Safe Haskell	None
Language	Haskell2010

Algebra.Prelude.Core

Synopsis

(%) :: (IsPolynomial poly, Division (Coefficient poly)) => Coefficient poly -> Coefficient poly -> poly
newtype Scalar r = Scalar {
- runScalar :: r
}
(.*.) :: Module (Scalar r) m => r -> m -> m
logBase2 :: Int -> Int
ceilingLogBase2 :: Int -> Int
seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b
filter :: (a -> Bool) -> [a] -> [a]
zip :: [a] -> [b] -> [(a, b)]
fst :: (a, b) -> a
snd :: (a, b) -> b
otherwise :: Bool
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
fromIntegral :: (Integral a, Num b) => a -> b
realToFrac :: (Real a, Fractional b) => a -> b
guard :: Alternative f => Bool -> f ()
join :: Monad m => m (m a) -> m a
class Bounded a where
- minBound :: a
- maxBound :: a
class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
class Eq a where
- (==) :: a -> a -> Bool
- (/=) :: a -> a -> Bool
class Fractional a => Floating a where
- pi :: a
- exp :: a -> a
- log :: a -> a
- sqrt :: a -> a
- (**) :: a -> a -> a
- logBase :: a -> a -> a
- sin :: a -> a
- cos :: a -> a
- tan :: a -> a
- asin :: a -> a
- acos :: a -> a
- atan :: a -> a
- sinh :: a -> a
- cosh :: a -> a
- tanh :: a -> a
- asinh :: a -> a
- acosh :: a -> a
- atanh :: a -> a
class Num a => Fractional a
class (Real a, Enum a) => Integral a where
- div :: a -> a -> a
- mod :: a -> a -> a
- toInteger :: a -> Integer
class Applicative m => Monad (m :: Type -> Type) where
- (>>=) :: m a -> (a -> m b) -> m b
- (>>) :: m a -> m b -> m b
- return :: a -> m a
class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- (<$) :: a -> f b -> f a
class Num a where
- abs :: a -> a
- signum :: a -> a
class Eq a => Ord a where
- compare :: a -> a -> Ordering
- (<) :: a -> a -> Bool
- (<=) :: a -> a -> Bool
- (>) :: a -> a -> Bool
- (>=) :: a -> a -> Bool
- max :: a -> a -> a
- min :: a -> a -> a
class Read a where
- readsPrec :: Int -> ReadS a
- readList :: ReadS [a]
class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
class (Real a, Fractional a) => RealFrac a where
- properFraction :: Integral b => a -> (b, a)
- truncate :: Integral b => a -> b
- round :: Integral b => a -> b
- ceiling :: Integral b => a -> b
- floor :: Integral b => a -> b
class Show a where
- showsPrec :: Int -> a -> ShowS
- show :: a -> String
- showList :: [a] -> ShowS
class Typeable (a :: k)
class Monad m => MonadFail (m :: Type -> Type) where
- fail :: String -> m a
class IsString a where
- fromString :: String -> a
class Functor f => Applicative (f :: Type -> Type) where
- pure :: a -> f a
- (<*>) :: f (a -> b) -> f a -> f b
- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
- (*>) :: f a -> f b -> f b
- (<*) :: f a -> f b -> f a
class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldr' :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldl' :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
class IsLabel (x :: Symbol) a where
- fromLabel :: a
(<>) :: Semigroup a => a -> a -> a
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
data Bool
- = False
- | True
data Char
data Double
data Float
data Int
data Int32
data Int64
data Integer
data Natural
data Maybe a
- = Nothing
- | Just a
data Ordering
- = LT
- | EQ
- | GT
data IO a
data Word
data Word8
data Word32
data Word64
data Either a b
- = Left a
- | Right b
ifThenElse :: Bool -> a -> a -> a
(^^) :: Division r => r -> Integer -> r
(^) :: Unital r => r -> Natural -> r
normaliseUnit :: UnitNormalForm r => r -> r
fromRational :: DivisionRing r => Rational -> r
fromInteger' :: Ring r => Integer -> r
fromInteger :: Num r => Integer -> r
type Rational = Fraction Integer
newtype WrapNum a = WrapNum {
- unwrapNum :: a
}
newtype WrapFractional a = WrapFractional {
- unwrapFractional :: a
}
newtype WrapIntegral a = WrapIntegral {
- unwrapIntegral :: a
}
newtype WrapAlgebra a = WrapAlgebra {
- unwrapAlgebra :: a
}
newtype Add a = Add {
- runAdd :: a
}
newtype Mult a = Mult {
- runMult :: a
}
type Ratio = Fraction
data Fraction d
numerator :: Fraction t -> t
denominator :: Fraction t -> t
class GCDDomain d => UFD d
class UFD d => PID d where
- egcd :: d -> d -> (d, d, d)
class (IntegralDomain d, UnitNormalForm d, DecidableZero d) => GCDDomain d where
- gcd :: d -> d -> d
- reduceFraction :: d -> d -> (d, d)
- lcm :: d -> d -> d
gcd' :: GCDDomain r => NonEmpty r -> r
class (Domain d, Commutative d) => IntegralDomain d where
- divides :: d -> d -> Bool
- maybeQuot :: d -> d -> Maybe d
class PID d => Euclidean d where
- degree :: d -> Maybe Natural
- divide :: d -> d -> (d, d)
- quot :: d -> d -> d
- rem :: d -> d -> d
euclid :: Euclidean d => d -> d -> [(d, d, d)]
prs :: Euclidean r => r -> r -> [(r, r, r)]
chineseRemainder :: Euclidean r => [(r, r)] -> r
class (ZeroProductSemiring d, Ring d) => Domain d
recipUnitWhole :: Integral r => r -> Maybe r
recipUnitIntegral :: Integral r => r -> Maybe r
isAssociateWhole :: Eq n => n -> n -> Bool
isAssociateIntegral :: (Eq n, Num n) => n -> n -> Bool
class (Monoidal r, Semiring r) => ZeroProductSemiring r
class (DecidableUnits r, DecidableAssociates r) => UnitNormalForm r where
- splitUnit :: r -> (r, r)
leadingUnit :: UnitNormalForm r => r -> r
class (Group r, Semiring r) => Rng r
class Ring r => LocalRing r
class (Division r, Ring r) => DivisionRing r
class (Rig r, Rng r) => Ring r
class (AdditiveOrder r, Rig r) => OrderedRig r
class (Semiring r, Unital r, Monoidal r) => Rig r where
- fromNatural :: Natural -> r
class Rig r => Characteristic r where
- char :: proxy r -> Natural
class Additive r => Quadrance r m where
- quadrance :: m -> r
class Order a => LocallyFiniteOrder a
class (Additive r, Order r) => AdditiveOrder r
class (Euclidean d, Division d) => Field d
class (Semiring r, Idempotent r) => Dioid r
class Monoidal r => DecidableZero r where
- isZero :: r -> Bool
class Unital r => DecidableUnits r where
- recipUnit :: r -> Maybe r
- isUnit :: r -> Bool
- (^?) :: Integral n => r -> n -> Maybe r
class Unital r => DecidableAssociates r where
- isAssociate :: r -> r -> Bool
newtype Covector r a = Covector {
- ($*) :: (a -> r) -> r
}
class Algebra r a => UnitalAlgebra r a where
- unit :: r -> a -> r
class Multiplicative r => Unital r where
- one :: r
- pow :: r -> Natural -> r
- productWith :: Foldable f => (a -> r) -> f a -> r
class Coalgebra r c => CounitalCoalgebra r c where
- counit :: (c -> r) -> r
class (UnitalAlgebra r a, CounitalCoalgebra r a) => Bialgebra r a
class (CocommutativeCoalgebra r a, TriviallyInvolutive r, InvolutiveCoalgebra r a) => TriviallyInvolutiveCoalgebra r a
class (InvolutiveBialgebra r h, TriviallyInvolutiveAlgebra r h, TriviallyInvolutiveCoalgebra r h) => TriviallyInvolutiveBialgebra r h
class (CommutativeAlgebra r a, TriviallyInvolutive r, InvolutiveAlgebra r a) => TriviallyInvolutiveAlgebra r a
class (Commutative r, InvolutiveMultiplication r) => TriviallyInvolutive r
class (Semiring r, InvolutiveMultiplication r) => InvolutiveSemiring r
class Multiplicative r => InvolutiveMultiplication r where
- adjoint :: r -> r
class (InvolutiveSemiring r, Coalgebra r c) => InvolutiveCoalgebra r c where
- coinv :: (c -> r) -> c -> r
class (Bialgebra r h, InvolutiveAlgebra r h, InvolutiveCoalgebra r h) => InvolutiveBialgebra r h
class (InvolutiveSemiring r, Algebra r a) => InvolutiveAlgebra r a where
- inv :: (a -> r) -> a -> r
class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h
class Algebra r a => IdempotentAlgebra r a
class Multiplicative r => Band r
class Bialgebra r h => HopfAlgebra r h where
- antipode :: (h -> r) -> h -> r
class Multiplicative m => Factorable m where
- factorWith :: (m -> m -> r) -> m -> NonEmpty r
class UnitalAlgebra r a => DivisionAlgebra r a where
- recipriocal :: (a -> r) -> a -> r
class Unital r => Division r where
- recip :: r -> r
- (/) :: r -> r -> r
- (\\) :: r -> r -> r
class (Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h
class Algebra r a => CommutativeAlgebra r a
class Multiplicative r => Commutative r
class Coalgebra r c => CocommutativeCoalgebra r c
class (Additive r, Abelian r, Multiplicative r) => Semiring r
class (Semiring r, Additive m) => RightModule r m where
- (*.) :: m -> r -> m
class Multiplicative r where
- (*) :: r -> r -> r
- pow1p :: r -> Natural -> r
- productWith1 :: Foldable1 f => (a -> r) -> f a -> r
class (LeftModule Natural m, RightModule Natural m) => Monoidal m where
- zero :: m
- sinnum :: Natural -> m -> m
- sumWith :: Foldable f => (a -> m) -> f a -> m
class (LeftModule r m, RightModule r m) => Module r m
class (Semiring r, Additive m) => LeftModule r m where
- (.*) :: r -> m -> m
class Semiring r => Coalgebra r c where
- comult :: (c -> r) -> c -> c -> r
class Semiring r => Algebra r a where
- mult :: (a -> a -> r) -> a -> r
class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r where
- (-) :: r -> r -> r
- negate :: r -> r
- subtract :: r -> r -> r
- times :: Integral n => n -> r -> r
class Additive m => Partitionable m where
- partitionWith :: (m -> m -> r) -> m -> NonEmpty r
class Additive r => Idempotent r
class Additive r where
- (+) :: r -> r -> r
- sinnum1p :: Natural -> r -> r
- sumWith1 :: Foldable1 f => (a -> r) -> f a -> r
class Additive r => Abelian r
charWord :: (Integral s, Bounded s) => proxy s -> Natural
charInt :: (Integral s, Bounded s) => proxy s -> Natural
zeroRep :: (Applicative m, Monoidal r) => m r
timesRep :: (Integral n, Functor m, Group r) => n -> m r -> m r
subtractRep :: (Applicative m, Group r) => m r -> m r -> m r
sinnumRep :: (Functor m, Monoidal r) => Natural -> m r -> m r
sinnum1pRep :: (Functor m, Additive r) => Natural -> m r -> m r
oneRep :: (Representable m, Unital r, UnitalAlgebra r (Rep m)) => m r
negateRep :: (Functor m, Group r) => m r -> m r
mulRep :: (Representable m, Algebra r (Rep m)) => m r -> m r -> m r
minusRep :: (Applicative m, Group r) => m r -> m r -> m r
fromNaturalRep :: (UnitalAlgebra r (Rep m), Representable m, Rig r) => Natural -> m r
fromIntegerRep :: (UnitalAlgebra r (Rep m), Representable m, Ring r) => Integer -> m r
addRep :: (Applicative m, Additive r) => m r -> m r -> m r
unitM :: CounitalCoalgebra r c => Covector r c
multM :: Coalgebra r c => c -> c -> Covector r c
invM :: InvolutiveAlgebra r h => h -> Covector r h
counitM :: UnitalAlgebra r a => a -> Covector r ()
convolveM :: (Algebra r c, Coalgebra r a) => (c -> Covector r a) -> (c -> Covector r a) -> c -> Covector r a
comultM :: Algebra r a => a -> Covector r (a, a)
coinvM :: InvolutiveCoalgebra r h => h -> Covector r h
antipodeM :: HopfAlgebra r h => h -> Covector r h
product :: (Foldable f, Unital r) => f r -> r
powBand :: Unital r => r -> Natural -> r
pow1pBand :: r -> Natural -> r
sum :: (Foldable f, Monoidal m) => f m -> m
sinnumIdempotent :: (Integral n, Idempotent r, Monoidal r) => n -> r -> r
product1 :: (Foldable1 f, Multiplicative r) => f r -> r
sum1 :: (Foldable1 f, Additive r) => f r -> r
sinnum1pIdempotent :: Natural -> r -> r
class (Vector Vector a, MVector MVector a) => Unbox a
data Vector a
data HashSet a
data HashMap k v
class Hashable a where
- hashWithSalt :: Int -> a -> Int
- hash :: a -> Int
type UVector = Vector
type SVector = Vector
type LText = Text
type LByteString = ByteString
terror :: HasCallStack => Text -> a
print :: (MonadIO m, Show a) => a -> m ()
equating :: Eq a => (b -> a) -> b -> b -> Bool
tshow :: Show a => a -> Text
textToString :: Text -> String
readMay :: Read a => Text -> Maybe a
readLn :: (MonadIO m, Read a) => m a
readIO :: (MonadIO m, Read a) => Text -> m a
putChar :: MonadIO m => Char -> m ()
map :: Functor f => (a -> b) -> f a -> f b
ltextToString :: LText -> String
intercalate :: Monoid w => w -> [w] -> w
getChar :: MonadIO m => m Char
fpToText :: FilePath -> Text
fpToString :: FilePath -> String
fpFromText :: Text -> FilePath
empty :: Monoid w => w
decodeUtf8 :: ByteString -> Text
concat :: Monoid w => [w] -> w
appendFile :: MonadIO m => FilePath -> Text -> m ()
(++) :: Monoid w => w -> w -> w
data Text
encodeUtf8 :: Text -> ByteString
(<.>) :: FilePath -> String -> FilePath
(</>) :: FilePath -> FilePath -> FilePath
data Set a
data Seq a
data Map k a
data IntSet
data IntMap a
data ByteString
not :: Bool -> Bool
(||) :: Bool -> Bool -> Bool
(&&) :: Bool -> Bool -> Bool
data SomeException
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
type String = [Char]
class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where
- mzero :: m a
- mplus :: m a -> m a -> m a
(=<<) :: Monad m => (a -> m b) -> m a -> m b
when :: Applicative f => Bool -> f () -> f ()
liftM :: Monad m => (a1 -> r) -> m a1 -> m r
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
ap :: Monad m => m (a -> b) -> m a -> m b
id :: a -> a
const :: a -> b -> a
(.) :: (b -> c) -> (a -> b) -> a -> c
flip :: (a -> b -> c) -> b -> a -> c
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
curry :: ((a, b) -> c) -> a -> b -> c
uncurry :: (a -> b -> c) -> (a, b) -> c
swap :: (a, b) -> (b, a)
(<$>) :: Functor f => (a -> b) -> f a -> f b
void :: Functor f => f a -> f ()
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
bool :: a -> a -> Bool -> a
maybe :: b -> (a -> b) -> Maybe a -> b
isJust :: Maybe a -> Bool
isNothing :: Maybe a -> Bool
fromMaybe :: a -> Maybe a -> a
maybeToList :: Maybe a -> [a]
listToMaybe :: [a] -> Maybe a
catMaybes :: [Maybe a] -> [a]
mapMaybe :: (a -> Maybe b) -> [a] -> [b]
head :: [a] -> a
uncons :: [a] -> Maybe (a, [a])
tail :: [a] -> [a]
last :: [a] -> a
init :: [a] -> [a]
foldl1' :: (a -> a -> a) -> [a] -> a
scanl :: (b -> a -> b) -> b -> [a] -> [b]
scanl1 :: (a -> a -> a) -> [a] -> [a]
scanl' :: (b -> a -> b) -> b -> [a] -> [b]
scanr :: (a -> b -> b) -> b -> [a] -> [b]
scanr1 :: (a -> a -> a) -> [a] -> [a]
iterate :: (a -> a) -> a -> [a]
iterate' :: (a -> a) -> a -> [a]
repeat :: a -> [a]
replicate :: Int -> a -> [a]
cycle :: [a] -> [a]
takeWhile :: (a -> Bool) -> [a] -> [a]
dropWhile :: (a -> Bool) -> [a] -> [a]
take :: Int -> [a] -> [a]
drop :: Int -> [a] -> [a]
splitAt :: Int -> [a] -> ([a], [a])
span :: (a -> Bool) -> [a] -> ([a], [a])
break :: (a -> Bool) -> [a] -> ([a], [a])
reverse :: [a] -> [a]
lookup :: Eq a => a -> [(a, b)] -> Maybe b
(!!) :: [a] -> Int -> a
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
unzip :: [(a, b)] -> ([a], [b])
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
type ShowS = String -> String
shows :: Show a => a -> ShowS
showChar :: Char -> ShowS
showString :: String -> ShowS
showParen :: Bool -> ShowS -> ShowS
even :: Integral a => a -> Bool
odd :: Integral a => a -> Bool
type ReadS a = String -> [(a, String)]
readParen :: Bool -> ReadS a -> ReadS a
class Storable a
newtype Down a = Down {
- getDown :: a
}
comparing :: Ord a => (b -> a) -> b -> b -> Ordering
either :: (a -> c) -> (b -> c) -> Either a b -> c
lefts :: [Either a b] -> [a]
rights :: [Either a b] -> [b]
partitionEithers :: [Either a b] -> ([a], [b])
reads :: Read a => ReadS a
dropWhileEnd :: (a -> Bool) -> [a] -> [a]
stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
elemIndex :: Eq a => a -> [a] -> Maybe Int
elemIndices :: Eq a => a -> [a] -> [Int]
findIndex :: (a -> Bool) -> [a] -> Maybe Int
findIndices :: (a -> Bool) -> [a] -> [Int]
isPrefixOf :: Eq a => [a] -> [a] -> Bool
isSuffixOf :: Eq a => [a] -> [a] -> Bool
isInfixOf :: Eq a => [a] -> [a] -> Bool
nub :: Eq a => [a] -> [a]
nubBy :: (a -> a -> Bool) -> [a] -> [a]
delete :: Eq a => a -> [a] -> [a]
deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
union :: Eq a => [a] -> [a] -> [a]
unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersect :: Eq a => [a] -> [a] -> [a]
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersperse :: a -> [a] -> [a]
transpose :: [[a]] -> [[a]]
partition :: (a -> Bool) -> [a] -> ([a], [a])
insert :: Ord a => a -> [a] -> [a]
insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
genericLength :: Num i => [a] -> i
genericTake :: Integral i => i -> [a] -> [a]
genericDrop :: Integral i => i -> [a] -> [a]
genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
genericIndex :: Integral i => [a] -> i -> a
genericReplicate :: Integral i => i -> a -> [a]
zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
group :: Eq a => [a] -> [[a]]
groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
inits :: [a] -> [[a]]
tails :: [a] -> [[a]]
subsequences :: [a] -> [[a]]
permutations :: [a] -> [[a]]
sort :: Ord a => [a] -> [a]
sortBy :: (a -> a -> Ordering) -> [a] -> [a]
sortOn :: Ord b => (a -> b) -> [a] -> [a]
unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
lines :: String -> [String]
unlines :: [String] -> String
words :: String -> [String]
unwords :: [String] -> String
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
asum :: (Foldable t, Alternative f) => t (f a) -> f a
msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
and :: Foldable t => t Bool -> Bool
or :: Foldable t => t Bool -> Bool
any :: Foldable t => (a -> Bool) -> t a -> Bool
all :: Foldable t => (a -> Bool) -> t a -> Bool
maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
notElem :: (Foldable t, Eq a) => a -> t a -> Bool
find :: Foldable t => (a -> Bool) -> t a -> Maybe a
class (Typeable e, Show e) => Exception e where
- toException :: e -> SomeException
- fromException :: SomeException -> Maybe e
- displayException :: e -> String
type IOError = IOException
data IOException
userError :: String -> IOError
type FilePath = String
data IOErrorType
ioError :: IOError -> IO a
tryIOError :: IO a -> IO (Either IOError a)
mkIOError :: IOErrorType -> String -> Maybe Handle -> Maybe FilePath -> IOError
isAlreadyExistsError :: IOError -> Bool
isDoesNotExistError :: IOError -> Bool
isAlreadyInUseError :: IOError -> Bool
isFullError :: IOError -> Bool
isEOFError :: IOError -> Bool
isIllegalOperation :: IOError -> Bool
isPermissionError :: IOError -> Bool
isUserError :: IOError -> Bool
isResourceVanishedError :: IOError -> Bool
alreadyExistsErrorType :: IOErrorType
doesNotExistErrorType :: IOErrorType
alreadyInUseErrorType :: IOErrorType
fullErrorType :: IOErrorType
eofErrorType :: IOErrorType
illegalOperationErrorType :: IOErrorType
permissionErrorType :: IOErrorType
userErrorType :: IOErrorType
resourceVanishedErrorType :: IOErrorType
isAlreadyExistsErrorType :: IOErrorType -> Bool
isDoesNotExistErrorType :: IOErrorType -> Bool
isAlreadyInUseErrorType :: IOErrorType -> Bool
isFullErrorType :: IOErrorType -> Bool
isEOFErrorType :: IOErrorType -> Bool
isIllegalOperationErrorType :: IOErrorType -> Bool
isPermissionErrorType :: IOErrorType -> Bool
isUserErrorType :: IOErrorType -> Bool
isResourceVanishedErrorType :: IOErrorType -> Bool
ioeGetErrorType :: IOError -> IOErrorType
ioeGetErrorString :: IOError -> String
ioeGetLocation :: IOError -> String
ioeGetHandle :: IOError -> Maybe Handle
ioeGetFileName :: IOError -> Maybe FilePath
ioeSetErrorType :: IOError -> IOErrorType -> IOError
ioeSetErrorString :: IOError -> String -> IOError
ioeSetLocation :: IOError -> String -> IOError
ioeSetHandle :: IOError -> Handle -> IOError
ioeSetFileName :: IOError -> FilePath -> IOError
modifyIOError :: (IOError -> IOError) -> IO a -> IO a
annotateIOError :: IOError -> String -> Maybe Handle -> Maybe FilePath -> IOError
catchIOError :: IO a -> (IOError -> IO a) -> IO a
putStr :: String -> IO ()
putStrLn :: String -> IO ()
getLine :: IO String
getContents :: IO String
interact :: (String -> String) -> IO ()
readFile :: FilePath -> IO String
writeFile :: FilePath -> String -> IO ()
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
forever :: Applicative f => f a -> f b
mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])
zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()
foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
replicateM :: Applicative m => Int -> m a -> m [a]
replicateM_ :: Applicative m => Int -> m a -> m ()
unless :: Applicative f => Bool -> f () -> f ()
(<$!>) :: Monad m => (a -> b) -> m a -> m b
mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a
class Monad m => MonadIO (m :: Type -> Type) where
- liftIO :: IO a -> m a
second :: Arrow a => a b c -> a (d, b) (d, c)
(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c')
first :: Arrow a => a b c -> a (b, d) (c, d)
(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c')
(<|>) :: Alternative f => f a -> f a -> f a
lift :: (MonadTrans t, Monad m) => m a -> t m a
module Algebra.Ring.Polynomial.Monomial
module Algebra.Ring.Polynomial.Class
type Polynomial r = OrderedPolynomial r Grevlex
transformMonomial :: (IsMonomialOrder m o', CoeffRing k, KnownNat m) => (USized n Int -> USized m Int) -> OrderedPolynomial k o n -> OrderedPolynomial k o' m
castPolynomial :: forall r n m o o'. (CoeffRing r, KnownNat n, KnownNat m, IsMonomialOrder n o, IsMonomialOrder m o') => OrderedPolynomial r o n -> OrderedPolynomial r o' m
changeOrder :: forall k n o o'. (CoeffRing k, Eq (Monomial n), IsMonomialOrder n o, IsMonomialOrder n o', KnownNat n) => o' -> OrderedPolynomial k o n -> OrderedPolynomial k o' n
changeOrderProxy :: forall k n o o'. (CoeffRing k, Eq (Monomial n), IsMonomialOrder n o, IsMonomialOrder n o', KnownNat n) => Proxy o' -> OrderedPolynomial k o n -> OrderedPolynomial k o' n
scastPolynomial :: (IsMonomialOrder n o, IsMonomialOrder m o', KnownNat m, CoeffRing r, KnownNat n) => SNat m -> OrderedPolynomial r o n -> OrderedPolynomial r o' m
newtype OrderedPolynomial r order n = Polynomial {
- _terms :: Map (OrderedMonomial order n) r
}
allVars :: forall k ord n. (IsMonomialOrder n ord, CoeffRing k, KnownNat n) => Sized n (OrderedPolynomial k ord n)
substVar :: (CoeffRing r, KnownNat n, IsMonomialOrder n ord, 1 <= n) => Ordinal n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n
homogenize :: forall k ord n. (CoeffRing k, KnownNat n, IsMonomialOrder (n + 1) ord, IsMonomialOrder n ord) => OrderedPolynomial k ord n -> OrderedPolynomial k ord (n + 1)
unhomogenize :: forall k ord n. (CoeffRing k, KnownNat n, IsMonomialOrder n ord, IsMonomialOrder (n + 1) ord) => OrderedPolynomial k ord (n + 1) -> OrderedPolynomial k ord n
normalize :: DecidableZero r => OrderedPolynomial r order n -> OrderedPolynomial r order n
varX :: forall r n order. (CoeffRing r, KnownNat n, IsMonomialOrder n order, 0 < n) => OrderedPolynomial r order n
getTerms :: OrderedPolynomial k order n -> [(k, OrderedMonomial order n)]
shiftR :: forall k r n ord. (CoeffRing r, KnownNat n, IsMonomialOrder n ord, IsMonomialOrder (k + n) ord) => SNat k -> OrderedPolynomial r ord n -> OrderedPolynomial r ord (k + n)
orderedBy :: OrderedPolynomial k o n -> o -> OrderedPolynomial k o n
mapCoeff :: (KnownNat n, CoeffRing b, IsMonomialOrder n ord) => (a -> b) -> OrderedPolynomial a ord n -> OrderedPolynomial b ord n
reversal :: (CoeffRing k, IsMonomialOrder 1 o) => Int -> OrderedPolynomial k o 1 -> OrderedPolynomial k o 1
padeApprox :: (Field r, DecidableUnits r, CoeffRing r, ZeroProductSemiring r, IsMonomialOrder 1 order) => Natural -> Natural -> OrderedPolynomial r order 1 -> (OrderedPolynomial r order 1, OrderedPolynomial r order 1)
eval :: (CoeffRing r, IsMonomialOrder n order, KnownNat n) => Sized n r -> OrderedPolynomial r order n -> r
evalUnivariate :: (CoeffRing b, IsMonomialOrder 1 order) => b -> OrderedPolynomial b order 1 -> b
substUnivariate :: (Module (Scalar r) b, Unital b, CoeffRing r, IsMonomialOrder 1 order) => b -> OrderedPolynomial r order 1 -> b
minpolRecurrent :: forall k. (Eq k, ZeroProductSemiring k, DecidableUnits k, DecidableZero k, Field k) => Natural -> [k] -> Polynomial k 1
class IsOrder (n :: Nat) ordering where
- cmpMonomial :: Proxy ordering -> MonomialOrder n
newtype PadPolyL n ord poly = PadPolyL {
- runPadPolyL :: OrderedPolynomial poly (Graded ord) n
}
padLeftPoly :: (IsMonomialOrder n ord, IsPolynomial poly) => SNat n -> ord -> poly -> PadPolyL n ord poly
module Algebra.Ring.Ideal
module Algebra.Normed
module Algebra.Internal

Documentation

(%) :: (IsPolynomial poly, Division (Coefficient poly)) => Coefficient poly -> Coefficient poly -> poly infixl 7 Source #

newtype Scalar r #

Scalar r provides almost the same type-instances as r, but it can also behave as a Module over r itself.

Constructors

Scalar
Fields runScalar :: r

Instances

Instances details

RightModule Integer r => RightModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Integer -> Scalar r #
RightModule Natural r => RightModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Natural -> Scalar r #
Semiring r => RightModule r (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> r -> Scalar r #
LeftModule Integer r => LeftModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Integer -> Scalar r -> Scalar r #
LeftModule Natural r => LeftModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Natural -> Scalar r -> Scalar r #
Semiring r => LeftModule r (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: r -> Scalar r -> Scalar r #
Enum r => Enum (Scalar r)
Instance details Defined in Algebra.Scalar Methods succ :: Scalar r -> Scalar r # pred :: Scalar r -> Scalar r # toEnum :: Int -> Scalar r # fromEnum :: Scalar r -> Int # enumFrom :: Scalar r -> [Scalar r] # enumFromThen :: Scalar r -> Scalar r -> [Scalar r] # enumFromTo :: Scalar r -> Scalar r -> [Scalar r] # enumFromThenTo :: Scalar r -> Scalar r -> Scalar r -> [Scalar r] #
Eq r => Eq (Scalar r)
Instance details Defined in Algebra.Scalar Methods (==) :: Scalar r -> Scalar r -> Bool # (/=) :: Scalar r -> Scalar r -> Bool #
Fractional r => Fractional (Scalar r)
Instance details Defined in Algebra.Scalar Methods (/) :: Scalar r -> Scalar r -> Scalar r # recip :: Scalar r -> Scalar r # fromRational :: Rational -> Scalar r #
Integral r => Integral (Scalar r)
Instance details Defined in Algebra.Scalar Methods quot :: Scalar r -> Scalar r -> Scalar r # rem :: Scalar r -> Scalar r -> Scalar r # div :: Scalar r -> Scalar r -> Scalar r # mod :: Scalar r -> Scalar r -> Scalar r # quotRem :: Scalar r -> Scalar r -> (Scalar r, Scalar r) # divMod :: Scalar r -> Scalar r -> (Scalar r, Scalar r) # toInteger :: Scalar r -> Integer #
Num r => Num (Scalar r)
Instance details Defined in Algebra.Scalar Methods (+) :: Scalar r -> Scalar r -> Scalar r # (-) :: Scalar r -> Scalar r -> Scalar r # (*) :: Scalar r -> Scalar r -> Scalar r # negate :: Scalar r -> Scalar r # abs :: Scalar r -> Scalar r # signum :: Scalar r -> Scalar r # fromInteger :: Integer -> Scalar r #
Ord r => Ord (Scalar r)
Instance details Defined in Algebra.Scalar Methods compare :: Scalar r -> Scalar r -> Ordering # (<) :: Scalar r -> Scalar r -> Bool # (<=) :: Scalar r -> Scalar r -> Bool # (>) :: Scalar r -> Scalar r -> Bool # (>=) :: Scalar r -> Scalar r -> Bool # max :: Scalar r -> Scalar r -> Scalar r # min :: Scalar r -> Scalar r -> Scalar r #
Read r => Read (Scalar r)
Instance details Defined in Algebra.Scalar Methods readsPrec :: Int -> ReadS (Scalar r) # readList :: ReadS [Scalar r] # readPrec :: ReadPrec (Scalar r) # readListPrec :: ReadPrec [Scalar r] #
Real r => Real (Scalar r)
Instance details Defined in Algebra.Scalar Methods toRational :: Scalar r -> Rational #
Show r => Show (Scalar r)
Instance details Defined in Algebra.Scalar Methods showsPrec :: Int -> Scalar r -> ShowS # show :: Scalar r -> String # showList :: [Scalar r] -> ShowS #
UnitNormalForm r => UnitNormalForm (Scalar r)
Instance details Defined in Algebra.Scalar Methods splitUnit :: Scalar r -> (Scalar r, Scalar r) #
Ring r => Ring (Scalar r)
Instance details Defined in Algebra.Scalar Methods fromInteger :: Integer -> Scalar r
Rig r => Rig (Scalar r)
Instance details Defined in Algebra.Scalar Methods fromNatural :: Natural -> Scalar r #
DecidableUnits r => DecidableUnits (Scalar r)
Instance details Defined in Algebra.Scalar Methods recipUnit :: Scalar r -> Maybe (Scalar r) # isUnit :: Scalar r -> Bool # (^?) :: Integral n => Scalar r -> n -> Maybe (Scalar r) #
DecidableAssociates r => DecidableAssociates (Scalar r)
Instance details Defined in Algebra.Scalar Methods isAssociate :: Scalar r -> Scalar r -> Bool #
Unital r => Unital (Scalar r)
Instance details Defined in Algebra.Scalar Methods one :: Scalar r # pow :: Scalar r -> Natural -> Scalar r # productWith :: Foldable f => (a -> Scalar r) -> f a -> Scalar r #
Division r => Division (Scalar r)
Instance details Defined in Algebra.Scalar Methods recip :: Scalar r -> Scalar r # (/) :: Scalar r -> Scalar r -> Scalar r # (\\) :: Scalar r -> Scalar r -> Scalar r # (^) :: Integral n => Scalar r -> n -> Scalar r
Commutative r => Commutative (Scalar r)
Instance details Defined in Algebra.Scalar
Semiring r => Semiring (Scalar r)
Instance details Defined in Algebra.Scalar
Multiplicative r => Multiplicative (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*) :: Scalar r -> Scalar r -> Scalar r # pow1p :: Scalar r -> Natural -> Scalar r # productWith1 :: Foldable1 f => (a -> Scalar r) -> f a -> Scalar r #
Monoidal r => Monoidal (Scalar r)
Instance details Defined in Algebra.Scalar Methods zero :: Scalar r # sinnum :: Natural -> Scalar r -> Scalar r # sumWith :: Foldable f => (a -> Scalar r) -> f a -> Scalar r #
Group r => Group (Scalar r)
Instance details Defined in Algebra.Scalar Methods (-) :: Scalar r -> Scalar r -> Scalar r # negate :: Scalar r -> Scalar r # subtract :: Scalar r -> Scalar r -> Scalar r # times :: Integral n => n -> Scalar r -> Scalar r #
Additive r => Additive (Scalar r)
Instance details Defined in Algebra.Scalar Methods (+) :: Scalar r -> Scalar r -> Scalar r # sinnum1p :: Natural -> Scalar r -> Scalar r # sumWith1 :: Foldable1 f => (a -> Scalar r) -> f a -> Scalar r #
Abelian r => Abelian (Scalar r)
Instance details Defined in Algebra.Scalar
Normed r => Normed (Scalar r)
Instance details Defined in Algebra.Scalar Associated Types type Norm (Scalar r) # Methods norm :: Scalar r -> Norm (Scalar r) # liftNorm :: Norm (Scalar r) -> Scalar r #
Semiring r => RightModule (Scalar r) (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Scalar r -> Scalar r #
(DecidableZero r, Semiring r) => RightModule (Scalar r) (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Scalar r -> Unipol r #
Semiring r => LeftModule (Scalar r) (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Scalar r -> Scalar r -> Scalar r #
(DecidableZero r, Semiring r) => LeftModule (Scalar r) (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Scalar r -> Unipol r -> Unipol r #
(Wraps vars poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Scalar r -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Scalar r -> LabPolynomial poly vars -> LabPolynomial poly vars #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Scalar r -> PadPolyL n ord poly #
(r ~ Coefficient poly, IsOrderedPolynomial poly) => RightModule (Scalar r) (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Scalar r -> Quotient poly ideal #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> PadPolyL n ord poly -> PadPolyL n ord poly #
(r ~ Coefficient poly, Field (Coefficient poly), IsOrderedPolynomial poly) => LeftModule (Scalar r) (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Scalar r -> Quotient poly ideal -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Scalar r -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
type Norm (Scalar r)
Instance details Defined in Algebra.Scalar type Norm (Scalar r) = Norm r

(.*.) :: Module (Scalar r) m => r -> m -> m infixr 8 #

logBase2 :: Int -> Int Source #

ceilingLogBase2 :: Int -> Int Source #

seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 #

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

filter :: (a -> Bool) -> [a] -> [a] #

$\mathcal{O}(n)$. filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

>>> filter odd [1, 2, 3]
[1,3]

zip :: [a] -> [b] -> [(a, b)] #

$\mathcal{O}(\min(m,n))$. zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.

fst :: (a, b) -> a #

Extract the first component of a pair.

snd :: (a, b) -> b #

Extract the second component of a pair.

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

guard :: Alternative f => Bool -> f () #

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

Expand

Common uses of guard include conditionally signaling an error in an error monad and conditionally rejecting the current choice in an Alternative-based parser.

As an example of signaling an error in the error monad Maybe, consider a safe division function safeDiv x y that returns Nothing when the denominator y is zero and Just (x `div` y) otherwise. For example:

>>> safeDiv 4 0
Nothing
>>> safeDiv 4 2
Just 2

A definition of safeDiv using guards, but not guard:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0    = Just (x `div` y)
            | otherwise = Nothing

A definition of safeDiv using guard and Monad do-notation:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y = do
  guard (y /= 0)
  return (x `div` y)

join :: Monad m => m (m a) -> m a #

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

Expand

A common use of join is to run an IO computation returned from an STM transaction, since STM transactions can't perform IO directly. Recall that

atomically :: STM a -> IO a

is used to run STM transactions atomically. So, by specializing the types of atomically and join to

atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

we can compose them as

join . atomically :: STM (IO b) -> IO b

to run an STM transaction and the IO action it returns.

class Bounded a where #

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a #

maxBound :: a #

Instances

Instances details

Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Bounded Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char # maxBound :: Char #
Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Bounded Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int8 # maxBound :: Int8 #
Bounded Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int16 # maxBound :: Int16 #
Bounded Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int32 # maxBound :: Int32 #
Bounded Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int64 # maxBound :: Int64 #
Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Bounded Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word # maxBound :: Word #
Bounded Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word8 # maxBound :: Word8 #
Bounded Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word16 # maxBound :: Word16 #
Bounded Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word32 # maxBound :: Word32 #
Bounded Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word64 # maxBound :: Word64 #
Bounded VecCount	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecCount # maxBound :: VecCount #
Bounded VecElem	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecElem # maxBound :: VecElem #
Bounded ()	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: () # maxBound :: () #
Bounded CDev
Instance details Defined in System.Posix.Types Methods minBound :: CDev # maxBound :: CDev #
Bounded CIno
Instance details Defined in System.Posix.Types Methods minBound :: CIno # maxBound :: CIno #
Bounded CMode
Instance details Defined in System.Posix.Types Methods minBound :: CMode # maxBound :: CMode #
Bounded COff
Instance details Defined in System.Posix.Types Methods minBound :: COff # maxBound :: COff #
Bounded CPid
Instance details Defined in System.Posix.Types Methods minBound :: CPid # maxBound :: CPid #
Bounded CSsize
Instance details Defined in System.Posix.Types Methods minBound :: CSsize # maxBound :: CSsize #
Bounded CGid
Instance details Defined in System.Posix.Types Methods minBound :: CGid # maxBound :: CGid #
Bounded CNlink
Instance details Defined in System.Posix.Types Methods minBound :: CNlink # maxBound :: CNlink #
Bounded CUid
Instance details Defined in System.Posix.Types Methods minBound :: CUid # maxBound :: CUid #
Bounded CTcflag
Instance details Defined in System.Posix.Types Methods minBound :: CTcflag # maxBound :: CTcflag #
Bounded CRLim
Instance details Defined in System.Posix.Types Methods minBound :: CRLim # maxBound :: CRLim #
Bounded CBlkSize
Instance details Defined in System.Posix.Types Methods minBound :: CBlkSize # maxBound :: CBlkSize #
Bounded CBlkCnt
Instance details Defined in System.Posix.Types Methods minBound :: CBlkCnt # maxBound :: CBlkCnt #
Bounded CClockId
Instance details Defined in System.Posix.Types Methods minBound :: CClockId # maxBound :: CClockId #
Bounded CFsBlkCnt
Instance details Defined in System.Posix.Types Methods minBound :: CFsBlkCnt # maxBound :: CFsBlkCnt #
Bounded CFsFilCnt
Instance details Defined in System.Posix.Types Methods minBound :: CFsFilCnt # maxBound :: CFsFilCnt #
Bounded CId
Instance details Defined in System.Posix.Types Methods minBound :: CId # maxBound :: CId #
Bounded CKey
Instance details Defined in System.Posix.Types Methods minBound :: CKey # maxBound :: CKey #
Bounded CSocklen
Instance details Defined in System.Posix.Types Methods minBound :: CSocklen # maxBound :: CSocklen #
Bounded CNfds
Instance details Defined in System.Posix.Types Methods minBound :: CNfds # maxBound :: CNfds #
Bounded Fd
Instance details Defined in System.Posix.Types Methods minBound :: Fd # maxBound :: Fd #
Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
Bounded Associativity	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: Associativity # maxBound :: Associativity #
Bounded SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: SourceUnpackedness # maxBound :: SourceUnpackedness #
Bounded SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: SourceStrictness # maxBound :: SourceStrictness #
Bounded DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods minBound :: DecidedStrictness # maxBound :: DecidedStrictness #
Bounded CChar
Instance details Defined in Foreign.C.Types Methods minBound :: CChar # maxBound :: CChar #
Bounded CSChar
Instance details Defined in Foreign.C.Types Methods minBound :: CSChar # maxBound :: CSChar #
Bounded CUChar
Instance details Defined in Foreign.C.Types Methods minBound :: CUChar # maxBound :: CUChar #
Bounded CShort
Instance details Defined in Foreign.C.Types Methods minBound :: CShort # maxBound :: CShort #
Bounded CUShort
Instance details Defined in Foreign.C.Types Methods minBound :: CUShort # maxBound :: CUShort #
Bounded CInt
Instance details Defined in Foreign.C.Types Methods minBound :: CInt # maxBound :: CInt #
Bounded CUInt
Instance details Defined in Foreign.C.Types Methods minBound :: CUInt # maxBound :: CUInt #
Bounded CLong
Instance details Defined in Foreign.C.Types Methods minBound :: CLong # maxBound :: CLong #
Bounded CULong
Instance details Defined in Foreign.C.Types Methods minBound :: CULong # maxBound :: CULong #
Bounded CLLong
Instance details Defined in Foreign.C.Types Methods minBound :: CLLong # maxBound :: CLLong #
Bounded CULLong
Instance details Defined in Foreign.C.Types Methods minBound :: CULLong # maxBound :: CULLong #
Bounded CBool
Instance details Defined in Foreign.C.Types Methods minBound :: CBool # maxBound :: CBool #
Bounded CPtrdiff
Instance details Defined in Foreign.C.Types Methods minBound :: CPtrdiff # maxBound :: CPtrdiff #
Bounded CSize
Instance details Defined in Foreign.C.Types Methods minBound :: CSize # maxBound :: CSize #
Bounded CWchar
Instance details Defined in Foreign.C.Types Methods minBound :: CWchar # maxBound :: CWchar #
Bounded CSigAtomic
Instance details Defined in Foreign.C.Types Methods minBound :: CSigAtomic # maxBound :: CSigAtomic #
Bounded CIntPtr
Instance details Defined in Foreign.C.Types Methods minBound :: CIntPtr # maxBound :: CIntPtr #
Bounded CUIntPtr
Instance details Defined in Foreign.C.Types Methods minBound :: CUIntPtr # maxBound :: CUIntPtr #
Bounded CIntMax
Instance details Defined in Foreign.C.Types Methods minBound :: CIntMax # maxBound :: CIntMax #
Bounded CUIntMax
Instance details Defined in Foreign.C.Types Methods minBound :: CUIntMax # maxBound :: CUIntMax #
Bounded GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Unicode Methods minBound :: GeneralCategory # maxBound :: GeneralCategory #
Bounded Extension
Instance details Defined in GHC.LanguageExtensions.Type Methods minBound :: Extension # maxBound :: Extension #
Bounded ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods minBound :: ComplexBasis # maxBound :: ComplexBasis #
Bounded a => Bounded (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods minBound :: Down a # maxBound :: Down a #
Bounded a => Bounded (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Min a # maxBound :: Min a #
Bounded a => Bounded (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Max a # maxBound :: Max a #
Bounded a => Bounded (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: First a # maxBound :: First a #
Bounded a => Bounded (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Last a # maxBound :: Last a #
Bounded m => Bounded (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m # maxBound :: WrappedMonoid m #
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Bounded a => Bounded (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a # maxBound :: Dual a #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
(KnownNat n, 0 < n) => Bounded (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods minBound :: Ordinal n # maxBound :: Ordinal n #
(Bounded a, Bounded b) => Bounded (a, b)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b) # maxBound :: (a, b) #
Bounded (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods minBound :: Proxy t # maxBound :: Proxy t #
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c) # maxBound :: (a, b, c) #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
(Applicative f, Bounded a) => Bounded (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods minBound :: Ap f a # maxBound :: Ap f a #
a ~ b => Bounded (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~: b # maxBound :: a :~: b #
Bounded b => Bounded (Tagged s b)
Instance details Defined in Data.Tagged Methods minBound :: Tagged s b # maxBound :: Tagged s b #
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d) # maxBound :: (a, b, c, d) #
a ~~ b => Bounded (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~~: b # maxBound :: a :~~: b #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e) # maxBound :: (a, b, c, d, e) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f) # maxBound :: (a, b, c, d, e, f) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g) # maxBound :: (a, b, c, d, e, f, g) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h) # maxBound :: (a, b, c, d, e, f, g, h) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i) # maxBound :: (a, b, c, d, e, f, g, h, i) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j) # maxBound :: (a, b, c, d, e, f, g, h, i, j) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Enum a where #

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

The calls succ maxBound and pred minBound should result in a runtime error.
fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
enumFrom and enumFromThen should be defined with an implicit bound, thus:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a #

Convert from an Int.

fromEnum :: a -> Int #

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a] #

Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example:

```
enumFrom 4 :: [Integer] = [4,5,6,7,...]
```

enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] #

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example:

enumFromThen 4 6 :: [Integer] = [4,6,8,10...]

enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] #

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example:

```
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
```
```
enumFromTo 42 1 :: [Integer] = []
```

enumFromThenTo :: a -> a -> a -> [a] #

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example:

enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]

```
enumFromThenTo 6 8 2 :: [Int] = []
```

Instances

Instances details

Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char # pred :: Char -> Char # toEnum :: Int -> Char # fromEnum :: Char -> Int # enumFrom :: Char -> [Char] # enumFromThen :: Char -> Char -> [Char] # enumFromTo :: Char -> Char -> [Char] # enumFromThenTo :: Char -> Char -> Char -> [Char] #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Enum Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int8 -> Int8 # pred :: Int8 -> Int8 # toEnum :: Int -> Int8 # fromEnum :: Int8 -> Int # enumFrom :: Int8 -> [Int8] # enumFromThen :: Int8 -> Int8 -> [Int8] # enumFromTo :: Int8 -> Int8 -> [Int8] # enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #
Enum Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int16 -> Int16 # pred :: Int16 -> Int16 # toEnum :: Int -> Int16 # fromEnum :: Int16 -> Int # enumFrom :: Int16 -> [Int16] # enumFromThen :: Int16 -> Int16 -> [Int16] # enumFromTo :: Int16 -> Int16 -> [Int16] # enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16] #
Enum Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int32 -> Int32 # pred :: Int32 -> Int32 # toEnum :: Int -> Int32 # fromEnum :: Int32 -> Int # enumFrom :: Int32 -> [Int32] # enumFromThen :: Int32 -> Int32 -> [Int32] # enumFromTo :: Int32 -> Int32 -> [Int32] # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] #
Enum Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int64 -> Int64 # pred :: Int64 -> Int64 # toEnum :: Int -> Int64 # fromEnum :: Int64 -> Int # enumFrom :: Int64 -> [Int64] # enumFromThen :: Int64 -> Int64 -> [Int64] # enumFromTo :: Int64 -> Int64 -> [Int64] # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] #
Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word # pred :: Word -> Word # toEnum :: Int -> Word # fromEnum :: Word -> Int # enumFrom :: Word -> [Word] # enumFromThen :: Word -> Word -> [Word] # enumFromTo :: Word -> Word -> [Word] # enumFromThenTo :: Word -> Word -> Word -> [Word] #
Enum Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word8 -> Word8 # pred :: Word8 -> Word8 # toEnum :: Int -> Word8 # fromEnum :: Word8 -> Int # enumFrom :: Word8 -> [Word8] # enumFromThen :: Word8 -> Word8 -> [Word8] # enumFromTo :: Word8 -> Word8 -> [Word8] # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] #
Enum Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word16 -> Word16 # pred :: Word16 -> Word16 # toEnum :: Int -> Word16 # fromEnum :: Word16 -> Int # enumFrom :: Word16 -> [Word16] # enumFromThen :: Word16 -> Word16 -> [Word16] # enumFromTo :: Word16 -> Word16 -> [Word16] # enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16] #
Enum Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word32 -> Word32 # pred :: Word32 -> Word32 # toEnum :: Int -> Word32 # fromEnum :: Word32 -> Int # enumFrom :: Word32 -> [Word32] # enumFromThen :: Word32 -> Word32 -> [Word32] # enumFromTo :: Word32 -> Word32 -> [Word32] # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] #
Enum Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word64 -> Word64 # pred :: Word64 -> Word64 # toEnum :: Int -> Word64 # fromEnum :: Word64 -> Int # enumFrom :: Word64 -> [Word64] # enumFromThen :: Word64 -> Word64 -> [Word64] # enumFromTo :: Word64 -> Word64 -> [Word64] # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] #
Enum VecCount	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods succ :: VecCount -> VecCount # pred :: VecCount -> VecCount # toEnum :: Int -> VecCount # fromEnum :: VecCount -> Int # enumFrom :: VecCount -> [VecCount] # enumFromThen :: VecCount -> VecCount -> [VecCount] # enumFromTo :: VecCount -> VecCount -> [VecCount] # enumFromThenTo :: VecCount -> VecCount -> VecCount -> [VecCount] #
Enum VecElem	Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods succ :: VecElem -> VecElem # pred :: VecElem -> VecElem # toEnum :: Int -> VecElem # fromEnum :: VecElem -> Int # enumFrom :: VecElem -> [VecElem] # enumFromThen :: VecElem -> VecElem -> [VecElem] # enumFromTo :: VecElem -> VecElem -> [VecElem] # enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] #
Enum ()	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: () -> () # pred :: () -> () # toEnum :: Int -> () # fromEnum :: () -> Int # enumFrom :: () -> [()] # enumFromThen :: () -> () -> [()] # enumFromTo :: () -> () -> [()] # enumFromThenTo :: () -> () -> () -> [()] #
Enum CDev
Instance details Defined in System.Posix.Types Methods succ :: CDev -> CDev # pred :: CDev -> CDev # toEnum :: Int -> CDev # fromEnum :: CDev -> Int # enumFrom :: CDev -> [CDev] # enumFromThen :: CDev -> CDev -> [CDev] # enumFromTo :: CDev -> CDev -> [CDev] # enumFromThenTo :: CDev -> CDev -> CDev -> [CDev] #
Enum CIno
Instance details Defined in System.Posix.Types Methods succ :: CIno -> CIno # pred :: CIno -> CIno # toEnum :: Int -> CIno # fromEnum :: CIno -> Int # enumFrom :: CIno -> [CIno] # enumFromThen :: CIno -> CIno -> [CIno] # enumFromTo :: CIno -> CIno -> [CIno] # enumFromThenTo :: CIno -> CIno -> CIno -> [CIno] #
Enum CMode
Instance details Defined in System.Posix.Types Methods succ :: CMode -> CMode # pred :: CMode -> CMode # toEnum :: Int -> CMode # fromEnum :: CMode -> Int # enumFrom :: CMode -> [CMode] # enumFromThen :: CMode -> CMode -> [CMode] # enumFromTo :: CMode -> CMode -> [CMode] # enumFromThenTo :: CMode -> CMode -> CMode -> [CMode] #
Enum COff
Instance details Defined in System.Posix.Types Methods succ :: COff -> COff # pred :: COff -> COff # toEnum :: Int -> COff # fromEnum :: COff -> Int # enumFrom :: COff -> [COff] # enumFromThen :: COff -> COff -> [COff] # enumFromTo :: COff -> COff -> [COff] # enumFromThenTo :: COff -> COff -> COff -> [COff] #
Enum CPid
Instance details Defined in System.Posix.Types Methods succ :: CPid -> CPid # pred :: CPid -> CPid # toEnum :: Int -> CPid # fromEnum :: CPid -> Int # enumFrom :: CPid -> [CPid] # enumFromThen :: CPid -> CPid -> [CPid] # enumFromTo :: CPid -> CPid -> [CPid] # enumFromThenTo :: CPid -> CPid -> CPid -> [CPid] #
Enum CSsize
Instance details Defined in System.Posix.Types Methods succ :: CSsize -> CSsize # pred :: CSsize -> CSsize # toEnum :: Int -> CSsize # fromEnum :: CSsize -> Int # enumFrom :: CSsize -> [CSsize] # enumFromThen :: CSsize -> CSsize -> [CSsize] # enumFromTo :: CSsize -> CSsize -> [CSsize] # enumFromThenTo :: CSsize -> CSsize -> CSsize -> [CSsize] #
Enum CGid
Instance details Defined in System.Posix.Types Methods succ :: CGid -> CGid # pred :: CGid -> CGid # toEnum :: Int -> CGid # fromEnum :: CGid -> Int # enumFrom :: CGid -> [CGid] # enumFromThen :: CGid -> CGid -> [CGid] # enumFromTo :: CGid -> CGid -> [CGid] # enumFromThenTo :: CGid -> CGid -> CGid -> [CGid] #
Enum CNlink
Instance details Defined in System.Posix.Types Methods succ :: CNlink -> CNlink # pred :: CNlink -> CNlink # toEnum :: Int -> CNlink # fromEnum :: CNlink -> Int # enumFrom :: CNlink -> [CNlink] # enumFromThen :: CNlink -> CNlink -> [CNlink] # enumFromTo :: CNlink -> CNlink -> [CNlink] # enumFromThenTo :: CNlink -> CNlink -> CNlink -> [CNlink] #
Enum CUid
Instance details Defined in System.Posix.Types Methods succ :: CUid -> CUid # pred :: CUid -> CUid # toEnum :: Int -> CUid # fromEnum :: CUid -> Int # enumFrom :: CUid -> [CUid] # enumFromThen :: CUid -> CUid -> [CUid] # enumFromTo :: CUid -> CUid -> [CUid] # enumFromThenTo :: CUid -> CUid -> CUid -> [CUid] #
Enum CCc
Instance details Defined in System.Posix.Types Methods succ :: CCc -> CCc # pred :: CCc -> CCc # toEnum :: Int -> CCc # fromEnum :: CCc -> Int # enumFrom :: CCc -> [CCc] # enumFromThen :: CCc -> CCc -> [CCc] # enumFromTo :: CCc -> CCc -> [CCc] # enumFromThenTo :: CCc -> CCc -> CCc -> [CCc] #
Enum CSpeed
Instance details Defined in System.Posix.Types Methods succ :: CSpeed -> CSpeed # pred :: CSpeed -> CSpeed # toEnum :: Int -> CSpeed # fromEnum :: CSpeed -> Int # enumFrom :: CSpeed -> [CSpeed] # enumFromThen :: CSpeed -> CSpeed -> [CSpeed] # enumFromTo :: CSpeed -> CSpeed -> [CSpeed] # enumFromThenTo :: CSpeed -> CSpeed -> CSpeed -> [CSpeed] #
Enum CTcflag
Instance details Defined in System.Posix.Types Methods succ :: CTcflag -> CTcflag # pred :: CTcflag -> CTcflag # toEnum :: Int -> CTcflag # fromEnum :: CTcflag -> Int # enumFrom :: CTcflag -> [CTcflag] # enumFromThen :: CTcflag -> CTcflag -> [CTcflag] # enumFromTo :: CTcflag -> CTcflag -> [CTcflag] # enumFromThenTo :: CTcflag -> CTcflag -> CTcflag -> [CTcflag] #
Enum CRLim
Instance details Defined in System.Posix.Types Methods succ :: CRLim -> CRLim # pred :: CRLim -> CRLim # toEnum :: Int -> CRLim # fromEnum :: CRLim -> Int # enumFrom :: CRLim -> [CRLim] # enumFromThen :: CRLim -> CRLim -> [CRLim] # enumFromTo :: CRLim -> CRLim -> [CRLim] # enumFromThenTo :: CRLim -> CRLim -> CRLim -> [CRLim] #
Enum CBlkSize
Instance details Defined in System.Posix.Types Methods succ :: CBlkSize -> CBlkSize # pred :: CBlkSize -> CBlkSize # toEnum :: Int -> CBlkSize # fromEnum :: CBlkSize -> Int # enumFrom :: CBlkSize -> [CBlkSize] # enumFromThen :: CBlkSize -> CBlkSize -> [CBlkSize] # enumFromTo :: CBlkSize -> CBlkSize -> [CBlkSize] # enumFromThenTo :: CBlkSize -> CBlkSize -> CBlkSize -> [CBlkSize] #
Enum CBlkCnt
Instance details Defined in System.Posix.Types Methods succ :: CBlkCnt -> CBlkCnt # pred :: CBlkCnt -> CBlkCnt # toEnum :: Int -> CBlkCnt # fromEnum :: CBlkCnt -> Int # enumFrom :: CBlkCnt -> [CBlkCnt] # enumFromThen :: CBlkCnt -> CBlkCnt -> [CBlkCnt] # enumFromTo :: CBlkCnt -> CBlkCnt -> [CBlkCnt] # enumFromThenTo :: CBlkCnt -> CBlkCnt -> CBlkCnt -> [CBlkCnt] #
Enum CClockId
Instance details Defined in System.Posix.Types Methods succ :: CClockId -> CClockId # pred :: CClockId -> CClockId # toEnum :: Int -> CClockId # fromEnum :: CClockId -> Int # enumFrom :: CClockId -> [CClockId] # enumFromThen :: CClockId -> CClockId -> [CClockId] # enumFromTo :: CClockId -> CClockId -> [CClockId] # enumFromThenTo :: CClockId -> CClockId -> CClockId -> [CClockId] #
Enum CFsBlkCnt
Instance details Defined in System.Posix.Types Methods succ :: CFsBlkCnt -> CFsBlkCnt # pred :: CFsBlkCnt -> CFsBlkCnt # toEnum :: Int -> CFsBlkCnt # fromEnum :: CFsBlkCnt -> Int # enumFrom :: CFsBlkCnt -> [CFsBlkCnt] # enumFromThen :: CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] # enumFromTo :: CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] # enumFromThenTo :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt -> [CFsBlkCnt] #
Enum CFsFilCnt
Instance details Defined in System.Posix.Types Methods succ :: CFsFilCnt -> CFsFilCnt # pred :: CFsFilCnt -> CFsFilCnt # toEnum :: Int -> CFsFilCnt # fromEnum :: CFsFilCnt -> Int # enumFrom :: CFsFilCnt -> [CFsFilCnt] # enumFromThen :: CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] # enumFromTo :: CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] # enumFromThenTo :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt -> [CFsFilCnt] #
Enum CId
Instance details Defined in System.Posix.Types Methods succ :: CId -> CId # pred :: CId -> CId # toEnum :: Int -> CId # fromEnum :: CId -> Int # enumFrom :: CId -> [CId] # enumFromThen :: CId -> CId -> [CId] # enumFromTo :: CId -> CId -> [CId] # enumFromThenTo :: CId -> CId -> CId -> [CId] #
Enum CKey
Instance details Defined in System.Posix.Types Methods succ :: CKey -> CKey # pred :: CKey -> CKey # toEnum :: Int -> CKey # fromEnum :: CKey -> Int # enumFrom :: CKey -> [CKey] # enumFromThen :: CKey -> CKey -> [CKey] # enumFromTo :: CKey -> CKey -> [CKey] # enumFromThenTo :: CKey -> CKey -> CKey -> [CKey] #
Enum CSocklen
Instance details Defined in System.Posix.Types Methods succ :: CSocklen -> CSocklen # pred :: CSocklen -> CSocklen # toEnum :: Int -> CSocklen # fromEnum :: CSocklen -> Int # enumFrom :: CSocklen -> [CSocklen] # enumFromThen :: CSocklen -> CSocklen -> [CSocklen] # enumFromTo :: CSocklen -> CSocklen -> [CSocklen] # enumFromThenTo :: CSocklen -> CSocklen -> CSocklen -> [CSocklen] #
Enum CNfds
Instance details Defined in System.Posix.Types Methods succ :: CNfds -> CNfds # pred :: CNfds -> CNfds # toEnum :: Int -> CNfds # fromEnum :: CNfds -> Int # enumFrom :: CNfds -> [CNfds] # enumFromThen :: CNfds -> CNfds -> [CNfds] # enumFromTo :: CNfds -> CNfds -> [CNfds] # enumFromThenTo :: CNfds -> CNfds -> CNfds -> [CNfds] #
Enum Fd
Instance details Defined in System.Posix.Types Methods succ :: Fd -> Fd # pred :: Fd -> Fd # toEnum :: Int -> Fd # fromEnum :: Fd -> Int # enumFrom :: Fd -> [Fd] # enumFromThen :: Fd -> Fd -> [Fd] # enumFromTo :: Fd -> Fd -> [Fd] # enumFromThenTo :: Fd -> Fd -> Fd -> [Fd] #
Enum Associativity	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: Associativity -> Associativity # pred :: Associativity -> Associativity # toEnum :: Int -> Associativity # fromEnum :: Associativity -> Int # enumFrom :: Associativity -> [Associativity] # enumFromThen :: Associativity -> Associativity -> [Associativity] # enumFromTo :: Associativity -> Associativity -> [Associativity] # enumFromThenTo :: Associativity -> Associativity -> Associativity -> [Associativity] #
Enum SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: SourceUnpackedness -> SourceUnpackedness # pred :: SourceUnpackedness -> SourceUnpackedness # toEnum :: Int -> SourceUnpackedness # fromEnum :: SourceUnpackedness -> Int # enumFrom :: SourceUnpackedness -> [SourceUnpackedness] # enumFromThen :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] # enumFromTo :: SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] # enumFromThenTo :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness -> [SourceUnpackedness] #
Enum SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: SourceStrictness -> SourceStrictness # pred :: SourceStrictness -> SourceStrictness # toEnum :: Int -> SourceStrictness # fromEnum :: SourceStrictness -> Int # enumFrom :: SourceStrictness -> [SourceStrictness] # enumFromThen :: SourceStrictness -> SourceStrictness -> [SourceStrictness] # enumFromTo :: SourceStrictness -> SourceStrictness -> [SourceStrictness] # enumFromThenTo :: SourceStrictness -> SourceStrictness -> SourceStrictness -> [SourceStrictness] #
Enum DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods succ :: DecidedStrictness -> DecidedStrictness # pred :: DecidedStrictness -> DecidedStrictness # toEnum :: Int -> DecidedStrictness # fromEnum :: DecidedStrictness -> Int # enumFrom :: DecidedStrictness -> [DecidedStrictness] # enumFromThen :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] # enumFromTo :: DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] # enumFromThenTo :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness -> [DecidedStrictness] #
Enum CChar
Instance details Defined in Foreign.C.Types Methods succ :: CChar -> CChar # pred :: CChar -> CChar # toEnum :: Int -> CChar # fromEnum :: CChar -> Int # enumFrom :: CChar -> [CChar] # enumFromThen :: CChar -> CChar -> [CChar] # enumFromTo :: CChar -> CChar -> [CChar] # enumFromThenTo :: CChar -> CChar -> CChar -> [CChar] #
Enum CSChar
Instance details Defined in Foreign.C.Types Methods succ :: CSChar -> CSChar # pred :: CSChar -> CSChar # toEnum :: Int -> CSChar # fromEnum :: CSChar -> Int # enumFrom :: CSChar -> [CSChar] # enumFromThen :: CSChar -> CSChar -> [CSChar] # enumFromTo :: CSChar -> CSChar -> [CSChar] # enumFromThenTo :: CSChar -> CSChar -> CSChar -> [CSChar] #
Enum CUChar
Instance details Defined in Foreign.C.Types Methods succ :: CUChar -> CUChar # pred :: CUChar -> CUChar # toEnum :: Int -> CUChar # fromEnum :: CUChar -> Int # enumFrom :: CUChar -> [CUChar] # enumFromThen :: CUChar -> CUChar -> [CUChar] # enumFromTo :: CUChar -> CUChar -> [CUChar] # enumFromThenTo :: CUChar -> CUChar -> CUChar -> [CUChar] #
Enum CShort
Instance details Defined in Foreign.C.Types Methods succ :: CShort -> CShort # pred :: CShort -> CShort # toEnum :: Int -> CShort # fromEnum :: CShort -> Int # enumFrom :: CShort -> [CShort] # enumFromThen :: CShort -> CShort -> [CShort] # enumFromTo :: CShort -> CShort -> [CShort] # enumFromThenTo :: CShort -> CShort -> CShort -> [CShort] #
Enum CUShort
Instance details Defined in Foreign.C.Types Methods succ :: CUShort -> CUShort # pred :: CUShort -> CUShort # toEnum :: Int -> CUShort # fromEnum :: CUShort -> Int # enumFrom :: CUShort -> [CUShort] # enumFromThen :: CUShort -> CUShort -> [CUShort] # enumFromTo :: CUShort -> CUShort -> [CUShort] # enumFromThenTo :: CUShort -> CUShort -> CUShort -> [CUShort] #
Enum CInt
Instance details Defined in Foreign.C.Types Methods succ :: CInt -> CInt # pred :: CInt -> CInt # toEnum :: Int -> CInt # fromEnum :: CInt -> Int # enumFrom :: CInt -> [CInt] # enumFromThen :: CInt -> CInt -> [CInt] # enumFromTo :: CInt -> CInt -> [CInt] # enumFromThenTo :: CInt -> CInt -> CInt -> [CInt] #
Enum CUInt
Instance details Defined in Foreign.C.Types Methods succ :: CUInt -> CUInt # pred :: CUInt -> CUInt # toEnum :: Int -> CUInt # fromEnum :: CUInt -> Int # enumFrom :: CUInt -> [CUInt] # enumFromThen :: CUInt -> CUInt -> [CUInt] # enumFromTo :: CUInt -> CUInt -> [CUInt] # enumFromThenTo :: CUInt -> CUInt -> CUInt -> [CUInt] #
Enum CLong
Instance details Defined in Foreign.C.Types Methods succ :: CLong -> CLong # pred :: CLong -> CLong # toEnum :: Int -> CLong # fromEnum :: CLong -> Int # enumFrom :: CLong -> [CLong] # enumFromThen :: CLong -> CLong -> [CLong] # enumFromTo :: CLong -> CLong -> [CLong] # enumFromThenTo :: CLong -> CLong -> CLong -> [CLong] #
Enum CULong
Instance details Defined in Foreign.C.Types Methods succ :: CULong -> CULong # pred :: CULong -> CULong # toEnum :: Int -> CULong # fromEnum :: CULong -> Int # enumFrom :: CULong -> [CULong] # enumFromThen :: CULong -> CULong -> [CULong] # enumFromTo :: CULong -> CULong -> [CULong] # enumFromThenTo :: CULong -> CULong -> CULong -> [CULong] #
Enum CLLong
Instance details Defined in Foreign.C.Types Methods succ :: CLLong -> CLLong # pred :: CLLong -> CLLong # toEnum :: Int -> CLLong # fromEnum :: CLLong -> Int # enumFrom :: CLLong -> [CLLong] # enumFromThen :: CLLong -> CLLong -> [CLLong] # enumFromTo :: CLLong -> CLLong -> [CLLong] # enumFromThenTo :: CLLong -> CLLong -> CLLong -> [CLLong] #
Enum CULLong
Instance details Defined in Foreign.C.Types Methods succ :: CULLong -> CULLong # pred :: CULLong -> CULLong # toEnum :: Int -> CULLong # fromEnum :: CULLong -> Int # enumFrom :: CULLong -> [CULLong] # enumFromThen :: CULLong -> CULLong -> [CULLong] # enumFromTo :: CULLong -> CULLong -> [CULLong] # enumFromThenTo :: CULLong -> CULLong -> CULLong -> [CULLong] #
Enum CBool
Instance details Defined in Foreign.C.Types Methods succ :: CBool -> CBool # pred :: CBool -> CBool # toEnum :: Int -> CBool # fromEnum :: CBool -> Int # enumFrom :: CBool -> [CBool] # enumFromThen :: CBool -> CBool -> [CBool] # enumFromTo :: CBool -> CBool -> [CBool] # enumFromThenTo :: CBool -> CBool -> CBool -> [CBool] #
Enum CFloat
Instance details Defined in Foreign.C.Types Methods succ :: CFloat -> CFloat # pred :: CFloat -> CFloat # toEnum :: Int -> CFloat # fromEnum :: CFloat -> Int # enumFrom :: CFloat -> [CFloat] # enumFromThen :: CFloat -> CFloat -> [CFloat] # enumFromTo :: CFloat -> CFloat -> [CFloat] # enumFromThenTo :: CFloat -> CFloat -> CFloat -> [CFloat] #
Enum CDouble
Instance details Defined in Foreign.C.Types Methods succ :: CDouble -> CDouble # pred :: CDouble -> CDouble # toEnum :: Int -> CDouble # fromEnum :: CDouble -> Int # enumFrom :: CDouble -> [CDouble] # enumFromThen :: CDouble -> CDouble -> [CDouble] # enumFromTo :: CDouble -> CDouble -> [CDouble] # enumFromThenTo :: CDouble -> CDouble -> CDouble -> [CDouble] #
Enum CPtrdiff
Instance details Defined in Foreign.C.Types Methods succ :: CPtrdiff -> CPtrdiff # pred :: CPtrdiff -> CPtrdiff # toEnum :: Int -> CPtrdiff # fromEnum :: CPtrdiff -> Int # enumFrom :: CPtrdiff -> [CPtrdiff] # enumFromThen :: CPtrdiff -> CPtrdiff -> [CPtrdiff] # enumFromTo :: CPtrdiff -> CPtrdiff -> [CPtrdiff] # enumFromThenTo :: CPtrdiff -> CPtrdiff -> CPtrdiff -> [CPtrdiff] #
Enum CSize
Instance details Defined in Foreign.C.Types Methods succ :: CSize -> CSize # pred :: CSize -> CSize # toEnum :: Int -> CSize # fromEnum :: CSize -> Int # enumFrom :: CSize -> [CSize] # enumFromThen :: CSize -> CSize -> [CSize] # enumFromTo :: CSize -> CSize -> [CSize] # enumFromThenTo :: CSize -> CSize -> CSize -> [CSize] #
Enum CWchar
Instance details Defined in Foreign.C.Types Methods succ :: CWchar -> CWchar # pred :: CWchar -> CWchar # toEnum :: Int -> CWchar # fromEnum :: CWchar -> Int # enumFrom :: CWchar -> [CWchar] # enumFromThen :: CWchar -> CWchar -> [CWchar] # enumFromTo :: CWchar -> CWchar -> [CWchar] # enumFromThenTo :: CWchar -> CWchar -> CWchar -> [CWchar] #
Enum CSigAtomic
Instance details Defined in Foreign.C.Types Methods succ :: CSigAtomic -> CSigAtomic # pred :: CSigAtomic -> CSigAtomic # toEnum :: Int -> CSigAtomic # fromEnum :: CSigAtomic -> Int # enumFrom :: CSigAtomic -> [CSigAtomic] # enumFromThen :: CSigAtomic -> CSigAtomic -> [CSigAtomic] # enumFromTo :: CSigAtomic -> CSigAtomic -> [CSigAtomic] # enumFromThenTo :: CSigAtomic -> CSigAtomic -> CSigAtomic -> [CSigAtomic] #
Enum CClock
Instance details Defined in Foreign.C.Types Methods succ :: CClock -> CClock # pred :: CClock -> CClock # toEnum :: Int -> CClock # fromEnum :: CClock -> Int # enumFrom :: CClock -> [CClock] # enumFromThen :: CClock -> CClock -> [CClock] # enumFromTo :: CClock -> CClock -> [CClock] # enumFromThenTo :: CClock -> CClock -> CClock -> [CClock] #
Enum CTime
Instance details Defined in Foreign.C.Types Methods succ :: CTime -> CTime # pred :: CTime -> CTime # toEnum :: Int -> CTime # fromEnum :: CTime -> Int # enumFrom :: CTime -> [CTime] # enumFromThen :: CTime -> CTime -> [CTime] # enumFromTo :: CTime -> CTime -> [CTime] # enumFromThenTo :: CTime -> CTime -> CTime -> [CTime] #
Enum CUSeconds
Instance details Defined in Foreign.C.Types Methods succ :: CUSeconds -> CUSeconds # pred :: CUSeconds -> CUSeconds # toEnum :: Int -> CUSeconds # fromEnum :: CUSeconds -> Int # enumFrom :: CUSeconds -> [CUSeconds] # enumFromThen :: CUSeconds -> CUSeconds -> [CUSeconds] # enumFromTo :: CUSeconds -> CUSeconds -> [CUSeconds] # enumFromThenTo :: CUSeconds -> CUSeconds -> CUSeconds -> [CUSeconds] #
Enum CSUSeconds
Instance details Defined in Foreign.C.Types Methods succ :: CSUSeconds -> CSUSeconds # pred :: CSUSeconds -> CSUSeconds # toEnum :: Int -> CSUSeconds # fromEnum :: CSUSeconds -> Int # enumFrom :: CSUSeconds -> [CSUSeconds] # enumFromThen :: CSUSeconds -> CSUSeconds -> [CSUSeconds] # enumFromTo :: CSUSeconds -> CSUSeconds -> [CSUSeconds] # enumFromThenTo :: CSUSeconds -> CSUSeconds -> CSUSeconds -> [CSUSeconds] #
Enum CIntPtr
Instance details Defined in Foreign.C.Types Methods succ :: CIntPtr -> CIntPtr # pred :: CIntPtr -> CIntPtr # toEnum :: Int -> CIntPtr # fromEnum :: CIntPtr -> Int # enumFrom :: CIntPtr -> [CIntPtr] # enumFromThen :: CIntPtr -> CIntPtr -> [CIntPtr] # enumFromTo :: CIntPtr -> CIntPtr -> [CIntPtr] # enumFromThenTo :: CIntPtr -> CIntPtr -> CIntPtr -> [CIntPtr] #
Enum CUIntPtr
Instance details Defined in Foreign.C.Types Methods succ :: CUIntPtr -> CUIntPtr # pred :: CUIntPtr -> CUIntPtr # toEnum :: Int -> CUIntPtr # fromEnum :: CUIntPtr -> Int # enumFrom :: CUIntPtr -> [CUIntPtr] # enumFromThen :: CUIntPtr -> CUIntPtr -> [CUIntPtr] # enumFromTo :: CUIntPtr -> CUIntPtr -> [CUIntPtr] # enumFromThenTo :: CUIntPtr -> CUIntPtr -> CUIntPtr -> [CUIntPtr] #
Enum CIntMax
Instance details Defined in Foreign.C.Types Methods succ :: CIntMax -> CIntMax # pred :: CIntMax -> CIntMax # toEnum :: Int -> CIntMax # fromEnum :: CIntMax -> Int # enumFrom :: CIntMax -> [CIntMax] # enumFromThen :: CIntMax -> CIntMax -> [CIntMax] # enumFromTo :: CIntMax -> CIntMax -> [CIntMax] # enumFromThenTo :: CIntMax -> CIntMax -> CIntMax -> [CIntMax] #
Enum CUIntMax
Instance details Defined in Foreign.C.Types Methods succ :: CUIntMax -> CUIntMax # pred :: CUIntMax -> CUIntMax # toEnum :: Int -> CUIntMax # fromEnum :: CUIntMax -> Int # enumFrom :: CUIntMax -> [CUIntMax] # enumFromThen :: CUIntMax -> CUIntMax -> [CUIntMax] # enumFromTo :: CUIntMax -> CUIntMax -> [CUIntMax] # enumFromThenTo :: CUIntMax -> CUIntMax -> CUIntMax -> [CUIntMax] #
Enum GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Unicode Methods succ :: GeneralCategory -> GeneralCategory # pred :: GeneralCategory -> GeneralCategory # toEnum :: Int -> GeneralCategory # fromEnum :: GeneralCategory -> Int # enumFrom :: GeneralCategory -> [GeneralCategory] # enumFromThen :: GeneralCategory -> GeneralCategory -> [GeneralCategory] # enumFromTo :: GeneralCategory -> GeneralCategory -> [GeneralCategory] # enumFromThenTo :: GeneralCategory -> GeneralCategory -> GeneralCategory -> [GeneralCategory] #
Enum Extension
Instance details Defined in GHC.LanguageExtensions.Type Methods succ :: Extension -> Extension # pred :: Extension -> Extension # toEnum :: Int -> Extension # fromEnum :: Extension -> Int # enumFrom :: Extension -> [Extension] # enumFromThen :: Extension -> Extension -> [Extension] # enumFromTo :: Extension -> Extension -> [Extension] # enumFromThenTo :: Extension -> Extension -> Extension -> [Extension] #
Enum ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods succ :: ComplexBasis -> ComplexBasis # pred :: ComplexBasis -> ComplexBasis # toEnum :: Int -> ComplexBasis # fromEnum :: ComplexBasis -> Int # enumFrom :: ComplexBasis -> [ComplexBasis] # enumFromThen :: ComplexBasis -> ComplexBasis -> [ComplexBasis] # enumFromTo :: ComplexBasis -> ComplexBasis -> [ComplexBasis] # enumFromThenTo :: ComplexBasis -> ComplexBasis -> ComplexBasis -> [ComplexBasis] #
Integral a => Enum (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods succ :: Ratio a -> Ratio a # pred :: Ratio a -> Ratio a # toEnum :: Int -> Ratio a # fromEnum :: Ratio a -> Int # enumFrom :: Ratio a -> [Ratio a] # enumFromThen :: Ratio a -> Ratio a -> [Ratio a] # enumFromTo :: Ratio a -> Ratio a -> [Ratio a] # enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #
Enum a => Enum (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods succ :: WrapFractional a -> WrapFractional a # pred :: WrapFractional a -> WrapFractional a # toEnum :: Int -> WrapFractional a # fromEnum :: WrapFractional a -> Int # enumFrom :: WrapFractional a -> [WrapFractional a] # enumFromThen :: WrapFractional a -> WrapFractional a -> [WrapFractional a] # enumFromTo :: WrapFractional a -> WrapFractional a -> [WrapFractional a] # enumFromThenTo :: WrapFractional a -> WrapFractional a -> WrapFractional a -> [WrapFractional a] #
Enum a => Enum (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods succ :: WrapIntegral a -> WrapIntegral a # pred :: WrapIntegral a -> WrapIntegral a # toEnum :: Int -> WrapIntegral a # fromEnum :: WrapIntegral a -> Int # enumFrom :: WrapIntegral a -> [WrapIntegral a] # enumFromThen :: WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] # enumFromTo :: WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] # enumFromThenTo :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] #
Enum a => Enum (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods succ :: Down a -> Down a # pred :: Down a -> Down a # toEnum :: Int -> Down a # fromEnum :: Down a -> Int # enumFrom :: Down a -> [Down a] # enumFromThen :: Down a -> Down a -> [Down a] # enumFromTo :: Down a -> Down a -> [Down a] # enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] #
Enum a => Enum (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Min a -> Min a # pred :: Min a -> Min a # toEnum :: Int -> Min a # fromEnum :: Min a -> Int # enumFrom :: Min a -> [Min a] # enumFromThen :: Min a -> Min a -> [Min a] # enumFromTo :: Min a -> Min a -> [Min a] # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #
Enum a => Enum (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Max a -> Max a # pred :: Max a -> Max a # toEnum :: Int -> Max a # fromEnum :: Max a -> Int # enumFrom :: Max a -> [Max a] # enumFromThen :: Max a -> Max a -> [Max a] # enumFromTo :: Max a -> Max a -> [Max a] # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #
Enum a => Enum (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: First a -> First a # pred :: First a -> First a # toEnum :: Int -> First a # fromEnum :: First a -> Int # enumFrom :: First a -> [First a] # enumFromThen :: First a -> First a -> [First a] # enumFromTo :: First a -> First a -> [First a] # enumFromThenTo :: First a -> First a -> First a -> [First a] #
Enum a => Enum (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Last a -> Last a # pred :: Last a -> Last a # toEnum :: Int -> Last a # fromEnum :: Last a -> Int # enumFrom :: Last a -> [Last a] # enumFromThen :: Last a -> Last a -> [Last a] # enumFromTo :: Last a -> Last a -> [Last a] # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #
Enum a => Enum (WrappedMonoid a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a # pred :: WrappedMonoid a -> WrappedMonoid a # toEnum :: Int -> WrappedMonoid a # fromEnum :: WrappedMonoid a -> Int # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> Identity a # toEnum :: Int -> Identity a # fromEnum :: Identity a -> Int # enumFrom :: Identity a -> [Identity a] # enumFromThen :: Identity a -> Identity a -> [Identity a] # enumFromTo :: Identity a -> Identity a -> [Identity a] # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] #
KnownNat n => Enum (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods succ :: Ordinal n -> Ordinal n # pred :: Ordinal n -> Ordinal n # toEnum :: Int -> Ordinal n # fromEnum :: Ordinal n -> Int # enumFrom :: Ordinal n -> [Ordinal n] # enumFromThen :: Ordinal n -> Ordinal n -> [Ordinal n] # enumFromTo :: Ordinal n -> Ordinal n -> [Ordinal n] # enumFromThenTo :: Ordinal n -> Ordinal n -> Ordinal n -> [Ordinal n] #
Enum r => Enum (Scalar r)
Instance details Defined in Algebra.Scalar Methods succ :: Scalar r -> Scalar r # pred :: Scalar r -> Scalar r # toEnum :: Int -> Scalar r # fromEnum :: Scalar r -> Int # enumFrom :: Scalar r -> [Scalar r] # enumFromThen :: Scalar r -> Scalar r -> [Scalar r] # enumFromTo :: Scalar r -> Scalar r -> [Scalar r] # enumFromThenTo :: Scalar r -> Scalar r -> Scalar r -> [Scalar r] #
Enum (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods succ :: Fixed a -> Fixed a # pred :: Fixed a -> Fixed a # toEnum :: Int -> Fixed a # fromEnum :: Fixed a -> Int # enumFrom :: Fixed a -> [Fixed a] # enumFromThen :: Fixed a -> Fixed a -> [Fixed a] # enumFromTo :: Fixed a -> Fixed a -> [Fixed a] # enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] #
Enum (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods succ :: Proxy s -> Proxy s # pred :: Proxy s -> Proxy s # toEnum :: Int -> Proxy s # fromEnum :: Proxy s -> Int # enumFrom :: Proxy s -> [Proxy s] # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Enum (f a) => Enum (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods succ :: Ap f a -> Ap f a # pred :: Ap f a -> Ap f a # toEnum :: Int -> Ap f a # fromEnum :: Ap f a -> Int # enumFrom :: Ap f a -> [Ap f a] # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] #
Enum (f a) => Enum (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a # pred :: Alt f a -> Alt f a # toEnum :: Int -> Alt f a # fromEnum :: Alt f a -> Int # enumFrom :: Alt f a -> [Alt f a] # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #
a ~ b => Enum (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b # pred :: (a :~: b) -> a :~: b # toEnum :: Int -> a :~: b # fromEnum :: (a :~: b) -> Int # enumFrom :: (a :~: b) -> [a :~: b] # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] #
Enum a => Enum (Tagged s a)
Instance details Defined in Data.Tagged Methods succ :: Tagged s a -> Tagged s a # pred :: Tagged s a -> Tagged s a # toEnum :: Int -> Tagged s a # fromEnum :: Tagged s a -> Int # enumFrom :: Tagged s a -> [Tagged s a] # enumFromThen :: Tagged s a -> Tagged s a -> [Tagged s a] # enumFromTo :: Tagged s a -> Tagged s a -> [Tagged s a] # enumFromThenTo :: Tagged s a -> Tagged s a -> Tagged s a -> [Tagged s a] #
a ~~ b => Enum (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~~: b) -> a :~~: b # pred :: (a :~~: b) -> a :~~: b # toEnum :: Int -> a :~~: b # fromEnum :: (a :~~: b) -> Int # enumFrom :: (a :~~: b) -> [a :~~: b] # enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] # enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] # enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

class Eq a where #

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity: x == x = True
Symmetry: x == y = y == x
Transitivity: if x == y && y == z = True, then x == z = True
Substitutivity: if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True
Negation: x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 #

(/=) :: a -> a -> Bool infix 4 #

Instances

Instances details

Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool # (/=) :: Char -> Char -> Bool #
Eq Double	Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Double)`False Also note that `Double`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Eq Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int8 -> Int8 -> Bool # (/=) :: Int8 -> Int8 -> Bool #
Eq Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int16 -> Int16 -> Bool # (/=) :: Int16 -> Int16 -> Bool #
Eq Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int32 -> Int32 -> Bool # (/=) :: Int32 -> Int32 -> Bool #
Eq Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int64 -> Int64 -> Bool # (/=) :: Int64 -> Int64 -> Bool #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool # (/=) :: Word -> Word -> Bool #
Eq Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word8 -> Word8 -> Bool # (/=) :: Word8 -> Word8 -> Bool #
Eq Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word16 -> Word16 -> Bool # (/=) :: Word16 -> Word16 -> Bool #
Eq Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word32 -> Word32 -> Bool # (/=) :: Word32 -> Word32 -> Bool #
Eq Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word64 -> Word64 -> Bool # (/=) :: Word64 -> Word64 -> Bool #
Eq SomeTypeRep
Instance details Defined in Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool #
Eq Exp
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Exp -> Exp -> Bool # (/=) :: Exp -> Exp -> Bool #
Eq Match
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Match -> Match -> Bool # (/=) :: Match -> Match -> Bool #
Eq Clause
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Clause -> Clause -> Bool # (/=) :: Clause -> Clause -> Bool #
Eq Pat
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Pat -> Pat -> Bool # (/=) :: Pat -> Pat -> Bool #
Eq Type
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Type -> Type -> Bool # (/=) :: Type -> Type -> Bool #
Eq Dec
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Dec -> Dec -> Bool # (/=) :: Dec -> Dec -> Bool #
Eq Name
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Name -> Name -> Bool # (/=) :: Name -> Name -> Bool #
Eq FunDep
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: FunDep -> FunDep -> Bool # (/=) :: FunDep -> FunDep -> Bool #
Eq InjectivityAnn
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: InjectivityAnn -> InjectivityAnn -> Bool # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool #
Eq Overlap
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Overlap -> Overlap -> Bool # (/=) :: Overlap -> Overlap -> Bool #
Eq ()
Instance details Defined in GHC.Classes Methods (==) :: () -> () -> Bool # (/=) :: () -> () -> Bool #
Eq TyCon
Instance details Defined in GHC.Classes Methods (==) :: TyCon -> TyCon -> Bool # (/=) :: TyCon -> TyCon -> Bool #
Eq Module
Instance details Defined in GHC.Classes Methods (==) :: Module -> Module -> Bool # (/=) :: Module -> Module -> Bool #
Eq TrName
Instance details Defined in GHC.Classes Methods (==) :: TrName -> TrName -> Bool # (/=) :: TrName -> TrName -> Bool #
Eq IntSet
Instance details Defined in Data.IntSet.Internal Methods (==) :: IntSet -> IntSet -> Bool # (/=) :: IntSet -> IntSet -> Bool #
Eq ByteString
Instance details Defined in Data.ByteString.Internal Methods (==) :: ByteString -> ByteString -> Bool # (/=) :: ByteString -> ByteString -> Bool #
Eq IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOException -> IOException -> Bool # (/=) :: IOException -> IOException -> Bool #
Eq IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool # (/=) :: IOErrorType -> IOErrorType -> Bool #
Eq Handle	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: Handle -> Handle -> Bool # (/=) :: Handle -> Handle -> Bool #
Eq Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods (==) :: Void -> Void -> Bool # (/=) :: Void -> Void -> Bool #
Eq SpecConstrAnnotation	Since: base-4.3.0.0
Instance details Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool #
Eq Unique
Instance details Defined in Data.Unique Methods (==) :: Unique -> Unique -> Bool # (/=) :: Unique -> Unique -> Bool #
Eq Version	Since: base-2.1
Instance details Defined in Data.Version Methods (==) :: Version -> Version -> Bool # (/=) :: Version -> Version -> Bool #
Eq ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: ThreadId -> ThreadId -> Bool # (/=) :: ThreadId -> ThreadId -> Bool #
Eq BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: BlockReason -> BlockReason -> Bool # (/=) :: BlockReason -> BlockReason -> Bool #
Eq ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: ThreadStatus -> ThreadStatus -> Bool # (/=) :: ThreadStatus -> ThreadStatus -> Bool #
Eq CDev
Instance details Defined in System.Posix.Types Methods (==) :: CDev -> CDev -> Bool # (/=) :: CDev -> CDev -> Bool #
Eq CIno
Instance details Defined in System.Posix.Types Methods (==) :: CIno -> CIno -> Bool # (/=) :: CIno -> CIno -> Bool #
Eq CMode
Instance details Defined in System.Posix.Types Methods (==) :: CMode -> CMode -> Bool # (/=) :: CMode -> CMode -> Bool #
Eq COff
Instance details Defined in System.Posix.Types Methods (==) :: COff -> COff -> Bool # (/=) :: COff -> COff -> Bool #
Eq CPid
Instance details Defined in System.Posix.Types Methods (==) :: CPid -> CPid -> Bool # (/=) :: CPid -> CPid -> Bool #
Eq CSsize
Instance details Defined in System.Posix.Types Methods (==) :: CSsize -> CSsize -> Bool # (/=) :: CSsize -> CSsize -> Bool #
Eq CGid
Instance details Defined in System.Posix.Types Methods (==) :: CGid -> CGid -> Bool # (/=) :: CGid -> CGid -> Bool #
Eq CNlink
Instance details Defined in System.Posix.Types Methods (==) :: CNlink -> CNlink -> Bool # (/=) :: CNlink -> CNlink -> Bool #
Eq CUid
Instance details Defined in System.Posix.Types Methods (==) :: CUid -> CUid -> Bool # (/=) :: CUid -> CUid -> Bool #
Eq CCc
Instance details Defined in System.Posix.Types Methods (==) :: CCc -> CCc -> Bool # (/=) :: CCc -> CCc -> Bool #
Eq CSpeed
Instance details Defined in System.Posix.Types Methods (==) :: CSpeed -> CSpeed -> Bool # (/=) :: CSpeed -> CSpeed -> Bool #
Eq CTcflag
Instance details Defined in System.Posix.Types Methods (==) :: CTcflag -> CTcflag -> Bool # (/=) :: CTcflag -> CTcflag -> Bool #
Eq CRLim
Instance details Defined in System.Posix.Types Methods (==) :: CRLim -> CRLim -> Bool # (/=) :: CRLim -> CRLim -> Bool #
Eq CBlkSize
Instance details Defined in System.Posix.Types Methods (==) :: CBlkSize -> CBlkSize -> Bool # (/=) :: CBlkSize -> CBlkSize -> Bool #
Eq CBlkCnt
Instance details Defined in System.Posix.Types Methods (==) :: CBlkCnt -> CBlkCnt -> Bool # (/=) :: CBlkCnt -> CBlkCnt -> Bool #
Eq CClockId
Instance details Defined in System.Posix.Types Methods (==) :: CClockId -> CClockId -> Bool # (/=) :: CClockId -> CClockId -> Bool #
Eq CFsBlkCnt
Instance details Defined in System.Posix.Types Methods (==) :: CFsBlkCnt -> CFsBlkCnt -> Bool # (/=) :: CFsBlkCnt -> CFsBlkCnt -> Bool #
Eq CFsFilCnt
Instance details Defined in System.Posix.Types Methods (==) :: CFsFilCnt -> CFsFilCnt -> Bool # (/=) :: CFsFilCnt -> CFsFilCnt -> Bool #
Eq CId
Instance details Defined in System.Posix.Types Methods (==) :: CId -> CId -> Bool # (/=) :: CId -> CId -> Bool #
Eq CKey
Instance details Defined in System.Posix.Types Methods (==) :: CKey -> CKey -> Bool # (/=) :: CKey -> CKey -> Bool #
Eq CTimer
Instance details Defined in System.Posix.Types Methods (==) :: CTimer -> CTimer -> Bool # (/=) :: CTimer -> CTimer -> Bool #
Eq CSocklen
Instance details Defined in System.Posix.Types Methods (==) :: CSocklen -> CSocklen -> Bool # (/=) :: CSocklen -> CSocklen -> Bool #
Eq CNfds
Instance details Defined in System.Posix.Types Methods (==) :: CNfds -> CNfds -> Bool # (/=) :: CNfds -> CNfds -> Bool #
Eq Fd
Instance details Defined in System.Posix.Types Methods (==) :: Fd -> Fd -> Bool # (/=) :: Fd -> Fd -> Bool #
Eq Errno	Since: base-2.1
Instance details Defined in Foreign.C.Error Methods (==) :: Errno -> Errno -> Bool # (/=) :: Errno -> Errno -> Bool #
Eq AsyncException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool #
Eq ArrayException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool #
Eq ExitCode
Instance details Defined in GHC.IO.Exception Methods (==) :: ExitCode -> ExitCode -> Bool # (/=) :: ExitCode -> ExitCode -> Bool #
Eq BufferMode	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: BufferMode -> BufferMode -> Bool # (/=) :: BufferMode -> BufferMode -> Bool #
Eq Newline	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: Newline -> Newline -> Bool # (/=) :: Newline -> Newline -> Bool #
Eq NewlineMode	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: NewlineMode -> NewlineMode -> Bool # (/=) :: NewlineMode -> NewlineMode -> Bool #
Eq MaskingState	Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods (==) :: MaskingState -> MaskingState -> Bool # (/=) :: MaskingState -> MaskingState -> Bool #
Eq ErrorCall	Since: base-4.7.0.0
Instance details Defined in GHC.Exception Methods (==) :: ErrorCall -> ErrorCall -> Bool # (/=) :: ErrorCall -> ErrorCall -> Bool #
Eq ArithException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool # (/=) :: ArithException -> ArithException -> Bool #
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Eq Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods (==) :: Fixity -> Fixity -> Bool # (/=) :: Fixity -> Fixity -> Bool #
Eq Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool #
Eq SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool #
Eq SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool #
Eq DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool #
Eq SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods (==) :: SomeSymbol -> SomeSymbol -> Bool # (/=) :: SomeSymbol -> SomeSymbol -> Bool #
Eq SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods (==) :: SomeNat -> SomeNat -> Bool # (/=) :: SomeNat -> SomeNat -> Bool #
Eq CChar
Instance details Defined in Foreign.C.Types Methods (==) :: CChar -> CChar -> Bool # (/=) :: CChar -> CChar -> Bool #
Eq CSChar
Instance details Defined in Foreign.C.Types Methods (==) :: CSChar -> CSChar -> Bool # (/=) :: CSChar -> CSChar -> Bool #
Eq CUChar
Instance details Defined in Foreign.C.Types Methods (==) :: CUChar -> CUChar -> Bool # (/=) :: CUChar -> CUChar -> Bool #
Eq CShort
Instance details Defined in Foreign.C.Types Methods (==) :: CShort -> CShort -> Bool # (/=) :: CShort -> CShort -> Bool #
Eq CUShort
Instance details Defined in Foreign.C.Types Methods (==) :: CUShort -> CUShort -> Bool # (/=) :: CUShort -> CUShort -> Bool #
Eq CInt
Instance details Defined in Foreign.C.Types Methods (==) :: CInt -> CInt -> Bool # (/=) :: CInt -> CInt -> Bool #
Eq CUInt
Instance details Defined in Foreign.C.Types Methods (==) :: CUInt -> CUInt -> Bool # (/=) :: CUInt -> CUInt -> Bool #
Eq CLong
Instance details Defined in Foreign.C.Types Methods (==) :: CLong -> CLong -> Bool # (/=) :: CLong -> CLong -> Bool #
Eq CULong
Instance details Defined in Foreign.C.Types Methods (==) :: CULong -> CULong -> Bool # (/=) :: CULong -> CULong -> Bool #
Eq CLLong
Instance details Defined in Foreign.C.Types Methods (==) :: CLLong -> CLLong -> Bool # (/=) :: CLLong -> CLLong -> Bool #
Eq CULLong
Instance details Defined in Foreign.C.Types Methods (==) :: CULLong -> CULLong -> Bool # (/=) :: CULLong -> CULLong -> Bool #
Eq CBool
Instance details Defined in Foreign.C.Types Methods (==) :: CBool -> CBool -> Bool # (/=) :: CBool -> CBool -> Bool #
Eq CFloat
Instance details Defined in Foreign.C.Types Methods (==) :: CFloat -> CFloat -> Bool # (/=) :: CFloat -> CFloat -> Bool #
Eq CDouble
Instance details Defined in Foreign.C.Types Methods (==) :: CDouble -> CDouble -> Bool # (/=) :: CDouble -> CDouble -> Bool #
Eq CPtrdiff
Instance details Defined in Foreign.C.Types Methods (==) :: CPtrdiff -> CPtrdiff -> Bool # (/=) :: CPtrdiff -> CPtrdiff -> Bool #
Eq CSize
Instance details Defined in Foreign.C.Types Methods (==) :: CSize -> CSize -> Bool # (/=) :: CSize -> CSize -> Bool #
Eq CWchar
Instance details Defined in Foreign.C.Types Methods (==) :: CWchar -> CWchar -> Bool # (/=) :: CWchar -> CWchar -> Bool #
Eq CSigAtomic
Instance details Defined in Foreign.C.Types Methods (==) :: CSigAtomic -> CSigAtomic -> Bool # (/=) :: CSigAtomic -> CSigAtomic -> Bool #
Eq CClock
Instance details Defined in Foreign.C.Types Methods (==) :: CClock -> CClock -> Bool # (/=) :: CClock -> CClock -> Bool #
Eq CTime
Instance details Defined in Foreign.C.Types Methods (==) :: CTime -> CTime -> Bool # (/=) :: CTime -> CTime -> Bool #
Eq CUSeconds
Instance details Defined in Foreign.C.Types Methods (==) :: CUSeconds -> CUSeconds -> Bool # (/=) :: CUSeconds -> CUSeconds -> Bool #
Eq CSUSeconds
Instance details Defined in Foreign.C.Types Methods (==) :: CSUSeconds -> CSUSeconds -> Bool # (/=) :: CSUSeconds -> CSUSeconds -> Bool #
Eq CIntPtr
Instance details Defined in Foreign.C.Types Methods (==) :: CIntPtr -> CIntPtr -> Bool # (/=) :: CIntPtr -> CIntPtr -> Bool #
Eq CUIntPtr
Instance details Defined in Foreign.C.Types Methods (==) :: CUIntPtr -> CUIntPtr -> Bool # (/=) :: CUIntPtr -> CUIntPtr -> Bool #
Eq CIntMax
Instance details Defined in Foreign.C.Types Methods (==) :: CIntMax -> CIntMax -> Bool # (/=) :: CIntMax -> CIntMax -> Bool #
Eq CUIntMax
Instance details Defined in Foreign.C.Types Methods (==) :: CUIntMax -> CUIntMax -> Bool # (/=) :: CUIntMax -> CUIntMax -> Bool #
Eq Fingerprint	Since: base-4.4.0.0
Instance details Defined in GHC.Fingerprint.Type Methods (==) :: Fingerprint -> Fingerprint -> Bool # (/=) :: Fingerprint -> Fingerprint -> Bool #
Eq Lexeme	Since: base-2.1
Instance details Defined in Text.Read.Lex Methods (==) :: Lexeme -> Lexeme -> Bool # (/=) :: Lexeme -> Lexeme -> Bool #
Eq Number	Since: base-4.6.0.0
Instance details Defined in Text.Read.Lex Methods (==) :: Number -> Number -> Bool # (/=) :: Number -> Number -> Bool #
Eq GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool # (/=) :: GeneralCategory -> GeneralCategory -> Bool #
Eq SrcLoc	Since: base-4.9.0.0
Instance details Defined in GHC.Stack.Types Methods (==) :: SrcLoc -> SrcLoc -> Bool # (/=) :: SrcLoc -> SrcLoc -> Bool #
Eq ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods (==) :: ShortByteString -> ShortByteString -> Bool # (/=) :: ShortByteString -> ShortByteString -> Bool #
Eq ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods (==) :: ByteString -> ByteString -> Bool # (/=) :: ByteString -> ByteString -> Bool #
Eq Extension
Instance details Defined in GHC.LanguageExtensions.Type Methods (==) :: Extension -> Extension -> Bool # (/=) :: Extension -> Extension -> Bool #
Eq ForeignSrcLang
Instance details Defined in GHC.ForeignSrcLang.Type Methods (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool #
Eq Lex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Lex -> Lex -> Bool # (/=) :: Lex -> Lex -> Bool #
Eq Revlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Revlex -> Revlex -> Bool # (/=) :: Revlex -> Revlex -> Bool #
Eq Grevlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Grevlex -> Grevlex -> Bool # (/=) :: Grevlex -> Grevlex -> Bool #
Eq Grlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Grlex -> Grlex -> Bool # (/=) :: Grlex -> Grlex -> Bool #
Eq SomeSNat
Instance details Defined in Data.Type.Natural Methods (==) :: SomeSNat -> SomeSNat -> Bool # (/=) :: SomeSNat -> SomeSNat -> Bool #
Eq BigNat
Instance details Defined in GHC.Integer.Type Methods (==) :: BigNat -> BigNat -> Bool # (/=) :: BigNat -> BigNat -> Bool #
Eq Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods (==) :: Doc -> Doc -> Bool # (/=) :: Doc -> Doc -> Bool #
Eq TextDetails
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: TextDetails -> TextDetails -> Bool # (/=) :: TextDetails -> TextDetails -> Bool #
Eq Style
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: Style -> Style -> Bool # (/=) :: Style -> Style -> Bool #
Eq Mode
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: Mode -> Mode -> Bool # (/=) :: Mode -> Mode -> Bool #
Eq ModName
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: ModName -> ModName -> Bool # (/=) :: ModName -> ModName -> Bool #
Eq PkgName
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: PkgName -> PkgName -> Bool # (/=) :: PkgName -> PkgName -> Bool #
Eq Module
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Module -> Module -> Bool # (/=) :: Module -> Module -> Bool #
Eq OccName
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: OccName -> OccName -> Bool # (/=) :: OccName -> OccName -> Bool #
Eq NameFlavour
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: NameFlavour -> NameFlavour -> Bool # (/=) :: NameFlavour -> NameFlavour -> Bool #
Eq NameSpace
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: NameSpace -> NameSpace -> Bool # (/=) :: NameSpace -> NameSpace -> Bool #
Eq Loc
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Loc -> Loc -> Bool # (/=) :: Loc -> Loc -> Bool #
Eq Info
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Info -> Info -> Bool # (/=) :: Info -> Info -> Bool #
Eq ModuleInfo
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: ModuleInfo -> ModuleInfo -> Bool # (/=) :: ModuleInfo -> ModuleInfo -> Bool #
Eq Fixity
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Fixity -> Fixity -> Bool # (/=) :: Fixity -> Fixity -> Bool #
Eq FixityDirection
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: FixityDirection -> FixityDirection -> Bool # (/=) :: FixityDirection -> FixityDirection -> Bool #
Eq Lit
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Lit -> Lit -> Bool # (/=) :: Lit -> Lit -> Bool #
Eq Bytes
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Bytes -> Bytes -> Bool # (/=) :: Bytes -> Bytes -> Bool #
Eq Body
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Body -> Body -> Bool # (/=) :: Body -> Body -> Bool #
Eq Guard
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Guard -> Guard -> Bool # (/=) :: Guard -> Guard -> Bool #
Eq Stmt
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Stmt -> Stmt -> Bool # (/=) :: Stmt -> Stmt -> Bool #
Eq Range
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Range -> Range -> Bool # (/=) :: Range -> Range -> Bool #
Eq DerivClause
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivClause -> DerivClause -> Bool # (/=) :: DerivClause -> DerivClause -> Bool #
Eq DerivStrategy
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivStrategy -> DerivStrategy -> Bool # (/=) :: DerivStrategy -> DerivStrategy -> Bool #
Eq TypeFamilyHead
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool #
Eq TySynEqn
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: TySynEqn -> TySynEqn -> Bool # (/=) :: TySynEqn -> TySynEqn -> Bool #
Eq Foreign
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Foreign -> Foreign -> Bool # (/=) :: Foreign -> Foreign -> Bool #
Eq Callconv
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Callconv -> Callconv -> Bool # (/=) :: Callconv -> Callconv -> Bool #
Eq Safety
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Safety -> Safety -> Bool # (/=) :: Safety -> Safety -> Bool #
Eq Pragma
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Pragma -> Pragma -> Bool # (/=) :: Pragma -> Pragma -> Bool #
Eq Inline
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Inline -> Inline -> Bool # (/=) :: Inline -> Inline -> Bool #
Eq RuleMatch
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: RuleMatch -> RuleMatch -> Bool # (/=) :: RuleMatch -> RuleMatch -> Bool #
Eq Phases
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Phases -> Phases -> Bool # (/=) :: Phases -> Phases -> Bool #
Eq RuleBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: RuleBndr -> RuleBndr -> Bool # (/=) :: RuleBndr -> RuleBndr -> Bool #
Eq AnnTarget
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: AnnTarget -> AnnTarget -> Bool # (/=) :: AnnTarget -> AnnTarget -> Bool #
Eq SourceUnpackedness
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool #
Eq SourceStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool #
Eq DecidedStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool #
Eq Con
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Con -> Con -> Bool # (/=) :: Con -> Con -> Bool #
Eq Bang
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Bang -> Bang -> Bool # (/=) :: Bang -> Bang -> Bool #
Eq PatSynDir
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: PatSynDir -> PatSynDir -> Bool # (/=) :: PatSynDir -> PatSynDir -> Bool #
Eq PatSynArgs
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: PatSynArgs -> PatSynArgs -> Bool # (/=) :: PatSynArgs -> PatSynArgs -> Bool #
Eq TyVarBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: TyVarBndr -> TyVarBndr -> Bool # (/=) :: TyVarBndr -> TyVarBndr -> Bool #
Eq FamilyResultSig
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: FamilyResultSig -> FamilyResultSig -> Bool # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool #
Eq TyLit
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: TyLit -> TyLit -> Bool # (/=) :: TyLit -> TyLit -> Bool #
Eq Role
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: Role -> Role -> Bool # (/=) :: Role -> Role -> Bool #
Eq AnnLookup
Instance details Defined in Language.Haskell.TH.Syntax Methods (==) :: AnnLookup -> AnnLookup -> Bool # (/=) :: AnnLookup -> AnnLookup -> Bool #
Eq WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: WrapOrdering -> WrapOrdering -> Bool # (/=) :: WrapOrdering -> WrapOrdering -> Bool #
Eq ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods (==) :: ByteArray -> ByteArray -> Bool # (/=) :: ByteArray -> ByteArray -> Bool #
Eq DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods (==) :: DefName -> DefName -> Bool # (/=) :: DefName -> DefName -> Bool #
Eq ConstructorInfo
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: ConstructorInfo -> ConstructorInfo -> Bool # (/=) :: ConstructorInfo -> ConstructorInfo -> Bool #
Eq DatatypeInfo
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: DatatypeInfo -> DatatypeInfo -> Bool # (/=) :: DatatypeInfo -> DatatypeInfo -> Bool #
Eq StdGen
Instance details Defined in System.Random.Internal Methods (==) :: StdGen -> StdGen -> Bool # (/=) :: StdGen -> StdGen -> Bool #
Eq ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods (==) :: ComplexBasis -> ComplexBasis -> Bool # (/=) :: ComplexBasis -> ComplexBasis -> Bool #
Eq DType
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DType -> DType -> Bool # (/=) :: DType -> DType -> Bool #
Eq DLetDec
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DLetDec -> DLetDec -> Bool # (/=) :: DLetDec -> DLetDec -> Bool #
Eq DTyVarBndr
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DTyVarBndr -> DTyVarBndr -> Bool # (/=) :: DTyVarBndr -> DTyVarBndr -> Bool #
Eq DCon
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DCon -> DCon -> Bool # (/=) :: DCon -> DCon -> Bool #
Eq DClause
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DClause -> DClause -> Bool # (/=) :: DClause -> DClause -> Bool #
Eq DExp
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DExp -> DExp -> Bool # (/=) :: DExp -> DExp -> Bool #
Eq DTypeFamilyHead
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DTypeFamilyHead -> DTypeFamilyHead -> Bool # (/=) :: DTypeFamilyHead -> DTypeFamilyHead -> Bool #
Eq ConstructorVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: ConstructorVariant -> ConstructorVariant -> Bool # (/=) :: ConstructorVariant -> ConstructorVariant -> Bool #
Eq DatatypeVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: DatatypeVariant -> DatatypeVariant -> Bool # (/=) :: DatatypeVariant -> DatatypeVariant -> Bool #
Eq FieldStrictness
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: FieldStrictness -> FieldStrictness -> Bool # (/=) :: FieldStrictness -> FieldStrictness -> Bool #
Eq Strictness
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: Strictness -> Strictness -> Bool # (/=) :: Strictness -> Strictness -> Bool #
Eq Unpackedness
Instance details Defined in Language.Haskell.TH.Datatype Methods (==) :: Unpackedness -> Unpackedness -> Bool # (/=) :: Unpackedness -> Unpackedness -> Bool #
Eq Specificity
Instance details Defined in Language.Haskell.TH.Datatype.TyVarBndr Methods (==) :: Specificity -> Specificity -> Bool # (/=) :: Specificity -> Specificity -> Bool #
Eq DConFields
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DConFields -> DConFields -> Bool # (/=) :: DConFields -> DConFields -> Bool #
Eq DDec
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DDec -> DDec -> Bool # (/=) :: DDec -> DDec -> Bool #
Eq DDerivClause
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DDerivClause -> DDerivClause -> Bool # (/=) :: DDerivClause -> DDerivClause -> Bool #
Eq DDerivStrategy
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DDerivStrategy -> DDerivStrategy -> Bool # (/=) :: DDerivStrategy -> DDerivStrategy -> Bool #
Eq DFamilyResultSig
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DFamilyResultSig -> DFamilyResultSig -> Bool # (/=) :: DFamilyResultSig -> DFamilyResultSig -> Bool #
Eq DForeign
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DForeign -> DForeign -> Bool # (/=) :: DForeign -> DForeign -> Bool #
Eq DInfo
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DInfo -> DInfo -> Bool # (/=) :: DInfo -> DInfo -> Bool #
Eq DMatch
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DMatch -> DMatch -> Bool # (/=) :: DMatch -> DMatch -> Bool #
Eq DPat
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DPat -> DPat -> Bool # (/=) :: DPat -> DPat -> Bool #
Eq DPatSynDir
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DPatSynDir -> DPatSynDir -> Bool # (/=) :: DPatSynDir -> DPatSynDir -> Bool #
Eq DPragma
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DPragma -> DPragma -> Bool # (/=) :: DPragma -> DPragma -> Bool #
Eq DRuleBndr
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DRuleBndr -> DRuleBndr -> Bool # (/=) :: DRuleBndr -> DRuleBndr -> Bool #
Eq DTySynEqn
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: DTySynEqn -> DTySynEqn -> Bool # (/=) :: DTySynEqn -> DTySynEqn -> Bool #
Eq NewOrData
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods (==) :: NewOrData -> NewOrData -> Bool # (/=) :: NewOrData -> NewOrData -> Bool #
Eq DFunArgs
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods (==) :: DFunArgs -> DFunArgs -> Bool # (/=) :: DFunArgs -> DFunArgs -> Bool #
Eq DTypeArg
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods (==) :: DTypeArg -> DTypeArg -> Bool # (/=) :: DTypeArg -> DTypeArg -> Bool #
Eq DVisFunArg
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods (==) :: DVisFunArg -> DVisFunArg -> Bool # (/=) :: DVisFunArg -> DVisFunArg -> Bool #
Eq CodePoint
Instance details Defined in Data.Text.Encoding Methods (==) :: CodePoint -> CodePoint -> Bool # (/=) :: CodePoint -> CodePoint -> Bool #
Eq DecoderState
Instance details Defined in Data.Text.Encoding Methods (==) :: DecoderState -> DecoderState -> Bool # (/=) :: DecoderState -> DecoderState -> Bool #
Eq GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: GradedStrategy -> GradedStrategy -> Bool # (/=) :: GradedStrategy -> GradedStrategy -> Bool #
Eq GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (/=) :: GrevlexStrategy -> GrevlexStrategy -> Bool #
Eq NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: NormalStrategy -> NormalStrategy -> Bool # (/=) :: NormalStrategy -> NormalStrategy -> Bool #
Eq a => Eq [a]
Instance details Defined in GHC.Classes Methods (==) :: [a] -> [a] -> Bool # (/=) :: [a] -> [a] -> Bool #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool # (/=) :: Maybe a -> Maybe a -> Bool #
Eq a => Eq (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Real Methods (==) :: Ratio a -> Ratio a -> Bool # (/=) :: Ratio a -> Ratio a -> Bool #
Eq (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods (==) :: Ptr a -> Ptr a -> Bool # (/=) :: Ptr a -> Ptr a -> Bool #
Eq (FunPtr a)
Instance details Defined in GHC.Ptr Methods (==) :: FunPtr a -> FunPtr a -> Bool # (/=) :: FunPtr a -> FunPtr a -> Bool #
Eq p => Eq (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: Par1 p -> Par1 p -> Bool # (/=) :: Par1 p -> Par1 p -> Bool #
Eq a => Eq (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapNum a -> WrapNum a -> Bool # (/=) :: WrapNum a -> WrapNum a -> Bool #
Eq a => Eq (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapFractional a -> WrapFractional a -> Bool # (/=) :: WrapFractional a -> WrapFractional a -> Bool #
Eq a => Eq (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapIntegral a -> WrapIntegral a -> Bool # (/=) :: WrapIntegral a -> WrapIntegral a -> Bool #
Eq a => Eq (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (/=) :: WrapAlgebra a -> WrapAlgebra a -> Bool #
Eq a => Eq (Add a)
Instance details Defined in AlgebraicPrelude Methods (==) :: Add a -> Add a -> Bool # (/=) :: Add a -> Add a -> Bool #
Eq a => Eq (Mult a)
Instance details Defined in AlgebraicPrelude Methods (==) :: Mult a -> Mult a -> Bool # (/=) :: Mult a -> Mult a -> Bool #
(Eq d, GCDDomain d) => Eq (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (==) :: Fraction d -> Fraction d -> Bool # (/=) :: Fraction d -> Fraction d -> Bool #
Eq a => Eq (Vector a)
Instance details Defined in Data.Vector Methods (==) :: Vector a -> Vector a -> Bool # (/=) :: Vector a -> Vector a -> Bool #
Eq a => Eq (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods (==) :: HashSet a -> HashSet a -> Bool # (/=) :: HashSet a -> HashSet a -> Bool #
Eq a => Eq (Set a)
Instance details Defined in Data.Set.Internal Methods (==) :: Set a -> Set a -> Bool # (/=) :: Set a -> Set a -> Bool #
Eq a => Eq (Seq a)
Instance details Defined in Data.Sequence.Internal Methods (==) :: Seq a -> Seq a -> Bool # (/=) :: Seq a -> Seq a -> Bool #
Eq a => Eq (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods (==) :: IntMap a -> IntMap a -> Bool # (/=) :: IntMap a -> IntMap a -> Bool #
Eq a => Eq (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods (==) :: Down a -> Down a -> Bool # (/=) :: Down a -> Down a -> Bool #
Eq a => Eq (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
Eq a => Eq (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Min a -> Min a -> Bool # (/=) :: Min a -> Min a -> Bool #
Eq a => Eq (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Max a -> Max a -> Bool # (/=) :: Max a -> Max a -> Bool #
Eq a => Eq (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Eq a => Eq (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Eq m => Eq (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #
Eq a => Eq (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Option a -> Option a -> Bool # (/=) :: Option a -> Option a -> Bool #
Eq (StableName a)	Since: base-2.1
Instance details Defined in GHC.StableName Methods (==) :: StableName a -> StableName a -> Bool # (/=) :: StableName a -> StableName a -> Bool #
Eq a => Eq (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (==) :: ZipList a -> ZipList a -> Bool # (/=) :: ZipList a -> ZipList a -> Bool #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Eq (TVar a)	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods (==) :: TVar a -> TVar a -> Bool # (/=) :: TVar a -> TVar a -> Bool #
Eq (IORef a)	Pointer equality. Since: base-4.0.0.0
Instance details Defined in GHC.IORef Methods (==) :: IORef a -> IORef a -> Bool # (/=) :: IORef a -> IORef a -> Bool #
Eq a => Eq (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Eq a => Eq (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Eq (MVar a)	Since: base-4.1.0.0
Instance details Defined in GHC.MVar Methods (==) :: MVar a -> MVar a -> Bool # (/=) :: MVar a -> MVar a -> Bool #
Eq a => Eq (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool # (/=) :: NonEmpty a -> NonEmpty a -> Bool #
Eq a => Eq (Tree a)
Instance details Defined in Data.Tree Methods (==) :: Tree a -> Tree a -> Bool # (/=) :: Tree a -> Tree a -> Bool #
Eq a => Eq (ViewL a)
Instance details Defined in Data.Sequence.Internal Methods (==) :: ViewL a -> ViewL a -> Bool # (/=) :: ViewL a -> ViewL a -> Bool #
Eq a => Eq (ViewR a)
Instance details Defined in Data.Sequence.Internal Methods (==) :: ViewR a -> ViewR a -> Bool # (/=) :: ViewR a -> ViewR a -> Bool #
Eq (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods (==) :: Ordinal n -> Ordinal n -> Bool # (/=) :: Ordinal n -> Ordinal n -> Bool #
Eq ord => Eq (Graded ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Graded ord -> Graded ord -> Bool # (/=) :: Graded ord -> Graded ord -> Bool #
Eq (IsTrue b)
Instance details Defined in Proof.Propositional Methods (==) :: IsTrue b -> IsTrue b -> Bool # (/=) :: IsTrue b -> IsTrue b -> Bool #
Eq (SOrdering ord)
Instance details Defined in Data.Type.Natural.Core Methods (==) :: SOrdering ord -> SOrdering ord -> Bool # (/=) :: SOrdering ord -> SOrdering ord -> Bool #
Eq (SBool ord)
Instance details Defined in Data.Type.Natural.Core Methods (==) :: SBool ord -> SBool ord -> Bool # (/=) :: SBool ord -> SBool ord -> Bool #
Eq (SNat n)
Instance details Defined in Data.Type.Natural.Core Methods (==) :: SNat n -> SNat n -> Bool # (/=) :: SNat n -> SNat n -> Bool #
Eq r => Eq (Scalar r)
Instance details Defined in Algebra.Scalar Methods (==) :: Scalar r -> Scalar r -> Bool # (/=) :: Scalar r -> Scalar r -> Bool #
Eq (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: Doc a -> Doc a -> Bool # (/=) :: Doc a -> Doc a -> Bool #
Eq a => Eq (AnnotDetails a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: AnnotDetails a -> AnnotDetails a -> Bool # (/=) :: AnnotDetails a -> AnnotDetails a -> Bool #
Eq a => Eq (Span a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: Span a -> Span a -> Bool # (/=) :: Span a -> Span a -> Bool #
Eq a => Eq (Complex a)
Instance details Defined in Numeric.Algebra.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
Eq (MutableByteArray s)
Instance details Defined in Data.Primitive.ByteArray Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool #
(Prim a, Eq a) => Eq (Vector a)
Instance details Defined in Data.Vector.Primitive Methods (==) :: Vector a -> Vector a -> Bool # (/=) :: Vector a -> Vector a -> Bool #
(Storable a, Eq a) => Eq (Vector a)
Instance details Defined in Data.Vector.Storable Methods (==) :: Vector a -> Vector a -> Bool # (/=) :: Vector a -> Vector a -> Bool #
Eq a => Eq (Array a)
Instance details Defined in Data.Primitive.Array Methods (==) :: Array a -> Array a -> Bool # (/=) :: Array a -> Array a -> Bool #
(Eq a, Prim a) => Eq (PrimArray a)
Instance details Defined in Data.Primitive.PrimArray Methods (==) :: PrimArray a -> PrimArray a -> Bool # (/=) :: PrimArray a -> PrimArray a -> Bool #
Eq a => Eq (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods (==) :: SmallArray a -> SmallArray a -> Bool # (/=) :: SmallArray a -> SmallArray a -> Bool #
Eq a => Eq (Hashed a)
Instance details Defined in Data.Hashable.Class Methods (==) :: Hashed a -> Hashed a -> Bool # (/=) :: Hashed a -> Hashed a -> Bool #
Eq g => Eq (StateGen g)
Instance details Defined in System.Random.Internal Methods (==) :: StateGen g -> StateGen g -> Bool # (/=) :: StateGen g -> StateGen g -> Bool #
Eq g => Eq (AtomicGen g)
Instance details Defined in System.Random.Stateful Methods (==) :: AtomicGen g -> AtomicGen g -> Bool # (/=) :: AtomicGen g -> AtomicGen g -> Bool #
Eq g => Eq (IOGen g)
Instance details Defined in System.Random.Stateful Methods (==) :: IOGen g -> IOGen g -> Bool # (/=) :: IOGen g -> IOGen g -> Bool #
Eq g => Eq (STGen g)
Instance details Defined in System.Random.Stateful Methods (==) :: STGen g -> STGen g -> Bool # (/=) :: STGen g -> STGen g -> Bool #
Eq s => Eq (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: SugarStrategy s -> SugarStrategy s -> Bool # (/=) :: SugarStrategy s -> SugarStrategy s -> Bool #
(Eq r, DecidableZero r) => Eq (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (==) :: Unipol r -> Unipol r -> Bool # (/=) :: Unipol r -> Unipol r -> Bool #
Eq (Heap a)
Instance details Defined in Data.Heap Methods (==) :: Heap a -> Heap a -> Bool # (/=) :: Heap a -> Heap a -> Bool #
Eq a => Eq (Matrix a)
Instance details Defined in Data.Matrix Methods (==) :: Matrix a -> Matrix a -> Bool # (/=) :: Matrix a -> Matrix a -> Bool #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool # (/=) :: Either a b -> Either a b -> Bool #
Eq (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: V1 p -> V1 p -> Bool # (/=) :: V1 p -> V1 p -> Bool #
Eq (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: U1 p -> U1 p -> Bool # (/=) :: U1 p -> U1 p -> Bool #
Eq (TypeRep a)	Since: base-2.1
Instance details Defined in Data.Typeable.Internal Methods (==) :: TypeRep a -> TypeRep a -> Bool # (/=) :: TypeRep a -> TypeRep a -> Bool #
(Eq a, Eq b) => Eq (a, b)
Instance details Defined in GHC.Classes Methods (==) :: (a, b) -> (a, b) -> Bool # (/=) :: (a, b) -> (a, b) -> Bool #
(Eq k, Eq v) => Eq (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods (==) :: HashMap k v -> HashMap k v -> Bool # (/=) :: HashMap k v -> HashMap k v -> Bool #
(Eq k, Eq a) => Eq (Map k a)
Instance details Defined in Data.Map.Internal Methods (==) :: Map k a -> Map k a -> Bool # (/=) :: Map k a -> Map k a -> Bool #
(Ix ix, Eq e, IArray UArray e) => Eq (UArray ix e)
Instance details Defined in Data.Array.Base Methods (==) :: UArray ix e -> UArray ix e -> Bool # (/=) :: UArray ix e -> UArray ix e -> Bool #
(Ix i, Eq e) => Eq (Array i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods (==) :: Array i e -> Array i e -> Bool # (/=) :: Array i e -> Array i e -> Bool #
Eq (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (==) :: Fixed a -> Fixed a -> Bool # (/=) :: Fixed a -> Fixed a -> Bool #
Eq a => Eq (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Arg a b -> Arg a b -> Bool # (/=) :: Arg a b -> Arg a b -> Bool #
Eq (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool # (/=) :: Proxy s -> Proxy s -> Bool #
Eq (STRef s a)	Pointer equality. Since: base-2.1
Instance details Defined in GHC.STRef Methods (==) :: STRef s a -> STRef s a -> Bool # (/=) :: STRef s a -> STRef s a -> Bool #
(Eq1 m, Eq a) => Eq (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods (==) :: MaybeT m a -> MaybeT m a -> Bool # (/=) :: MaybeT m a -> MaybeT m a -> Bool #
(Eq1 m, Eq a) => Eq (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods (==) :: ListT m a -> ListT m a -> Bool # (/=) :: ListT m a -> ListT m a -> Bool #
(Eq k, Eq v) => Eq (Leaf k v)
Instance details Defined in Data.HashMap.Internal Methods (==) :: Leaf k v -> Leaf k v -> Bool # (/=) :: Leaf k v -> Leaf k v -> Bool #
(Eq i, Eq a) => Eq (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods (==) :: Level i a -> Level i a -> Bool # (/=) :: Level i a -> Level i a -> Bool #
Eq (f a) => Eq (SomeSized f a)
Instance details Defined in Data.Sized Methods (==) :: SomeSized f a -> SomeSized f a -> Bool # (/=) :: SomeSized f a -> SomeSized f a -> Bool #
(Eq a, Eq b) => Eq (These a b)
Instance details Defined in Data.These Methods (==) :: These a b -> These a b -> Bool # (/=) :: These a b -> These a b -> Bool #
(Eq1 w, Eq a) => Eq (CoiterT w a)
Instance details Defined in Control.Comonad.Trans.Coiter Methods (==) :: CoiterT w a -> CoiterT w a -> Bool # (/=) :: CoiterT w a -> CoiterT w a -> Bool #
(Eq1 m, Eq a) => Eq (IterT m a)
Instance details Defined in Control.Monad.Trans.Iter Methods (==) :: IterT m a -> IterT m a -> Bool # (/=) :: IterT m a -> IterT m a -> Bool #
(Eq1 f, Eq a) => Eq (Cofree f a)
Instance details Defined in Control.Comonad.Cofree Methods (==) :: Cofree f a -> Cofree f a -> Bool # (/=) :: Cofree f a -> Cofree f a -> Bool #
(Eq1 f, Eq a) => Eq (Free f a)
Instance details Defined in Control.Monad.Free Methods (==) :: Free f a -> Free f a -> Bool # (/=) :: Free f a -> Free f a -> Bool #
(Eq1 f, Eq a) => Eq (Yoneda f a)
Instance details Defined in Data.Functor.Yoneda Methods (==) :: Yoneda f a -> Yoneda f a -> Bool # (/=) :: Yoneda f a -> Yoneda f a -> Bool #
Eq (MutableArray s a)
Instance details Defined in Data.Primitive.Array Methods (==) :: MutableArray s a -> MutableArray s a -> Bool # (/=) :: MutableArray s a -> MutableArray s a -> Bool #
Eq (MutablePrimArray s a)
Instance details Defined in Data.Primitive.PrimArray Methods (==) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool # (/=) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool #
Eq (SmallMutableArray s a)
Instance details Defined in Data.Primitive.SmallArray Methods (==) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # (/=) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool #
Eq p => Eq (Entry p a)
Instance details Defined in Data.Heap Methods (==) :: Entry p a -> Entry p a -> Bool # (/=) :: Entry p a -> Entry p a -> Bool #
(Wraps vars poly, Eq poly) => Eq (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (==) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (/=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool #
Eq (f p) => Eq (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: Rec1 f p -> Rec1 f p -> Bool # (/=) :: Rec1 f p -> Rec1 f p -> Bool #
Eq (URec (Ptr ()) p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Char p -> URec Char p -> Bool # (/=) :: URec Char p -> URec Char p -> Bool #
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Word p -> URec Word p -> Bool # (/=) :: URec Word p -> URec Word p -> Bool #
(Eq a, Eq b, Eq c) => Eq (a, b, c)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c) -> (a, b, c) -> Bool # (/=) :: (a, b, c) -> (a, b, c) -> Bool #
Eq (STUArray s i e)
Instance details Defined in Data.Array.Base Methods (==) :: STUArray s i e -> STUArray s i e -> Bool # (/=) :: STUArray s i e -> STUArray s i e -> Bool #
Eq (STArray s i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods (==) :: STArray s i e -> STArray s i e -> Bool # (/=) :: STArray s i e -> STArray s i e -> Bool #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Eq (f a) => Eq (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool # (/=) :: Ap f a -> Ap f a -> Bool #
Eq (f a) => Eq (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool # (/=) :: Alt f a -> Alt f a -> Bool #
Eq (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool # (/=) :: (a :~: b) -> (a :~: b) -> Bool #
(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods (==) :: ExceptT e m a -> ExceptT e m a -> Bool # (/=) :: ExceptT e m a -> ExceptT e m a -> Bool #
Eq (OrderedMonomial ordering n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: OrderedMonomial ordering n -> OrderedMonomial ordering n -> Bool # (/=) :: OrderedMonomial ordering n -> OrderedMonomial ordering n -> Bool #
(Eq1 f, Eq a) => Eq (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods (==) :: IdentityT f a -> IdentityT f a -> Bool # (/=) :: IdentityT f a -> IdentityT f a -> Bool #
(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods (==) :: ErrorT e m a -> ErrorT e m a -> Bool # (/=) :: ErrorT e m a -> ErrorT e m a -> Bool #
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods (==) :: WriterT w m a -> WriterT w m a -> Bool # (/=) :: WriterT w m a -> WriterT w m a -> Bool #
(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods (==) :: WriterT w m a -> WriterT w m a -> Bool # (/=) :: WriterT w m a -> WriterT w m a -> Bool #
(Eq1 f, Eq a) => Eq (Reverse f a)
Instance details Defined in Data.Functor.Reverse Methods (==) :: Reverse f a -> Reverse f a -> Bool # (/=) :: Reverse f a -> Reverse f a -> Bool #
Eq a => Eq (Constant a b)
Instance details Defined in Data.Functor.Constant Methods (==) :: Constant a b -> Constant a b -> Bool # (/=) :: Constant a b -> Constant a b -> Bool #
(Eq1 f, Eq a) => Eq (Backwards f a)
Instance details Defined in Control.Applicative.Backwards Methods (==) :: Backwards f a -> Backwards f a -> Bool # (/=) :: Backwards f a -> Backwards f a -> Bool #
Eq (f a) => Eq (Sized f n a)
Instance details Defined in Data.Sized.Internal Methods (==) :: Sized f n a -> Sized f n a -> Bool # (/=) :: Sized f n a -> Sized f n a -> Bool #
Eq (f a) => Eq (Flipped f a n)
Instance details Defined in Data.Sized.Flipped Methods (==) :: Flipped f a n -> Flipped f a n -> Bool # (/=) :: Flipped f a n -> Flipped f a n -> Bool #
Eq (f a) => Eq (CApp f a)
Instance details Defined in Control.Subcategory.Applicative Methods (==) :: CApp f a -> CApp f a -> Bool # (/=) :: CApp f a -> CApp f a -> Bool #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Eq (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (==) :: PadPolyL n ord poly -> PadPolyL n ord poly -> Bool # (/=) :: PadPolyL n ord poly -> PadPolyL n ord poly -> Bool #
Eq b => Eq (Tagged s b)
Instance details Defined in Data.Tagged Methods (==) :: Tagged s b -> Tagged s b -> Bool # (/=) :: Tagged s b -> Tagged s b -> Bool #
Eq (w (CofreeF f a (CofreeT f w a))) => Eq (CofreeT f w a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods (==) :: CofreeT f w a -> CofreeT f w a -> Bool # (/=) :: CofreeT f w a -> CofreeT f w a -> Bool #
(Eq a, Eq (f b)) => Eq (CofreeF f a b)
Instance details Defined in Control.Comonad.Trans.Cofree Methods (==) :: CofreeF f a b -> CofreeF f a b -> Bool # (/=) :: CofreeF f a b -> CofreeF f a b -> Bool #
Eq (p (Fix p a) a) => Eq (Fix p a)
Instance details Defined in Data.Bifunctor.Fix Methods (==) :: Fix p a -> Fix p a -> Bool # (/=) :: Fix p a -> Fix p a -> Bool #
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a)
Instance details Defined in Control.Monad.Trans.Free Methods (==) :: FreeT f m a -> FreeT f m a -> Bool # (/=) :: FreeT f m a -> FreeT f m a -> Bool #
(Eq a, Eq (f b)) => Eq (FreeF f a b)
Instance details Defined in Control.Monad.Trans.Free Methods (==) :: FreeF f a b -> FreeF f a b -> Bool # (/=) :: FreeF f a b -> FreeF f a b -> Bool #
Eq (p a a) => Eq (Join p a)
Instance details Defined in Data.Bifunctor.Join Methods (==) :: Join p a -> Join p a -> Bool # (/=) :: Join p a -> Join p a -> Bool #
Eq (f a) => Eq (CZippy f a)
Instance details Defined in Control.Subcategory.Zip Methods (==) :: CZippy f a -> CZippy f a -> Bool # (/=) :: CZippy f a -> CZippy f a -> Bool #
Eq poly => Eq (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (==) :: Quotient poly ideal -> Quotient poly ideal -> Bool # (/=) :: Quotient poly ideal -> Quotient poly ideal -> Bool #
Eq c => Eq (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: K1 i c p -> K1 i c p -> Bool # (/=) :: K1 i c p -> K1 i c p -> Bool #
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :+: g) p -> (f :+: g) p -> Bool # (/=) :: (f :+: g) p -> (f :+: g) p -> Bool #
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :: g) p -> (f :: g) p -> Bool # (/=) :: (f :: g) p -> (f :: g) p -> Bool #
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool # (/=) :: Product f g a -> Product f g a -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods (==) :: Sum f g a -> Sum f g a -> Bool # (/=) :: Sum f g a -> Sum f g a -> Bool #
Eq (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~~: b) -> (a :~~: b) -> Bool # (/=) :: (a :~~: b) -> (a :~~: b) -> Bool #
Eq r => Eq (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (==) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> Bool # (/=) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> Bool #
Eq (f p) => Eq (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: M1 i c f p -> M1 i c f p -> Bool # (/=) :: M1 i c f p -> M1 i c f p -> Bool #
Eq (f (g p)) => Eq ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :.: g) p -> (f :.: g) p -> Bool # (/=) :: (f :.: g) p -> (f :.: g) p -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #
(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods (==) :: Compose f g a -> Compose f g a -> Bool # (/=) :: Compose f g a -> Compose f g a -> Bool #
Eq (f a) => Eq (Clown f a b)
Instance details Defined in Data.Bifunctor.Clown Methods (==) :: Clown f a b -> Clown f a b -> Bool # (/=) :: Clown f a b -> Clown f a b -> Bool #
Eq (p b a) => Eq (Flip p a b)
Instance details Defined in Data.Bifunctor.Flip Methods (==) :: Flip p a b -> Flip p a b -> Bool # (/=) :: Flip p a b -> Flip p a b -> Bool #
Eq (g b) => Eq (Joker g a b)
Instance details Defined in Data.Bifunctor.Joker Methods (==) :: Joker g a b -> Joker g a b -> Bool # (/=) :: Joker g a b -> Joker g a b -> Bool #
Eq (p a b) => Eq (WrappedBifunctor p a b)
Instance details Defined in Data.Bifunctor.Wrapped Methods (==) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # (/=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #
(Eq (f a b), Eq (g a b)) => Eq (Product f g a b)
Instance details Defined in Data.Bifunctor.Product Methods (==) :: Product f g a b -> Product f g a b -> Bool # (/=) :: Product f g a b -> Product f g a b -> Bool #
(Eq (p a b), Eq (q a b)) => Eq (Sum p q a b)
Instance details Defined in Data.Bifunctor.Sum Methods (==) :: Sum p q a b -> Sum p q a b -> Bool # (/=) :: Sum p q a b -> Sum p q a b -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #
Eq (f (p a b)) => Eq (Tannen f p a b)
Instance details Defined in Data.Bifunctor.Tannen Methods (==) :: Tannen f p a b -> Tannen f p a b -> Bool # (/=) :: Tannen f p a b -> Tannen f p a b -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #
Eq (p (f a) (g b)) => Eq (Biff p f g a b)
Instance details Defined in Data.Bifunctor.Biff Methods (==) :: Biff p f g a b -> Biff p f g a b -> Bool # (/=) :: Biff p f g a b -> Biff p f g a b -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

class Fractional a => Floating a where #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:

exp (a + b) = exp a * exp b
exp (fromInteger 0) = fromInteger 1

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a #

exp :: a -> a #

log :: a -> a #

sqrt :: a -> a #

(**) :: a -> a -> a infixr 8 #

logBase :: a -> a -> a #

sin :: a -> a #

cos :: a -> a #

tan :: a -> a #

asin :: a -> a #

acos :: a -> a #

atan :: a -> a #

sinh :: a -> a #

cosh :: a -> a #

tanh :: a -> a #

asinh :: a -> a #

acosh :: a -> a #

atanh :: a -> a #

Instances

Instances details

Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Floating CFloat
Instance details Defined in Foreign.C.Types Methods pi :: CFloat # exp :: CFloat -> CFloat # log :: CFloat -> CFloat # sqrt :: CFloat -> CFloat # (**) :: CFloat -> CFloat -> CFloat # logBase :: CFloat -> CFloat -> CFloat # sin :: CFloat -> CFloat # cos :: CFloat -> CFloat # tan :: CFloat -> CFloat # asin :: CFloat -> CFloat # acos :: CFloat -> CFloat # atan :: CFloat -> CFloat # sinh :: CFloat -> CFloat # cosh :: CFloat -> CFloat # tanh :: CFloat -> CFloat # asinh :: CFloat -> CFloat # acosh :: CFloat -> CFloat # atanh :: CFloat -> CFloat # log1p :: CFloat -> CFloat # expm1 :: CFloat -> CFloat # log1pexp :: CFloat -> CFloat # log1mexp :: CFloat -> CFloat #
Floating CDouble
Instance details Defined in Foreign.C.Types Methods pi :: CDouble # exp :: CDouble -> CDouble # log :: CDouble -> CDouble # sqrt :: CDouble -> CDouble # (**) :: CDouble -> CDouble -> CDouble # logBase :: CDouble -> CDouble -> CDouble # sin :: CDouble -> CDouble # cos :: CDouble -> CDouble # tan :: CDouble -> CDouble # asin :: CDouble -> CDouble # acos :: CDouble -> CDouble # atan :: CDouble -> CDouble # sinh :: CDouble -> CDouble # cosh :: CDouble -> CDouble # tanh :: CDouble -> CDouble # asinh :: CDouble -> CDouble # acosh :: CDouble -> CDouble # atanh :: CDouble -> CDouble # log1p :: CDouble -> CDouble # expm1 :: CDouble -> CDouble # log1pexp :: CDouble -> CDouble # log1mexp :: CDouble -> CDouble #
Floating a => Floating (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods pi :: Down a # exp :: Down a -> Down a # log :: Down a -> Down a # sqrt :: Down a -> Down a # (**) :: Down a -> Down a -> Down a # logBase :: Down a -> Down a -> Down a # sin :: Down a -> Down a # cos :: Down a -> Down a # tan :: Down a -> Down a # asin :: Down a -> Down a # acos :: Down a -> Down a # atan :: Down a -> Down a # sinh :: Down a -> Down a # cosh :: Down a -> Down a # tanh :: Down a -> Down a # asinh :: Down a -> Down a # acosh :: Down a -> Down a # atanh :: Down a -> Down a # log1p :: Down a -> Down a # expm1 :: Down a -> Down a # log1pexp :: Down a -> Down a # log1mexp :: Down a -> Down a #
RealFloat a => Floating (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods pi :: Complex a # exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # acosh :: Complex a -> Complex a # atanh :: Complex a -> Complex a # log1p :: Complex a -> Complex a # expm1 :: Complex a -> Complex a # log1pexp :: Complex a -> Complex a # log1mexp :: Complex a -> Complex a #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods pi :: Identity a # exp :: Identity a -> Identity a # log :: Identity a -> Identity a # sqrt :: Identity a -> Identity a # (**) :: Identity a -> Identity a -> Identity a # logBase :: Identity a -> Identity a -> Identity a # sin :: Identity a -> Identity a # cos :: Identity a -> Identity a # tan :: Identity a -> Identity a # asin :: Identity a -> Identity a # acos :: Identity a -> Identity a # atan :: Identity a -> Identity a # sinh :: Identity a -> Identity a # cosh :: Identity a -> Identity a # tanh :: Identity a -> Identity a # asinh :: Identity a -> Identity a # acosh :: Identity a -> Identity a # atanh :: Identity a -> Identity a # log1p :: Identity a -> Identity a # expm1 :: Identity a -> Identity a # log1pexp :: Identity a -> Identity a # log1mexp :: Identity a -> Identity a #
Floating a => Floating (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods pi :: Op a b # exp :: Op a b -> Op a b # log :: Op a b -> Op a b # sqrt :: Op a b -> Op a b # (**) :: Op a b -> Op a b -> Op a b # logBase :: Op a b -> Op a b -> Op a b # sin :: Op a b -> Op a b # cos :: Op a b -> Op a b # tan :: Op a b -> Op a b # asin :: Op a b -> Op a b # acos :: Op a b -> Op a b # atan :: Op a b -> Op a b # sinh :: Op a b -> Op a b # cosh :: Op a b -> Op a b # tanh :: Op a b -> Op a b # asinh :: Op a b -> Op a b # acosh :: Op a b -> Op a b # atanh :: Op a b -> Op a b # log1p :: Op a b -> Op a b # expm1 :: Op a b -> Op a b # log1pexp :: Op a b -> Op a b # log1mexp :: Op a b -> Op a b #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #
Floating a => Floating (Tagged s a)
Instance details Defined in Data.Tagged Methods pi :: Tagged s a # exp :: Tagged s a -> Tagged s a # log :: Tagged s a -> Tagged s a # sqrt :: Tagged s a -> Tagged s a # (**) :: Tagged s a -> Tagged s a -> Tagged s a # logBase :: Tagged s a -> Tagged s a -> Tagged s a # sin :: Tagged s a -> Tagged s a # cos :: Tagged s a -> Tagged s a # tan :: Tagged s a -> Tagged s a # asin :: Tagged s a -> Tagged s a # acos :: Tagged s a -> Tagged s a # atan :: Tagged s a -> Tagged s a # sinh :: Tagged s a -> Tagged s a # cosh :: Tagged s a -> Tagged s a # tanh :: Tagged s a -> Tagged s a # asinh :: Tagged s a -> Tagged s a # acosh :: Tagged s a -> Tagged s a # atanh :: Tagged s a -> Tagged s a # log1p :: Tagged s a -> Tagged s a # expm1 :: Tagged s a -> Tagged s a # log1pexp :: Tagged s a -> Tagged s a # log1mexp :: Tagged s a -> Tagged s a #

class Num a => Fractional a #

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse: x * recip x = recip x * x = fromInteger 1

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Instances

Instances details

Fractional CFloat
Instance details Defined in Foreign.C.Types Methods (/) :: CFloat -> CFloat -> CFloat # recip :: CFloat -> CFloat # fromRational :: Rational -> CFloat #
Fractional CDouble
Instance details Defined in Foreign.C.Types Methods (/) :: CDouble -> CDouble -> CDouble # recip :: CDouble -> CDouble # fromRational :: Rational -> CDouble #
Integral a => Fractional (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (/) :: Ratio a -> Ratio a -> Ratio a # recip :: Ratio a -> Ratio a # fromRational :: Rational -> Ratio a #
Fractional a => Fractional (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (/) :: WrapFractional a -> WrapFractional a -> WrapFractional a # recip :: WrapFractional a -> WrapFractional a # fromRational :: Rational -> WrapFractional a #
(DivisionRing a, UnitNormalForm a) => Fractional (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (/) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # recip :: WrapAlgebra a -> WrapAlgebra a # fromRational :: Rational -> WrapAlgebra a #
Fractional a => Fractional (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods (/) :: Down a -> Down a -> Down a # recip :: Down a -> Down a # fromRational :: Rational -> Down a #
RealFloat a => Fractional (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a # recip :: Identity a -> Identity a # fromRational :: Rational -> Identity a #
Fractional r => Fractional (Scalar r)
Instance details Defined in Algebra.Scalar Methods (/) :: Scalar r -> Scalar r -> Scalar r # recip :: Scalar r -> Scalar r # fromRational :: Rational -> Scalar r #
HasResolution a => Fractional (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (/) :: Fixed a -> Fixed a -> Fixed a # recip :: Fixed a -> Fixed a # fromRational :: Rational -> Fixed a #
Fractional a => Fractional (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods (/) :: Op a b -> Op a b -> Op a b # recip :: Op a b -> Op a b # fromRational :: Rational -> Op a b #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #
Fractional a => Fractional (Tagged s a)
Instance details Defined in Data.Tagged Methods (/) :: Tagged s a -> Tagged s a -> Tagged s a # recip :: Tagged s a -> Tagged s a # fromRational :: Rational -> Tagged s a #

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Minimal complete definition

quotRem, toInteger

Methods

div :: a -> a -> a infixl 7 #

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 #

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

toInteger :: a -> Integer #

conversion to Integer

Instances

Instances details

Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Integral Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int8 -> Int8 -> Int8 # rem :: Int8 -> Int8 -> Int8 # div :: Int8 -> Int8 -> Int8 # mod :: Int8 -> Int8 -> Int8 # quotRem :: Int8 -> Int8 -> (Int8, Int8) # divMod :: Int8 -> Int8 -> (Int8, Int8) # toInteger :: Int8 -> Integer #
Integral Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int16 -> Int16 -> Int16 # rem :: Int16 -> Int16 -> Int16 # div :: Int16 -> Int16 -> Int16 # mod :: Int16 -> Int16 -> Int16 # quotRem :: Int16 -> Int16 -> (Int16, Int16) # divMod :: Int16 -> Int16 -> (Int16, Int16) # toInteger :: Int16 -> Integer #
Integral Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int32 -> Int32 -> Int32 # rem :: Int32 -> Int32 -> Int32 # div :: Int32 -> Int32 -> Int32 # mod :: Int32 -> Int32 -> Int32 # quotRem :: Int32 -> Int32 -> (Int32, Int32) # divMod :: Int32 -> Int32 -> (Int32, Int32) # toInteger :: Int32 -> Integer #
Integral Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int64 -> Int64 -> Int64 # rem :: Int64 -> Int64 -> Int64 # div :: Int64 -> Int64 -> Int64 # mod :: Int64 -> Int64 -> Int64 # quotRem :: Int64 -> Int64 -> (Int64, Int64) # divMod :: Int64 -> Int64 -> (Int64, Int64) # toInteger :: Int64 -> Integer #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
Integral Word	Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # div :: Word -> Word -> Word # mod :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) # divMod :: Word -> Word -> (Word, Word) # toInteger :: Word -> Integer #
Integral Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word8 -> Word8 -> Word8 # rem :: Word8 -> Word8 -> Word8 # div :: Word8 -> Word8 -> Word8 # mod :: Word8 -> Word8 -> Word8 # quotRem :: Word8 -> Word8 -> (Word8, Word8) # divMod :: Word8 -> Word8 -> (Word8, Word8) # toInteger :: Word8 -> Integer #
Integral Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word16 -> Word16 -> Word16 # rem :: Word16 -> Word16 -> Word16 # div :: Word16 -> Word16 -> Word16 # mod :: Word16 -> Word16 -> Word16 # quotRem :: Word16 -> Word16 -> (Word16, Word16) # divMod :: Word16 -> Word16 -> (Word16, Word16) # toInteger :: Word16 -> Integer #
Integral Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word32 -> Word32 -> Word32 # rem :: Word32 -> Word32 -> Word32 # div :: Word32 -> Word32 -> Word32 # mod :: Word32 -> Word32 -> Word32 # quotRem :: Word32 -> Word32 -> (Word32, Word32) # divMod :: Word32 -> Word32 -> (Word32, Word32) # toInteger :: Word32 -> Integer #
Integral Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word64 -> Word64 -> Word64 # rem :: Word64 -> Word64 -> Word64 # div :: Word64 -> Word64 -> Word64 # mod :: Word64 -> Word64 -> Word64 # quotRem :: Word64 -> Word64 -> (Word64, Word64) # divMod :: Word64 -> Word64 -> (Word64, Word64) # toInteger :: Word64 -> Integer #
Integral CDev
Instance details Defined in System.Posix.Types Methods quot :: CDev -> CDev -> CDev # rem :: CDev -> CDev -> CDev # div :: CDev -> CDev -> CDev # mod :: CDev -> CDev -> CDev # quotRem :: CDev -> CDev -> (CDev, CDev) # divMod :: CDev -> CDev -> (CDev, CDev) # toInteger :: CDev -> Integer #
Integral CIno
Instance details Defined in System.Posix.Types Methods quot :: CIno -> CIno -> CIno # rem :: CIno -> CIno -> CIno # div :: CIno -> CIno -> CIno # mod :: CIno -> CIno -> CIno # quotRem :: CIno -> CIno -> (CIno, CIno) # divMod :: CIno -> CIno -> (CIno, CIno) # toInteger :: CIno -> Integer #
Integral CMode
Instance details Defined in System.Posix.Types Methods quot :: CMode -> CMode -> CMode # rem :: CMode -> CMode -> CMode # div :: CMode -> CMode -> CMode # mod :: CMode -> CMode -> CMode # quotRem :: CMode -> CMode -> (CMode, CMode) # divMod :: CMode -> CMode -> (CMode, CMode) # toInteger :: CMode -> Integer #
Integral COff
Instance details Defined in System.Posix.Types Methods quot :: COff -> COff -> COff # rem :: COff -> COff -> COff # div :: COff -> COff -> COff # mod :: COff -> COff -> COff # quotRem :: COff -> COff -> (COff, COff) # divMod :: COff -> COff -> (COff, COff) # toInteger :: COff -> Integer #
Integral CPid
Instance details Defined in System.Posix.Types Methods quot :: CPid -> CPid -> CPid # rem :: CPid -> CPid -> CPid # div :: CPid -> CPid -> CPid # mod :: CPid -> CPid -> CPid # quotRem :: CPid -> CPid -> (CPid, CPid) # divMod :: CPid -> CPid -> (CPid, CPid) # toInteger :: CPid -> Integer #
Integral CSsize
Instance details Defined in System.Posix.Types Methods quot :: CSsize -> CSsize -> CSsize # rem :: CSsize -> CSsize -> CSsize # div :: CSsize -> CSsize -> CSsize # mod :: CSsize -> CSsize -> CSsize # quotRem :: CSsize -> CSsize -> (CSsize, CSsize) # divMod :: CSsize -> CSsize -> (CSsize, CSsize) # toInteger :: CSsize -> Integer #
Integral CGid
Instance details Defined in System.Posix.Types Methods quot :: CGid -> CGid -> CGid # rem :: CGid -> CGid -> CGid # div :: CGid -> CGid -> CGid # mod :: CGid -> CGid -> CGid # quotRem :: CGid -> CGid -> (CGid, CGid) # divMod :: CGid -> CGid -> (CGid, CGid) # toInteger :: CGid -> Integer #
Integral CNlink
Instance details Defined in System.Posix.Types Methods quot :: CNlink -> CNlink -> CNlink # rem :: CNlink -> CNlink -> CNlink # div :: CNlink -> CNlink -> CNlink # mod :: CNlink -> CNlink -> CNlink # quotRem :: CNlink -> CNlink -> (CNlink, CNlink) # divMod :: CNlink -> CNlink -> (CNlink, CNlink) # toInteger :: CNlink -> Integer #
Integral CUid
Instance details Defined in System.Posix.Types Methods quot :: CUid -> CUid -> CUid # rem :: CUid -> CUid -> CUid # div :: CUid -> CUid -> CUid # mod :: CUid -> CUid -> CUid # quotRem :: CUid -> CUid -> (CUid, CUid) # divMod :: CUid -> CUid -> (CUid, CUid) # toInteger :: CUid -> Integer #
Integral CTcflag
Instance details Defined in System.Posix.Types Methods quot :: CTcflag -> CTcflag -> CTcflag # rem :: CTcflag -> CTcflag -> CTcflag # div :: CTcflag -> CTcflag -> CTcflag # mod :: CTcflag -> CTcflag -> CTcflag # quotRem :: CTcflag -> CTcflag -> (CTcflag, CTcflag) # divMod :: CTcflag -> CTcflag -> (CTcflag, CTcflag) # toInteger :: CTcflag -> Integer #
Integral CRLim
Instance details Defined in System.Posix.Types Methods quot :: CRLim -> CRLim -> CRLim # rem :: CRLim -> CRLim -> CRLim # div :: CRLim -> CRLim -> CRLim # mod :: CRLim -> CRLim -> CRLim # quotRem :: CRLim -> CRLim -> (CRLim, CRLim) # divMod :: CRLim -> CRLim -> (CRLim, CRLim) # toInteger :: CRLim -> Integer #
Integral CBlkSize
Instance details Defined in System.Posix.Types Methods quot :: CBlkSize -> CBlkSize -> CBlkSize # rem :: CBlkSize -> CBlkSize -> CBlkSize # div :: CBlkSize -> CBlkSize -> CBlkSize # mod :: CBlkSize -> CBlkSize -> CBlkSize # quotRem :: CBlkSize -> CBlkSize -> (CBlkSize, CBlkSize) # divMod :: CBlkSize -> CBlkSize -> (CBlkSize, CBlkSize) # toInteger :: CBlkSize -> Integer #
Integral CBlkCnt
Instance details Defined in System.Posix.Types Methods quot :: CBlkCnt -> CBlkCnt -> CBlkCnt # rem :: CBlkCnt -> CBlkCnt -> CBlkCnt # div :: CBlkCnt -> CBlkCnt -> CBlkCnt # mod :: CBlkCnt -> CBlkCnt -> CBlkCnt # quotRem :: CBlkCnt -> CBlkCnt -> (CBlkCnt, CBlkCnt) # divMod :: CBlkCnt -> CBlkCnt -> (CBlkCnt, CBlkCnt) # toInteger :: CBlkCnt -> Integer #
Integral CClockId
Instance details Defined in System.Posix.Types Methods quot :: CClockId -> CClockId -> CClockId # rem :: CClockId -> CClockId -> CClockId # div :: CClockId -> CClockId -> CClockId # mod :: CClockId -> CClockId -> CClockId # quotRem :: CClockId -> CClockId -> (CClockId, CClockId) # divMod :: CClockId -> CClockId -> (CClockId, CClockId) # toInteger :: CClockId -> Integer #
Integral CFsBlkCnt
Instance details Defined in System.Posix.Types Methods quot :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # rem :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # div :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # mod :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # quotRem :: CFsBlkCnt -> CFsBlkCnt -> (CFsBlkCnt, CFsBlkCnt) # divMod :: CFsBlkCnt -> CFsBlkCnt -> (CFsBlkCnt, CFsBlkCnt) # toInteger :: CFsBlkCnt -> Integer #
Integral CFsFilCnt
Instance details Defined in System.Posix.Types Methods quot :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # rem :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # div :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # mod :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # quotRem :: CFsFilCnt -> CFsFilCnt -> (CFsFilCnt, CFsFilCnt) # divMod :: CFsFilCnt -> CFsFilCnt -> (CFsFilCnt, CFsFilCnt) # toInteger :: CFsFilCnt -> Integer #
Integral CId
Instance details Defined in System.Posix.Types Methods quot :: CId -> CId -> CId # rem :: CId -> CId -> CId # div :: CId -> CId -> CId # mod :: CId -> CId -> CId # quotRem :: CId -> CId -> (CId, CId) # divMod :: CId -> CId -> (CId, CId) # toInteger :: CId -> Integer #
Integral CKey
Instance details Defined in System.Posix.Types Methods quot :: CKey -> CKey -> CKey # rem :: CKey -> CKey -> CKey # div :: CKey -> CKey -> CKey # mod :: CKey -> CKey -> CKey # quotRem :: CKey -> CKey -> (CKey, CKey) # divMod :: CKey -> CKey -> (CKey, CKey) # toInteger :: CKey -> Integer #
Integral CSocklen
Instance details Defined in System.Posix.Types Methods quot :: CSocklen -> CSocklen -> CSocklen # rem :: CSocklen -> CSocklen -> CSocklen # div :: CSocklen -> CSocklen -> CSocklen # mod :: CSocklen -> CSocklen -> CSocklen # quotRem :: CSocklen -> CSocklen -> (CSocklen, CSocklen) # divMod :: CSocklen -> CSocklen -> (CSocklen, CSocklen) # toInteger :: CSocklen -> Integer #
Integral CNfds
Instance details Defined in System.Posix.Types Methods quot :: CNfds -> CNfds -> CNfds # rem :: CNfds -> CNfds -> CNfds # div :: CNfds -> CNfds -> CNfds # mod :: CNfds -> CNfds -> CNfds # quotRem :: CNfds -> CNfds -> (CNfds, CNfds) # divMod :: CNfds -> CNfds -> (CNfds, CNfds) # toInteger :: CNfds -> Integer #
Integral Fd
Instance details Defined in System.Posix.Types Methods quot :: Fd -> Fd -> Fd # rem :: Fd -> Fd -> Fd # div :: Fd -> Fd -> Fd # mod :: Fd -> Fd -> Fd # quotRem :: Fd -> Fd -> (Fd, Fd) # divMod :: Fd -> Fd -> (Fd, Fd) # toInteger :: Fd -> Integer #
Integral CChar
Instance details Defined in Foreign.C.Types Methods quot :: CChar -> CChar -> CChar # rem :: CChar -> CChar -> CChar # div :: CChar -> CChar -> CChar # mod :: CChar -> CChar -> CChar # quotRem :: CChar -> CChar -> (CChar, CChar) # divMod :: CChar -> CChar -> (CChar, CChar) # toInteger :: CChar -> Integer #
Integral CSChar
Instance details Defined in Foreign.C.Types Methods quot :: CSChar -> CSChar -> CSChar # rem :: CSChar -> CSChar -> CSChar # div :: CSChar -> CSChar -> CSChar # mod :: CSChar -> CSChar -> CSChar # quotRem :: CSChar -> CSChar -> (CSChar, CSChar) # divMod :: CSChar -> CSChar -> (CSChar, CSChar) # toInteger :: CSChar -> Integer #
Integral CUChar
Instance details Defined in Foreign.C.Types Methods quot :: CUChar -> CUChar -> CUChar # rem :: CUChar -> CUChar -> CUChar # div :: CUChar -> CUChar -> CUChar # mod :: CUChar -> CUChar -> CUChar # quotRem :: CUChar -> CUChar -> (CUChar, CUChar) # divMod :: CUChar -> CUChar -> (CUChar, CUChar) # toInteger :: CUChar -> Integer #
Integral CShort
Instance details Defined in Foreign.C.Types Methods quot :: CShort -> CShort -> CShort # rem :: CShort -> CShort -> CShort # div :: CShort -> CShort -> CShort # mod :: CShort -> CShort -> CShort # quotRem :: CShort -> CShort -> (CShort, CShort) # divMod :: CShort -> CShort -> (CShort, CShort) # toInteger :: CShort -> Integer #
Integral CUShort
Instance details Defined in Foreign.C.Types Methods quot :: CUShort -> CUShort -> CUShort # rem :: CUShort -> CUShort -> CUShort # div :: CUShort -> CUShort -> CUShort # mod :: CUShort -> CUShort -> CUShort # quotRem :: CUShort -> CUShort -> (CUShort, CUShort) # divMod :: CUShort -> CUShort -> (CUShort, CUShort) # toInteger :: CUShort -> Integer #
Integral CInt
Instance details Defined in Foreign.C.Types Methods quot :: CInt -> CInt -> CInt # rem :: CInt -> CInt -> CInt # div :: CInt -> CInt -> CInt # mod :: CInt -> CInt -> CInt # quotRem :: CInt -> CInt -> (CInt, CInt) # divMod :: CInt -> CInt -> (CInt, CInt) # toInteger :: CInt -> Integer #
Integral CUInt
Instance details Defined in Foreign.C.Types Methods quot :: CUInt -> CUInt -> CUInt # rem :: CUInt -> CUInt -> CUInt # div :: CUInt -> CUInt -> CUInt # mod :: CUInt -> CUInt -> CUInt # quotRem :: CUInt -> CUInt -> (CUInt, CUInt) # divMod :: CUInt -> CUInt -> (CUInt, CUInt) # toInteger :: CUInt -> Integer #
Integral CLong
Instance details Defined in Foreign.C.Types Methods quot :: CLong -> CLong -> CLong # rem :: CLong -> CLong -> CLong # div :: CLong -> CLong -> CLong # mod :: CLong -> CLong -> CLong # quotRem :: CLong -> CLong -> (CLong, CLong) # divMod :: CLong -> CLong -> (CLong, CLong) # toInteger :: CLong -> Integer #
Integral CULong
Instance details Defined in Foreign.C.Types Methods quot :: CULong -> CULong -> CULong # rem :: CULong -> CULong -> CULong # div :: CULong -> CULong -> CULong # mod :: CULong -> CULong -> CULong # quotRem :: CULong -> CULong -> (CULong, CULong) # divMod :: CULong -> CULong -> (CULong, CULong) # toInteger :: CULong -> Integer #
Integral CLLong
Instance details Defined in Foreign.C.Types Methods quot :: CLLong -> CLLong -> CLLong # rem :: CLLong -> CLLong -> CLLong # div :: CLLong -> CLLong -> CLLong # mod :: CLLong -> CLLong -> CLLong # quotRem :: CLLong -> CLLong -> (CLLong, CLLong) # divMod :: CLLong -> CLLong -> (CLLong, CLLong) # toInteger :: CLLong -> Integer #
Integral CULLong
Instance details Defined in Foreign.C.Types Methods quot :: CULLong -> CULLong -> CULLong # rem :: CULLong -> CULLong -> CULLong # div :: CULLong -> CULLong -> CULLong # mod :: CULLong -> CULLong -> CULLong # quotRem :: CULLong -> CULLong -> (CULLong, CULLong) # divMod :: CULLong -> CULLong -> (CULLong, CULLong) # toInteger :: CULLong -> Integer #
Integral CBool
Instance details Defined in Foreign.C.Types Methods quot :: CBool -> CBool -> CBool # rem :: CBool -> CBool -> CBool # div :: CBool -> CBool -> CBool # mod :: CBool -> CBool -> CBool # quotRem :: CBool -> CBool -> (CBool, CBool) # divMod :: CBool -> CBool -> (CBool, CBool) # toInteger :: CBool -> Integer #
Integral CPtrdiff
Instance details Defined in Foreign.C.Types Methods quot :: CPtrdiff -> CPtrdiff -> CPtrdiff # rem :: CPtrdiff -> CPtrdiff -> CPtrdiff # div :: CPtrdiff -> CPtrdiff -> CPtrdiff # mod :: CPtrdiff -> CPtrdiff -> CPtrdiff # quotRem :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) # divMod :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) # toInteger :: CPtrdiff -> Integer #
Integral CSize
Instance details Defined in Foreign.C.Types Methods quot :: CSize -> CSize -> CSize # rem :: CSize -> CSize -> CSize # div :: CSize -> CSize -> CSize # mod :: CSize -> CSize -> CSize # quotRem :: CSize -> CSize -> (CSize, CSize) # divMod :: CSize -> CSize -> (CSize, CSize) # toInteger :: CSize -> Integer #
Integral CWchar
Instance details Defined in Foreign.C.Types Methods quot :: CWchar -> CWchar -> CWchar # rem :: CWchar -> CWchar -> CWchar # div :: CWchar -> CWchar -> CWchar # mod :: CWchar -> CWchar -> CWchar # quotRem :: CWchar -> CWchar -> (CWchar, CWchar) # divMod :: CWchar -> CWchar -> (CWchar, CWchar) # toInteger :: CWchar -> Integer #
Integral CSigAtomic
Instance details Defined in Foreign.C.Types Methods quot :: CSigAtomic -> CSigAtomic -> CSigAtomic # rem :: CSigAtomic -> CSigAtomic -> CSigAtomic # div :: CSigAtomic -> CSigAtomic -> CSigAtomic # mod :: CSigAtomic -> CSigAtomic -> CSigAtomic # quotRem :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) # divMod :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) # toInteger :: CSigAtomic -> Integer #
Integral CIntPtr
Instance details Defined in Foreign.C.Types Methods quot :: CIntPtr -> CIntPtr -> CIntPtr # rem :: CIntPtr -> CIntPtr -> CIntPtr # div :: CIntPtr -> CIntPtr -> CIntPtr # mod :: CIntPtr -> CIntPtr -> CIntPtr # quotRem :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) # divMod :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) # toInteger :: CIntPtr -> Integer #
Integral CUIntPtr
Instance details Defined in Foreign.C.Types Methods quot :: CUIntPtr -> CUIntPtr -> CUIntPtr # rem :: CUIntPtr -> CUIntPtr -> CUIntPtr # div :: CUIntPtr -> CUIntPtr -> CUIntPtr # mod :: CUIntPtr -> CUIntPtr -> CUIntPtr # quotRem :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) # divMod :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) # toInteger :: CUIntPtr -> Integer #
Integral CIntMax
Instance details Defined in Foreign.C.Types Methods quot :: CIntMax -> CIntMax -> CIntMax # rem :: CIntMax -> CIntMax -> CIntMax # div :: CIntMax -> CIntMax -> CIntMax # mod :: CIntMax -> CIntMax -> CIntMax # quotRem :: CIntMax -> CIntMax -> (CIntMax, CIntMax) # divMod :: CIntMax -> CIntMax -> (CIntMax, CIntMax) # toInteger :: CIntMax -> Integer #
Integral CUIntMax
Instance details Defined in Foreign.C.Types Methods quot :: CUIntMax -> CUIntMax -> CUIntMax # rem :: CUIntMax -> CUIntMax -> CUIntMax # div :: CUIntMax -> CUIntMax -> CUIntMax # mod :: CUIntMax -> CUIntMax -> CUIntMax # quotRem :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) # divMod :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) # toInteger :: CUIntMax -> Integer #
Integral a => Integral (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods quot :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # rem :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # div :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # mod :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # quotRem :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # divMod :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # toInteger :: WrapIntegral a -> Integer #
Integral a => Integral (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods quot :: Down a -> Down a -> Down a # rem :: Down a -> Down a -> Down a # div :: Down a -> Down a -> Down a # mod :: Down a -> Down a -> Down a # quotRem :: Down a -> Down a -> (Down a, Down a) # divMod :: Down a -> Down a -> (Down a, Down a) # toInteger :: Down a -> Integer #
Integral a => Integral (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # toInteger :: Identity a -> Integer #
Integral r => Integral (Scalar r)
Instance details Defined in Algebra.Scalar Methods quot :: Scalar r -> Scalar r -> Scalar r # rem :: Scalar r -> Scalar r -> Scalar r # div :: Scalar r -> Scalar r -> Scalar r # mod :: Scalar r -> Scalar r -> Scalar r # quotRem :: Scalar r -> Scalar r -> (Scalar r, Scalar r) # divMod :: Scalar r -> Scalar r -> (Scalar r, Scalar r) # toInteger :: Scalar r -> Integer #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #
Integral a => Integral (Tagged s a)
Instance details Defined in Data.Tagged Methods quot :: Tagged s a -> Tagged s a -> Tagged s a # rem :: Tagged s a -> Tagged s a -> Tagged s a # div :: Tagged s a -> Tagged s a -> Tagged s a # mod :: Tagged s a -> Tagged s a -> Tagged s a # quotRem :: Tagged s a -> Tagged s a -> (Tagged s a, Tagged s a) # divMod :: Tagged s a -> Tagged s a -> (Tagged s a, Tagged s a) # toInteger :: Tagged s a -> Integer #

class Applicative m => Monad (m :: Type -> Type) where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following:

Left identity: return a >>= k = k a
Right identity: m >>= return = m
Associativity: m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

```
pure = return
```

m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

The above laws imply:

```
fmap f xs  =  xs >>= return . f
```
```
(>>) = (*>)
```

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

(>>) :: m a -> m b -> m b infixl 1 #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

'as >> bs' can be understood as the do expression

do as
   bs

return :: a -> m a #

Inject a value into the monadic type.

Instances

Instances details

Monad []	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] # (>>) :: [a] -> [b] -> [b] # return :: a -> [a] #
Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a #
Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a #
Monad Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b # (>>) :: Par1 a -> Par1 b -> Par1 b # return :: a -> Par1 a #
Monad Q
Instance details Defined in Language.Haskell.TH.Syntax Methods (>>=) :: Q a -> (a -> Q b) -> Q b # (>>) :: Q a -> Q b -> Q b # return :: a -> Q a #
Monad Vector
Instance details Defined in Data.Vector Methods (>>=) :: Vector a -> (a -> Vector b) -> Vector b # (>>) :: Vector a -> Vector b -> Vector b # return :: a -> Vector a #
Monad Seq
Instance details Defined in Data.Sequence.Internal Methods (>>=) :: Seq a -> (a -> Seq b) -> Seq b # (>>) :: Seq a -> Seq b -> Seq b # return :: a -> Seq a #
Monad Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b # (>>) :: Down a -> Down b -> Down b # return :: a -> Down a #
Monad Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a #
Monad Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b # (>>) :: Min a -> Min b -> Min b # return :: a -> Min a #
Monad Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b # (>>) :: Max a -> Max b -> Max b # return :: a -> Max a #
Monad First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a #
Monad Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a #
Monad Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Option a -> (a -> Option b) -> Option b # (>>) :: Option a -> Option b -> Option b # return :: a -> Option a #
Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a #
Monad STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b # (>>) :: STM a -> STM b -> STM b # return :: a -> STM a #
Monad First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a #
Monad Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a #
Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a #
Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a #
Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a #
Monad ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods (>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b # (>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b # return :: a -> ReadPrec a #
Monad ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b # (>>) :: ReadP a -> ReadP b -> ReadP b # return :: a -> ReadP a #
Monad NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # return :: a -> NonEmpty a #
Monad Tree
Instance details Defined in Data.Tree Methods (>>=) :: Tree a -> (a -> Tree b) -> Tree b # (>>) :: Tree a -> Tree b -> Tree b # return :: a -> Tree a #
Monad Id
Instance details Defined in Data.Vector.Fusion.Util Methods (>>=) :: Id a -> (a -> Id b) -> Id b # (>>) :: Id a -> Id b -> Id b # return :: a -> Id a #
Monad Complex
Instance details Defined in Numeric.Algebra.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a #
Monad P	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: P a -> (a -> P b) -> P b # (>>) :: P a -> P b -> P b # return :: a -> P a #
Monad Box
Instance details Defined in Data.Vector.Fusion.Util Methods (>>=) :: Box a -> (a -> Box b) -> Box b # (>>) :: Box a -> Box b -> Box b # return :: a -> Box a #
Monad Array
Instance details Defined in Data.Primitive.Array Methods (>>=) :: Array a -> (a -> Array b) -> Array b # (>>) :: Array a -> Array b -> Array b # return :: a -> Array a #
Monad SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods (>>=) :: SmallArray a -> (a -> SmallArray b) -> SmallArray b # (>>) :: SmallArray a -> SmallArray b -> SmallArray b # return :: a -> SmallArray a #
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a #
Monad (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b # (>>) :: U1 a -> U1 b -> U1 b # return :: a -> U1 a #
Monoid a => Monad ((,) a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) # (>>) :: (a, a0) -> (a, b) -> (a, b) # return :: a0 -> (a, a0) #
Monad (Covector r)
Instance details Defined in Numeric.Covector Methods (>>=) :: Covector r a -> (a -> Covector r b) -> Covector r b # (>>) :: Covector r a -> Covector r b -> Covector r b # return :: a -> Covector r a #
Monad (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b # (>>) :: ST s a -> ST s b -> ST s b # return :: a -> ST s a #
Monad (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b # (>>) :: ST s a -> ST s b -> ST s b # return :: a -> ST s a #
Monad m => Monad (WrappedMonad m)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a #
ArrowApply a => Monad (ArrowMonad a)	Since: base-2.1
Instance details Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 #
Monad (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a #
Monad m => Monad (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods (>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b # (>>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # return :: a -> MaybeT m a #
Monad m => Monad (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods (>>=) :: CatchT m a -> (a -> CatchT m b) -> CatchT m b # (>>) :: CatchT m a -> CatchT m b -> CatchT m b # return :: a -> CatchT m a #
Monad m => Monad (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods (>>=) :: ListT m a -> (a -> ListT m b) -> ListT m b # (>>) :: ListT m a -> ListT m b -> ListT m b # return :: a -> ListT m a #
Monad (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # (>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # return :: a -> ReifiedFold s a #
Monad (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # (>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # return :: a -> ReifiedGetter s a #
Monad f => Monad (WrappedPoly f)
Instance details Defined in Data.MonoTraversable Methods (>>=) :: WrappedPoly f a -> (a -> WrappedPoly f b) -> WrappedPoly f b # (>>) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f b # return :: a -> WrappedPoly f a #
Semigroup a => Monad (These a)
Instance details Defined in Data.These Methods (>>=) :: These a a0 -> (a0 -> These a b) -> These a b # (>>) :: These a a0 -> These a b -> These a b # return :: a0 -> These a a0 #
Monad f => Monad (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods (>>=) :: WrapFunctor f a -> (a -> WrapFunctor f b) -> WrapFunctor f b # (>>) :: WrapFunctor f a -> WrapFunctor f b -> WrapFunctor f b # return :: a -> WrapFunctor f a #
Monad m => Monad (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods (>>=) :: IterT m a -> (a -> IterT m b) -> IterT m b # (>>) :: IterT m a -> IterT m b -> IterT m b # return :: a -> IterT m a #
Representable f => Monad (Co f)
Instance details Defined in Data.Functor.Rep Methods (>>=) :: Co f a -> (a -> Co f b) -> Co f b # (>>) :: Co f a -> Co f b -> Co f b # return :: a -> Co f a #
Alternative f => Monad (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods (>>=) :: Cofree f a -> (a -> Cofree f b) -> Cofree f b # (>>) :: Cofree f a -> Cofree f b -> Cofree f b # return :: a -> Cofree f a #
Functor f => Monad (Free f)
Instance details Defined in Control.Monad.Free Methods (>>=) :: Free f a -> (a -> Free f b) -> Free f b # (>>) :: Free f a -> Free f b -> Free f b # return :: a -> Free f a #
Monad m => Monad (Yoneda m)
Instance details Defined in Data.Functor.Yoneda Methods (>>=) :: Yoneda m a -> (a -> Yoneda m b) -> Yoneda m b # (>>) :: Yoneda m a -> Yoneda m b -> Yoneda m b # return :: a -> Yoneda m a #
Monad f => Monad (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b # (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # return :: a -> Rec1 f a #
(Monoid a, Monoid b) => Monad ((,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) # (>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) # return :: a0 -> (a, b, a0) #
Monad m => Monad (Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b # (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b # return :: a0 -> Kleisli m a a0 #
Monad f => Monad (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b # (>>) :: Ap f a -> Ap f b -> Ap f b # return :: a -> Ap f a #
Monad f => Monad (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b # (>>) :: Alt f a -> Alt f b -> Alt f b # return :: a -> Alt f a #
(Applicative f, Monad f) => Monad (WhenMissing f x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a #
Monad m => Monad (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods (>>=) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b # (>>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # return :: a -> ExceptT e m a #
Monad m => Monad (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods (>>=) :: IdentityT m a -> (a -> IdentityT m b) -> IdentityT m b # (>>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # return :: a -> IdentityT m a #
(Monad m, Error e) => Monad (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods (>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b # (>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # return :: a -> ErrorT e m a #
Monad m => Monad (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods (>>=) :: ReaderT r m a -> (a -> ReaderT r m b) -> ReaderT r m b # (>>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # return :: a -> ReaderT r m a #
Monad m => Monad (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a #
Monad m => Monad (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods (>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b # (>>) :: StateT s m a -> StateT s m b -> StateT s m b # return :: a -> StateT s m a #
(Monoid w, Monad m) => Monad (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a #
(Monoid w, Monad m) => Monad (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods (>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b # (>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # return :: a -> WriterT w m a #
Monad m => Monad (Reverse m)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods (>>=) :: Reverse m a -> (a -> Reverse m b) -> Reverse m b # (>>) :: Reverse m a -> Reverse m b -> Reverse m b # return :: a -> Reverse m a #
Monad (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>=) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # (>>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # return :: a0 -> Indexed i a a0 #
Monad (Tagged s)
Instance details Defined in Data.Tagged Methods (>>=) :: Tagged s a -> (a -> Tagged s b) -> Tagged s b # (>>) :: Tagged s a -> Tagged s b -> Tagged s b # return :: a -> Tagged s a #
(Alternative f, Monad w) => Monad (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods (>>=) :: CofreeT f w a -> (a -> CofreeT f w b) -> CofreeT f w b # (>>) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w b # return :: a -> CofreeT f w a #
(Functor f, Monad m) => Monad (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods (>>=) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b # (>>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # return :: a -> FreeT f m a #
Monad m => Monad (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods (>>=) :: RandT g m a -> (a -> RandT g m b) -> RandT g m b # (>>) :: RandT g m a -> RandT g m b -> RandT g m b # return :: a -> RandT g m a #
Monad m => Monad (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods (>>=) :: RandT g m a -> (a -> RandT g m b) -> RandT g m b # (>>) :: RandT g m a -> RandT g m b -> RandT g m b # return :: a -> RandT g m a #
(Monad (Rep p), Representable p) => Monad (Prep p)
Instance details Defined in Data.Profunctor.Rep Methods (>>=) :: Prep p a -> (a -> Prep p b) -> Prep p b # (>>) :: Prep p a -> Prep p b -> Prep p b # return :: a -> Prep p a #
Monad ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b # (>>) :: (r -> a) -> (r -> b) -> r -> b # return :: a -> r -> a #
(Monad f, Monad g) => Monad (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b # (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # return :: a -> (f :*: g) a #
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) # (>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) # return :: a0 -> (a, b, c, a0) #
(Monad f, Monad g) => Monad (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a #
(Monad f, Applicative f) => Monad (WhenMatched f x y)	Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a #
(Applicative f, Monad f) => Monad (WhenMissing f k x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))` . Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a #
Monad (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods (>>=) :: ContT r m a -> (a -> ContT r m b) -> ContT r m b # (>>) :: ContT r m a -> ContT r m b -> ContT r m b # return :: a -> ContT r m a #
Monad (Costar f a)
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Costar f a a0 -> (a0 -> Costar f a b) -> Costar f a b # (>>) :: Costar f a a0 -> Costar f a b -> Costar f a b # return :: a0 -> Costar f a a0 #
Monad f => Monad (Star f a)
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Star f a a0 -> (a0 -> Star f a b) -> Star f a b # (>>) :: Star f a a0 -> Star f a b -> Star f a b # return :: a0 -> Star f a a0 #
Monad f => Monad (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # return :: a -> M1 i c f a #
(Monad f, Applicative f) => Monad (WhenMatched f k x y)	Equivalent to `ReaderT k (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a #
(Monoid w, Monad m) => Monad (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a #
(Monoid w, Monad m) => Monad (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods (>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b # (>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # return :: a -> RWST r w s m a #

class Functor (f :: Type -> Type) where #

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity: fmap id == id
Composition: fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b #

Using ApplicativeDo: 'fmap f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

(<$) :: a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

Instances

Instances details

Functor []	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] # (<$) :: a -> [b] -> [a] #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b # (<$) :: a -> Par1 b -> Par1 a #
Functor Q
Instance details Defined in Language.Haskell.TH.Syntax Methods fmap :: (a -> b) -> Q a -> Q b # (<$) :: a -> Q b -> Q a #
Functor Vector
Instance details Defined in Data.Vector Methods fmap :: (a -> b) -> Vector a -> Vector b # (<$) :: a -> Vector b -> Vector a #
Functor Seq
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b # (<$) :: a -> Seq b -> Seq a #
Functor IntMap
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> IntMap a -> IntMap b # (<$) :: a -> IntMap b -> IntMap a #
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b # (<$) :: a -> Down b -> Down a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b # (<$) :: a -> Min b -> Min a #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b # (<$) :: a -> Max b -> Max a #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Option a -> Option b # (<$) :: a -> Option b -> Option a #
Functor ArgOrder	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgOrder a -> ArgOrder b # (<$) :: a -> ArgOrder b -> ArgOrder a #
Functor OptDescr	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> OptDescr a -> OptDescr b # (<$) :: a -> OptDescr b -> OptDescr a #
Functor ArgDescr	Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgDescr a -> ArgDescr b # (<$) :: a -> ArgDescr b -> ArgDescr a #
Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b # (<$) :: a -> ZipList b -> ZipList a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
Functor Handler	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b # (<$) :: a -> Handler b -> Handler a #
Functor STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b # (<$) :: a -> STM b -> STM a #
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Functor ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods fmap :: (a -> b) -> ReadPrec a -> ReadPrec b # (<$) :: a -> ReadPrec b -> ReadPrec a #
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b # (<$) :: a -> ReadP b -> ReadP a #
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b # (<$) :: a -> NonEmpty b -> NonEmpty a #
Functor Tree
Instance details Defined in Data.Tree Methods fmap :: (a -> b) -> Tree a -> Tree b # (<$) :: a -> Tree b -> Tree a #
Functor FingerTree
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a #
Functor Digit
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Digit a -> Digit b # (<$) :: a -> Digit b -> Digit a #
Functor Node
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Node a -> Node b # (<$) :: a -> Node b -> Node a #
Functor Elem
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Elem a -> Elem b # (<$) :: a -> Elem b -> Elem a #
Functor ViewL
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewL a -> ViewL b # (<$) :: a -> ViewL b -> ViewL a #
Functor ViewR
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewR a -> ViewR b # (<$) :: a -> ViewR b -> ViewR a #
Functor Ideal
Instance details Defined in Algebra.Ring.Ideal Methods fmap :: (a -> b) -> Ideal a -> Ideal b # (<$) :: a -> Ideal b -> Ideal a #
Functor Doc
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> Doc a -> Doc b # (<$) :: a -> Doc b -> Doc a #
Functor AnnotDetails
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b # (<$) :: a -> AnnotDetails b -> AnnotDetails a #
Functor Span
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> Span a -> Span b # (<$) :: a -> Span b -> Span a #
Functor Id
Instance details Defined in Data.Vector.Fusion.Util Methods fmap :: (a -> b) -> Id a -> Id b # (<$) :: a -> Id b -> Id a #
Functor Complex
Instance details Defined in Numeric.Algebra.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Functor P	Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b # (<$) :: a -> P b -> P a #
Functor Box
Instance details Defined in Data.Vector.Fusion.Util Methods fmap :: (a -> b) -> Box a -> Box b # (<$) :: a -> Box b -> Box a #
Functor Array
Instance details Defined in Data.Primitive.Array Methods fmap :: (a -> b) -> Array a -> Array b # (<$) :: a -> Array b -> Array a #
Functor SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods fmap :: (a -> b) -> SmallArray a -> SmallArray b # (<$) :: a -> SmallArray b -> SmallArray a #
Functor Forest
Instance details Defined in Data.Heap Methods fmap :: (a -> b) -> Forest a -> Forest b # (<$) :: a -> Forest b -> Forest a #
Functor Tree
Instance details Defined in Data.Heap Methods fmap :: (a -> b) -> Tree a -> Tree b # (<$) :: a -> Tree b -> Tree a #
Functor Matrix
Instance details Defined in Data.Matrix Methods fmap :: (a -> b) -> Matrix a -> Matrix b # (<$) :: a -> Matrix b -> Matrix a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Functor (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b # (<$) :: a -> U1 b -> U1 a #
Functor ((,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) # (<$) :: a0 -> (a, b) -> (a, a0) #
Functor (Covector r)
Instance details Defined in Numeric.Covector Methods fmap :: (a -> b) -> Covector r a -> Covector r b # (<$) :: a -> Covector r b -> Covector r a #
Functor (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods fmap :: (a -> b) -> HashMap k a -> HashMap k b # (<$) :: a -> HashMap k b -> HashMap k a #
Functor (Map k)
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b # (<$) :: a -> Map k b -> Map k a #
Functor (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b # (<$) :: a -> ST s b -> ST s a #
Functor (Array i)	Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b # (<$) :: a -> Array i b -> Array i a #
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Functor (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fmap :: (a -> b) -> ST s a -> ST s b # (<$) :: a -> ST s b -> ST s a #
Monad m => Functor (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a #
Arrow a => Functor (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Functor m => Functor (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods fmap :: (a -> b) -> MaybeT m a -> MaybeT m b # (<$) :: a -> MaybeT m b -> MaybeT m a #
Monad m => Functor (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods fmap :: (a -> b) -> CatchT m a -> CatchT m b # (<$) :: a -> CatchT m b -> CatchT m a #
Functor m => Functor (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods fmap :: (a -> b) -> ListT m a -> ListT m b # (<$) :: a -> ListT m b -> ListT m a #
Functor (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fmap :: (a -> b) -> Level i a -> Level i b # (<$) :: a -> Level i b -> Level i a #
Functor (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (<$) :: a -> ReifiedFold s b -> ReifiedFold s a #
Functor (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (<$) :: a -> ReifiedGetter s b -> ReifiedGetter s a #
Functor f => Functor (WrappedPoly f)
Instance details Defined in Data.MonoTraversable Methods fmap :: (a -> b) -> WrappedPoly f a -> WrappedPoly f b # (<$) :: a -> WrappedPoly f b -> WrappedPoly f a #
Functor (These a)
Instance details Defined in Data.These Methods fmap :: (a0 -> b) -> These a a0 -> These a b # (<$) :: a0 -> These a b -> These a a0 #
Functor f => Functor (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods fmap :: (a -> b) -> WrapFunctor f a -> WrapFunctor f b # (<$) :: a -> WrapFunctor f b -> WrapFunctor f a #
Functor (Alt f)
Instance details Defined in Control.Alternative.Free Methods fmap :: (a -> b) -> Alt f a -> Alt f b # (<$) :: a -> Alt f b -> Alt f a #
Functor (AltF f)
Instance details Defined in Control.Alternative.Free Methods fmap :: (a -> b) -> AltF f a -> AltF f b # (<$) :: a -> AltF f b -> AltF f a #
Functor w => Functor (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods fmap :: (a -> b) -> CoiterT w a -> CoiterT w b # (<$) :: a -> CoiterT w b -> CoiterT w a #
Monad m => Functor (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods fmap :: (a -> b) -> IterT m a -> IterT m b # (<$) :: a -> IterT m b -> IterT m a #
Functor f => Functor (MaybeApply f)
Instance details Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> MaybeApply f a -> MaybeApply f b # (<$) :: a -> MaybeApply f b -> MaybeApply f a #
Functor f => Functor (WrappedApplicative f)
Instance details Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # (<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a #
Functor f => Functor (Indexing f)
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a -> b) -> Indexing f a -> Indexing f b # (<$) :: a -> Indexing f b -> Indexing f a #
Functor f => Functor (Co f)
Instance details Defined in Data.Functor.Rep Methods fmap :: (a -> b) -> Co f a -> Co f b # (<$) :: a -> Co f b -> Co f a #
Functor f => Functor (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods fmap :: (a -> b) -> Cofree f a -> Cofree f b # (<$) :: a -> Cofree f b -> Cofree f a #
Functor f => Functor (Free f)
Instance details Defined in Control.Monad.Free Methods fmap :: (a -> b) -> Free f a -> Free f b # (<$) :: a -> Free f b -> Free f a #
Functor (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods fmap :: (a -> b) -> Yoneda f a -> Yoneda f b # (<$) :: a -> Yoneda f b -> Yoneda f a #
Functor (StateL s)
Instance details Defined in Data.Key Methods fmap :: (a -> b) -> StateL s a -> StateL s b # (<$) :: a -> StateL s b -> StateL s a #
Functor (StateR s)
Instance details Defined in Data.Key Methods fmap :: (a -> b) -> StateR s a -> StateR s b # (<$) :: a -> StateR s b -> StateR s a #
Functor f => Functor (Act f)
Instance details Defined in Data.Key Methods fmap :: (a -> b) -> Act f a -> Act f b # (<$) :: a -> Act f b -> Act f a #
Functor f => Functor (Indexing64 f)
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a -> b) -> Indexing64 f a -> Indexing64 f b # (<$) :: a -> Indexing64 f b -> Indexing64 f a #
Functor (Entry p)
Instance details Defined in Data.Heap Methods fmap :: (a -> b) -> Entry p a -> Entry p b # (<$) :: a -> Entry p b -> Entry p a #
Functor f => Functor (First1 f)
Instance details Defined in Control.Lens.Lens Methods fmap :: (a -> b) -> First1 f a -> First1 f b # (<$) :: a -> First1 f b -> First1 f a #
Functor f => Functor (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Rec1 f a -> Rec1 f b # (<$) :: a -> Rec1 f b -> Rec1 f a #
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
Functor (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b # (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #
Functor ((,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) # (<$) :: a0 -> (a, b, b0) -> (a, b, a0) #
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Functor m => Functor (Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b # (<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Functor f => Functor (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b # (<$) :: a -> Ap f b -> Ap f a #
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b # (<$) :: a -> Alt f b -> Alt f a #
(Applicative f, Monad f) => Functor (WhenMissing f x)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a #
Functor m => Functor (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b # (<$) :: a -> ExceptT e m b -> ExceptT e m a #
Functor m => Functor (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods fmap :: (a -> b) -> IdentityT m a -> IdentityT m b # (<$) :: a -> IdentityT m b -> IdentityT m a #
Functor m => Functor (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b # (<$) :: a -> ErrorT e m b -> ErrorT e m a #
Functor m => Functor (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b # (<$) :: a -> ReaderT r m b -> ReaderT r m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor f => Functor (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods fmap :: (a -> b) -> Reverse f a -> Reverse f b # (<$) :: a -> Reverse f b -> Reverse f a #
Functor (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods fmap :: (a0 -> b) -> Constant a a0 -> Constant a b # (<$) :: a0 -> Constant a b -> Constant a a0 #
Functor f => Functor (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods fmap :: (a -> b) -> Backwards f a -> Backwards f b # (<$) :: a -> Backwards f b -> Backwards f a #
Functor f => Functor (Sized f n)
Instance details Defined in Data.Sized.Internal Methods fmap :: (a -> b) -> Sized f n a -> Sized f n b # (<$) :: a -> Sized f n b -> Sized f n a #
Monad m => Functor (Bundle m v)
Instance details Defined in Data.Vector.Fusion.Bundle.Monadic Methods fmap :: (a -> b) -> Bundle m v a -> Bundle m v b # (<$) :: a -> Bundle m v b -> Bundle m v a #
Functor (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> Context a b a0 -> Context a b b0 # (<$) :: a0 -> Context a b b0 -> Context a b a0 #
Functor (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (<$) :: a0 -> Indexed i a b -> Indexed i a a0 #
Functor (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s b # (<$) :: a -> ReifiedIndexedFold i s b -> ReifiedIndexedFold i s a #
Functor (ReifiedIndexedGetter i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (<$) :: a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a #
Functor f => Functor (CAlt f)
Instance details Defined in Control.Subcategory.Alternative Methods fmap :: (a -> b) -> CAlt f a -> CAlt f b # (<$) :: a -> CAlt f b -> CAlt f a #
Functor f => Functor (CApp f)
Instance details Defined in Control.Subcategory.Applicative Methods fmap :: (a -> b) -> CApp f a -> CApp f b # (<$) :: a -> CApp f b -> CApp f a #
Functor (Tagged s)
Instance details Defined in Data.Tagged Methods fmap :: (a -> b) -> Tagged s a -> Tagged s b # (<$) :: a -> Tagged s b -> Tagged s a #
Functor g => Functor (ApT f g)
Instance details Defined in Control.Applicative.Trans.Free Methods fmap :: (a -> b) -> ApT f g a -> ApT f g b # (<$) :: a -> ApT f g b -> ApT f g a #
Functor g => Functor (ApF f g)
Instance details Defined in Control.Applicative.Trans.Free Methods fmap :: (a -> b) -> ApF f g a -> ApF f g b # (<$) :: a -> ApF f g b -> ApF f g a #
(Functor f, Functor w) => Functor (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods fmap :: (a -> b) -> CofreeT f w a -> CofreeT f w b # (<$) :: a -> CofreeT f w b -> CofreeT f w a #
Functor f => Functor (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods fmap :: (a0 -> b) -> CofreeF f a a0 -> CofreeF f a b # (<$) :: a0 -> CofreeF f a b -> CofreeF f a a0 #
(Functor f, Functor g) => Functor (ComposeCF f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods fmap :: (a -> b) -> ComposeCF f g a -> ComposeCF f g b # (<$) :: a -> ComposeCF f g b -> ComposeCF f g a #
(Functor f, Functor g) => Functor (ComposeFC f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods fmap :: (a -> b) -> ComposeFC f g a -> ComposeFC f g b # (<$) :: a -> ComposeFC f g b -> ComposeFC f g a #
(Contravariant f, Contravariant g) => Functor (Compose f g)
Instance details Defined in Data.Functor.Contravariant.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b # (<$) :: a -> Compose f g b -> Compose f g a #
Bifunctor p => Functor (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods fmap :: (a -> b) -> Fix p a -> Fix p b # (<$) :: a -> Fix p b -> Fix p a #
(Functor f, Monad m) => Functor (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods fmap :: (a -> b) -> FreeT f m a -> FreeT f m b # (<$) :: a -> FreeT f m b -> FreeT f m a #
Functor f => Functor (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods fmap :: (a0 -> b) -> FreeF f a a0 -> FreeF f a b # (<$) :: a0 -> FreeF f a b -> FreeF f a a0 #
Bifunctor p => Functor (Join p)
Instance details Defined in Data.Bifunctor.Join Methods fmap :: (a -> b) -> Join p a -> Join p b # (<$) :: a -> Join p b -> Join p a #
Functor f => Functor (Static f a)
Instance details Defined in Data.Semigroupoid.Static Methods fmap :: (a0 -> b) -> Static f a a0 -> Static f a b # (<$) :: a0 -> Static f a b -> Static f a a0 #
Functor w => Functor (TracedT m w)
Instance details Defined in Control.Comonad.Trans.Traced Methods fmap :: (a -> b) -> TracedT m w a -> TracedT m w b # (<$) :: a -> TracedT m w b -> TracedT m w a #
Functor m => Functor (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods fmap :: (a -> b) -> RandT g m a -> RandT g m b # (<$) :: a -> RandT g m b -> RandT g m a #
Functor m => Functor (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods fmap :: (a -> b) -> RandT g m a -> RandT g m b # (<$) :: a -> RandT g m b -> RandT g m a #
Functor (Day f g)
Instance details Defined in Data.Functor.Day Methods fmap :: (a -> b) -> Day f g a -> Day f g b # (<$) :: a -> Day f g b -> Day f g a #
Profunctor p => Functor (Coprep p)
Instance details Defined in Data.Profunctor.Rep Methods fmap :: (a -> b) -> Coprep p a -> Coprep p b # (<$) :: a -> Coprep p b -> Coprep p a #
Profunctor p => Functor (Prep p)
Instance details Defined in Data.Profunctor.Rep Methods fmap :: (a -> b) -> Prep p a -> Prep p b # (<$) :: a -> Prep p b -> Prep p a #
Functor f => Functor (CZippy f)
Instance details Defined in Control.Subcategory.Zip Methods fmap :: (a -> b) -> CZippy f a -> CZippy f b # (<$) :: a -> CZippy f b -> CZippy f a #
Functor (Mag a b)
Instance details Defined in Data.Biapplicative Methods fmap :: (a0 -> b0) -> Mag a b a0 -> Mag a b b0 # (<$) :: a0 -> Mag a b b0 -> Mag a b a0 #
Functor (Flows i b)
Instance details Defined in Control.Lens.Internal.Level Methods fmap :: (a -> b0) -> Flows i b a -> Flows i b b0 # (<$) :: a -> Flows i b b0 -> Flows i b a #
Functor (Mafic a b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a0 -> b0) -> Mafic a b a0 -> Mafic a b b0 # (<$) :: a0 -> Mafic a b b0 -> Mafic a b a0 #
Functor (Holes t m)
Instance details Defined in Control.Lens.Traversal Methods fmap :: (a -> b) -> Holes t m a -> Holes t m b # (<$) :: a -> Holes t m b -> Holes t m a #
Functor (CopastroSum p a)
Instance details Defined in Data.Profunctor.Choice Methods fmap :: (a0 -> b) -> CopastroSum p a a0 -> CopastroSum p a b # (<$) :: a0 -> CopastroSum p a b -> CopastroSum p a a0 #
Functor (CotambaraSum p a)
Instance details Defined in Data.Profunctor.Choice Methods fmap :: (a0 -> b) -> CotambaraSum p a a0 -> CotambaraSum p a b # (<$) :: a0 -> CotambaraSum p a b -> CotambaraSum p a a0 #
Functor (PastroSum p a)
Instance details Defined in Data.Profunctor.Choice Methods fmap :: (a0 -> b) -> PastroSum p a a0 -> PastroSum p a b # (<$) :: a0 -> PastroSum p a b -> PastroSum p a a0 #
Profunctor p => Functor (TambaraSum p a)
Instance details Defined in Data.Profunctor.Choice Methods fmap :: (a0 -> b) -> TambaraSum p a a0 -> TambaraSum p a b # (<$) :: a0 -> TambaraSum p a b -> TambaraSum p a a0 #
Functor ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b # (<$) :: a -> (r -> b) -> r -> a #
Functor (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b # (<$) :: a -> K1 i c b -> K1 i c a #
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
(Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
Functor ((,,,) a b c)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) # (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b # (<$) :: a -> Sum f g b -> Sum f g a #
Functor f => Functor (WhenMatched f x y)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a #
(Applicative f, Monad f) => Functor (WhenMissing f k x)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a #
Functor (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods fmap :: (a -> b) -> ContT r m a -> ContT r m b # (<$) :: a -> ContT r m b -> ContT r m a #
Functor (Exchange a b s)
Instance details Defined in Control.Lens.Internal.Iso Methods fmap :: (a0 -> b0) -> Exchange a b s a0 -> Exchange a b s b0 # (<$) :: a0 -> Exchange a b s b0 -> Exchange a b s a0 #
Functor (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (<$) :: a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Functor (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (<$) :: a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
Functor (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a -> b0) -> Magma i t b a -> Magma i t b b0 # (<$) :: a -> Magma i t b b0 -> Magma i t b a #
Functor (Costar f a)
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Costar f a a0 -> Costar f a b # (<$) :: a0 -> Costar f a b -> Costar f a a0 #
Functor (Forget r a :: Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Forget r a a0 -> Forget r a b # (<$) :: a0 -> Forget r a b -> Forget r a a0 #
Functor f => Functor (Star f a)
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Star f a a0 -> Star f a b # (<$) :: a0 -> Star f a b -> Star f a a0 #
Functor (Pretext p a b)
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> Pretext p a b a0 -> Pretext p a b b0 # (<$) :: a0 -> Pretext p a b b0 -> Pretext p a b a0 #
Functor (Molten i a b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a0 -> b0) -> Molten i a b a0 -> Molten i a b b0 # (<$) :: a0 -> Molten i a b b0 -> Molten i a b a0 #
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b # (<$) :: a -> M1 i c f b -> M1 i c f a #
(Functor f, Functor g) => Functor (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
(Functor f, Functor g) => Functor (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b # (<$) :: a -> Compose f g b -> Compose f g a #
Functor f => Functor (WhenMatched f k x y)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
Reifies s (ReifiedApplicative f) => Functor (ReflectedApplicative f s)
Instance details Defined in Data.Reflection Methods fmap :: (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # (<$) :: a -> ReflectedApplicative f s b -> ReflectedApplicative f s a #
Functor (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods fmap :: (a0 -> b) -> Clown f a a0 -> Clown f a b # (<$) :: a0 -> Clown f a b -> Clown f a a0 #
Bifunctor p => Functor (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods fmap :: (a0 -> b) -> Flip p a a0 -> Flip p a b # (<$) :: a0 -> Flip p a b -> Flip p a a0 #
Functor g => Functor (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods fmap :: (a0 -> b) -> Joker g a a0 -> Joker g a b # (<$) :: a0 -> Joker g a b -> Joker g a a0 #
Bifunctor p => Functor (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods fmap :: (a0 -> b) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b # (<$) :: a0 -> WrappedBifunctor p a b -> WrappedBifunctor p a a0 #
Functor (TakingWhile p f a b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a0 -> b0) -> TakingWhile p f a b a0 -> TakingWhile p f a b b0 # (<$) :: a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
Functor (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> BazaarT p g a b a0 -> BazaarT p g a b b0 # (<$) :: a0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #
Functor (BazaarT1 p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> BazaarT1 p g a b a0 -> BazaarT1 p g a b b0 # (<$) :: a0 -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #
Functor (PretextT p g a b)
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> PretextT p g a b a0 -> PretextT p g a b b0 # (<$) :: a0 -> PretextT p g a b b0 -> PretextT p g a b a0 #
(Functor f, Bifunctor p) => Functor (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods fmap :: (a0 -> b) -> Tannen f p a a0 -> Tannen f p a b # (<$) :: a0 -> Tannen f p a b -> Tannen f p a a0 #
Profunctor p => Functor (Procompose p q a)
Instance details Defined in Data.Profunctor.Composition Methods fmap :: (a0 -> b) -> Procompose p q a a0 -> Procompose p q a b # (<$) :: a0 -> Procompose p q a b -> Procompose p q a a0 #
Profunctor p => Functor (Rift p q a)
Instance details Defined in Data.Profunctor.Composition Methods fmap :: (a0 -> b) -> Rift p q a a0 -> Rift p q a b # (<$) :: a0 -> Rift p q a b -> Rift p q a a0 #
(Bifunctor p, Functor g) => Functor (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods fmap :: (a0 -> b) -> Biff p f g a a0 -> Biff p f g a b # (<$) :: a0 -> Biff p f g a b -> Biff p f g a a0 #

class Num a where #

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+): (x + y) + z = x + (y + z)
Commutativity of (+): x + y = y + x
fromInteger 0 is the additive identity: x + fromInteger 0 = x
negate gives the additive inverse: x + negate x = fromInteger 0
Associativity of (*): (x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity: x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+): a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

abs :: a -> a #

Absolute value.

signum :: a -> a #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

Instances

Instances details

Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Num Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int8 -> Int8 -> Int8 # (-) :: Int8 -> Int8 -> Int8 # (*) :: Int8 -> Int8 -> Int8 # negate :: Int8 -> Int8 # abs :: Int8 -> Int8 # signum :: Int8 -> Int8 # fromInteger :: Integer -> Int8 #
Num Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int16 -> Int16 -> Int16 # (-) :: Int16 -> Int16 -> Int16 # (*) :: Int16 -> Int16 -> Int16 # negate :: Int16 -> Int16 # abs :: Int16 -> Int16 # signum :: Int16 -> Int16 # fromInteger :: Integer -> Int16 #
Num Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int32 -> Int32 -> Int32 # (-) :: Int32 -> Int32 -> Int32 # (*) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # abs :: Int32 -> Int32 # signum :: Int32 -> Int32 # fromInteger :: Integer -> Int32 #
Num Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int64 -> Int64 -> Int64 # (-) :: Int64 -> Int64 -> Int64 # (*) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # abs :: Int64 -> Int64 # signum :: Int64 -> Int64 # fromInteger :: Integer -> Int64 #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Num Word	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word # (-) :: Word -> Word -> Word # (*) :: Word -> Word -> Word # negate :: Word -> Word # abs :: Word -> Word # signum :: Word -> Word # fromInteger :: Integer -> Word #
Num Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word8 -> Word8 -> Word8 # (-) :: Word8 -> Word8 -> Word8 # (*) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # abs :: Word8 -> Word8 # signum :: Word8 -> Word8 # fromInteger :: Integer -> Word8 #
Num Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word16 -> Word16 -> Word16 # (-) :: Word16 -> Word16 -> Word16 # (*) :: Word16 -> Word16 -> Word16 # negate :: Word16 -> Word16 # abs :: Word16 -> Word16 # signum :: Word16 -> Word16 # fromInteger :: Integer -> Word16 #
Num Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word32 -> Word32 -> Word32 # (-) :: Word32 -> Word32 -> Word32 # (*) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # abs :: Word32 -> Word32 # signum :: Word32 -> Word32 # fromInteger :: Integer -> Word32 #
Num Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word64 -> Word64 -> Word64 # (-) :: Word64 -> Word64 -> Word64 # (*) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # abs :: Word64 -> Word64 # signum :: Word64 -> Word64 # fromInteger :: Integer -> Word64 #
Num CDev
Instance details Defined in System.Posix.Types Methods (+) :: CDev -> CDev -> CDev # (-) :: CDev -> CDev -> CDev # (*) :: CDev -> CDev -> CDev # negate :: CDev -> CDev # abs :: CDev -> CDev # signum :: CDev -> CDev # fromInteger :: Integer -> CDev #
Num CIno
Instance details Defined in System.Posix.Types Methods (+) :: CIno -> CIno -> CIno # (-) :: CIno -> CIno -> CIno # (*) :: CIno -> CIno -> CIno # negate :: CIno -> CIno # abs :: CIno -> CIno # signum :: CIno -> CIno # fromInteger :: Integer -> CIno #
Num CMode
Instance details Defined in System.Posix.Types Methods (+) :: CMode -> CMode -> CMode # (-) :: CMode -> CMode -> CMode # (*) :: CMode -> CMode -> CMode # negate :: CMode -> CMode # abs :: CMode -> CMode # signum :: CMode -> CMode # fromInteger :: Integer -> CMode #
Num COff
Instance details Defined in System.Posix.Types Methods (+) :: COff -> COff -> COff # (-) :: COff -> COff -> COff # (*) :: COff -> COff -> COff # negate :: COff -> COff # abs :: COff -> COff # signum :: COff -> COff # fromInteger :: Integer -> COff #
Num CPid
Instance details Defined in System.Posix.Types Methods (+) :: CPid -> CPid -> CPid # (-) :: CPid -> CPid -> CPid # (*) :: CPid -> CPid -> CPid # negate :: CPid -> CPid # abs :: CPid -> CPid # signum :: CPid -> CPid # fromInteger :: Integer -> CPid #
Num CSsize
Instance details Defined in System.Posix.Types Methods (+) :: CSsize -> CSsize -> CSsize # (-) :: CSsize -> CSsize -> CSsize # (*) :: CSsize -> CSsize -> CSsize # negate :: CSsize -> CSsize # abs :: CSsize -> CSsize # signum :: CSsize -> CSsize # fromInteger :: Integer -> CSsize #
Num CGid
Instance details Defined in System.Posix.Types Methods (+) :: CGid -> CGid -> CGid # (-) :: CGid -> CGid -> CGid # (*) :: CGid -> CGid -> CGid # negate :: CGid -> CGid # abs :: CGid -> CGid # signum :: CGid -> CGid # fromInteger :: Integer -> CGid #
Num CNlink
Instance details Defined in System.Posix.Types Methods (+) :: CNlink -> CNlink -> CNlink # (-) :: CNlink -> CNlink -> CNlink # (*) :: CNlink -> CNlink -> CNlink # negate :: CNlink -> CNlink # abs :: CNlink -> CNlink # signum :: CNlink -> CNlink # fromInteger :: Integer -> CNlink #
Num CUid
Instance details Defined in System.Posix.Types Methods (+) :: CUid -> CUid -> CUid # (-) :: CUid -> CUid -> CUid # (*) :: CUid -> CUid -> CUid # negate :: CUid -> CUid # abs :: CUid -> CUid # signum :: CUid -> CUid # fromInteger :: Integer -> CUid #
Num CCc
Instance details Defined in System.Posix.Types Methods (+) :: CCc -> CCc -> CCc # (-) :: CCc -> CCc -> CCc # (*) :: CCc -> CCc -> CCc # negate :: CCc -> CCc # abs :: CCc -> CCc # signum :: CCc -> CCc # fromInteger :: Integer -> CCc #
Num CSpeed
Instance details Defined in System.Posix.Types Methods (+) :: CSpeed -> CSpeed -> CSpeed # (-) :: CSpeed -> CSpeed -> CSpeed # (*) :: CSpeed -> CSpeed -> CSpeed # negate :: CSpeed -> CSpeed # abs :: CSpeed -> CSpeed # signum :: CSpeed -> CSpeed # fromInteger :: Integer -> CSpeed #
Num CTcflag
Instance details Defined in System.Posix.Types Methods (+) :: CTcflag -> CTcflag -> CTcflag # (-) :: CTcflag -> CTcflag -> CTcflag # (*) :: CTcflag -> CTcflag -> CTcflag # negate :: CTcflag -> CTcflag # abs :: CTcflag -> CTcflag # signum :: CTcflag -> CTcflag # fromInteger :: Integer -> CTcflag #
Num CRLim
Instance details Defined in System.Posix.Types Methods (+) :: CRLim -> CRLim -> CRLim # (-) :: CRLim -> CRLim -> CRLim # (*) :: CRLim -> CRLim -> CRLim # negate :: CRLim -> CRLim # abs :: CRLim -> CRLim # signum :: CRLim -> CRLim # fromInteger :: Integer -> CRLim #
Num CBlkSize
Instance details Defined in System.Posix.Types Methods (+) :: CBlkSize -> CBlkSize -> CBlkSize # (-) :: CBlkSize -> CBlkSize -> CBlkSize # (*) :: CBlkSize -> CBlkSize -> CBlkSize # negate :: CBlkSize -> CBlkSize # abs :: CBlkSize -> CBlkSize # signum :: CBlkSize -> CBlkSize # fromInteger :: Integer -> CBlkSize #
Num CBlkCnt
Instance details Defined in System.Posix.Types Methods (+) :: CBlkCnt -> CBlkCnt -> CBlkCnt # (-) :: CBlkCnt -> CBlkCnt -> CBlkCnt # (*) :: CBlkCnt -> CBlkCnt -> CBlkCnt # negate :: CBlkCnt -> CBlkCnt # abs :: CBlkCnt -> CBlkCnt # signum :: CBlkCnt -> CBlkCnt # fromInteger :: Integer -> CBlkCnt #
Num CClockId
Instance details Defined in System.Posix.Types Methods (+) :: CClockId -> CClockId -> CClockId # (-) :: CClockId -> CClockId -> CClockId # (*) :: CClockId -> CClockId -> CClockId # negate :: CClockId -> CClockId # abs :: CClockId -> CClockId # signum :: CClockId -> CClockId # fromInteger :: Integer -> CClockId #
Num CFsBlkCnt
Instance details Defined in System.Posix.Types Methods (+) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # (-) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # (*) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # negate :: CFsBlkCnt -> CFsBlkCnt # abs :: CFsBlkCnt -> CFsBlkCnt # signum :: CFsBlkCnt -> CFsBlkCnt # fromInteger :: Integer -> CFsBlkCnt #
Num CFsFilCnt
Instance details Defined in System.Posix.Types Methods (+) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # (-) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # (*) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # negate :: CFsFilCnt -> CFsFilCnt # abs :: CFsFilCnt -> CFsFilCnt # signum :: CFsFilCnt -> CFsFilCnt # fromInteger :: Integer -> CFsFilCnt #
Num CId
Instance details Defined in System.Posix.Types Methods (+) :: CId -> CId -> CId # (-) :: CId -> CId -> CId # (*) :: CId -> CId -> CId # negate :: CId -> CId # abs :: CId -> CId # signum :: CId -> CId # fromInteger :: Integer -> CId #
Num CKey
Instance details Defined in System.Posix.Types Methods (+) :: CKey -> CKey -> CKey # (-) :: CKey -> CKey -> CKey # (*) :: CKey -> CKey -> CKey # negate :: CKey -> CKey # abs :: CKey -> CKey # signum :: CKey -> CKey # fromInteger :: Integer -> CKey #
Num CSocklen
Instance details Defined in System.Posix.Types Methods (+) :: CSocklen -> CSocklen -> CSocklen # (-) :: CSocklen -> CSocklen -> CSocklen # (*) :: CSocklen -> CSocklen -> CSocklen # negate :: CSocklen -> CSocklen # abs :: CSocklen -> CSocklen # signum :: CSocklen -> CSocklen # fromInteger :: Integer -> CSocklen #
Num CNfds
Instance details Defined in System.Posix.Types Methods (+) :: CNfds -> CNfds -> CNfds # (-) :: CNfds -> CNfds -> CNfds # (*) :: CNfds -> CNfds -> CNfds # negate :: CNfds -> CNfds # abs :: CNfds -> CNfds # signum :: CNfds -> CNfds # fromInteger :: Integer -> CNfds #
Num Fd
Instance details Defined in System.Posix.Types Methods (+) :: Fd -> Fd -> Fd # (-) :: Fd -> Fd -> Fd # (*) :: Fd -> Fd -> Fd # negate :: Fd -> Fd # abs :: Fd -> Fd # signum :: Fd -> Fd # fromInteger :: Integer -> Fd #
Num CChar
Instance details Defined in Foreign.C.Types Methods (+) :: CChar -> CChar -> CChar # (-) :: CChar -> CChar -> CChar # (*) :: CChar -> CChar -> CChar # negate :: CChar -> CChar # abs :: CChar -> CChar # signum :: CChar -> CChar # fromInteger :: Integer -> CChar #
Num CSChar
Instance details Defined in Foreign.C.Types Methods (+) :: CSChar -> CSChar -> CSChar # (-) :: CSChar -> CSChar -> CSChar # (*) :: CSChar -> CSChar -> CSChar # negate :: CSChar -> CSChar # abs :: CSChar -> CSChar # signum :: CSChar -> CSChar # fromInteger :: Integer -> CSChar #
Num CUChar
Instance details Defined in Foreign.C.Types Methods (+) :: CUChar -> CUChar -> CUChar # (-) :: CUChar -> CUChar -> CUChar # (*) :: CUChar -> CUChar -> CUChar # negate :: CUChar -> CUChar # abs :: CUChar -> CUChar # signum :: CUChar -> CUChar # fromInteger :: Integer -> CUChar #
Num CShort
Instance details Defined in Foreign.C.Types Methods (+) :: CShort -> CShort -> CShort # (-) :: CShort -> CShort -> CShort # (*) :: CShort -> CShort -> CShort # negate :: CShort -> CShort # abs :: CShort -> CShort # signum :: CShort -> CShort # fromInteger :: Integer -> CShort #
Num CUShort
Instance details Defined in Foreign.C.Types Methods (+) :: CUShort -> CUShort -> CUShort # (-) :: CUShort -> CUShort -> CUShort # (*) :: CUShort -> CUShort -> CUShort # negate :: CUShort -> CUShort # abs :: CUShort -> CUShort # signum :: CUShort -> CUShort # fromInteger :: Integer -> CUShort #
Num CInt
Instance details Defined in Foreign.C.Types Methods (+) :: CInt -> CInt -> CInt # (-) :: CInt -> CInt -> CInt # (*) :: CInt -> CInt -> CInt # negate :: CInt -> CInt # abs :: CInt -> CInt # signum :: CInt -> CInt # fromInteger :: Integer -> CInt #
Num CUInt
Instance details Defined in Foreign.C.Types Methods (+) :: CUInt -> CUInt -> CUInt # (-) :: CUInt -> CUInt -> CUInt # (*) :: CUInt -> CUInt -> CUInt # negate :: CUInt -> CUInt # abs :: CUInt -> CUInt # signum :: CUInt -> CUInt # fromInteger :: Integer -> CUInt #
Num CLong
Instance details Defined in Foreign.C.Types Methods (+) :: CLong -> CLong -> CLong # (-) :: CLong -> CLong -> CLong # (*) :: CLong -> CLong -> CLong # negate :: CLong -> CLong # abs :: CLong -> CLong # signum :: CLong -> CLong # fromInteger :: Integer -> CLong #
Num CULong
Instance details Defined in Foreign.C.Types Methods (+) :: CULong -> CULong -> CULong # (-) :: CULong -> CULong -> CULong # (*) :: CULong -> CULong -> CULong # negate :: CULong -> CULong # abs :: CULong -> CULong # signum :: CULong -> CULong # fromInteger :: Integer -> CULong #
Num CLLong
Instance details Defined in Foreign.C.Types Methods (+) :: CLLong -> CLLong -> CLLong # (-) :: CLLong -> CLLong -> CLLong # (*) :: CLLong -> CLLong -> CLLong # negate :: CLLong -> CLLong # abs :: CLLong -> CLLong # signum :: CLLong -> CLLong # fromInteger :: Integer -> CLLong #
Num CULLong
Instance details Defined in Foreign.C.Types Methods (+) :: CULLong -> CULLong -> CULLong # (-) :: CULLong -> CULLong -> CULLong # (*) :: CULLong -> CULLong -> CULLong # negate :: CULLong -> CULLong # abs :: CULLong -> CULLong # signum :: CULLong -> CULLong # fromInteger :: Integer -> CULLong #
Num CBool
Instance details Defined in Foreign.C.Types Methods (+) :: CBool -> CBool -> CBool # (-) :: CBool -> CBool -> CBool # (*) :: CBool -> CBool -> CBool # negate :: CBool -> CBool # abs :: CBool -> CBool # signum :: CBool -> CBool # fromInteger :: Integer -> CBool #
Num CFloat
Instance details Defined in Foreign.C.Types Methods (+) :: CFloat -> CFloat -> CFloat # (-) :: CFloat -> CFloat -> CFloat # (*) :: CFloat -> CFloat -> CFloat # negate :: CFloat -> CFloat # abs :: CFloat -> CFloat # signum :: CFloat -> CFloat # fromInteger :: Integer -> CFloat #
Num CDouble
Instance details Defined in Foreign.C.Types Methods (+) :: CDouble -> CDouble -> CDouble # (-) :: CDouble -> CDouble -> CDouble # (*) :: CDouble -> CDouble -> CDouble # negate :: CDouble -> CDouble # abs :: CDouble -> CDouble # signum :: CDouble -> CDouble # fromInteger :: Integer -> CDouble #
Num CPtrdiff
Instance details Defined in Foreign.C.Types Methods (+) :: CPtrdiff -> CPtrdiff -> CPtrdiff # (-) :: CPtrdiff -> CPtrdiff -> CPtrdiff # (*) :: CPtrdiff -> CPtrdiff -> CPtrdiff # negate :: CPtrdiff -> CPtrdiff # abs :: CPtrdiff -> CPtrdiff # signum :: CPtrdiff -> CPtrdiff # fromInteger :: Integer -> CPtrdiff #
Num CSize
Instance details Defined in Foreign.C.Types Methods (+) :: CSize -> CSize -> CSize # (-) :: CSize -> CSize -> CSize # (*) :: CSize -> CSize -> CSize # negate :: CSize -> CSize # abs :: CSize -> CSize # signum :: CSize -> CSize # fromInteger :: Integer -> CSize #
Num CWchar
Instance details Defined in Foreign.C.Types Methods (+) :: CWchar -> CWchar -> CWchar # (-) :: CWchar -> CWchar -> CWchar # (*) :: CWchar -> CWchar -> CWchar # negate :: CWchar -> CWchar # abs :: CWchar -> CWchar # signum :: CWchar -> CWchar # fromInteger :: Integer -> CWchar #
Num CSigAtomic
Instance details Defined in Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic # negate :: CSigAtomic -> CSigAtomic # abs :: CSigAtomic -> CSigAtomic # signum :: CSigAtomic -> CSigAtomic # fromInteger :: Integer -> CSigAtomic #
Num CClock
Instance details Defined in Foreign.C.Types Methods (+) :: CClock -> CClock -> CClock # (-) :: CClock -> CClock -> CClock # (*) :: CClock -> CClock -> CClock # negate :: CClock -> CClock # abs :: CClock -> CClock # signum :: CClock -> CClock # fromInteger :: Integer -> CClock #
Num CTime
Instance details Defined in Foreign.C.Types Methods (+) :: CTime -> CTime -> CTime # (-) :: CTime -> CTime -> CTime # (*) :: CTime -> CTime -> CTime # negate :: CTime -> CTime # abs :: CTime -> CTime # signum :: CTime -> CTime # fromInteger :: Integer -> CTime #
Num CUSeconds
Instance details Defined in Foreign.C.Types Methods (+) :: CUSeconds -> CUSeconds -> CUSeconds # (-) :: CUSeconds -> CUSeconds -> CUSeconds # (*) :: CUSeconds -> CUSeconds -> CUSeconds # negate :: CUSeconds -> CUSeconds # abs :: CUSeconds -> CUSeconds # signum :: CUSeconds -> CUSeconds # fromInteger :: Integer -> CUSeconds #
Num CSUSeconds
Instance details Defined in Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds # negate :: CSUSeconds -> CSUSeconds # abs :: CSUSeconds -> CSUSeconds # signum :: CSUSeconds -> CSUSeconds # fromInteger :: Integer -> CSUSeconds #
Num CIntPtr
Instance details Defined in Foreign.C.Types Methods (+) :: CIntPtr -> CIntPtr -> CIntPtr # (-) :: CIntPtr -> CIntPtr -> CIntPtr # (*) :: CIntPtr -> CIntPtr -> CIntPtr # negate :: CIntPtr -> CIntPtr # abs :: CIntPtr -> CIntPtr # signum :: CIntPtr -> CIntPtr # fromInteger :: Integer -> CIntPtr #
Num CUIntPtr
Instance details Defined in Foreign.C.Types Methods (+) :: CUIntPtr -> CUIntPtr -> CUIntPtr # (-) :: CUIntPtr -> CUIntPtr -> CUIntPtr # (*) :: CUIntPtr -> CUIntPtr -> CUIntPtr # negate :: CUIntPtr -> CUIntPtr # abs :: CUIntPtr -> CUIntPtr # signum :: CUIntPtr -> CUIntPtr # fromInteger :: Integer -> CUIntPtr #
Num CIntMax
Instance details Defined in Foreign.C.Types Methods (+) :: CIntMax -> CIntMax -> CIntMax # (-) :: CIntMax -> CIntMax -> CIntMax # (*) :: CIntMax -> CIntMax -> CIntMax # negate :: CIntMax -> CIntMax # abs :: CIntMax -> CIntMax # signum :: CIntMax -> CIntMax # fromInteger :: Integer -> CIntMax #
Num CUIntMax
Instance details Defined in Foreign.C.Types Methods (+) :: CUIntMax -> CUIntMax -> CUIntMax # (-) :: CUIntMax -> CUIntMax -> CUIntMax # (*) :: CUIntMax -> CUIntMax -> CUIntMax # negate :: CUIntMax -> CUIntMax # abs :: CUIntMax -> CUIntMax # signum :: CUIntMax -> CUIntMax # fromInteger :: Integer -> CUIntMax #
Num CodePoint
Instance details Defined in Data.Text.Encoding Methods (+) :: CodePoint -> CodePoint -> CodePoint # (-) :: CodePoint -> CodePoint -> CodePoint # (*) :: CodePoint -> CodePoint -> CodePoint # negate :: CodePoint -> CodePoint # abs :: CodePoint -> CodePoint # signum :: CodePoint -> CodePoint # fromInteger :: Integer -> CodePoint #
Num DecoderState
Instance details Defined in Data.Text.Encoding Methods (+) :: DecoderState -> DecoderState -> DecoderState # (-) :: DecoderState -> DecoderState -> DecoderState # (*) :: DecoderState -> DecoderState -> DecoderState # negate :: DecoderState -> DecoderState # abs :: DecoderState -> DecoderState # signum :: DecoderState -> DecoderState # fromInteger :: Integer -> DecoderState #
Integral a => Num (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a # (-) :: Ratio a -> Ratio a -> Ratio a # (*) :: Ratio a -> Ratio a -> Ratio a # negate :: Ratio a -> Ratio a # abs :: Ratio a -> Ratio a # signum :: Ratio a -> Ratio a # fromInteger :: Integer -> Ratio a #
Num a => Num (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapNum a -> WrapNum a -> WrapNum a # (-) :: WrapNum a -> WrapNum a -> WrapNum a # (*) :: WrapNum a -> WrapNum a -> WrapNum a # negate :: WrapNum a -> WrapNum a # abs :: WrapNum a -> WrapNum a # signum :: WrapNum a -> WrapNum a # fromInteger :: Integer -> WrapNum a #
Num a => Num (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (-) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (*) :: WrapFractional a -> WrapFractional a -> WrapFractional a # negate :: WrapFractional a -> WrapFractional a # abs :: WrapFractional a -> WrapFractional a # signum :: WrapFractional a -> WrapFractional a # fromInteger :: Integer -> WrapFractional a #
Num a => Num (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # (-) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # (*) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # negate :: WrapIntegral a -> WrapIntegral a # abs :: WrapIntegral a -> WrapIntegral a # signum :: WrapIntegral a -> WrapIntegral a # fromInteger :: Integer -> WrapIntegral a #
(Ring a, UnitNormalForm a) => Num (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (-) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (*) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # negate :: WrapAlgebra a -> WrapAlgebra a # abs :: WrapAlgebra a -> WrapAlgebra a # signum :: WrapAlgebra a -> WrapAlgebra a # fromInteger :: Integer -> WrapAlgebra a #
Num a => Num (Add a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Add a -> Add a -> Add a # (-) :: Add a -> Add a -> Add a # (*) :: Add a -> Add a -> Add a # negate :: Add a -> Add a # abs :: Add a -> Add a # signum :: Add a -> Add a # fromInteger :: Integer -> Add a #
Num a => Num (Mult a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Mult a -> Mult a -> Mult a # (-) :: Mult a -> Mult a -> Mult a # (*) :: Mult a -> Mult a -> Mult a # negate :: Mult a -> Mult a # abs :: Mult a -> Mult a # signum :: Mult a -> Mult a # fromInteger :: Integer -> Mult a #
Num a => Num (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (+) :: Down a -> Down a -> Down a # (-) :: Down a -> Down a -> Down a # (*) :: Down a -> Down a -> Down a # negate :: Down a -> Down a # abs :: Down a -> Down a # signum :: Down a -> Down a # fromInteger :: Integer -> Down a #
RealFloat a => Num (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a # (-) :: Complex a -> Complex a -> Complex a # (*) :: Complex a -> Complex a -> Complex a # negate :: Complex a -> Complex a # abs :: Complex a -> Complex a # signum :: Complex a -> Complex a # fromInteger :: Integer -> Complex a #
Num a => Num (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a # (-) :: Min a -> Min a -> Min a # (*) :: Min a -> Min a -> Min a # negate :: Min a -> Min a # abs :: Min a -> Min a # signum :: Min a -> Min a # fromInteger :: Integer -> Min a #
Num a => Num (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a # (-) :: Max a -> Max a -> Max a # (*) :: Max a -> Max a -> Max a # negate :: Max a -> Max a # abs :: Max a -> Max a # signum :: Max a -> Max a # fromInteger :: Integer -> Max a #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a # (-) :: Identity a -> Identity a -> Identity a # (*) :: Identity a -> Identity a -> Identity a # negate :: Identity a -> Identity a # abs :: Identity a -> Identity a # signum :: Identity a -> Identity a # fromInteger :: Integer -> Identity a #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
KnownNat n => Num (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods (+) :: Ordinal n -> Ordinal n -> Ordinal n # (-) :: Ordinal n -> Ordinal n -> Ordinal n # (*) :: Ordinal n -> Ordinal n -> Ordinal n # negate :: Ordinal n -> Ordinal n # abs :: Ordinal n -> Ordinal n # signum :: Ordinal n -> Ordinal n # fromInteger :: Integer -> Ordinal n #
Num r => Num (Scalar r)
Instance details Defined in Algebra.Scalar Methods (+) :: Scalar r -> Scalar r -> Scalar r # (-) :: Scalar r -> Scalar r -> Scalar r # (*) :: Scalar r -> Scalar r -> Scalar r # negate :: Scalar r -> Scalar r # abs :: Scalar r -> Scalar r # signum :: Scalar r -> Scalar r # fromInteger :: Integer -> Scalar r #
CoeffRing r => Num (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (+) :: Unipol r -> Unipol r -> Unipol r # (-) :: Unipol r -> Unipol r -> Unipol r # (*) :: Unipol r -> Unipol r -> Unipol r # negate :: Unipol r -> Unipol r # abs :: Unipol r -> Unipol r # signum :: Unipol r -> Unipol r # fromInteger :: Integer -> Unipol r #
Num a => Num (Matrix a)
Instance details Defined in Data.Matrix Methods (+) :: Matrix a -> Matrix a -> Matrix a # (-) :: Matrix a -> Matrix a -> Matrix a # (*) :: Matrix a -> Matrix a -> Matrix a # negate :: Matrix a -> Matrix a # abs :: Matrix a -> Matrix a # signum :: Matrix a -> Matrix a # fromInteger :: Integer -> Matrix a #
HasResolution a => Num (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (+) :: Fixed a -> Fixed a -> Fixed a # (-) :: Fixed a -> Fixed a -> Fixed a # (*) :: Fixed a -> Fixed a -> Fixed a # negate :: Fixed a -> Fixed a # abs :: Fixed a -> Fixed a # signum :: Fixed a -> Fixed a # fromInteger :: Integer -> Fixed a #
Num a => Num (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods (+) :: Op a b -> Op a b -> Op a b # (-) :: Op a b -> Op a b -> Op a b # (*) :: Op a b -> Op a b -> Op a b # negate :: Op a b -> Op a b # abs :: Op a b -> Op a b # signum :: Op a b -> Op a b # fromInteger :: Integer -> Op a b #
(Wraps vars poly, Num poly) => Num (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (+) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # (-) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # (*) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # negate :: LabPolynomial poly vars -> LabPolynomial poly vars # abs :: LabPolynomial poly vars -> LabPolynomial poly vars # signum :: LabPolynomial poly vars -> LabPolynomial poly vars # fromInteger :: Integer -> LabPolynomial poly vars #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
(Applicative f, Num a) => Num (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a # (-) :: Ap f a -> Ap f a -> Ap f a # (*) :: Ap f a -> Ap f a -> Ap f a # negate :: Ap f a -> Ap f a # abs :: Ap f a -> Ap f a # signum :: Ap f a -> Ap f a # fromInteger :: Integer -> Ap f a #
Num (f a) => Num (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a # (-) :: Alt f a -> Alt f a -> Alt f a # (*) :: Alt f a -> Alt f a -> Alt f a # negate :: Alt f a -> Alt f a # abs :: Alt f a -> Alt f a # signum :: Alt f a -> Alt f a # fromInteger :: Integer -> Alt f a #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Num (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # (-) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # (*) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # negate :: PadPolyL n ord poly -> PadPolyL n ord poly # abs :: PadPolyL n ord poly -> PadPolyL n ord poly # signum :: PadPolyL n ord poly -> PadPolyL n ord poly # fromInteger :: Integer -> PadPolyL n ord poly #
Num a => Num (Tagged s a)
Instance details Defined in Data.Tagged Methods (+) :: Tagged s a -> Tagged s a -> Tagged s a # (-) :: Tagged s a -> Tagged s a -> Tagged s a # (*) :: Tagged s a -> Tagged s a -> Tagged s a # negate :: Tagged s a -> Tagged s a # abs :: Tagged s a -> Tagged s a # signum :: Tagged s a -> Tagged s a # fromInteger :: Integer -> Tagged s a #
(Field (Coefficient poly), UnitNormalForm poly, IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Num (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (+) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # (-) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # (*) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # negate :: Quotient poly ideal -> Quotient poly ideal # abs :: Quotient poly ideal -> Quotient poly ideal # signum :: Quotient poly ideal -> Quotient poly ideal # fromInteger :: Integer -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Num (OrderedPolynomial r order n) Source #	We provide Num instance to use trivial injection R into R[X]. Do not use signum or abs.
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # (-) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # (*) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # negate :: OrderedPolynomial r order n -> OrderedPolynomial r order n # abs :: OrderedPolynomial r order n -> OrderedPolynomial r order n # signum :: OrderedPolynomial r order n -> OrderedPolynomial r order n # fromInteger :: Integer -> OrderedPolynomial r order n #

class Eq a => Ord a where #

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

Transitivity: if x <= y && y <= z = True, then x <= z = True
Reflexivity: x <= x = True
Antisymmetry: if x <= y && y <= x = True, then x == y = True

Note that the following operator interactions are expected to hold:

x >= y = y <= x
x < y = x <= y && x /= y
x > y = y < x
x < y = compare x y == LT
x > y = compare x y == GT
x == y = compare x y == EQ
min x y == if x <= y then x else y = True
max x y == if x >= y then x else y = True

Note that (7.) and (8.) do not require min and max to return either of their arguments. The result is merely required to equal one of the arguments in terms of (==).

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering #

(<) :: a -> a -> Bool infix 4 #

(<=) :: a -> a -> Bool infix 4 #

(>) :: a -> a -> Bool infix 4 #

(>=) :: a -> a -> Bool infix 4 #

max :: a -> a -> a #

min :: a -> a -> a #

Instances

Instances details

Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
Ord Char
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering # (<) :: Char -> Char -> Bool # (<=) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool # (>=) :: Char -> Char -> Bool # max :: Char -> Char -> Char # min :: Char -> Char -> Char #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Ord Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int8 -> Int8 -> Ordering # (<) :: Int8 -> Int8 -> Bool # (<=) :: Int8 -> Int8 -> Bool # (>) :: Int8 -> Int8 -> Bool # (>=) :: Int8 -> Int8 -> Bool # max :: Int8 -> Int8 -> Int8 # min :: Int8 -> Int8 -> Int8 #
Ord Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int16 -> Int16 -> Ordering # (<) :: Int16 -> Int16 -> Bool # (<=) :: Int16 -> Int16 -> Bool # (>) :: Int16 -> Int16 -> Bool # (>=) :: Int16 -> Int16 -> Bool # max :: Int16 -> Int16 -> Int16 # min :: Int16 -> Int16 -> Int16 #
Ord Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int32 -> Int32 -> Ordering # (<) :: Int32 -> Int32 -> Bool # (<=) :: Int32 -> Int32 -> Bool # (>) :: Int32 -> Int32 -> Bool # (>=) :: Int32 -> Int32 -> Bool # max :: Int32 -> Int32 -> Int32 # min :: Int32 -> Int32 -> Int32 #
Ord Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int64 -> Int64 -> Ordering # (<) :: Int64 -> Int64 -> Bool # (<=) :: Int64 -> Int64 -> Bool # (>) :: Int64 -> Int64 -> Bool # (>=) :: Int64 -> Int64 -> Bool # max :: Int64 -> Int64 -> Int64 # min :: Int64 -> Int64 -> Int64 #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
Ord Word
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering # (<) :: Word -> Word -> Bool # (<=) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool # (>=) :: Word -> Word -> Bool # max :: Word -> Word -> Word # min :: Word -> Word -> Word #
Ord Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word8 -> Word8 -> Ordering # (<) :: Word8 -> Word8 -> Bool # (<=) :: Word8 -> Word8 -> Bool # (>) :: Word8 -> Word8 -> Bool # (>=) :: Word8 -> Word8 -> Bool # max :: Word8 -> Word8 -> Word8 # min :: Word8 -> Word8 -> Word8 #
Ord Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word16 -> Word16 -> Ordering # (<) :: Word16 -> Word16 -> Bool # (<=) :: Word16 -> Word16 -> Bool # (>) :: Word16 -> Word16 -> Bool # (>=) :: Word16 -> Word16 -> Bool # max :: Word16 -> Word16 -> Word16 # min :: Word16 -> Word16 -> Word16 #
Ord Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word32 -> Word32 -> Ordering # (<) :: Word32 -> Word32 -> Bool # (<=) :: Word32 -> Word32 -> Bool # (>) :: Word32 -> Word32 -> Bool # (>=) :: Word32 -> Word32 -> Bool # max :: Word32 -> Word32 -> Word32 # min :: Word32 -> Word32 -> Word32 #
Ord Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word64 -> Word64 -> Ordering # (<) :: Word64 -> Word64 -> Bool # (<=) :: Word64 -> Word64 -> Bool # (>) :: Word64 -> Word64 -> Bool # (>=) :: Word64 -> Word64 -> Bool # max :: Word64 -> Word64 -> Word64 # min :: Word64 -> Word64 -> Word64 #
Ord SomeTypeRep
Instance details Defined in Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering # (<) :: SomeTypeRep -> SomeTypeRep -> Bool # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool # (>) :: SomeTypeRep -> SomeTypeRep -> Bool # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep #
Ord Exp
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Exp -> Exp -> Ordering # (<) :: Exp -> Exp -> Bool # (<=) :: Exp -> Exp -> Bool # (>) :: Exp -> Exp -> Bool # (>=) :: Exp -> Exp -> Bool # max :: Exp -> Exp -> Exp # min :: Exp -> Exp -> Exp #
Ord Match
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Match -> Match -> Ordering # (<) :: Match -> Match -> Bool # (<=) :: Match -> Match -> Bool # (>) :: Match -> Match -> Bool # (>=) :: Match -> Match -> Bool # max :: Match -> Match -> Match # min :: Match -> Match -> Match #
Ord Clause
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Clause -> Clause -> Ordering # (<) :: Clause -> Clause -> Bool # (<=) :: Clause -> Clause -> Bool # (>) :: Clause -> Clause -> Bool # (>=) :: Clause -> Clause -> Bool # max :: Clause -> Clause -> Clause # min :: Clause -> Clause -> Clause #
Ord Pat
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Pat -> Pat -> Ordering # (<) :: Pat -> Pat -> Bool # (<=) :: Pat -> Pat -> Bool # (>) :: Pat -> Pat -> Bool # (>=) :: Pat -> Pat -> Bool # max :: Pat -> Pat -> Pat # min :: Pat -> Pat -> Pat #
Ord Type
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Type -> Type -> Ordering # (<) :: Type -> Type -> Bool # (<=) :: Type -> Type -> Bool # (>) :: Type -> Type -> Bool # (>=) :: Type -> Type -> Bool # max :: Type -> Type -> Type # min :: Type -> Type -> Type #
Ord Dec
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Dec -> Dec -> Ordering # (<) :: Dec -> Dec -> Bool # (<=) :: Dec -> Dec -> Bool # (>) :: Dec -> Dec -> Bool # (>=) :: Dec -> Dec -> Bool # max :: Dec -> Dec -> Dec # min :: Dec -> Dec -> Dec #
Ord Name
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Name -> Name -> Ordering # (<) :: Name -> Name -> Bool # (<=) :: Name -> Name -> Bool # (>) :: Name -> Name -> Bool # (>=) :: Name -> Name -> Bool # max :: Name -> Name -> Name # min :: Name -> Name -> Name #
Ord FunDep
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: FunDep -> FunDep -> Ordering # (<) :: FunDep -> FunDep -> Bool # (<=) :: FunDep -> FunDep -> Bool # (>) :: FunDep -> FunDep -> Bool # (>=) :: FunDep -> FunDep -> Bool # max :: FunDep -> FunDep -> FunDep # min :: FunDep -> FunDep -> FunDep #
Ord InjectivityAnn
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: InjectivityAnn -> InjectivityAnn -> Ordering # (<) :: InjectivityAnn -> InjectivityAnn -> Bool # (<=) :: InjectivityAnn -> InjectivityAnn -> Bool # (>) :: InjectivityAnn -> InjectivityAnn -> Bool # (>=) :: InjectivityAnn -> InjectivityAnn -> Bool # max :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn # min :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn #
Ord Overlap
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Overlap -> Overlap -> Ordering # (<) :: Overlap -> Overlap -> Bool # (<=) :: Overlap -> Overlap -> Bool # (>) :: Overlap -> Overlap -> Bool # (>=) :: Overlap -> Overlap -> Bool # max :: Overlap -> Overlap -> Overlap # min :: Overlap -> Overlap -> Overlap #
Ord ()
Instance details Defined in GHC.Classes Methods compare :: () -> () -> Ordering # (<) :: () -> () -> Bool # (<=) :: () -> () -> Bool # (>) :: () -> () -> Bool # (>=) :: () -> () -> Bool # max :: () -> () -> () # min :: () -> () -> () #
Ord TyCon
Instance details Defined in GHC.Classes Methods compare :: TyCon -> TyCon -> Ordering # (<) :: TyCon -> TyCon -> Bool # (<=) :: TyCon -> TyCon -> Bool # (>) :: TyCon -> TyCon -> Bool # (>=) :: TyCon -> TyCon -> Bool # max :: TyCon -> TyCon -> TyCon # min :: TyCon -> TyCon -> TyCon #
Ord IntSet
Instance details Defined in Data.IntSet.Internal Methods compare :: IntSet -> IntSet -> Ordering # (<) :: IntSet -> IntSet -> Bool # (<=) :: IntSet -> IntSet -> Bool # (>) :: IntSet -> IntSet -> Bool # (>=) :: IntSet -> IntSet -> Bool # max :: IntSet -> IntSet -> IntSet # min :: IntSet -> IntSet -> IntSet #
Ord ByteString
Instance details Defined in Data.ByteString.Internal Methods compare :: ByteString -> ByteString -> Ordering # (<) :: ByteString -> ByteString -> Bool # (<=) :: ByteString -> ByteString -> Bool # (>) :: ByteString -> ByteString -> Bool # (>=) :: ByteString -> ByteString -> Bool # max :: ByteString -> ByteString -> ByteString # min :: ByteString -> ByteString -> ByteString #
Ord Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods compare :: Void -> Void -> Ordering # (<) :: Void -> Void -> Bool # (<=) :: Void -> Void -> Bool # (>) :: Void -> Void -> Bool # (>=) :: Void -> Void -> Bool # max :: Void -> Void -> Void # min :: Void -> Void -> Void #
Ord Unique
Instance details Defined in Data.Unique Methods compare :: Unique -> Unique -> Ordering # (<) :: Unique -> Unique -> Bool # (<=) :: Unique -> Unique -> Bool # (>) :: Unique -> Unique -> Bool # (>=) :: Unique -> Unique -> Bool # max :: Unique -> Unique -> Unique # min :: Unique -> Unique -> Unique #
Ord Version	Since: base-2.1
Instance details Defined in Data.Version Methods compare :: Version -> Version -> Ordering # (<) :: Version -> Version -> Bool # (<=) :: Version -> Version -> Bool # (>) :: Version -> Version -> Bool # (>=) :: Version -> Version -> Bool # max :: Version -> Version -> Version # min :: Version -> Version -> Version #
Ord ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: ThreadId -> ThreadId -> Ordering # (<) :: ThreadId -> ThreadId -> Bool # (<=) :: ThreadId -> ThreadId -> Bool # (>) :: ThreadId -> ThreadId -> Bool # (>=) :: ThreadId -> ThreadId -> Bool # max :: ThreadId -> ThreadId -> ThreadId # min :: ThreadId -> ThreadId -> ThreadId #
Ord BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: BlockReason -> BlockReason -> Ordering # (<) :: BlockReason -> BlockReason -> Bool # (<=) :: BlockReason -> BlockReason -> Bool # (>) :: BlockReason -> BlockReason -> Bool # (>=) :: BlockReason -> BlockReason -> Bool # max :: BlockReason -> BlockReason -> BlockReason # min :: BlockReason -> BlockReason -> BlockReason #
Ord ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods compare :: ThreadStatus -> ThreadStatus -> Ordering # (<) :: ThreadStatus -> ThreadStatus -> Bool # (<=) :: ThreadStatus -> ThreadStatus -> Bool # (>) :: ThreadStatus -> ThreadStatus -> Bool # (>=) :: ThreadStatus -> ThreadStatus -> Bool # max :: ThreadStatus -> ThreadStatus -> ThreadStatus # min :: ThreadStatus -> ThreadStatus -> ThreadStatus #
Ord CDev
Instance details Defined in System.Posix.Types Methods compare :: CDev -> CDev -> Ordering # (<) :: CDev -> CDev -> Bool # (<=) :: CDev -> CDev -> Bool # (>) :: CDev -> CDev -> Bool # (>=) :: CDev -> CDev -> Bool # max :: CDev -> CDev -> CDev # min :: CDev -> CDev -> CDev #
Ord CIno
Instance details Defined in System.Posix.Types Methods compare :: CIno -> CIno -> Ordering # (<) :: CIno -> CIno -> Bool # (<=) :: CIno -> CIno -> Bool # (>) :: CIno -> CIno -> Bool # (>=) :: CIno -> CIno -> Bool # max :: CIno -> CIno -> CIno # min :: CIno -> CIno -> CIno #
Ord CMode
Instance details Defined in System.Posix.Types Methods compare :: CMode -> CMode -> Ordering # (<) :: CMode -> CMode -> Bool # (<=) :: CMode -> CMode -> Bool # (>) :: CMode -> CMode -> Bool # (>=) :: CMode -> CMode -> Bool # max :: CMode -> CMode -> CMode # min :: CMode -> CMode -> CMode #
Ord COff
Instance details Defined in System.Posix.Types Methods compare :: COff -> COff -> Ordering # (<) :: COff -> COff -> Bool # (<=) :: COff -> COff -> Bool # (>) :: COff -> COff -> Bool # (>=) :: COff -> COff -> Bool # max :: COff -> COff -> COff # min :: COff -> COff -> COff #
Ord CPid
Instance details Defined in System.Posix.Types Methods compare :: CPid -> CPid -> Ordering # (<) :: CPid -> CPid -> Bool # (<=) :: CPid -> CPid -> Bool # (>) :: CPid -> CPid -> Bool # (>=) :: CPid -> CPid -> Bool # max :: CPid -> CPid -> CPid # min :: CPid -> CPid -> CPid #
Ord CSsize
Instance details Defined in System.Posix.Types Methods compare :: CSsize -> CSsize -> Ordering # (<) :: CSsize -> CSsize -> Bool # (<=) :: CSsize -> CSsize -> Bool # (>) :: CSsize -> CSsize -> Bool # (>=) :: CSsize -> CSsize -> Bool # max :: CSsize -> CSsize -> CSsize # min :: CSsize -> CSsize -> CSsize #
Ord CGid
Instance details Defined in System.Posix.Types Methods compare :: CGid -> CGid -> Ordering # (<) :: CGid -> CGid -> Bool # (<=) :: CGid -> CGid -> Bool # (>) :: CGid -> CGid -> Bool # (>=) :: CGid -> CGid -> Bool # max :: CGid -> CGid -> CGid # min :: CGid -> CGid -> CGid #
Ord CNlink
Instance details Defined in System.Posix.Types Methods compare :: CNlink -> CNlink -> Ordering # (<) :: CNlink -> CNlink -> Bool # (<=) :: CNlink -> CNlink -> Bool # (>) :: CNlink -> CNlink -> Bool # (>=) :: CNlink -> CNlink -> Bool # max :: CNlink -> CNlink -> CNlink # min :: CNlink -> CNlink -> CNlink #
Ord CUid
Instance details Defined in System.Posix.Types Methods compare :: CUid -> CUid -> Ordering # (<) :: CUid -> CUid -> Bool # (<=) :: CUid -> CUid -> Bool # (>) :: CUid -> CUid -> Bool # (>=) :: CUid -> CUid -> Bool # max :: CUid -> CUid -> CUid # min :: CUid -> CUid -> CUid #
Ord CCc
Instance details Defined in System.Posix.Types Methods compare :: CCc -> CCc -> Ordering # (<) :: CCc -> CCc -> Bool # (<=) :: CCc -> CCc -> Bool # (>) :: CCc -> CCc -> Bool # (>=) :: CCc -> CCc -> Bool # max :: CCc -> CCc -> CCc # min :: CCc -> CCc -> CCc #
Ord CSpeed
Instance details Defined in System.Posix.Types Methods compare :: CSpeed -> CSpeed -> Ordering # (<) :: CSpeed -> CSpeed -> Bool # (<=) :: CSpeed -> CSpeed -> Bool # (>) :: CSpeed -> CSpeed -> Bool # (>=) :: CSpeed -> CSpeed -> Bool # max :: CSpeed -> CSpeed -> CSpeed # min :: CSpeed -> CSpeed -> CSpeed #
Ord CTcflag
Instance details Defined in System.Posix.Types Methods compare :: CTcflag -> CTcflag -> Ordering # (<) :: CTcflag -> CTcflag -> Bool # (<=) :: CTcflag -> CTcflag -> Bool # (>) :: CTcflag -> CTcflag -> Bool # (>=) :: CTcflag -> CTcflag -> Bool # max :: CTcflag -> CTcflag -> CTcflag # min :: CTcflag -> CTcflag -> CTcflag #
Ord CRLim
Instance details Defined in System.Posix.Types Methods compare :: CRLim -> CRLim -> Ordering # (<) :: CRLim -> CRLim -> Bool # (<=) :: CRLim -> CRLim -> Bool # (>) :: CRLim -> CRLim -> Bool # (>=) :: CRLim -> CRLim -> Bool # max :: CRLim -> CRLim -> CRLim # min :: CRLim -> CRLim -> CRLim #
Ord CBlkSize
Instance details Defined in System.Posix.Types Methods compare :: CBlkSize -> CBlkSize -> Ordering # (<) :: CBlkSize -> CBlkSize -> Bool # (<=) :: CBlkSize -> CBlkSize -> Bool # (>) :: CBlkSize -> CBlkSize -> Bool # (>=) :: CBlkSize -> CBlkSize -> Bool # max :: CBlkSize -> CBlkSize -> CBlkSize # min :: CBlkSize -> CBlkSize -> CBlkSize #
Ord CBlkCnt
Instance details Defined in System.Posix.Types Methods compare :: CBlkCnt -> CBlkCnt -> Ordering # (<) :: CBlkCnt -> CBlkCnt -> Bool # (<=) :: CBlkCnt -> CBlkCnt -> Bool # (>) :: CBlkCnt -> CBlkCnt -> Bool # (>=) :: CBlkCnt -> CBlkCnt -> Bool # max :: CBlkCnt -> CBlkCnt -> CBlkCnt # min :: CBlkCnt -> CBlkCnt -> CBlkCnt #
Ord CClockId
Instance details Defined in System.Posix.Types Methods compare :: CClockId -> CClockId -> Ordering # (<) :: CClockId -> CClockId -> Bool # (<=) :: CClockId -> CClockId -> Bool # (>) :: CClockId -> CClockId -> Bool # (>=) :: CClockId -> CClockId -> Bool # max :: CClockId -> CClockId -> CClockId # min :: CClockId -> CClockId -> CClockId #
Ord CFsBlkCnt
Instance details Defined in System.Posix.Types Methods compare :: CFsBlkCnt -> CFsBlkCnt -> Ordering # (<) :: CFsBlkCnt -> CFsBlkCnt -> Bool # (<=) :: CFsBlkCnt -> CFsBlkCnt -> Bool # (>) :: CFsBlkCnt -> CFsBlkCnt -> Bool # (>=) :: CFsBlkCnt -> CFsBlkCnt -> Bool # max :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt # min :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt #
Ord CFsFilCnt
Instance details Defined in System.Posix.Types Methods compare :: CFsFilCnt -> CFsFilCnt -> Ordering # (<) :: CFsFilCnt -> CFsFilCnt -> Bool # (<=) :: CFsFilCnt -> CFsFilCnt -> Bool # (>) :: CFsFilCnt -> CFsFilCnt -> Bool # (>=) :: CFsFilCnt -> CFsFilCnt -> Bool # max :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt # min :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt #
Ord CId
Instance details Defined in System.Posix.Types Methods compare :: CId -> CId -> Ordering # (<) :: CId -> CId -> Bool # (<=) :: CId -> CId -> Bool # (>) :: CId -> CId -> Bool # (>=) :: CId -> CId -> Bool # max :: CId -> CId -> CId # min :: CId -> CId -> CId #
Ord CKey
Instance details Defined in System.Posix.Types Methods compare :: CKey -> CKey -> Ordering # (<) :: CKey -> CKey -> Bool # (<=) :: CKey -> CKey -> Bool # (>) :: CKey -> CKey -> Bool # (>=) :: CKey -> CKey -> Bool # max :: CKey -> CKey -> CKey # min :: CKey -> CKey -> CKey #
Ord CTimer
Instance details Defined in System.Posix.Types Methods compare :: CTimer -> CTimer -> Ordering # (<) :: CTimer -> CTimer -> Bool # (<=) :: CTimer -> CTimer -> Bool # (>) :: CTimer -> CTimer -> Bool # (>=) :: CTimer -> CTimer -> Bool # max :: CTimer -> CTimer -> CTimer # min :: CTimer -> CTimer -> CTimer #
Ord CSocklen
Instance details Defined in System.Posix.Types Methods compare :: CSocklen -> CSocklen -> Ordering # (<) :: CSocklen -> CSocklen -> Bool # (<=) :: CSocklen -> CSocklen -> Bool # (>) :: CSocklen -> CSocklen -> Bool # (>=) :: CSocklen -> CSocklen -> Bool # max :: CSocklen -> CSocklen -> CSocklen # min :: CSocklen -> CSocklen -> CSocklen #
Ord CNfds
Instance details Defined in System.Posix.Types Methods compare :: CNfds -> CNfds -> Ordering # (<) :: CNfds -> CNfds -> Bool # (<=) :: CNfds -> CNfds -> Bool # (>) :: CNfds -> CNfds -> Bool # (>=) :: CNfds -> CNfds -> Bool # max :: CNfds -> CNfds -> CNfds # min :: CNfds -> CNfds -> CNfds #
Ord Fd
Instance details Defined in System.Posix.Types Methods compare :: Fd -> Fd -> Ordering # (<) :: Fd -> Fd -> Bool # (<=) :: Fd -> Fd -> Bool # (>) :: Fd -> Fd -> Bool # (>=) :: Fd -> Fd -> Bool # max :: Fd -> Fd -> Fd # min :: Fd -> Fd -> Fd #
Ord AsyncException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering # (<) :: AsyncException -> AsyncException -> Bool # (<=) :: AsyncException -> AsyncException -> Bool # (>) :: AsyncException -> AsyncException -> Bool # (>=) :: AsyncException -> AsyncException -> Bool # max :: AsyncException -> AsyncException -> AsyncException # min :: AsyncException -> AsyncException -> AsyncException #
Ord ArrayException	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering # (<) :: ArrayException -> ArrayException -> Bool # (<=) :: ArrayException -> ArrayException -> Bool # (>) :: ArrayException -> ArrayException -> Bool # (>=) :: ArrayException -> ArrayException -> Bool # max :: ArrayException -> ArrayException -> ArrayException # min :: ArrayException -> ArrayException -> ArrayException #
Ord ExitCode
Instance details Defined in GHC.IO.Exception Methods compare :: ExitCode -> ExitCode -> Ordering # (<) :: ExitCode -> ExitCode -> Bool # (<=) :: ExitCode -> ExitCode -> Bool # (>) :: ExitCode -> ExitCode -> Bool # (>=) :: ExitCode -> ExitCode -> Bool # max :: ExitCode -> ExitCode -> ExitCode # min :: ExitCode -> ExitCode -> ExitCode #
Ord BufferMode	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods compare :: BufferMode -> BufferMode -> Ordering # (<) :: BufferMode -> BufferMode -> Bool # (<=) :: BufferMode -> BufferMode -> Bool # (>) :: BufferMode -> BufferMode -> Bool # (>=) :: BufferMode -> BufferMode -> Bool # max :: BufferMode -> BufferMode -> BufferMode # min :: BufferMode -> BufferMode -> BufferMode #
Ord Newline	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods compare :: Newline -> Newline -> Ordering # (<) :: Newline -> Newline -> Bool # (<=) :: Newline -> Newline -> Bool # (>) :: Newline -> Newline -> Bool # (>=) :: Newline -> Newline -> Bool # max :: Newline -> Newline -> Newline # min :: Newline -> Newline -> Newline #
Ord NewlineMode	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods compare :: NewlineMode -> NewlineMode -> Ordering # (<) :: NewlineMode -> NewlineMode -> Bool # (<=) :: NewlineMode -> NewlineMode -> Bool # (>) :: NewlineMode -> NewlineMode -> Bool # (>=) :: NewlineMode -> NewlineMode -> Bool # max :: NewlineMode -> NewlineMode -> NewlineMode # min :: NewlineMode -> NewlineMode -> NewlineMode #
Ord ErrorCall	Since: base-4.7.0.0
Instance details Defined in GHC.Exception Methods compare :: ErrorCall -> ErrorCall -> Ordering # (<) :: ErrorCall -> ErrorCall -> Bool # (<=) :: ErrorCall -> ErrorCall -> Bool # (>) :: ErrorCall -> ErrorCall -> Bool # (>=) :: ErrorCall -> ErrorCall -> Bool # max :: ErrorCall -> ErrorCall -> ErrorCall # min :: ErrorCall -> ErrorCall -> ErrorCall #
Ord ArithException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods compare :: ArithException -> ArithException -> Ordering # (<) :: ArithException -> ArithException -> Bool # (<=) :: ArithException -> ArithException -> Bool # (>) :: ArithException -> ArithException -> Bool # (>=) :: ArithException -> ArithException -> Bool # max :: ArithException -> ArithException -> ArithException # min :: ArithException -> ArithException -> ArithException #
Ord All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering # (<) :: All -> All -> Bool # (<=) :: All -> All -> Bool # (>) :: All -> All -> Bool # (>=) :: All -> All -> Bool # max :: All -> All -> All # min :: All -> All -> All #
Ord Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering # (<) :: Any -> Any -> Bool # (<=) :: Any -> Any -> Bool # (>) :: Any -> Any -> Bool # (>=) :: Any -> Any -> Bool # max :: Any -> Any -> Any # min :: Any -> Any -> Any #
Ord Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods compare :: Fixity -> Fixity -> Ordering # (<) :: Fixity -> Fixity -> Bool # (<=) :: Fixity -> Fixity -> Bool # (>) :: Fixity -> Fixity -> Bool # (>=) :: Fixity -> Fixity -> Bool # max :: Fixity -> Fixity -> Fixity # min :: Fixity -> Fixity -> Fixity #
Ord Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods compare :: Associativity -> Associativity -> Ordering # (<) :: Associativity -> Associativity -> Bool # (<=) :: Associativity -> Associativity -> Bool # (>) :: Associativity -> Associativity -> Bool # (>=) :: Associativity -> Associativity -> Bool # max :: Associativity -> Associativity -> Associativity # min :: Associativity -> Associativity -> Associativity #
Ord SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness #
Ord SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness #
Ord DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness #
Ord SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods compare :: SomeSymbol -> SomeSymbol -> Ordering # (<) :: SomeSymbol -> SomeSymbol -> Bool # (<=) :: SomeSymbol -> SomeSymbol -> Bool # (>) :: SomeSymbol -> SomeSymbol -> Bool # (>=) :: SomeSymbol -> SomeSymbol -> Bool # max :: SomeSymbol -> SomeSymbol -> SomeSymbol # min :: SomeSymbol -> SomeSymbol -> SomeSymbol #
Ord SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods compare :: SomeNat -> SomeNat -> Ordering # (<) :: SomeNat -> SomeNat -> Bool # (<=) :: SomeNat -> SomeNat -> Bool # (>) :: SomeNat -> SomeNat -> Bool # (>=) :: SomeNat -> SomeNat -> Bool # max :: SomeNat -> SomeNat -> SomeNat # min :: SomeNat -> SomeNat -> SomeNat #
Ord CChar
Instance details Defined in Foreign.C.Types Methods compare :: CChar -> CChar -> Ordering # (<) :: CChar -> CChar -> Bool # (<=) :: CChar -> CChar -> Bool # (>) :: CChar -> CChar -> Bool # (>=) :: CChar -> CChar -> Bool # max :: CChar -> CChar -> CChar # min :: CChar -> CChar -> CChar #
Ord CSChar
Instance details Defined in Foreign.C.Types Methods compare :: CSChar -> CSChar -> Ordering # (<) :: CSChar -> CSChar -> Bool # (<=) :: CSChar -> CSChar -> Bool # (>) :: CSChar -> CSChar -> Bool # (>=) :: CSChar -> CSChar -> Bool # max :: CSChar -> CSChar -> CSChar # min :: CSChar -> CSChar -> CSChar #
Ord CUChar
Instance details Defined in Foreign.C.Types Methods compare :: CUChar -> CUChar -> Ordering # (<) :: CUChar -> CUChar -> Bool # (<=) :: CUChar -> CUChar -> Bool # (>) :: CUChar -> CUChar -> Bool # (>=) :: CUChar -> CUChar -> Bool # max :: CUChar -> CUChar -> CUChar # min :: CUChar -> CUChar -> CUChar #
Ord CShort
Instance details Defined in Foreign.C.Types Methods compare :: CShort -> CShort -> Ordering # (<) :: CShort -> CShort -> Bool # (<=) :: CShort -> CShort -> Bool # (>) :: CShort -> CShort -> Bool # (>=) :: CShort -> CShort -> Bool # max :: CShort -> CShort -> CShort # min :: CShort -> CShort -> CShort #
Ord CUShort
Instance details Defined in Foreign.C.Types Methods compare :: CUShort -> CUShort -> Ordering # (<) :: CUShort -> CUShort -> Bool # (<=) :: CUShort -> CUShort -> Bool # (>) :: CUShort -> CUShort -> Bool # (>=) :: CUShort -> CUShort -> Bool # max :: CUShort -> CUShort -> CUShort # min :: CUShort -> CUShort -> CUShort #
Ord CInt
Instance details Defined in Foreign.C.Types Methods compare :: CInt -> CInt -> Ordering # (<) :: CInt -> CInt -> Bool # (<=) :: CInt -> CInt -> Bool # (>) :: CInt -> CInt -> Bool # (>=) :: CInt -> CInt -> Bool # max :: CInt -> CInt -> CInt # min :: CInt -> CInt -> CInt #
Ord CUInt
Instance details Defined in Foreign.C.Types Methods compare :: CUInt -> CUInt -> Ordering # (<) :: CUInt -> CUInt -> Bool # (<=) :: CUInt -> CUInt -> Bool # (>) :: CUInt -> CUInt -> Bool # (>=) :: CUInt -> CUInt -> Bool # max :: CUInt -> CUInt -> CUInt # min :: CUInt -> CUInt -> CUInt #
Ord CLong
Instance details Defined in Foreign.C.Types Methods compare :: CLong -> CLong -> Ordering # (<) :: CLong -> CLong -> Bool # (<=) :: CLong -> CLong -> Bool # (>) :: CLong -> CLong -> Bool # (>=) :: CLong -> CLong -> Bool # max :: CLong -> CLong -> CLong # min :: CLong -> CLong -> CLong #
Ord CULong
Instance details Defined in Foreign.C.Types Methods compare :: CULong -> CULong -> Ordering # (<) :: CULong -> CULong -> Bool # (<=) :: CULong -> CULong -> Bool # (>) :: CULong -> CULong -> Bool # (>=) :: CULong -> CULong -> Bool # max :: CULong -> CULong -> CULong # min :: CULong -> CULong -> CULong #
Ord CLLong
Instance details Defined in Foreign.C.Types Methods compare :: CLLong -> CLLong -> Ordering # (<) :: CLLong -> CLLong -> Bool # (<=) :: CLLong -> CLLong -> Bool # (>) :: CLLong -> CLLong -> Bool # (>=) :: CLLong -> CLLong -> Bool # max :: CLLong -> CLLong -> CLLong # min :: CLLong -> CLLong -> CLLong #
Ord CULLong
Instance details Defined in Foreign.C.Types Methods compare :: CULLong -> CULLong -> Ordering # (<) :: CULLong -> CULLong -> Bool # (<=) :: CULLong -> CULLong -> Bool # (>) :: CULLong -> CULLong -> Bool # (>=) :: CULLong -> CULLong -> Bool # max :: CULLong -> CULLong -> CULLong # min :: CULLong -> CULLong -> CULLong #
Ord CBool
Instance details Defined in Foreign.C.Types Methods compare :: CBool -> CBool -> Ordering # (<) :: CBool -> CBool -> Bool # (<=) :: CBool -> CBool -> Bool # (>) :: CBool -> CBool -> Bool # (>=) :: CBool -> CBool -> Bool # max :: CBool -> CBool -> CBool # min :: CBool -> CBool -> CBool #
Ord CFloat
Instance details Defined in Foreign.C.Types Methods compare :: CFloat -> CFloat -> Ordering # (<) :: CFloat -> CFloat -> Bool # (<=) :: CFloat -> CFloat -> Bool # (>) :: CFloat -> CFloat -> Bool # (>=) :: CFloat -> CFloat -> Bool # max :: CFloat -> CFloat -> CFloat # min :: CFloat -> CFloat -> CFloat #
Ord CDouble
Instance details Defined in Foreign.C.Types Methods compare :: CDouble -> CDouble -> Ordering # (<) :: CDouble -> CDouble -> Bool # (<=) :: CDouble -> CDouble -> Bool # (>) :: CDouble -> CDouble -> Bool # (>=) :: CDouble -> CDouble -> Bool # max :: CDouble -> CDouble -> CDouble # min :: CDouble -> CDouble -> CDouble #
Ord CPtrdiff
Instance details Defined in Foreign.C.Types Methods compare :: CPtrdiff -> CPtrdiff -> Ordering # (<) :: CPtrdiff -> CPtrdiff -> Bool # (<=) :: CPtrdiff -> CPtrdiff -> Bool # (>) :: CPtrdiff -> CPtrdiff -> Bool # (>=) :: CPtrdiff -> CPtrdiff -> Bool # max :: CPtrdiff -> CPtrdiff -> CPtrdiff # min :: CPtrdiff -> CPtrdiff -> CPtrdiff #
Ord CSize
Instance details Defined in Foreign.C.Types Methods compare :: CSize -> CSize -> Ordering # (<) :: CSize -> CSize -> Bool # (<=) :: CSize -> CSize -> Bool # (>) :: CSize -> CSize -> Bool # (>=) :: CSize -> CSize -> Bool # max :: CSize -> CSize -> CSize # min :: CSize -> CSize -> CSize #
Ord CWchar
Instance details Defined in Foreign.C.Types Methods compare :: CWchar -> CWchar -> Ordering # (<) :: CWchar -> CWchar -> Bool # (<=) :: CWchar -> CWchar -> Bool # (>) :: CWchar -> CWchar -> Bool # (>=) :: CWchar -> CWchar -> Bool # max :: CWchar -> CWchar -> CWchar # min :: CWchar -> CWchar -> CWchar #
Ord CSigAtomic
Instance details Defined in Foreign.C.Types Methods compare :: CSigAtomic -> CSigAtomic -> Ordering # (<) :: CSigAtomic -> CSigAtomic -> Bool # (<=) :: CSigAtomic -> CSigAtomic -> Bool # (>) :: CSigAtomic -> CSigAtomic -> Bool # (>=) :: CSigAtomic -> CSigAtomic -> Bool # max :: CSigAtomic -> CSigAtomic -> CSigAtomic # min :: CSigAtomic -> CSigAtomic -> CSigAtomic #
Ord CClock
Instance details Defined in Foreign.C.Types Methods compare :: CClock -> CClock -> Ordering # (<) :: CClock -> CClock -> Bool # (<=) :: CClock -> CClock -> Bool # (>) :: CClock -> CClock -> Bool # (>=) :: CClock -> CClock -> Bool # max :: CClock -> CClock -> CClock # min :: CClock -> CClock -> CClock #
Ord CTime
Instance details Defined in Foreign.C.Types Methods compare :: CTime -> CTime -> Ordering # (<) :: CTime -> CTime -> Bool # (<=) :: CTime -> CTime -> Bool # (>) :: CTime -> CTime -> Bool # (>=) :: CTime -> CTime -> Bool # max :: CTime -> CTime -> CTime # min :: CTime -> CTime -> CTime #
Ord CUSeconds
Instance details Defined in Foreign.C.Types Methods compare :: CUSeconds -> CUSeconds -> Ordering # (<) :: CUSeconds -> CUSeconds -> Bool # (<=) :: CUSeconds -> CUSeconds -> Bool # (>) :: CUSeconds -> CUSeconds -> Bool # (>=) :: CUSeconds -> CUSeconds -> Bool # max :: CUSeconds -> CUSeconds -> CUSeconds # min :: CUSeconds -> CUSeconds -> CUSeconds #
Ord CSUSeconds
Instance details Defined in Foreign.C.Types Methods compare :: CSUSeconds -> CSUSeconds -> Ordering # (<) :: CSUSeconds -> CSUSeconds -> Bool # (<=) :: CSUSeconds -> CSUSeconds -> Bool # (>) :: CSUSeconds -> CSUSeconds -> Bool # (>=) :: CSUSeconds -> CSUSeconds -> Bool # max :: CSUSeconds -> CSUSeconds -> CSUSeconds # min :: CSUSeconds -> CSUSeconds -> CSUSeconds #
Ord CIntPtr
Instance details Defined in Foreign.C.Types Methods compare :: CIntPtr -> CIntPtr -> Ordering # (<) :: CIntPtr -> CIntPtr -> Bool # (<=) :: CIntPtr -> CIntPtr -> Bool # (>) :: CIntPtr -> CIntPtr -> Bool # (>=) :: CIntPtr -> CIntPtr -> Bool # max :: CIntPtr -> CIntPtr -> CIntPtr # min :: CIntPtr -> CIntPtr -> CIntPtr #
Ord CUIntPtr
Instance details Defined in Foreign.C.Types Methods compare :: CUIntPtr -> CUIntPtr -> Ordering # (<) :: CUIntPtr -> CUIntPtr -> Bool # (<=) :: CUIntPtr -> CUIntPtr -> Bool # (>) :: CUIntPtr -> CUIntPtr -> Bool # (>=) :: CUIntPtr -> CUIntPtr -> Bool # max :: CUIntPtr -> CUIntPtr -> CUIntPtr # min :: CUIntPtr -> CUIntPtr -> CUIntPtr #
Ord CIntMax
Instance details Defined in Foreign.C.Types Methods compare :: CIntMax -> CIntMax -> Ordering # (<) :: CIntMax -> CIntMax -> Bool # (<=) :: CIntMax -> CIntMax -> Bool # (>) :: CIntMax -> CIntMax -> Bool # (>=) :: CIntMax -> CIntMax -> Bool # max :: CIntMax -> CIntMax -> CIntMax # min :: CIntMax -> CIntMax -> CIntMax #
Ord CUIntMax
Instance details Defined in Foreign.C.Types Methods compare :: CUIntMax -> CUIntMax -> Ordering # (<) :: CUIntMax -> CUIntMax -> Bool # (<=) :: CUIntMax -> CUIntMax -> Bool # (>) :: CUIntMax -> CUIntMax -> Bool # (>=) :: CUIntMax -> CUIntMax -> Bool # max :: CUIntMax -> CUIntMax -> CUIntMax # min :: CUIntMax -> CUIntMax -> CUIntMax #
Ord Fingerprint	Since: base-4.4.0.0
Instance details Defined in GHC.Fingerprint.Type Methods compare :: Fingerprint -> Fingerprint -> Ordering # (<) :: Fingerprint -> Fingerprint -> Bool # (<=) :: Fingerprint -> Fingerprint -> Bool # (>) :: Fingerprint -> Fingerprint -> Bool # (>=) :: Fingerprint -> Fingerprint -> Bool # max :: Fingerprint -> Fingerprint -> Fingerprint # min :: Fingerprint -> Fingerprint -> Fingerprint #
Ord GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Unicode Methods compare :: GeneralCategory -> GeneralCategory -> Ordering # (<) :: GeneralCategory -> GeneralCategory -> Bool # (<=) :: GeneralCategory -> GeneralCategory -> Bool # (>) :: GeneralCategory -> GeneralCategory -> Bool # (>=) :: GeneralCategory -> GeneralCategory -> Bool # max :: GeneralCategory -> GeneralCategory -> GeneralCategory # min :: GeneralCategory -> GeneralCategory -> GeneralCategory #
Ord ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods compare :: ShortByteString -> ShortByteString -> Ordering # (<) :: ShortByteString -> ShortByteString -> Bool # (<=) :: ShortByteString -> ShortByteString -> Bool # (>) :: ShortByteString -> ShortByteString -> Bool # (>=) :: ShortByteString -> ShortByteString -> Bool # max :: ShortByteString -> ShortByteString -> ShortByteString # min :: ShortByteString -> ShortByteString -> ShortByteString #
Ord ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods compare :: ByteString -> ByteString -> Ordering # (<) :: ByteString -> ByteString -> Bool # (<=) :: ByteString -> ByteString -> Bool # (>) :: ByteString -> ByteString -> Bool # (>=) :: ByteString -> ByteString -> Bool # max :: ByteString -> ByteString -> ByteString # min :: ByteString -> ByteString -> ByteString #
Ord Lex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Lex -> Lex -> Ordering # (<) :: Lex -> Lex -> Bool # (<=) :: Lex -> Lex -> Bool # (>) :: Lex -> Lex -> Bool # (>=) :: Lex -> Lex -> Bool # max :: Lex -> Lex -> Lex # min :: Lex -> Lex -> Lex #
Ord Revlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Revlex -> Revlex -> Ordering # (<) :: Revlex -> Revlex -> Bool # (<=) :: Revlex -> Revlex -> Bool # (>) :: Revlex -> Revlex -> Bool # (>=) :: Revlex -> Revlex -> Bool # max :: Revlex -> Revlex -> Revlex # min :: Revlex -> Revlex -> Revlex #
Ord Grevlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Grevlex -> Grevlex -> Ordering # (<) :: Grevlex -> Grevlex -> Bool # (<=) :: Grevlex -> Grevlex -> Bool # (>) :: Grevlex -> Grevlex -> Bool # (>=) :: Grevlex -> Grevlex -> Bool # max :: Grevlex -> Grevlex -> Grevlex # min :: Grevlex -> Grevlex -> Grevlex #
Ord Grlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Grlex -> Grlex -> Ordering # (<) :: Grlex -> Grlex -> Bool # (<=) :: Grlex -> Grlex -> Bool # (>) :: Grlex -> Grlex -> Bool # (>=) :: Grlex -> Grlex -> Bool # max :: Grlex -> Grlex -> Grlex # min :: Grlex -> Grlex -> Grlex #
Ord BigNat
Instance details Defined in GHC.Integer.Type Methods compare :: BigNat -> BigNat -> Ordering # (<) :: BigNat -> BigNat -> Bool # (<=) :: BigNat -> BigNat -> Bool # (>) :: BigNat -> BigNat -> Bool # (>=) :: BigNat -> BigNat -> Bool # max :: BigNat -> BigNat -> BigNat # min :: BigNat -> BigNat -> BigNat #
Ord ModName
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: ModName -> ModName -> Ordering # (<) :: ModName -> ModName -> Bool # (<=) :: ModName -> ModName -> Bool # (>) :: ModName -> ModName -> Bool # (>=) :: ModName -> ModName -> Bool # max :: ModName -> ModName -> ModName # min :: ModName -> ModName -> ModName #
Ord PkgName
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: PkgName -> PkgName -> Ordering # (<) :: PkgName -> PkgName -> Bool # (<=) :: PkgName -> PkgName -> Bool # (>) :: PkgName -> PkgName -> Bool # (>=) :: PkgName -> PkgName -> Bool # max :: PkgName -> PkgName -> PkgName # min :: PkgName -> PkgName -> PkgName #
Ord Module
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Module -> Module -> Ordering # (<) :: Module -> Module -> Bool # (<=) :: Module -> Module -> Bool # (>) :: Module -> Module -> Bool # (>=) :: Module -> Module -> Bool # max :: Module -> Module -> Module # min :: Module -> Module -> Module #
Ord OccName
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: OccName -> OccName -> Ordering # (<) :: OccName -> OccName -> Bool # (<=) :: OccName -> OccName -> Bool # (>) :: OccName -> OccName -> Bool # (>=) :: OccName -> OccName -> Bool # max :: OccName -> OccName -> OccName # min :: OccName -> OccName -> OccName #
Ord NameFlavour
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: NameFlavour -> NameFlavour -> Ordering # (<) :: NameFlavour -> NameFlavour -> Bool # (<=) :: NameFlavour -> NameFlavour -> Bool # (>) :: NameFlavour -> NameFlavour -> Bool # (>=) :: NameFlavour -> NameFlavour -> Bool # max :: NameFlavour -> NameFlavour -> NameFlavour # min :: NameFlavour -> NameFlavour -> NameFlavour #
Ord NameSpace
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: NameSpace -> NameSpace -> Ordering # (<) :: NameSpace -> NameSpace -> Bool # (<=) :: NameSpace -> NameSpace -> Bool # (>) :: NameSpace -> NameSpace -> Bool # (>=) :: NameSpace -> NameSpace -> Bool # max :: NameSpace -> NameSpace -> NameSpace # min :: NameSpace -> NameSpace -> NameSpace #
Ord Loc
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Loc -> Loc -> Ordering # (<) :: Loc -> Loc -> Bool # (<=) :: Loc -> Loc -> Bool # (>) :: Loc -> Loc -> Bool # (>=) :: Loc -> Loc -> Bool # max :: Loc -> Loc -> Loc # min :: Loc -> Loc -> Loc #
Ord Info
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Info -> Info -> Ordering # (<) :: Info -> Info -> Bool # (<=) :: Info -> Info -> Bool # (>) :: Info -> Info -> Bool # (>=) :: Info -> Info -> Bool # max :: Info -> Info -> Info # min :: Info -> Info -> Info #
Ord ModuleInfo
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: ModuleInfo -> ModuleInfo -> Ordering # (<) :: ModuleInfo -> ModuleInfo -> Bool # (<=) :: ModuleInfo -> ModuleInfo -> Bool # (>) :: ModuleInfo -> ModuleInfo -> Bool # (>=) :: ModuleInfo -> ModuleInfo -> Bool # max :: ModuleInfo -> ModuleInfo -> ModuleInfo # min :: ModuleInfo -> ModuleInfo -> ModuleInfo #
Ord Fixity
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Fixity -> Fixity -> Ordering # (<) :: Fixity -> Fixity -> Bool # (<=) :: Fixity -> Fixity -> Bool # (>) :: Fixity -> Fixity -> Bool # (>=) :: Fixity -> Fixity -> Bool # max :: Fixity -> Fixity -> Fixity # min :: Fixity -> Fixity -> Fixity #
Ord FixityDirection
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: FixityDirection -> FixityDirection -> Ordering # (<) :: FixityDirection -> FixityDirection -> Bool # (<=) :: FixityDirection -> FixityDirection -> Bool # (>) :: FixityDirection -> FixityDirection -> Bool # (>=) :: FixityDirection -> FixityDirection -> Bool # max :: FixityDirection -> FixityDirection -> FixityDirection # min :: FixityDirection -> FixityDirection -> FixityDirection #
Ord Lit
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Lit -> Lit -> Ordering # (<) :: Lit -> Lit -> Bool # (<=) :: Lit -> Lit -> Bool # (>) :: Lit -> Lit -> Bool # (>=) :: Lit -> Lit -> Bool # max :: Lit -> Lit -> Lit # min :: Lit -> Lit -> Lit #
Ord Bytes
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Bytes -> Bytes -> Ordering # (<) :: Bytes -> Bytes -> Bool # (<=) :: Bytes -> Bytes -> Bool # (>) :: Bytes -> Bytes -> Bool # (>=) :: Bytes -> Bytes -> Bool # max :: Bytes -> Bytes -> Bytes # min :: Bytes -> Bytes -> Bytes #
Ord Body
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Body -> Body -> Ordering # (<) :: Body -> Body -> Bool # (<=) :: Body -> Body -> Bool # (>) :: Body -> Body -> Bool # (>=) :: Body -> Body -> Bool # max :: Body -> Body -> Body # min :: Body -> Body -> Body #
Ord Guard
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Guard -> Guard -> Ordering # (<) :: Guard -> Guard -> Bool # (<=) :: Guard -> Guard -> Bool # (>) :: Guard -> Guard -> Bool # (>=) :: Guard -> Guard -> Bool # max :: Guard -> Guard -> Guard # min :: Guard -> Guard -> Guard #
Ord Stmt
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Stmt -> Stmt -> Ordering # (<) :: Stmt -> Stmt -> Bool # (<=) :: Stmt -> Stmt -> Bool # (>) :: Stmt -> Stmt -> Bool # (>=) :: Stmt -> Stmt -> Bool # max :: Stmt -> Stmt -> Stmt # min :: Stmt -> Stmt -> Stmt #
Ord Range
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Range -> Range -> Ordering # (<) :: Range -> Range -> Bool # (<=) :: Range -> Range -> Bool # (>) :: Range -> Range -> Bool # (>=) :: Range -> Range -> Bool # max :: Range -> Range -> Range # min :: Range -> Range -> Range #
Ord DerivClause
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: DerivClause -> DerivClause -> Ordering # (<) :: DerivClause -> DerivClause -> Bool # (<=) :: DerivClause -> DerivClause -> Bool # (>) :: DerivClause -> DerivClause -> Bool # (>=) :: DerivClause -> DerivClause -> Bool # max :: DerivClause -> DerivClause -> DerivClause # min :: DerivClause -> DerivClause -> DerivClause #
Ord DerivStrategy
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: DerivStrategy -> DerivStrategy -> Ordering # (<) :: DerivStrategy -> DerivStrategy -> Bool # (<=) :: DerivStrategy -> DerivStrategy -> Bool # (>) :: DerivStrategy -> DerivStrategy -> Bool # (>=) :: DerivStrategy -> DerivStrategy -> Bool # max :: DerivStrategy -> DerivStrategy -> DerivStrategy # min :: DerivStrategy -> DerivStrategy -> DerivStrategy #
Ord TypeFamilyHead
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: TypeFamilyHead -> TypeFamilyHead -> Ordering # (<) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (<=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # max :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead # min :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead #
Ord TySynEqn
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: TySynEqn -> TySynEqn -> Ordering # (<) :: TySynEqn -> TySynEqn -> Bool # (<=) :: TySynEqn -> TySynEqn -> Bool # (>) :: TySynEqn -> TySynEqn -> Bool # (>=) :: TySynEqn -> TySynEqn -> Bool # max :: TySynEqn -> TySynEqn -> TySynEqn # min :: TySynEqn -> TySynEqn -> TySynEqn #
Ord Foreign
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Foreign -> Foreign -> Ordering # (<) :: Foreign -> Foreign -> Bool # (<=) :: Foreign -> Foreign -> Bool # (>) :: Foreign -> Foreign -> Bool # (>=) :: Foreign -> Foreign -> Bool # max :: Foreign -> Foreign -> Foreign # min :: Foreign -> Foreign -> Foreign #
Ord Callconv
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Callconv -> Callconv -> Ordering # (<) :: Callconv -> Callconv -> Bool # (<=) :: Callconv -> Callconv -> Bool # (>) :: Callconv -> Callconv -> Bool # (>=) :: Callconv -> Callconv -> Bool # max :: Callconv -> Callconv -> Callconv # min :: Callconv -> Callconv -> Callconv #
Ord Safety
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Safety -> Safety -> Ordering # (<) :: Safety -> Safety -> Bool # (<=) :: Safety -> Safety -> Bool # (>) :: Safety -> Safety -> Bool # (>=) :: Safety -> Safety -> Bool # max :: Safety -> Safety -> Safety # min :: Safety -> Safety -> Safety #
Ord Pragma
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Pragma -> Pragma -> Ordering # (<) :: Pragma -> Pragma -> Bool # (<=) :: Pragma -> Pragma -> Bool # (>) :: Pragma -> Pragma -> Bool # (>=) :: Pragma -> Pragma -> Bool # max :: Pragma -> Pragma -> Pragma # min :: Pragma -> Pragma -> Pragma #
Ord Inline
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Inline -> Inline -> Ordering # (<) :: Inline -> Inline -> Bool # (<=) :: Inline -> Inline -> Bool # (>) :: Inline -> Inline -> Bool # (>=) :: Inline -> Inline -> Bool # max :: Inline -> Inline -> Inline # min :: Inline -> Inline -> Inline #
Ord RuleMatch
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: RuleMatch -> RuleMatch -> Ordering # (<) :: RuleMatch -> RuleMatch -> Bool # (<=) :: RuleMatch -> RuleMatch -> Bool # (>) :: RuleMatch -> RuleMatch -> Bool # (>=) :: RuleMatch -> RuleMatch -> Bool # max :: RuleMatch -> RuleMatch -> RuleMatch # min :: RuleMatch -> RuleMatch -> RuleMatch #
Ord Phases
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Phases -> Phases -> Ordering # (<) :: Phases -> Phases -> Bool # (<=) :: Phases -> Phases -> Bool # (>) :: Phases -> Phases -> Bool # (>=) :: Phases -> Phases -> Bool # max :: Phases -> Phases -> Phases # min :: Phases -> Phases -> Phases #
Ord RuleBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: RuleBndr -> RuleBndr -> Ordering # (<) :: RuleBndr -> RuleBndr -> Bool # (<=) :: RuleBndr -> RuleBndr -> Bool # (>) :: RuleBndr -> RuleBndr -> Bool # (>=) :: RuleBndr -> RuleBndr -> Bool # max :: RuleBndr -> RuleBndr -> RuleBndr # min :: RuleBndr -> RuleBndr -> RuleBndr #
Ord AnnTarget
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: AnnTarget -> AnnTarget -> Ordering # (<) :: AnnTarget -> AnnTarget -> Bool # (<=) :: AnnTarget -> AnnTarget -> Bool # (>) :: AnnTarget -> AnnTarget -> Bool # (>=) :: AnnTarget -> AnnTarget -> Bool # max :: AnnTarget -> AnnTarget -> AnnTarget # min :: AnnTarget -> AnnTarget -> AnnTarget #
Ord SourceUnpackedness
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness #
Ord SourceStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness #
Ord DecidedStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness #
Ord Con
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Con -> Con -> Ordering # (<) :: Con -> Con -> Bool # (<=) :: Con -> Con -> Bool # (>) :: Con -> Con -> Bool # (>=) :: Con -> Con -> Bool # max :: Con -> Con -> Con # min :: Con -> Con -> Con #
Ord Bang
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Bang -> Bang -> Ordering # (<) :: Bang -> Bang -> Bool # (<=) :: Bang -> Bang -> Bool # (>) :: Bang -> Bang -> Bool # (>=) :: Bang -> Bang -> Bool # max :: Bang -> Bang -> Bang # min :: Bang -> Bang -> Bang #
Ord PatSynDir
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: PatSynDir -> PatSynDir -> Ordering # (<) :: PatSynDir -> PatSynDir -> Bool # (<=) :: PatSynDir -> PatSynDir -> Bool # (>) :: PatSynDir -> PatSynDir -> Bool # (>=) :: PatSynDir -> PatSynDir -> Bool # max :: PatSynDir -> PatSynDir -> PatSynDir # min :: PatSynDir -> PatSynDir -> PatSynDir #
Ord PatSynArgs
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: PatSynArgs -> PatSynArgs -> Ordering # (<) :: PatSynArgs -> PatSynArgs -> Bool # (<=) :: PatSynArgs -> PatSynArgs -> Bool # (>) :: PatSynArgs -> PatSynArgs -> Bool # (>=) :: PatSynArgs -> PatSynArgs -> Bool # max :: PatSynArgs -> PatSynArgs -> PatSynArgs # min :: PatSynArgs -> PatSynArgs -> PatSynArgs #
Ord TyVarBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: TyVarBndr -> TyVarBndr -> Ordering # (<) :: TyVarBndr -> TyVarBndr -> Bool # (<=) :: TyVarBndr -> TyVarBndr -> Bool # (>) :: TyVarBndr -> TyVarBndr -> Bool # (>=) :: TyVarBndr -> TyVarBndr -> Bool # max :: TyVarBndr -> TyVarBndr -> TyVarBndr # min :: TyVarBndr -> TyVarBndr -> TyVarBndr #
Ord FamilyResultSig
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: FamilyResultSig -> FamilyResultSig -> Ordering # (<) :: FamilyResultSig -> FamilyResultSig -> Bool # (<=) :: FamilyResultSig -> FamilyResultSig -> Bool # (>) :: FamilyResultSig -> FamilyResultSig -> Bool # (>=) :: FamilyResultSig -> FamilyResultSig -> Bool # max :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig # min :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig #
Ord TyLit
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: TyLit -> TyLit -> Ordering # (<) :: TyLit -> TyLit -> Bool # (<=) :: TyLit -> TyLit -> Bool # (>) :: TyLit -> TyLit -> Bool # (>=) :: TyLit -> TyLit -> Bool # max :: TyLit -> TyLit -> TyLit # min :: TyLit -> TyLit -> TyLit #
Ord Role
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: Role -> Role -> Ordering # (<) :: Role -> Role -> Bool # (<=) :: Role -> Role -> Bool # (>) :: Role -> Role -> Bool # (>=) :: Role -> Role -> Bool # max :: Role -> Role -> Role # min :: Role -> Role -> Role #
Ord AnnLookup
Instance details Defined in Language.Haskell.TH.Syntax Methods compare :: AnnLookup -> AnnLookup -> Ordering # (<) :: AnnLookup -> AnnLookup -> Bool # (<=) :: AnnLookup -> AnnLookup -> Bool # (>) :: AnnLookup -> AnnLookup -> Bool # (>=) :: AnnLookup -> AnnLookup -> Bool # max :: AnnLookup -> AnnLookup -> AnnLookup # min :: AnnLookup -> AnnLookup -> AnnLookup #
Ord WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: WrapOrdering -> WrapOrdering -> Ordering # (<) :: WrapOrdering -> WrapOrdering -> Bool # (<=) :: WrapOrdering -> WrapOrdering -> Bool # (>) :: WrapOrdering -> WrapOrdering -> Bool # (>=) :: WrapOrdering -> WrapOrdering -> Bool # max :: WrapOrdering -> WrapOrdering -> WrapOrdering # min :: WrapOrdering -> WrapOrdering -> WrapOrdering #
Ord ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods compare :: ByteArray -> ByteArray -> Ordering # (<) :: ByteArray -> ByteArray -> Bool # (<=) :: ByteArray -> ByteArray -> Bool # (>) :: ByteArray -> ByteArray -> Bool # (>=) :: ByteArray -> ByteArray -> Bool # max :: ByteArray -> ByteArray -> ByteArray # min :: ByteArray -> ByteArray -> ByteArray #
Ord DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods compare :: DefName -> DefName -> Ordering # (<) :: DefName -> DefName -> Bool # (<=) :: DefName -> DefName -> Bool # (>) :: DefName -> DefName -> Bool # (>=) :: DefName -> DefName -> Bool # max :: DefName -> DefName -> DefName # min :: DefName -> DefName -> DefName #
Ord ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods compare :: ComplexBasis -> ComplexBasis -> Ordering # (<) :: ComplexBasis -> ComplexBasis -> Bool # (<=) :: ComplexBasis -> ComplexBasis -> Bool # (>) :: ComplexBasis -> ComplexBasis -> Bool # (>=) :: ComplexBasis -> ComplexBasis -> Bool # max :: ComplexBasis -> ComplexBasis -> ComplexBasis # min :: ComplexBasis -> ComplexBasis -> ComplexBasis #
Ord ConstructorVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods compare :: ConstructorVariant -> ConstructorVariant -> Ordering # (<) :: ConstructorVariant -> ConstructorVariant -> Bool # (<=) :: ConstructorVariant -> ConstructorVariant -> Bool # (>) :: ConstructorVariant -> ConstructorVariant -> Bool # (>=) :: ConstructorVariant -> ConstructorVariant -> Bool # max :: ConstructorVariant -> ConstructorVariant -> ConstructorVariant # min :: ConstructorVariant -> ConstructorVariant -> ConstructorVariant #
Ord DatatypeVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods compare :: DatatypeVariant -> DatatypeVariant -> Ordering # (<) :: DatatypeVariant -> DatatypeVariant -> Bool # (<=) :: DatatypeVariant -> DatatypeVariant -> Bool # (>) :: DatatypeVariant -> DatatypeVariant -> Bool # (>=) :: DatatypeVariant -> DatatypeVariant -> Bool # max :: DatatypeVariant -> DatatypeVariant -> DatatypeVariant # min :: DatatypeVariant -> DatatypeVariant -> DatatypeVariant #
Ord FieldStrictness
Instance details Defined in Language.Haskell.TH.Datatype Methods compare :: FieldStrictness -> FieldStrictness -> Ordering # (<) :: FieldStrictness -> FieldStrictness -> Bool # (<=) :: FieldStrictness -> FieldStrictness -> Bool # (>) :: FieldStrictness -> FieldStrictness -> Bool # (>=) :: FieldStrictness -> FieldStrictness -> Bool # max :: FieldStrictness -> FieldStrictness -> FieldStrictness # min :: FieldStrictness -> FieldStrictness -> FieldStrictness #
Ord Strictness
Instance details Defined in Language.Haskell.TH.Datatype Methods compare :: Strictness -> Strictness -> Ordering # (<) :: Strictness -> Strictness -> Bool # (<=) :: Strictness -> Strictness -> Bool # (>) :: Strictness -> Strictness -> Bool # (>=) :: Strictness -> Strictness -> Bool # max :: Strictness -> Strictness -> Strictness # min :: Strictness -> Strictness -> Strictness #
Ord Unpackedness
Instance details Defined in Language.Haskell.TH.Datatype Methods compare :: Unpackedness -> Unpackedness -> Ordering # (<) :: Unpackedness -> Unpackedness -> Bool # (<=) :: Unpackedness -> Unpackedness -> Bool # (>) :: Unpackedness -> Unpackedness -> Bool # (>=) :: Unpackedness -> Unpackedness -> Bool # max :: Unpackedness -> Unpackedness -> Unpackedness # min :: Unpackedness -> Unpackedness -> Unpackedness #
Ord Specificity
Instance details Defined in Language.Haskell.TH.Datatype.TyVarBndr Methods compare :: Specificity -> Specificity -> Ordering # (<) :: Specificity -> Specificity -> Bool # (<=) :: Specificity -> Specificity -> Bool # (>) :: Specificity -> Specificity -> Bool # (>=) :: Specificity -> Specificity -> Bool # max :: Specificity -> Specificity -> Specificity # min :: Specificity -> Specificity -> Specificity #
Ord GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: GradedStrategy -> GradedStrategy -> Ordering # (<) :: GradedStrategy -> GradedStrategy -> Bool # (<=) :: GradedStrategy -> GradedStrategy -> Bool # (>) :: GradedStrategy -> GradedStrategy -> Bool # (>=) :: GradedStrategy -> GradedStrategy -> Bool # max :: GradedStrategy -> GradedStrategy -> GradedStrategy # min :: GradedStrategy -> GradedStrategy -> GradedStrategy #
Ord GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: GrevlexStrategy -> GrevlexStrategy -> Ordering # (<) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (<=) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (>) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (>=) :: GrevlexStrategy -> GrevlexStrategy -> Bool # max :: GrevlexStrategy -> GrevlexStrategy -> GrevlexStrategy # min :: GrevlexStrategy -> GrevlexStrategy -> GrevlexStrategy #
Ord NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: NormalStrategy -> NormalStrategy -> Ordering # (<) :: NormalStrategy -> NormalStrategy -> Bool # (<=) :: NormalStrategy -> NormalStrategy -> Bool # (>) :: NormalStrategy -> NormalStrategy -> Bool # (>=) :: NormalStrategy -> NormalStrategy -> Bool # max :: NormalStrategy -> NormalStrategy -> NormalStrategy # min :: NormalStrategy -> NormalStrategy -> NormalStrategy #
Ord a => Ord [a]
Instance details Defined in GHC.Classes Methods compare :: [a] -> [a] -> Ordering # (<) :: [a] -> [a] -> Bool # (<=) :: [a] -> [a] -> Bool # (>) :: [a] -> [a] -> Bool # (>=) :: [a] -> [a] -> Bool # max :: [a] -> [a] -> [a] # min :: [a] -> [a] -> [a] #
Ord a => Ord (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering # (<) :: Maybe a -> Maybe a -> Bool # (<=) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool # (>=) :: Maybe a -> Maybe a -> Bool # max :: Maybe a -> Maybe a -> Maybe a # min :: Maybe a -> Maybe a -> Maybe a #
Integral a => Ord (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods compare :: Ratio a -> Ratio a -> Ordering # (<) :: Ratio a -> Ratio a -> Bool # (<=) :: Ratio a -> Ratio a -> Bool # (>) :: Ratio a -> Ratio a -> Bool # (>=) :: Ratio a -> Ratio a -> Bool # max :: Ratio a -> Ratio a -> Ratio a # min :: Ratio a -> Ratio a -> Ratio a #
Ord (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods compare :: Ptr a -> Ptr a -> Ordering # (<) :: Ptr a -> Ptr a -> Bool # (<=) :: Ptr a -> Ptr a -> Bool # (>) :: Ptr a -> Ptr a -> Bool # (>=) :: Ptr a -> Ptr a -> Bool # max :: Ptr a -> Ptr a -> Ptr a # min :: Ptr a -> Ptr a -> Ptr a #
Ord (FunPtr a)
Instance details Defined in GHC.Ptr Methods compare :: FunPtr a -> FunPtr a -> Ordering # (<) :: FunPtr a -> FunPtr a -> Bool # (<=) :: FunPtr a -> FunPtr a -> Bool # (>) :: FunPtr a -> FunPtr a -> Bool # (>=) :: FunPtr a -> FunPtr a -> Bool # max :: FunPtr a -> FunPtr a -> FunPtr a # min :: FunPtr a -> FunPtr a -> FunPtr a #
Ord p => Ord (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: Par1 p -> Par1 p -> Ordering # (<) :: Par1 p -> Par1 p -> Bool # (<=) :: Par1 p -> Par1 p -> Bool # (>) :: Par1 p -> Par1 p -> Bool # (>=) :: Par1 p -> Par1 p -> Bool # max :: Par1 p -> Par1 p -> Par1 p # min :: Par1 p -> Par1 p -> Par1 p #
Ord a => Ord (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapNum a -> WrapNum a -> Ordering # (<) :: WrapNum a -> WrapNum a -> Bool # (<=) :: WrapNum a -> WrapNum a -> Bool # (>) :: WrapNum a -> WrapNum a -> Bool # (>=) :: WrapNum a -> WrapNum a -> Bool # max :: WrapNum a -> WrapNum a -> WrapNum a # min :: WrapNum a -> WrapNum a -> WrapNum a #
Ord a => Ord (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapFractional a -> WrapFractional a -> Ordering # (<) :: WrapFractional a -> WrapFractional a -> Bool # (<=) :: WrapFractional a -> WrapFractional a -> Bool # (>) :: WrapFractional a -> WrapFractional a -> Bool # (>=) :: WrapFractional a -> WrapFractional a -> Bool # max :: WrapFractional a -> WrapFractional a -> WrapFractional a # min :: WrapFractional a -> WrapFractional a -> WrapFractional a #
Ord a => Ord (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapIntegral a -> WrapIntegral a -> Ordering # (<) :: WrapIntegral a -> WrapIntegral a -> Bool # (<=) :: WrapIntegral a -> WrapIntegral a -> Bool # (>) :: WrapIntegral a -> WrapIntegral a -> Bool # (>=) :: WrapIntegral a -> WrapIntegral a -> Bool # max :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # min :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
Ord a => Ord (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapAlgebra a -> WrapAlgebra a -> Ordering # (<) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (<=) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (>) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (>=) :: WrapAlgebra a -> WrapAlgebra a -> Bool # max :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # min :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
Ord a => Ord (Add a)
Instance details Defined in AlgebraicPrelude Methods compare :: Add a -> Add a -> Ordering # (<) :: Add a -> Add a -> Bool # (<=) :: Add a -> Add a -> Bool # (>) :: Add a -> Add a -> Bool # (>=) :: Add a -> Add a -> Bool # max :: Add a -> Add a -> Add a # min :: Add a -> Add a -> Add a #
Ord a => Ord (Mult a)
Instance details Defined in AlgebraicPrelude Methods compare :: Mult a -> Mult a -> Ordering # (<) :: Mult a -> Mult a -> Bool # (<=) :: Mult a -> Mult a -> Bool # (>) :: Mult a -> Mult a -> Bool # (>=) :: Mult a -> Mult a -> Bool # max :: Mult a -> Mult a -> Mult a # min :: Mult a -> Mult a -> Mult a #
(Ord d, GCDDomain d) => Ord (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods compare :: Fraction d -> Fraction d -> Ordering # (<) :: Fraction d -> Fraction d -> Bool # (<=) :: Fraction d -> Fraction d -> Bool # (>) :: Fraction d -> Fraction d -> Bool # (>=) :: Fraction d -> Fraction d -> Bool # max :: Fraction d -> Fraction d -> Fraction d # min :: Fraction d -> Fraction d -> Fraction d #
Ord a => Ord (Vector a)
Instance details Defined in Data.Vector Methods compare :: Vector a -> Vector a -> Ordering # (<) :: Vector a -> Vector a -> Bool # (<=) :: Vector a -> Vector a -> Bool # (>) :: Vector a -> Vector a -> Bool # (>=) :: Vector a -> Vector a -> Bool # max :: Vector a -> Vector a -> Vector a # min :: Vector a -> Vector a -> Vector a #
Ord a => Ord (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods compare :: HashSet a -> HashSet a -> Ordering # (<) :: HashSet a -> HashSet a -> Bool # (<=) :: HashSet a -> HashSet a -> Bool # (>) :: HashSet a -> HashSet a -> Bool # (>=) :: HashSet a -> HashSet a -> Bool # max :: HashSet a -> HashSet a -> HashSet a # min :: HashSet a -> HashSet a -> HashSet a #
Ord a => Ord (Set a)
Instance details Defined in Data.Set.Internal Methods compare :: Set a -> Set a -> Ordering # (<) :: Set a -> Set a -> Bool # (<=) :: Set a -> Set a -> Bool # (>) :: Set a -> Set a -> Bool # (>=) :: Set a -> Set a -> Bool # max :: Set a -> Set a -> Set a # min :: Set a -> Set a -> Set a #
Ord a => Ord (Seq a)
Instance details Defined in Data.Sequence.Internal Methods compare :: Seq a -> Seq a -> Ordering # (<) :: Seq a -> Seq a -> Bool # (<=) :: Seq a -> Seq a -> Bool # (>) :: Seq a -> Seq a -> Bool # (>=) :: Seq a -> Seq a -> Bool # max :: Seq a -> Seq a -> Seq a # min :: Seq a -> Seq a -> Seq a #
Ord a => Ord (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods compare :: IntMap a -> IntMap a -> Ordering # (<) :: IntMap a -> IntMap a -> Bool # (<=) :: IntMap a -> IntMap a -> Bool # (>) :: IntMap a -> IntMap a -> Bool # (>=) :: IntMap a -> IntMap a -> Bool # max :: IntMap a -> IntMap a -> IntMap a # min :: IntMap a -> IntMap a -> IntMap a #
Ord a => Ord (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods compare :: Down a -> Down a -> Ordering # (<) :: Down a -> Down a -> Bool # (<=) :: Down a -> Down a -> Bool # (>) :: Down a -> Down a -> Bool # (>=) :: Down a -> Down a -> Bool # max :: Down a -> Down a -> Down a # min :: Down a -> Down a -> Down a #
Ord a => Ord (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Min a -> Min a -> Ordering # (<) :: Min a -> Min a -> Bool # (<=) :: Min a -> Min a -> Bool # (>) :: Min a -> Min a -> Bool # (>=) :: Min a -> Min a -> Bool # max :: Min a -> Min a -> Min a # min :: Min a -> Min a -> Min a #
Ord a => Ord (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Max a -> Max a -> Ordering # (<) :: Max a -> Max a -> Bool # (<=) :: Max a -> Max a -> Bool # (>) :: Max a -> Max a -> Bool # (>=) :: Max a -> Max a -> Bool # max :: Max a -> Max a -> Max a # min :: Max a -> Max a -> Max a #
Ord a => Ord (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Ord a => Ord (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Ord m => Ord (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #
Ord a => Ord (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Option a -> Option a -> Ordering # (<) :: Option a -> Option a -> Bool # (<=) :: Option a -> Option a -> Bool # (>) :: Option a -> Option a -> Bool # (>=) :: Option a -> Option a -> Bool # max :: Option a -> Option a -> Option a # min :: Option a -> Option a -> Option a #
Ord a => Ord (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods compare :: ZipList a -> ZipList a -> Ordering # (<) :: ZipList a -> ZipList a -> Bool # (<=) :: ZipList a -> ZipList a -> Bool # (>) :: ZipList a -> ZipList a -> Bool # (>=) :: ZipList a -> ZipList a -> Bool # max :: ZipList a -> ZipList a -> ZipList a # min :: ZipList a -> ZipList a -> ZipList a #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering # (<) :: Identity a -> Identity a -> Bool # (<=) :: Identity a -> Identity a -> Bool # (>) :: Identity a -> Identity a -> Bool # (>=) :: Identity a -> Identity a -> Bool # max :: Identity a -> Identity a -> Identity a # min :: Identity a -> Identity a -> Identity a #
Ord a => Ord (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Ord a => Ord (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Ord a => Ord (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Ord a => Ord (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Ord a => Ord (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering # (<) :: Product a -> Product a -> Bool # (<=) :: Product a -> Product a -> Bool # (>) :: Product a -> Product a -> Bool # (>=) :: Product a -> Product a -> Bool # max :: Product a -> Product a -> Product a # min :: Product a -> Product a -> Product a #
Ord a => Ord (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering # (<) :: NonEmpty a -> NonEmpty a -> Bool # (<=) :: NonEmpty a -> NonEmpty a -> Bool # (>) :: NonEmpty a -> NonEmpty a -> Bool # (>=) :: NonEmpty a -> NonEmpty a -> Bool # max :: NonEmpty a -> NonEmpty a -> NonEmpty a # min :: NonEmpty a -> NonEmpty a -> NonEmpty a #
Ord a => Ord (Tree a)	Since: containers-0.6.5
Instance details Defined in Data.Tree Methods compare :: Tree a -> Tree a -> Ordering # (<) :: Tree a -> Tree a -> Bool # (<=) :: Tree a -> Tree a -> Bool # (>) :: Tree a -> Tree a -> Bool # (>=) :: Tree a -> Tree a -> Bool # max :: Tree a -> Tree a -> Tree a # min :: Tree a -> Tree a -> Tree a #
Ord a => Ord (ViewL a)
Instance details Defined in Data.Sequence.Internal Methods compare :: ViewL a -> ViewL a -> Ordering # (<) :: ViewL a -> ViewL a -> Bool # (<=) :: ViewL a -> ViewL a -> Bool # (>) :: ViewL a -> ViewL a -> Bool # (>=) :: ViewL a -> ViewL a -> Bool # max :: ViewL a -> ViewL a -> ViewL a # min :: ViewL a -> ViewL a -> ViewL a #
Ord a => Ord (ViewR a)
Instance details Defined in Data.Sequence.Internal Methods compare :: ViewR a -> ViewR a -> Ordering # (<) :: ViewR a -> ViewR a -> Bool # (<=) :: ViewR a -> ViewR a -> Bool # (>) :: ViewR a -> ViewR a -> Bool # (>=) :: ViewR a -> ViewR a -> Bool # max :: ViewR a -> ViewR a -> ViewR a # min :: ViewR a -> ViewR a -> ViewR a #
Ord (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods compare :: Ordinal n -> Ordinal n -> Ordering # (<) :: Ordinal n -> Ordinal n -> Bool # (<=) :: Ordinal n -> Ordinal n -> Bool # (>) :: Ordinal n -> Ordinal n -> Bool # (>=) :: Ordinal n -> Ordinal n -> Bool # max :: Ordinal n -> Ordinal n -> Ordinal n # min :: Ordinal n -> Ordinal n -> Ordinal n #
Ord ord => Ord (Graded ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Graded ord -> Graded ord -> Ordering # (<) :: Graded ord -> Graded ord -> Bool # (<=) :: Graded ord -> Graded ord -> Bool # (>) :: Graded ord -> Graded ord -> Bool # (>=) :: Graded ord -> Graded ord -> Bool # max :: Graded ord -> Graded ord -> Graded ord # min :: Graded ord -> Graded ord -> Graded ord #
Ord (IsTrue b)
Instance details Defined in Proof.Propositional Methods compare :: IsTrue b -> IsTrue b -> Ordering # (<) :: IsTrue b -> IsTrue b -> Bool # (<=) :: IsTrue b -> IsTrue b -> Bool # (>) :: IsTrue b -> IsTrue b -> Bool # (>=) :: IsTrue b -> IsTrue b -> Bool # max :: IsTrue b -> IsTrue b -> IsTrue b # min :: IsTrue b -> IsTrue b -> IsTrue b #
Ord (SNat n)
Instance details Defined in Data.Type.Natural.Core Methods compare :: SNat n -> SNat n -> Ordering # (<) :: SNat n -> SNat n -> Bool # (<=) :: SNat n -> SNat n -> Bool # (>) :: SNat n -> SNat n -> Bool # (>=) :: SNat n -> SNat n -> Bool # max :: SNat n -> SNat n -> SNat n # min :: SNat n -> SNat n -> SNat n #
Ord r => Ord (Scalar r)
Instance details Defined in Algebra.Scalar Methods compare :: Scalar r -> Scalar r -> Ordering # (<) :: Scalar r -> Scalar r -> Bool # (<=) :: Scalar r -> Scalar r -> Bool # (>) :: Scalar r -> Scalar r -> Bool # (>=) :: Scalar r -> Scalar r -> Bool # max :: Scalar r -> Scalar r -> Scalar r # min :: Scalar r -> Scalar r -> Scalar r #
(Prim a, Ord a) => Ord (Vector a)
Instance details Defined in Data.Vector.Primitive Methods compare :: Vector a -> Vector a -> Ordering # (<) :: Vector a -> Vector a -> Bool # (<=) :: Vector a -> Vector a -> Bool # (>) :: Vector a -> Vector a -> Bool # (>=) :: Vector a -> Vector a -> Bool # max :: Vector a -> Vector a -> Vector a # min :: Vector a -> Vector a -> Vector a #
(Storable a, Ord a) => Ord (Vector a)
Instance details Defined in Data.Vector.Storable Methods compare :: Vector a -> Vector a -> Ordering # (<) :: Vector a -> Vector a -> Bool # (<=) :: Vector a -> Vector a -> Bool # (>) :: Vector a -> Vector a -> Bool # (>=) :: Vector a -> Vector a -> Bool # max :: Vector a -> Vector a -> Vector a # min :: Vector a -> Vector a -> Vector a #
Ord a => Ord (Array a)
Instance details Defined in Data.Primitive.Array Methods compare :: Array a -> Array a -> Ordering # (<) :: Array a -> Array a -> Bool # (<=) :: Array a -> Array a -> Bool # (>) :: Array a -> Array a -> Bool # (>=) :: Array a -> Array a -> Bool # max :: Array a -> Array a -> Array a # min :: Array a -> Array a -> Array a #
(Ord a, Prim a) => Ord (PrimArray a)
Instance details Defined in Data.Primitive.PrimArray Methods compare :: PrimArray a -> PrimArray a -> Ordering # (<) :: PrimArray a -> PrimArray a -> Bool # (<=) :: PrimArray a -> PrimArray a -> Bool # (>) :: PrimArray a -> PrimArray a -> Bool # (>=) :: PrimArray a -> PrimArray a -> Bool # max :: PrimArray a -> PrimArray a -> PrimArray a # min :: PrimArray a -> PrimArray a -> PrimArray a #
Ord a => Ord (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods compare :: SmallArray a -> SmallArray a -> Ordering # (<) :: SmallArray a -> SmallArray a -> Bool # (<=) :: SmallArray a -> SmallArray a -> Bool # (>) :: SmallArray a -> SmallArray a -> Bool # (>=) :: SmallArray a -> SmallArray a -> Bool # max :: SmallArray a -> SmallArray a -> SmallArray a # min :: SmallArray a -> SmallArray a -> SmallArray a #
Ord a => Ord (Hashed a)
Instance details Defined in Data.Hashable.Class Methods compare :: Hashed a -> Hashed a -> Ordering # (<) :: Hashed a -> Hashed a -> Bool # (<=) :: Hashed a -> Hashed a -> Bool # (>) :: Hashed a -> Hashed a -> Bool # (>=) :: Hashed a -> Hashed a -> Bool # max :: Hashed a -> Hashed a -> Hashed a # min :: Hashed a -> Hashed a -> Hashed a #
Ord g => Ord (StateGen g)
Instance details Defined in System.Random.Internal Methods compare :: StateGen g -> StateGen g -> Ordering # (<) :: StateGen g -> StateGen g -> Bool # (<=) :: StateGen g -> StateGen g -> Bool # (>) :: StateGen g -> StateGen g -> Bool # (>=) :: StateGen g -> StateGen g -> Bool # max :: StateGen g -> StateGen g -> StateGen g # min :: StateGen g -> StateGen g -> StateGen g #
Ord g => Ord (AtomicGen g)
Instance details Defined in System.Random.Stateful Methods compare :: AtomicGen g -> AtomicGen g -> Ordering # (<) :: AtomicGen g -> AtomicGen g -> Bool # (<=) :: AtomicGen g -> AtomicGen g -> Bool # (>) :: AtomicGen g -> AtomicGen g -> Bool # (>=) :: AtomicGen g -> AtomicGen g -> Bool # max :: AtomicGen g -> AtomicGen g -> AtomicGen g # min :: AtomicGen g -> AtomicGen g -> AtomicGen g #
Ord g => Ord (IOGen g)
Instance details Defined in System.Random.Stateful Methods compare :: IOGen g -> IOGen g -> Ordering # (<) :: IOGen g -> IOGen g -> Bool # (<=) :: IOGen g -> IOGen g -> Bool # (>) :: IOGen g -> IOGen g -> Bool # (>=) :: IOGen g -> IOGen g -> Bool # max :: IOGen g -> IOGen g -> IOGen g # min :: IOGen g -> IOGen g -> IOGen g #
Ord g => Ord (STGen g)
Instance details Defined in System.Random.Stateful Methods compare :: STGen g -> STGen g -> Ordering # (<) :: STGen g -> STGen g -> Bool # (<=) :: STGen g -> STGen g -> Bool # (>) :: STGen g -> STGen g -> Bool # (>=) :: STGen g -> STGen g -> Bool # max :: STGen g -> STGen g -> STGen g # min :: STGen g -> STGen g -> STGen g #
Ord s => Ord (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: SugarStrategy s -> SugarStrategy s -> Ordering # (<) :: SugarStrategy s -> SugarStrategy s -> Bool # (<=) :: SugarStrategy s -> SugarStrategy s -> Bool # (>) :: SugarStrategy s -> SugarStrategy s -> Bool # (>=) :: SugarStrategy s -> SugarStrategy s -> Bool # max :: SugarStrategy s -> SugarStrategy s -> SugarStrategy s # min :: SugarStrategy s -> SugarStrategy s -> SugarStrategy s #
(Ord r, DecidableZero r) => Ord (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods compare :: Unipol r -> Unipol r -> Ordering # (<) :: Unipol r -> Unipol r -> Bool # (<=) :: Unipol r -> Unipol r -> Bool # (>) :: Unipol r -> Unipol r -> Bool # (>=) :: Unipol r -> Unipol r -> Bool # max :: Unipol r -> Unipol r -> Unipol r # min :: Unipol r -> Unipol r -> Unipol r #
Ord (Heap a)
Instance details Defined in Data.Heap Methods compare :: Heap a -> Heap a -> Ordering # (<) :: Heap a -> Heap a -> Bool # (<=) :: Heap a -> Heap a -> Bool # (>) :: Heap a -> Heap a -> Bool # (>=) :: Heap a -> Heap a -> Bool # max :: Heap a -> Heap a -> Heap a # min :: Heap a -> Heap a -> Heap a #
(Ord a, Ord b) => Ord (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering # (<) :: Either a b -> Either a b -> Bool # (<=) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool # (>=) :: Either a b -> Either a b -> Bool # max :: Either a b -> Either a b -> Either a b # min :: Either a b -> Either a b -> Either a b #
Ord (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: V1 p -> V1 p -> Ordering # (<) :: V1 p -> V1 p -> Bool # (<=) :: V1 p -> V1 p -> Bool # (>) :: V1 p -> V1 p -> Bool # (>=) :: V1 p -> V1 p -> Bool # max :: V1 p -> V1 p -> V1 p # min :: V1 p -> V1 p -> V1 p #
Ord (U1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: U1 p -> U1 p -> Ordering # (<) :: U1 p -> U1 p -> Bool # (<=) :: U1 p -> U1 p -> Bool # (>) :: U1 p -> U1 p -> Bool # (>=) :: U1 p -> U1 p -> Bool # max :: U1 p -> U1 p -> U1 p # min :: U1 p -> U1 p -> U1 p #
Ord (TypeRep a)	Since: base-4.4.0.0
Instance details Defined in Data.Typeable.Internal Methods compare :: TypeRep a -> TypeRep a -> Ordering # (<) :: TypeRep a -> TypeRep a -> Bool # (<=) :: TypeRep a -> TypeRep a -> Bool # (>) :: TypeRep a -> TypeRep a -> Bool # (>=) :: TypeRep a -> TypeRep a -> Bool # max :: TypeRep a -> TypeRep a -> TypeRep a # min :: TypeRep a -> TypeRep a -> TypeRep a #
(Ord a, Ord b) => Ord (a, b)
Instance details Defined in GHC.Classes Methods compare :: (a, b) -> (a, b) -> Ordering # (<) :: (a, b) -> (a, b) -> Bool # (<=) :: (a, b) -> (a, b) -> Bool # (>) :: (a, b) -> (a, b) -> Bool # (>=) :: (a, b) -> (a, b) -> Bool # max :: (a, b) -> (a, b) -> (a, b) # min :: (a, b) -> (a, b) -> (a, b) #
(Ord k, Ord v) => Ord (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods compare :: HashMap k v -> HashMap k v -> Ordering # (<) :: HashMap k v -> HashMap k v -> Bool # (<=) :: HashMap k v -> HashMap k v -> Bool # (>) :: HashMap k v -> HashMap k v -> Bool # (>=) :: HashMap k v -> HashMap k v -> Bool # max :: HashMap k v -> HashMap k v -> HashMap k v # min :: HashMap k v -> HashMap k v -> HashMap k v #
(Ord k, Ord v) => Ord (Map k v)
Instance details Defined in Data.Map.Internal Methods compare :: Map k v -> Map k v -> Ordering # (<) :: Map k v -> Map k v -> Bool # (<=) :: Map k v -> Map k v -> Bool # (>) :: Map k v -> Map k v -> Bool # (>=) :: Map k v -> Map k v -> Bool # max :: Map k v -> Map k v -> Map k v # min :: Map k v -> Map k v -> Map k v #
(Ix ix, Ord e, IArray UArray e) => Ord (UArray ix e)
Instance details Defined in Data.Array.Base Methods compare :: UArray ix e -> UArray ix e -> Ordering # (<) :: UArray ix e -> UArray ix e -> Bool # (<=) :: UArray ix e -> UArray ix e -> Bool # (>) :: UArray ix e -> UArray ix e -> Bool # (>=) :: UArray ix e -> UArray ix e -> Bool # max :: UArray ix e -> UArray ix e -> UArray ix e # min :: UArray ix e -> UArray ix e -> UArray ix e #
(Ix i, Ord e) => Ord (Array i e)	Since: base-2.1
Instance details Defined in GHC.Arr Methods compare :: Array i e -> Array i e -> Ordering # (<) :: Array i e -> Array i e -> Bool # (<=) :: Array i e -> Array i e -> Bool # (>) :: Array i e -> Array i e -> Bool # (>=) :: Array i e -> Array i e -> Bool # max :: Array i e -> Array i e -> Array i e # min :: Array i e -> Array i e -> Array i e #
Ord (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods compare :: Fixed a -> Fixed a -> Ordering # (<) :: Fixed a -> Fixed a -> Bool # (<=) :: Fixed a -> Fixed a -> Bool # (>) :: Fixed a -> Fixed a -> Bool # (>=) :: Fixed a -> Fixed a -> Bool # max :: Fixed a -> Fixed a -> Fixed a # min :: Fixed a -> Fixed a -> Fixed a #
Ord a => Ord (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Arg a b -> Arg a b -> Ordering # (<) :: Arg a b -> Arg a b -> Bool # (<=) :: Arg a b -> Arg a b -> Bool # (>) :: Arg a b -> Arg a b -> Bool # (>=) :: Arg a b -> Arg a b -> Bool # max :: Arg a b -> Arg a b -> Arg a b # min :: Arg a b -> Arg a b -> Arg a b #
Ord (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods compare :: Proxy s -> Proxy s -> Ordering # (<) :: Proxy s -> Proxy s -> Bool # (<=) :: Proxy s -> Proxy s -> Bool # (>) :: Proxy s -> Proxy s -> Bool # (>=) :: Proxy s -> Proxy s -> Bool # max :: Proxy s -> Proxy s -> Proxy s # min :: Proxy s -> Proxy s -> Proxy s #
(Ord1 m, Ord a) => Ord (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods compare :: MaybeT m a -> MaybeT m a -> Ordering # (<) :: MaybeT m a -> MaybeT m a -> Bool # (<=) :: MaybeT m a -> MaybeT m a -> Bool # (>) :: MaybeT m a -> MaybeT m a -> Bool # (>=) :: MaybeT m a -> MaybeT m a -> Bool # max :: MaybeT m a -> MaybeT m a -> MaybeT m a # min :: MaybeT m a -> MaybeT m a -> MaybeT m a #
(Ord1 m, Ord a) => Ord (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods compare :: ListT m a -> ListT m a -> Ordering # (<) :: ListT m a -> ListT m a -> Bool # (<=) :: ListT m a -> ListT m a -> Bool # (>) :: ListT m a -> ListT m a -> Bool # (>=) :: ListT m a -> ListT m a -> Bool # max :: ListT m a -> ListT m a -> ListT m a # min :: ListT m a -> ListT m a -> ListT m a #
(Ord i, Ord a) => Ord (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods compare :: Level i a -> Level i a -> Ordering # (<) :: Level i a -> Level i a -> Bool # (<=) :: Level i a -> Level i a -> Bool # (>) :: Level i a -> Level i a -> Bool # (>=) :: Level i a -> Level i a -> Bool # max :: Level i a -> Level i a -> Level i a # min :: Level i a -> Level i a -> Level i a #
(Ord a, Ord b) => Ord (These a b)
Instance details Defined in Data.These Methods compare :: These a b -> These a b -> Ordering # (<) :: These a b -> These a b -> Bool # (<=) :: These a b -> These a b -> Bool # (>) :: These a b -> These a b -> Bool # (>=) :: These a b -> These a b -> Bool # max :: These a b -> These a b -> These a b # min :: These a b -> These a b -> These a b #
(Ord1 w, Ord a) => Ord (CoiterT w a)
Instance details Defined in Control.Comonad.Trans.Coiter Methods compare :: CoiterT w a -> CoiterT w a -> Ordering # (<) :: CoiterT w a -> CoiterT w a -> Bool # (<=) :: CoiterT w a -> CoiterT w a -> Bool # (>) :: CoiterT w a -> CoiterT w a -> Bool # (>=) :: CoiterT w a -> CoiterT w a -> Bool # max :: CoiterT w a -> CoiterT w a -> CoiterT w a # min :: CoiterT w a -> CoiterT w a -> CoiterT w a #
(Ord1 m, Ord a) => Ord (IterT m a)
Instance details Defined in Control.Monad.Trans.Iter Methods compare :: IterT m a -> IterT m a -> Ordering # (<) :: IterT m a -> IterT m a -> Bool # (<=) :: IterT m a -> IterT m a -> Bool # (>) :: IterT m a -> IterT m a -> Bool # (>=) :: IterT m a -> IterT m a -> Bool # max :: IterT m a -> IterT m a -> IterT m a # min :: IterT m a -> IterT m a -> IterT m a #
(Ord1 f, Ord a) => Ord (Cofree f a)
Instance details Defined in Control.Comonad.Cofree Methods compare :: Cofree f a -> Cofree f a -> Ordering # (<) :: Cofree f a -> Cofree f a -> Bool # (<=) :: Cofree f a -> Cofree f a -> Bool # (>) :: Cofree f a -> Cofree f a -> Bool # (>=) :: Cofree f a -> Cofree f a -> Bool # max :: Cofree f a -> Cofree f a -> Cofree f a # min :: Cofree f a -> Cofree f a -> Cofree f a #
(Ord1 f, Ord a) => Ord (Free f a)
Instance details Defined in Control.Monad.Free Methods compare :: Free f a -> Free f a -> Ordering # (<) :: Free f a -> Free f a -> Bool # (<=) :: Free f a -> Free f a -> Bool # (>) :: Free f a -> Free f a -> Bool # (>=) :: Free f a -> Free f a -> Bool # max :: Free f a -> Free f a -> Free f a # min :: Free f a -> Free f a -> Free f a #
(Ord1 f, Ord a) => Ord (Yoneda f a)
Instance details Defined in Data.Functor.Yoneda Methods compare :: Yoneda f a -> Yoneda f a -> Ordering # (<) :: Yoneda f a -> Yoneda f a -> Bool # (<=) :: Yoneda f a -> Yoneda f a -> Bool # (>) :: Yoneda f a -> Yoneda f a -> Bool # (>=) :: Yoneda f a -> Yoneda f a -> Bool # max :: Yoneda f a -> Yoneda f a -> Yoneda f a # min :: Yoneda f a -> Yoneda f a -> Yoneda f a #
Ord p => Ord (Entry p a)
Instance details Defined in Data.Heap Methods compare :: Entry p a -> Entry p a -> Ordering # (<) :: Entry p a -> Entry p a -> Bool # (<=) :: Entry p a -> Entry p a -> Bool # (>) :: Entry p a -> Entry p a -> Bool # (>=) :: Entry p a -> Entry p a -> Bool # max :: Entry p a -> Entry p a -> Entry p a # min :: Entry p a -> Entry p a -> Entry p a #
(Wraps vars poly, Ord poly) => Ord (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods compare :: LabPolynomial poly vars -> LabPolynomial poly vars -> Ordering # (<) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (<=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (>) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (>=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # max :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # min :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
Ord (f p) => Ord (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: Rec1 f p -> Rec1 f p -> Ordering # (<) :: Rec1 f p -> Rec1 f p -> Bool # (<=) :: Rec1 f p -> Rec1 f p -> Bool # (>) :: Rec1 f p -> Rec1 f p -> Bool # (>=) :: Rec1 f p -> Rec1 f p -> Bool # max :: Rec1 f p -> Rec1 f p -> Rec1 f p # min :: Rec1 f p -> Rec1 f p -> Rec1 f p #
Ord (URec (Ptr ()) p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #
Ord (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering # (<) :: URec Char p -> URec Char p -> Bool # (<=) :: URec Char p -> URec Char p -> Bool # (>) :: URec Char p -> URec Char p -> Bool # (>=) :: URec Char p -> URec Char p -> Bool # max :: URec Char p -> URec Char p -> URec Char p # min :: URec Char p -> URec Char p -> URec Char p #
Ord (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Ord (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Ord (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering # (<) :: URec Word p -> URec Word p -> Bool # (<=) :: URec Word p -> URec Word p -> Bool # (>) :: URec Word p -> URec Word p -> Bool # (>=) :: URec Word p -> URec Word p -> Bool # max :: URec Word p -> URec Word p -> URec Word p # min :: URec Word p -> URec Word p -> URec Word p #
(Ord a, Ord b, Ord c) => Ord (a, b, c)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c) -> (a, b, c) -> Ordering # (<) :: (a, b, c) -> (a, b, c) -> Bool # (<=) :: (a, b, c) -> (a, b, c) -> Bool # (>) :: (a, b, c) -> (a, b, c) -> Bool # (>=) :: (a, b, c) -> (a, b, c) -> Bool # max :: (a, b, c) -> (a, b, c) -> (a, b, c) # min :: (a, b, c) -> (a, b, c) -> (a, b, c) #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Ord (f a) => Ord (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods compare :: Ap f a -> Ap f a -> Ordering # (<) :: Ap f a -> Ap f a -> Bool # (<=) :: Ap f a -> Ap f a -> Bool # (>) :: Ap f a -> Ap f a -> Bool # (>=) :: Ap f a -> Ap f a -> Bool # max :: Ap f a -> Ap f a -> Ap f a # min :: Ap f a -> Ap f a -> Ap f a #
Ord (f a) => Ord (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering # (<) :: Alt f a -> Alt f a -> Bool # (<=) :: Alt f a -> Alt f a -> Bool # (>) :: Alt f a -> Alt f a -> Bool # (>=) :: Alt f a -> Alt f a -> Bool # max :: Alt f a -> Alt f a -> Alt f a # min :: Alt f a -> Alt f a -> Alt f a #
Ord (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~: b) -> (a :~: b) -> Ordering # (<) :: (a :~: b) -> (a :~: b) -> Bool # (<=) :: (a :~: b) -> (a :~: b) -> Bool # (>) :: (a :~: b) -> (a :~: b) -> Bool # (>=) :: (a :~: b) -> (a :~: b) -> Bool # max :: (a :~: b) -> (a :~: b) -> a :~: b # min :: (a :~: b) -> (a :~: b) -> a :~: b #
(Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods compare :: ExceptT e m a -> ExceptT e m a -> Ordering # (<) :: ExceptT e m a -> ExceptT e m a -> Bool # (<=) :: ExceptT e m a -> ExceptT e m a -> Bool # (>) :: ExceptT e m a -> ExceptT e m a -> Bool # (>=) :: ExceptT e m a -> ExceptT e m a -> Bool # max :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a # min :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #
(Eq (Monomial n), IsOrder n name) => Ord (OrderedMonomial name n)	Special ordering for ordered-monomials.
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: OrderedMonomial name n -> OrderedMonomial name n -> Ordering # (<) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (<=) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (>) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (>=) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # max :: OrderedMonomial name n -> OrderedMonomial name n -> OrderedMonomial name n # min :: OrderedMonomial name n -> OrderedMonomial name n -> OrderedMonomial name n #
(Ord1 f, Ord a) => Ord (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods compare :: IdentityT f a -> IdentityT f a -> Ordering # (<) :: IdentityT f a -> IdentityT f a -> Bool # (<=) :: IdentityT f a -> IdentityT f a -> Bool # (>) :: IdentityT f a -> IdentityT f a -> Bool # (>=) :: IdentityT f a -> IdentityT f a -> Bool # max :: IdentityT f a -> IdentityT f a -> IdentityT f a # min :: IdentityT f a -> IdentityT f a -> IdentityT f a #
(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods compare :: ErrorT e m a -> ErrorT e m a -> Ordering # (<) :: ErrorT e m a -> ErrorT e m a -> Bool # (<=) :: ErrorT e m a -> ErrorT e m a -> Bool # (>) :: ErrorT e m a -> ErrorT e m a -> Bool # (>=) :: ErrorT e m a -> ErrorT e m a -> Bool # max :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a # min :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #
(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods compare :: WriterT w m a -> WriterT w m a -> Ordering # (<) :: WriterT w m a -> WriterT w m a -> Bool # (<=) :: WriterT w m a -> WriterT w m a -> Bool # (>) :: WriterT w m a -> WriterT w m a -> Bool # (>=) :: WriterT w m a -> WriterT w m a -> Bool # max :: WriterT w m a -> WriterT w m a -> WriterT w m a # min :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods compare :: WriterT w m a -> WriterT w m a -> Ordering # (<) :: WriterT w m a -> WriterT w m a -> Bool # (<=) :: WriterT w m a -> WriterT w m a -> Bool # (>) :: WriterT w m a -> WriterT w m a -> Bool # (>=) :: WriterT w m a -> WriterT w m a -> Bool # max :: WriterT w m a -> WriterT w m a -> WriterT w m a # min :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Ord1 f, Ord a) => Ord (Reverse f a)
Instance details Defined in Data.Functor.Reverse Methods compare :: Reverse f a -> Reverse f a -> Ordering # (<) :: Reverse f a -> Reverse f a -> Bool # (<=) :: Reverse f a -> Reverse f a -> Bool # (>) :: Reverse f a -> Reverse f a -> Bool # (>=) :: Reverse f a -> Reverse f a -> Bool # max :: Reverse f a -> Reverse f a -> Reverse f a # min :: Reverse f a -> Reverse f a -> Reverse f a #
Ord a => Ord (Constant a b)
Instance details Defined in Data.Functor.Constant Methods compare :: Constant a b -> Constant a b -> Ordering # (<) :: Constant a b -> Constant a b -> Bool # (<=) :: Constant a b -> Constant a b -> Bool # (>) :: Constant a b -> Constant a b -> Bool # (>=) :: Constant a b -> Constant a b -> Bool # max :: Constant a b -> Constant a b -> Constant a b # min :: Constant a b -> Constant a b -> Constant a b #
(Ord1 f, Ord a) => Ord (Backwards f a)
Instance details Defined in Control.Applicative.Backwards Methods compare :: Backwards f a -> Backwards f a -> Ordering # (<) :: Backwards f a -> Backwards f a -> Bool # (<=) :: Backwards f a -> Backwards f a -> Bool # (>) :: Backwards f a -> Backwards f a -> Bool # (>=) :: Backwards f a -> Backwards f a -> Bool # max :: Backwards f a -> Backwards f a -> Backwards f a # min :: Backwards f a -> Backwards f a -> Backwards f a #
Ord (f a) => Ord (Sized f n a)
Instance details Defined in Data.Sized.Internal Methods compare :: Sized f n a -> Sized f n a -> Ordering # (<) :: Sized f n a -> Sized f n a -> Bool # (<=) :: Sized f n a -> Sized f n a -> Bool # (>) :: Sized f n a -> Sized f n a -> Bool # (>=) :: Sized f n a -> Sized f n a -> Bool # max :: Sized f n a -> Sized f n a -> Sized f n a # min :: Sized f n a -> Sized f n a -> Sized f n a #
Ord (f a) => Ord (Flipped f a n)
Instance details Defined in Data.Sized.Flipped Methods compare :: Flipped f a n -> Flipped f a n -> Ordering # (<) :: Flipped f a n -> Flipped f a n -> Bool # (<=) :: Flipped f a n -> Flipped f a n -> Bool # (>) :: Flipped f a n -> Flipped f a n -> Bool # (>=) :: Flipped f a n -> Flipped f a n -> Bool # max :: Flipped f a n -> Flipped f a n -> Flipped f a n # min :: Flipped f a n -> Flipped f a n -> Flipped f a n #
Ord (f a) => Ord (CApp f a)
Instance details Defined in Control.Subcategory.Applicative Methods compare :: CApp f a -> CApp f a -> Ordering # (<) :: CApp f a -> CApp f a -> Bool # (<=) :: CApp f a -> CApp f a -> Bool # (>) :: CApp f a -> CApp f a -> Bool # (>=) :: CApp f a -> CApp f a -> Bool # max :: CApp f a -> CApp f a -> CApp f a # min :: CApp f a -> CApp f a -> CApp f a #
Ord b => Ord (Tagged s b)
Instance details Defined in Data.Tagged Methods compare :: Tagged s b -> Tagged s b -> Ordering # (<) :: Tagged s b -> Tagged s b -> Bool # (<=) :: Tagged s b -> Tagged s b -> Bool # (>) :: Tagged s b -> Tagged s b -> Bool # (>=) :: Tagged s b -> Tagged s b -> Bool # max :: Tagged s b -> Tagged s b -> Tagged s b # min :: Tagged s b -> Tagged s b -> Tagged s b #
Ord (w (CofreeF f a (CofreeT f w a))) => Ord (CofreeT f w a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods compare :: CofreeT f w a -> CofreeT f w a -> Ordering # (<) :: CofreeT f w a -> CofreeT f w a -> Bool # (<=) :: CofreeT f w a -> CofreeT f w a -> Bool # (>) :: CofreeT f w a -> CofreeT f w a -> Bool # (>=) :: CofreeT f w a -> CofreeT f w a -> Bool # max :: CofreeT f w a -> CofreeT f w a -> CofreeT f w a # min :: CofreeT f w a -> CofreeT f w a -> CofreeT f w a #
(Ord a, Ord (f b)) => Ord (CofreeF f a b)
Instance details Defined in Control.Comonad.Trans.Cofree Methods compare :: CofreeF f a b -> CofreeF f a b -> Ordering # (<) :: CofreeF f a b -> CofreeF f a b -> Bool # (<=) :: CofreeF f a b -> CofreeF f a b -> Bool # (>) :: CofreeF f a b -> CofreeF f a b -> Bool # (>=) :: CofreeF f a b -> CofreeF f a b -> Bool # max :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b # min :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b #
Ord (p (Fix p a) a) => Ord (Fix p a)
Instance details Defined in Data.Bifunctor.Fix Methods compare :: Fix p a -> Fix p a -> Ordering # (<) :: Fix p a -> Fix p a -> Bool # (<=) :: Fix p a -> Fix p a -> Bool # (>) :: Fix p a -> Fix p a -> Bool # (>=) :: Fix p a -> Fix p a -> Bool # max :: Fix p a -> Fix p a -> Fix p a # min :: Fix p a -> Fix p a -> Fix p a #
(Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a)
Instance details Defined in Control.Monad.Trans.Free Methods compare :: FreeT f m a -> FreeT f m a -> Ordering # (<) :: FreeT f m a -> FreeT f m a -> Bool # (<=) :: FreeT f m a -> FreeT f m a -> Bool # (>) :: FreeT f m a -> FreeT f m a -> Bool # (>=) :: FreeT f m a -> FreeT f m a -> Bool # max :: FreeT f m a -> FreeT f m a -> FreeT f m a # min :: FreeT f m a -> FreeT f m a -> FreeT f m a #
(Ord a, Ord (f b)) => Ord (FreeF f a b)
Instance details Defined in Control.Monad.Trans.Free Methods compare :: FreeF f a b -> FreeF f a b -> Ordering # (<) :: FreeF f a b -> FreeF f a b -> Bool # (<=) :: FreeF f a b -> FreeF f a b -> Bool # (>) :: FreeF f a b -> FreeF f a b -> Bool # (>=) :: FreeF f a b -> FreeF f a b -> Bool # max :: FreeF f a b -> FreeF f a b -> FreeF f a b # min :: FreeF f a b -> FreeF f a b -> FreeF f a b #
Ord (p a a) => Ord (Join p a)
Instance details Defined in Data.Bifunctor.Join Methods compare :: Join p a -> Join p a -> Ordering # (<) :: Join p a -> Join p a -> Bool # (<=) :: Join p a -> Join p a -> Bool # (>) :: Join p a -> Join p a -> Bool # (>=) :: Join p a -> Join p a -> Bool # max :: Join p a -> Join p a -> Join p a # min :: Join p a -> Join p a -> Join p a #
Ord (f a) => Ord (CZippy f a)
Instance details Defined in Control.Subcategory.Zip Methods compare :: CZippy f a -> CZippy f a -> Ordering # (<) :: CZippy f a -> CZippy f a -> Bool # (<=) :: CZippy f a -> CZippy f a -> Bool # (>) :: CZippy f a -> CZippy f a -> Bool # (>=) :: CZippy f a -> CZippy f a -> Bool # max :: CZippy f a -> CZippy f a -> CZippy f a # min :: CZippy f a -> CZippy f a -> CZippy f a #
Ord c => Ord (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: K1 i c p -> K1 i c p -> Ordering # (<) :: K1 i c p -> K1 i c p -> Bool # (<=) :: K1 i c p -> K1 i c p -> Bool # (>) :: K1 i c p -> K1 i c p -> Bool # (>=) :: K1 i c p -> K1 i c p -> Bool # max :: K1 i c p -> K1 i c p -> K1 i c p # min :: K1 i c p -> K1 i c p -> K1 i c p #
(Ord (f p), Ord (g p)) => Ord ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :+: g) p -> (f :+: g) p -> Ordering # (<) :: (f :+: g) p -> (f :+: g) p -> Bool # (<=) :: (f :+: g) p -> (f :+: g) p -> Bool # (>) :: (f :+: g) p -> (f :+: g) p -> Bool # (>=) :: (f :+: g) p -> (f :+: g) p -> Bool # max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p # min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #
(Ord (f p), Ord (g p)) => Ord ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :: g) p -> (f :: g) p -> Ordering # (<) :: (f :: g) p -> (f :: g) p -> Bool # (<=) :: (f :: g) p -> (f :: g) p -> Bool # (>) :: (f :: g) p -> (f :: g) p -> Bool # (>=) :: (f :: g) p -> (f :: g) p -> Bool # max :: (f :: g) p -> (f :: g) p -> (f :: g) p # min :: (f :: g) p -> (f :: g) p -> (f :: g) p #
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering # (<) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (>) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #
(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # max :: Product f g a -> Product f g a -> Product f g a # min :: Product f g a -> Product f g a -> Product f g a #
(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods compare :: Sum f g a -> Sum f g a -> Ordering # (<) :: Sum f g a -> Sum f g a -> Bool # (<=) :: Sum f g a -> Sum f g a -> Bool # (>) :: Sum f g a -> Sum f g a -> Bool # (>=) :: Sum f g a -> Sum f g a -> Bool # max :: Sum f g a -> Sum f g a -> Sum f g a # min :: Sum f g a -> Sum f g a -> Sum f g a #
Ord (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~~: b) -> (a :~~: b) -> Ordering # (<) :: (a :~~: b) -> (a :~~: b) -> Bool # (<=) :: (a :~~: b) -> (a :~~: b) -> Bool # (>) :: (a :~~: b) -> (a :~~: b) -> Bool # (>=) :: (a :~~: b) -> (a :~~: b) -> Bool # max :: (a :~~: b) -> (a :~~: b) -> a :~~: b # min :: (a :~~: b) -> (a :~~: b) -> a :~~: b #
(CoeffRing r, IsOrder n ord, Ord r) => Ord (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods compare :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Ordering # (<) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (<=) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (>) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (>=) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # max :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # min :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #
Ord (f p) => Ord (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: M1 i c f p -> M1 i c f p -> Ordering # (<) :: M1 i c f p -> M1 i c f p -> Bool # (<=) :: M1 i c f p -> M1 i c f p -> Bool # (>) :: M1 i c f p -> M1 i c f p -> Bool # (>=) :: M1 i c f p -> M1 i c f p -> Bool # max :: M1 i c f p -> M1 i c f p -> M1 i c f p # min :: M1 i c f p -> M1 i c f p -> M1 i c f p #
Ord (f (g p)) => Ord ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :.: g) p -> (f :.: g) p -> Ordering # (<) :: (f :.: g) p -> (f :.: g) p -> Bool # (<=) :: (f :.: g) p -> (f :.: g) p -> Bool # (>) :: (f :.: g) p -> (f :.: g) p -> Bool # (>=) :: (f :.: g) p -> (f :.: g) p -> Bool # max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #
(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods compare :: Compose f g a -> Compose f g a -> Ordering # (<) :: Compose f g a -> Compose f g a -> Bool # (<=) :: Compose f g a -> Compose f g a -> Bool # (>) :: Compose f g a -> Compose f g a -> Bool # (>=) :: Compose f g a -> Compose f g a -> Bool # max :: Compose f g a -> Compose f g a -> Compose f g a # min :: Compose f g a -> Compose f g a -> Compose f g a #
Ord (f a) => Ord (Clown f a b)
Instance details Defined in Data.Bifunctor.Clown Methods compare :: Clown f a b -> Clown f a b -> Ordering # (<) :: Clown f a b -> Clown f a b -> Bool # (<=) :: Clown f a b -> Clown f a b -> Bool # (>) :: Clown f a b -> Clown f a b -> Bool # (>=) :: Clown f a b -> Clown f a b -> Bool # max :: Clown f a b -> Clown f a b -> Clown f a b # min :: Clown f a b -> Clown f a b -> Clown f a b #
Ord (p b a) => Ord (Flip p a b)
Instance details Defined in Data.Bifunctor.Flip Methods compare :: Flip p a b -> Flip p a b -> Ordering # (<) :: Flip p a b -> Flip p a b -> Bool # (<=) :: Flip p a b -> Flip p a b -> Bool # (>) :: Flip p a b -> Flip p a b -> Bool # (>=) :: Flip p a b -> Flip p a b -> Bool # max :: Flip p a b -> Flip p a b -> Flip p a b # min :: Flip p a b -> Flip p a b -> Flip p a b #
Ord (g b) => Ord (Joker g a b)
Instance details Defined in Data.Bifunctor.Joker Methods compare :: Joker g a b -> Joker g a b -> Ordering # (<) :: Joker g a b -> Joker g a b -> Bool # (<=) :: Joker g a b -> Joker g a b -> Bool # (>) :: Joker g a b -> Joker g a b -> Bool # (>=) :: Joker g a b -> Joker g a b -> Bool # max :: Joker g a b -> Joker g a b -> Joker g a b # min :: Joker g a b -> Joker g a b -> Joker g a b #
Ord (p a b) => Ord (WrappedBifunctor p a b)
Instance details Defined in Data.Bifunctor.Wrapped Methods compare :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Ordering # (<) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # (<=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # (>) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # (>=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool # max :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> WrappedBifunctor p a b # min :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> WrappedBifunctor p a b #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #
(Ord (f a b), Ord (g a b)) => Ord (Product f g a b)
Instance details Defined in Data.Bifunctor.Product Methods compare :: Product f g a b -> Product f g a b -> Ordering # (<) :: Product f g a b -> Product f g a b -> Bool # (<=) :: Product f g a b -> Product f g a b -> Bool # (>) :: Product f g a b -> Product f g a b -> Bool # (>=) :: Product f g a b -> Product f g a b -> Bool # max :: Product f g a b -> Product f g a b -> Product f g a b # min :: Product f g a b -> Product f g a b -> Product f g a b #
(Ord (p a b), Ord (q a b)) => Ord (Sum p q a b)
Instance details Defined in Data.Bifunctor.Sum Methods compare :: Sum p q a b -> Sum p q a b -> Ordering # (<) :: Sum p q a b -> Sum p q a b -> Bool # (<=) :: Sum p q a b -> Sum p q a b -> Bool # (>) :: Sum p q a b -> Sum p q a b -> Bool # (>=) :: Sum p q a b -> Sum p q a b -> Bool # max :: Sum p q a b -> Sum p q a b -> Sum p q a b # min :: Sum p q a b -> Sum p q a b -> Sum p q a b #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #
Ord (f (p a b)) => Ord (Tannen f p a b)
Instance details Defined in Data.Bifunctor.Tannen Methods compare :: Tannen f p a b -> Tannen f p a b -> Ordering # (<) :: Tannen f p a b -> Tannen f p a b -> Bool # (<=) :: Tannen f p a b -> Tannen f p a b -> Bool # (>) :: Tannen f p a b -> Tannen f p a b -> Bool # (>=) :: Tannen f p a b -> Tannen f p a b -> Bool # max :: Tannen f p a b -> Tannen f p a b -> Tannen f p a b # min :: Tannen f p a b -> Tannen f p a b -> Tannen f p a b #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #
Ord (p (f a) (g b)) => Ord (Biff p f g a b)
Instance details Defined in Data.Bifunctor.Biff Methods compare :: Biff p f g a b -> Biff p f g a b -> Ordering # (<) :: Biff p f g a b -> Biff p f g a b -> Bool # (<=) :: Biff p f g a b -> Biff p f g a b -> Bool # (>) :: Biff p f g a b -> Biff p f g a b -> Bool # (>=) :: Biff p f g a b -> Biff p f g a b -> Bool # max :: Biff p f g a b -> Biff p f g a b -> Biff p f g a b # min :: Biff p f g a b -> Biff p f g a b -> Biff p f g a b #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)
Instance details Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Read a where #

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.

readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.

As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec #

Arguments

:: Int	the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> ReadS a

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

(x,"") is an element of (readsPrec d (showsPrec d x "")).

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a] #

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Instances details

Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Read Char	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char # readList :: ReadS [Char] # readPrec :: ReadPrec Char # readListPrec :: ReadPrec [Char] #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Read Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int8 # readList :: ReadS [Int8] # readPrec :: ReadPrec Int8 # readListPrec :: ReadPrec [Int8] #
Read Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int16 # readList :: ReadS [Int16] # readPrec :: ReadPrec Int16 # readListPrec :: ReadPrec [Int16] #
Read Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int32 # readList :: ReadS [Int32] # readPrec :: ReadPrec Int32 # readListPrec :: ReadPrec [Int32] #
Read Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int64 # readList :: ReadS [Int64] # readPrec :: ReadPrec Int64 # readListPrec :: ReadPrec [Int64] #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Read Word	Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word # readList :: ReadS [Word] # readPrec :: ReadPrec Word # readListPrec :: ReadPrec [Word] #
Read Word8	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word8 # readList :: ReadS [Word8] # readPrec :: ReadPrec Word8 # readListPrec :: ReadPrec [Word8] #
Read Word16	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word16 # readList :: ReadS [Word16] # readPrec :: ReadPrec Word16 # readListPrec :: ReadPrec [Word16] #
Read Word32	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word32 # readList :: ReadS [Word32] # readPrec :: ReadPrec Word32 # readListPrec :: ReadPrec [Word32] #
Read Word64	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word64 # readList :: ReadS [Word64] # readPrec :: ReadPrec Word64 # readListPrec :: ReadPrec [Word64] #
Read ()	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS () # readList :: ReadS [()] # readPrec :: ReadPrec () # readListPrec :: ReadPrec [()] #
Read IntSet
Instance details Defined in Data.IntSet.Internal Methods readsPrec :: Int -> ReadS IntSet # readList :: ReadS [IntSet] # readPrec :: ReadPrec IntSet # readListPrec :: ReadPrec [IntSet] #
Read ByteString
Instance details Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] #
Read Void	Reading a `Void` value is always a parse error, considering `Void` as a data type with no constructors. Since: base-4.8.0.0
Instance details Defined in Data.Void Methods readsPrec :: Int -> ReadS Void # readList :: ReadS [Void] # readPrec :: ReadPrec Void # readListPrec :: ReadPrec [Void] #
Read Version	Since: base-2.1
Instance details Defined in Data.Version Methods readsPrec :: Int -> ReadS Version # readList :: ReadS [Version] # readPrec :: ReadPrec Version # readListPrec :: ReadPrec [Version] #
Read CDev
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CDev # readList :: ReadS [CDev] # readPrec :: ReadPrec CDev # readListPrec :: ReadPrec [CDev] #
Read CIno
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CIno # readList :: ReadS [CIno] # readPrec :: ReadPrec CIno # readListPrec :: ReadPrec [CIno] #
Read CMode
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CMode # readList :: ReadS [CMode] # readPrec :: ReadPrec CMode # readListPrec :: ReadPrec [CMode] #
Read COff
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS COff # readList :: ReadS [COff] # readPrec :: ReadPrec COff # readListPrec :: ReadPrec [COff] #
Read CPid
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CPid # readList :: ReadS [CPid] # readPrec :: ReadPrec CPid # readListPrec :: ReadPrec [CPid] #
Read CSsize
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CSsize # readList :: ReadS [CSsize] # readPrec :: ReadPrec CSsize # readListPrec :: ReadPrec [CSsize] #
Read CGid
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CGid # readList :: ReadS [CGid] # readPrec :: ReadPrec CGid # readListPrec :: ReadPrec [CGid] #
Read CNlink
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CNlink # readList :: ReadS [CNlink] # readPrec :: ReadPrec CNlink # readListPrec :: ReadPrec [CNlink] #
Read CUid
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CUid # readList :: ReadS [CUid] # readPrec :: ReadPrec CUid # readListPrec :: ReadPrec [CUid] #
Read CCc
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CCc # readList :: ReadS [CCc] # readPrec :: ReadPrec CCc # readListPrec :: ReadPrec [CCc] #
Read CSpeed
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CSpeed # readList :: ReadS [CSpeed] # readPrec :: ReadPrec CSpeed # readListPrec :: ReadPrec [CSpeed] #
Read CTcflag
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CTcflag # readList :: ReadS [CTcflag] # readPrec :: ReadPrec CTcflag # readListPrec :: ReadPrec [CTcflag] #
Read CRLim
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CRLim # readList :: ReadS [CRLim] # readPrec :: ReadPrec CRLim # readListPrec :: ReadPrec [CRLim] #
Read CBlkSize
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CBlkSize # readList :: ReadS [CBlkSize] # readPrec :: ReadPrec CBlkSize # readListPrec :: ReadPrec [CBlkSize] #
Read CBlkCnt
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CBlkCnt # readList :: ReadS [CBlkCnt] # readPrec :: ReadPrec CBlkCnt # readListPrec :: ReadPrec [CBlkCnt] #
Read CClockId
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CClockId # readList :: ReadS [CClockId] # readPrec :: ReadPrec CClockId # readListPrec :: ReadPrec [CClockId] #
Read CFsBlkCnt
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CFsBlkCnt # readList :: ReadS [CFsBlkCnt] # readPrec :: ReadPrec CFsBlkCnt # readListPrec :: ReadPrec [CFsBlkCnt] #
Read CFsFilCnt
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CFsFilCnt # readList :: ReadS [CFsFilCnt] # readPrec :: ReadPrec CFsFilCnt # readListPrec :: ReadPrec [CFsFilCnt] #
Read CId
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CId # readList :: ReadS [CId] # readPrec :: ReadPrec CId # readListPrec :: ReadPrec [CId] #
Read CKey
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CKey # readList :: ReadS [CKey] # readPrec :: ReadPrec CKey # readListPrec :: ReadPrec [CKey] #
Read CSocklen
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CSocklen # readList :: ReadS [CSocklen] # readPrec :: ReadPrec CSocklen # readListPrec :: ReadPrec [CSocklen] #
Read CNfds
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS CNfds # readList :: ReadS [CNfds] # readPrec :: ReadPrec CNfds # readListPrec :: ReadPrec [CNfds] #
Read Fd
Instance details Defined in System.Posix.Types Methods readsPrec :: Int -> ReadS Fd # readList :: ReadS [Fd] # readPrec :: ReadPrec Fd # readListPrec :: ReadPrec [Fd] #
Read ExitCode
Instance details Defined in GHC.IO.Exception Methods readsPrec :: Int -> ReadS ExitCode # readList :: ReadS [ExitCode] # readPrec :: ReadPrec ExitCode # readListPrec :: ReadPrec [ExitCode] #
Read BufferMode	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode # readList :: ReadS [BufferMode] # readPrec :: ReadPrec BufferMode # readListPrec :: ReadPrec [BufferMode] #
Read Newline	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS Newline # readList :: ReadS [Newline] # readPrec :: ReadPrec Newline # readListPrec :: ReadPrec [Newline] #
Read NewlineMode	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode # readList :: ReadS [NewlineMode] # readPrec :: ReadPrec NewlineMode # readListPrec :: ReadPrec [NewlineMode] #
Read All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Read Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Read Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Fixity # readList :: ReadS [Fixity] # readPrec :: ReadPrec Fixity # readListPrec :: ReadPrec [Fixity] #
Read Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # readPrec :: ReadPrec Associativity # readListPrec :: ReadPrec [Associativity] #
Read SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # readPrec :: ReadPrec SourceUnpackedness # readListPrec :: ReadPrec [SourceUnpackedness] #
Read SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # readPrec :: ReadPrec SourceStrictness # readListPrec :: ReadPrec [SourceStrictness] #
Read DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # readPrec :: ReadPrec DecidedStrictness # readListPrec :: ReadPrec [DecidedStrictness] #
Read SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods readsPrec :: Int -> ReadS SomeSymbol # readList :: ReadS [SomeSymbol] # readPrec :: ReadPrec SomeSymbol # readListPrec :: ReadPrec [SomeSymbol] #
Read SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods readsPrec :: Int -> ReadS SomeNat # readList :: ReadS [SomeNat] # readPrec :: ReadPrec SomeNat # readListPrec :: ReadPrec [SomeNat] #
Read CChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CChar # readList :: ReadS [CChar] # readPrec :: ReadPrec CChar # readListPrec :: ReadPrec [CChar] #
Read CSChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSChar # readList :: ReadS [CSChar] # readPrec :: ReadPrec CSChar # readListPrec :: ReadPrec [CSChar] #
Read CUChar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUChar # readList :: ReadS [CUChar] # readPrec :: ReadPrec CUChar # readListPrec :: ReadPrec [CUChar] #
Read CShort
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CShort # readList :: ReadS [CShort] # readPrec :: ReadPrec CShort # readListPrec :: ReadPrec [CShort] #
Read CUShort
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUShort # readList :: ReadS [CUShort] # readPrec :: ReadPrec CUShort # readListPrec :: ReadPrec [CUShort] #
Read CInt
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CInt # readList :: ReadS [CInt] # readPrec :: ReadPrec CInt # readListPrec :: ReadPrec [CInt] #
Read CUInt
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUInt # readList :: ReadS [CUInt] # readPrec :: ReadPrec CUInt # readListPrec :: ReadPrec [CUInt] #
Read CLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CLong # readList :: ReadS [CLong] # readPrec :: ReadPrec CLong # readListPrec :: ReadPrec [CLong] #
Read CULong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CULong # readList :: ReadS [CULong] # readPrec :: ReadPrec CULong # readListPrec :: ReadPrec [CULong] #
Read CLLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CLLong # readList :: ReadS [CLLong] # readPrec :: ReadPrec CLLong # readListPrec :: ReadPrec [CLLong] #
Read CULLong
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CULLong # readList :: ReadS [CULLong] # readPrec :: ReadPrec CULLong # readListPrec :: ReadPrec [CULLong] #
Read CBool
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CBool # readList :: ReadS [CBool] # readPrec :: ReadPrec CBool # readListPrec :: ReadPrec [CBool] #
Read CFloat
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CFloat # readList :: ReadS [CFloat] # readPrec :: ReadPrec CFloat # readListPrec :: ReadPrec [CFloat] #
Read CDouble
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CDouble # readList :: ReadS [CDouble] # readPrec :: ReadPrec CDouble # readListPrec :: ReadPrec [CDouble] #
Read CPtrdiff
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CPtrdiff # readList :: ReadS [CPtrdiff] # readPrec :: ReadPrec CPtrdiff # readListPrec :: ReadPrec [CPtrdiff] #
Read CSize
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSize # readList :: ReadS [CSize] # readPrec :: ReadPrec CSize # readListPrec :: ReadPrec [CSize] #
Read CWchar
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CWchar # readList :: ReadS [CWchar] # readPrec :: ReadPrec CWchar # readListPrec :: ReadPrec [CWchar] #
Read CSigAtomic
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSigAtomic # readList :: ReadS [CSigAtomic] # readPrec :: ReadPrec CSigAtomic # readListPrec :: ReadPrec [CSigAtomic] #
Read CClock
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CClock # readList :: ReadS [CClock] # readPrec :: ReadPrec CClock # readListPrec :: ReadPrec [CClock] #
Read CTime
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CTime # readList :: ReadS [CTime] # readPrec :: ReadPrec CTime # readListPrec :: ReadPrec [CTime] #
Read CUSeconds
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUSeconds # readList :: ReadS [CUSeconds] # readPrec :: ReadPrec CUSeconds # readListPrec :: ReadPrec [CUSeconds] #
Read CSUSeconds
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSUSeconds # readList :: ReadS [CSUSeconds] # readPrec :: ReadPrec CSUSeconds # readListPrec :: ReadPrec [CSUSeconds] #
Read CIntPtr
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CIntPtr # readList :: ReadS [CIntPtr] # readPrec :: ReadPrec CIntPtr # readListPrec :: ReadPrec [CIntPtr] #
Read CUIntPtr
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUIntPtr # readList :: ReadS [CUIntPtr] # readPrec :: ReadPrec CUIntPtr # readListPrec :: ReadPrec [CUIntPtr] #
Read CIntMax
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CIntMax # readList :: ReadS [CIntMax] # readPrec :: ReadPrec CIntMax # readListPrec :: ReadPrec [CIntMax] #
Read CUIntMax
Instance details Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CUIntMax # readList :: ReadS [CUIntMax] # readPrec :: ReadPrec CUIntMax # readListPrec :: ReadPrec [CUIntMax] #
Read Lexeme	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Lexeme # readList :: ReadS [Lexeme] # readPrec :: ReadPrec Lexeme # readListPrec :: ReadPrec [Lexeme] #
Read GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # readPrec :: ReadPrec GeneralCategory # readListPrec :: ReadPrec [GeneralCategory] #
Read ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # readPrec :: ReadPrec ShortByteString # readListPrec :: ReadPrec [ShortByteString] #
Read ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] #
Read WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods readsPrec :: Int -> ReadS WrapOrdering # readList :: ReadS [WrapOrdering] # readPrec :: ReadPrec WrapOrdering # readListPrec :: ReadPrec [WrapOrdering] #
Read ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods readsPrec :: Int -> ReadS ComplexBasis # readList :: ReadS [ComplexBasis] # readPrec :: ReadPrec ComplexBasis # readListPrec :: ReadPrec [ComplexBasis] #
Read DatatypeVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods readsPrec :: Int -> ReadS DatatypeVariant # readList :: ReadS [DatatypeVariant] # readPrec :: ReadPrec DatatypeVariant # readListPrec :: ReadPrec [DatatypeVariant] #
Read GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS GradedStrategy # readList :: ReadS [GradedStrategy] # readPrec :: ReadPrec GradedStrategy # readListPrec :: ReadPrec [GradedStrategy] #
Read GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS GrevlexStrategy # readList :: ReadS [GrevlexStrategy] # readPrec :: ReadPrec GrevlexStrategy # readListPrec :: ReadPrec [GrevlexStrategy] #
Read NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS NormalStrategy # readList :: ReadS [NormalStrategy] # readPrec :: ReadPrec NormalStrategy # readListPrec :: ReadPrec [NormalStrategy] #
Read a => Read [a]	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS [a] # readList :: ReadS [[a]] # readPrec :: ReadPrec [a] # readListPrec :: ReadPrec [[a]] #
Read a => Read (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) # readList :: ReadS [Maybe a] # readPrec :: ReadPrec (Maybe a) # readListPrec :: ReadPrec [Maybe a] #
(Integral a, Read a) => Read (Ratio a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Ratio a) # readList :: ReadS [Ratio a] # readPrec :: ReadPrec (Ratio a) # readListPrec :: ReadPrec [Ratio a] #
Read p => Read (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (Par1 p) # readList :: ReadS [Par1 p] # readPrec :: ReadPrec (Par1 p) # readListPrec :: ReadPrec [Par1 p] #
Read a => Read (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapNum a) # readList :: ReadS [WrapNum a] # readPrec :: ReadPrec (WrapNum a) # readListPrec :: ReadPrec [WrapNum a] #
Read a => Read (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapFractional a) # readList :: ReadS [WrapFractional a] # readPrec :: ReadPrec (WrapFractional a) # readListPrec :: ReadPrec [WrapFractional a] #
Read a => Read (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapIntegral a) # readList :: ReadS [WrapIntegral a] # readPrec :: ReadPrec (WrapIntegral a) # readListPrec :: ReadPrec [WrapIntegral a] #
Read a => Read (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapAlgebra a) # readList :: ReadS [WrapAlgebra a] # readPrec :: ReadPrec (WrapAlgebra a) # readListPrec :: ReadPrec [WrapAlgebra a] #
Read a => Read (Add a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (Add a) # readList :: ReadS [Add a] # readPrec :: ReadPrec (Add a) # readListPrec :: ReadPrec [Add a] #
Read a => Read (Mult a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (Mult a) # readList :: ReadS [Mult a] # readPrec :: ReadPrec (Mult a) # readListPrec :: ReadPrec [Mult a] #
Read a => Read (Vector a)
Instance details Defined in Data.Vector Methods readsPrec :: Int -> ReadS (Vector a) # readList :: ReadS [Vector a] # readPrec :: ReadPrec (Vector a) # readListPrec :: ReadPrec [Vector a] #
(Eq a, Hashable a, Read a) => Read (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods readsPrec :: Int -> ReadS (HashSet a) # readList :: ReadS [HashSet a] # readPrec :: ReadPrec (HashSet a) # readListPrec :: ReadPrec [HashSet a] #
(Read a, Ord a) => Read (Set a)
Instance details Defined in Data.Set.Internal Methods readsPrec :: Int -> ReadS (Set a) # readList :: ReadS [Set a] # readPrec :: ReadPrec (Set a) # readListPrec :: ReadPrec [Set a] #
Read a => Read (Seq a)
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (Seq a) # readList :: ReadS [Seq a] # readPrec :: ReadPrec (Seq a) # readListPrec :: ReadPrec [Seq a] #
Read e => Read (IntMap e)
Instance details Defined in Data.IntMap.Internal Methods readsPrec :: Int -> ReadS (IntMap e) # readList :: ReadS [IntMap e] # readPrec :: ReadPrec (IntMap e) # readListPrec :: ReadPrec [IntMap e] #
Read a => Read (Down a)	This instance would be equivalent to the derived instances of the `Down` newtype if the `getDown` field were removed Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods readsPrec :: Int -> ReadS (Down a) # readList :: ReadS [Down a] # readPrec :: ReadPrec (Down a) # readListPrec :: ReadPrec [Down a] #
Read a => Read (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
Read a => Read (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Min a) # readList :: ReadS [Min a] # readPrec :: ReadPrec (Min a) # readListPrec :: ReadPrec [Min a] #
Read a => Read (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Max a) # readList :: ReadS [Max a] # readPrec :: ReadPrec (Max a) # readListPrec :: ReadPrec [Max a] #
Read a => Read (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Read a => Read (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Read m => Read (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] #
Read a => Read (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Option a) # readList :: ReadS [Option a] # readPrec :: ReadPrec (Option a) # readListPrec :: ReadPrec [Option a] #
Read a => Read (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods readsPrec :: Int -> ReadS (ZipList a) # readList :: ReadS [ZipList a] # readPrec :: ReadPrec (ZipList a) # readListPrec :: ReadPrec [ZipList a] #
Read a => Read (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Read a => Read (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Read a => Read (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Read a => Read (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Read a => Read (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Read a => Read (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Read a => Read (NonEmpty a)	Since: base-4.11.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (NonEmpty a) # readList :: ReadS [NonEmpty a] # readPrec :: ReadPrec (NonEmpty a) # readListPrec :: ReadPrec [NonEmpty a] #
Read a => Read (Tree a)
Instance details Defined in Data.Tree Methods readsPrec :: Int -> ReadS (Tree a) # readList :: ReadS [Tree a] # readPrec :: ReadPrec (Tree a) # readListPrec :: ReadPrec [Tree a] #
Read a => Read (ViewL a)
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewL a) # readList :: ReadS [ViewL a] # readPrec :: ReadPrec (ViewL a) # readListPrec :: ReadPrec [ViewL a] #
Read a => Read (ViewR a)
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (ViewR a) # readList :: ReadS [ViewR a] # readPrec :: ReadPrec (ViewR a) # readListPrec :: ReadPrec [ViewR a] #
Read ord => Read (Graded ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods readsPrec :: Int -> ReadS (Graded ord) # readList :: ReadS [Graded ord] # readPrec :: ReadPrec (Graded ord) # readListPrec :: ReadPrec [Graded ord] #
Read (IsTrue 'True)
Instance details Defined in Proof.Propositional Methods readsPrec :: Int -> ReadS (IsTrue 'True) # readList :: ReadS [IsTrue 'True] # readPrec :: ReadPrec (IsTrue 'True) # readListPrec :: ReadPrec [IsTrue 'True] #
Read r => Read (Scalar r)
Instance details Defined in Algebra.Scalar Methods readsPrec :: Int -> ReadS (Scalar r) # readList :: ReadS [Scalar r] # readPrec :: ReadPrec (Scalar r) # readListPrec :: ReadPrec [Scalar r] #
Read a => Read (Complex a)
Instance details Defined in Numeric.Algebra.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
(Read a, Prim a) => Read (Vector a)
Instance details Defined in Data.Vector.Primitive Methods readsPrec :: Int -> ReadS (Vector a) # readList :: ReadS [Vector a] # readPrec :: ReadPrec (Vector a) # readListPrec :: ReadPrec [Vector a] #
(Read a, Storable a) => Read (Vector a)
Instance details Defined in Data.Vector.Storable Methods readsPrec :: Int -> ReadS (Vector a) # readList :: ReadS [Vector a] # readPrec :: ReadPrec (Vector a) # readListPrec :: ReadPrec [Vector a] #
Read a => Read (Array a)
Instance details Defined in Data.Primitive.Array Methods readsPrec :: Int -> ReadS (Array a) # readList :: ReadS [Array a] # readPrec :: ReadPrec (Array a) # readListPrec :: ReadPrec [Array a] #
Read a => Read (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods readsPrec :: Int -> ReadS (SmallArray a) # readList :: ReadS [SmallArray a] # readPrec :: ReadPrec (SmallArray a) # readListPrec :: ReadPrec [SmallArray a] #
Read s => Read (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS (SugarStrategy s) # readList :: ReadS [SugarStrategy s] # readPrec :: ReadPrec (SugarStrategy s) # readListPrec :: ReadPrec [SugarStrategy s] #
(Ord a, Read a) => Read (Heap a)
Instance details Defined in Data.Heap Methods readsPrec :: Int -> ReadS (Heap a) # readList :: ReadS [Heap a] # readPrec :: ReadPrec (Heap a) # readListPrec :: ReadPrec [Heap a] #
Read a => Read (Forest a)
Instance details Defined in Data.Heap Methods readsPrec :: Int -> ReadS (Forest a) # readList :: ReadS [Forest a] # readPrec :: ReadPrec (Forest a) # readListPrec :: ReadPrec [Forest a] #
Read a => Read (Tree a)
Instance details Defined in Data.Heap Methods readsPrec :: Int -> ReadS (Tree a) # readList :: ReadS [Tree a] # readPrec :: ReadPrec (Tree a) # readListPrec :: ReadPrec [Tree a] #
(Read a, Read b) => Read (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) # readList :: ReadS [Either a b] # readPrec :: ReadPrec (Either a b) # readListPrec :: ReadPrec [Either a b] #
Read (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (V1 p) # readList :: ReadS [V1 p] # readPrec :: ReadPrec (V1 p) # readListPrec :: ReadPrec [V1 p] #
Read (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (U1 p) # readList :: ReadS [U1 p] # readPrec :: ReadPrec (U1 p) # readListPrec :: ReadPrec [U1 p] #
(Read a, Read b) => Read (a, b)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b) # readList :: ReadS [(a, b)] # readPrec :: ReadPrec (a, b) # readListPrec :: ReadPrec [(a, b)] #
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e)
Instance details Defined in Data.HashMap.Internal Methods readsPrec :: Int -> ReadS (HashMap k e) # readList :: ReadS [HashMap k e] # readPrec :: ReadPrec (HashMap k e) # readListPrec :: ReadPrec [HashMap k e] #
(Ord k, Read k, Read e) => Read (Map k e)
Instance details Defined in Data.Map.Internal Methods readsPrec :: Int -> ReadS (Map k e) # readList :: ReadS [Map k e] # readPrec :: ReadPrec (Map k e) # readListPrec :: ReadPrec [Map k e] #
(Ix ix, Read ix, Read e, IArray UArray e) => Read (UArray ix e)
Instance details Defined in Data.Array.Base Methods readsPrec :: Int -> ReadS (UArray ix e) # readList :: ReadS [UArray ix e] # readPrec :: ReadPrec (UArray ix e) # readListPrec :: ReadPrec [UArray ix e] #
(Ix a, Read a, Read b) => Read (Array a b)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Array a b) # readList :: ReadS [Array a b] # readPrec :: ReadPrec (Array a b) # readListPrec :: ReadPrec [Array a b] #
HasResolution a => Read (Fixed a)	Since: base-4.3.0.0
Instance details Defined in Data.Fixed Methods readsPrec :: Int -> ReadS (Fixed a) # readList :: ReadS [Fixed a] # readPrec :: ReadPrec (Fixed a) # readListPrec :: ReadPrec [Fixed a] #
(Read a, Read b) => Read (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Arg a b) # readList :: ReadS [Arg a b] # readPrec :: ReadPrec (Arg a b) # readListPrec :: ReadPrec [Arg a b] #
Read (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods readsPrec :: Int -> ReadS (Proxy t) # readList :: ReadS [Proxy t] # readPrec :: ReadPrec (Proxy t) # readListPrec :: ReadPrec [Proxy t] #
(Read1 m, Read a) => Read (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods readsPrec :: Int -> ReadS (MaybeT m a) # readList :: ReadS [MaybeT m a] # readPrec :: ReadPrec (MaybeT m a) # readListPrec :: ReadPrec [MaybeT m a] #
(Read1 m, Read a) => Read (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods readsPrec :: Int -> ReadS (ListT m a) # readList :: ReadS [ListT m a] # readPrec :: ReadPrec (ListT m a) # readListPrec :: ReadPrec [ListT m a] #
(Read i, Read a) => Read (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods readsPrec :: Int -> ReadS (Level i a) # readList :: ReadS [Level i a] # readPrec :: ReadPrec (Level i a) # readListPrec :: ReadPrec [Level i a] #
(Read a, Read b) => Read (These a b)
Instance details Defined in Data.These Methods readsPrec :: Int -> ReadS (These a b) # readList :: ReadS [These a b] # readPrec :: ReadPrec (These a b) # readListPrec :: ReadPrec [These a b] #
(Read1 w, Read a) => Read (CoiterT w a)
Instance details Defined in Control.Comonad.Trans.Coiter Methods readsPrec :: Int -> ReadS (CoiterT w a) # readList :: ReadS [CoiterT w a] # readPrec :: ReadPrec (CoiterT w a) # readListPrec :: ReadPrec [CoiterT w a] #
(Read1 m, Read a) => Read (IterT m a)
Instance details Defined in Control.Monad.Trans.Iter Methods readsPrec :: Int -> ReadS (IterT m a) # readList :: ReadS [IterT m a] # readPrec :: ReadPrec (IterT m a) # readListPrec :: ReadPrec [IterT m a] #
(Read1 f, Read a) => Read (Cofree f a)
Instance details Defined in Control.Comonad.Cofree Methods readsPrec :: Int -> ReadS (Cofree f a) # readList :: ReadS [Cofree f a] # readPrec :: ReadPrec (Cofree f a) # readListPrec :: ReadPrec [Cofree f a] #
(Read1 f, Read a) => Read (Free f a)
Instance details Defined in Control.Monad.Free Methods readsPrec :: Int -> ReadS (Free f a) # readList :: ReadS [Free f a] # readPrec :: ReadPrec (Free f a) # readListPrec :: ReadPrec [Free f a] #
(Functor f, Read (f a)) => Read (Yoneda f a)
Instance details Defined in Data.Functor.Yoneda Methods readsPrec :: Int -> ReadS (Yoneda f a) # readList :: ReadS [Yoneda f a] # readPrec :: ReadPrec (Yoneda f a) # readListPrec :: ReadPrec [Yoneda f a] #
(Read p, Read a) => Read (Entry p a)
Instance details Defined in Data.Heap Methods readsPrec :: Int -> ReadS (Entry p a) # readList :: ReadS [Entry p a] # readPrec :: ReadPrec (Entry p a) # readListPrec :: ReadPrec [Entry p a] #
Read (f p) => Read (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (Rec1 f p) # readList :: ReadS [Rec1 f p] # readPrec :: ReadPrec (Rec1 f p) # readListPrec :: ReadPrec [Rec1 f p] #
(Read a, Read b, Read c) => Read (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c) # readList :: ReadS [(a, b, c)] # readPrec :: ReadPrec (a, b, c) # readListPrec :: ReadPrec [(a, b, c)] #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Read (f a) => Read (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Ap f a) # readList :: ReadS [Ap f a] # readPrec :: ReadPrec (Ap f a) # readListPrec :: ReadPrec [Ap f a] #
Read (f a) => Read (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) # readList :: ReadS [Alt f a] # readPrec :: ReadPrec (Alt f a) # readListPrec :: ReadPrec [Alt f a] #
a ~ b => Read (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~: b) # readList :: ReadS [a :~: b] # readPrec :: ReadPrec (a :~: b) # readListPrec :: ReadPrec [a :~: b] #
(Read e, Read1 m, Read a) => Read (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods readsPrec :: Int -> ReadS (ExceptT e m a) # readList :: ReadS [ExceptT e m a] # readPrec :: ReadPrec (ExceptT e m a) # readListPrec :: ReadPrec [ExceptT e m a] #
(Read1 f, Read a) => Read (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods readsPrec :: Int -> ReadS (IdentityT f a) # readList :: ReadS [IdentityT f a] # readPrec :: ReadPrec (IdentityT f a) # readListPrec :: ReadPrec [IdentityT f a] #
(Read e, Read1 m, Read a) => Read (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods readsPrec :: Int -> ReadS (ErrorT e m a) # readList :: ReadS [ErrorT e m a] # readPrec :: ReadPrec (ErrorT e m a) # readListPrec :: ReadPrec [ErrorT e m a] #
(Read w, Read1 m, Read a) => Read (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods readsPrec :: Int -> ReadS (WriterT w m a) # readList :: ReadS [WriterT w m a] # readPrec :: ReadPrec (WriterT w m a) # readListPrec :: ReadPrec [WriterT w m a] #
(Read w, Read1 m, Read a) => Read (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods readsPrec :: Int -> ReadS (WriterT w m a) # readList :: ReadS [WriterT w m a] # readPrec :: ReadPrec (WriterT w m a) # readListPrec :: ReadPrec [WriterT w m a] #
(Read1 f, Read a) => Read (Reverse f a)
Instance details Defined in Data.Functor.Reverse Methods readsPrec :: Int -> ReadS (Reverse f a) # readList :: ReadS [Reverse f a] # readPrec :: ReadPrec (Reverse f a) # readListPrec :: ReadPrec [Reverse f a] #
Read a => Read (Constant a b)
Instance details Defined in Data.Functor.Constant Methods readsPrec :: Int -> ReadS (Constant a b) # readList :: ReadS [Constant a b] # readPrec :: ReadPrec (Constant a b) # readListPrec :: ReadPrec [Constant a b] #
(Read1 f, Read a) => Read (Backwards f a)
Instance details Defined in Control.Applicative.Backwards Methods readsPrec :: Int -> ReadS (Backwards f a) # readList :: ReadS [Backwards f a] # readPrec :: ReadPrec (Backwards f a) # readListPrec :: ReadPrec [Backwards f a] #
Read (f a) => Read (CApp f a)
Instance details Defined in Control.Subcategory.Applicative Methods readsPrec :: Int -> ReadS (CApp f a) # readList :: ReadS [CApp f a] # readPrec :: ReadPrec (CApp f a) # readListPrec :: ReadPrec [CApp f a] #
Read b => Read (Tagged s b)
Instance details Defined in Data.Tagged Methods readsPrec :: Int -> ReadS (Tagged s b) # readList :: ReadS [Tagged s b] # readPrec :: ReadPrec (Tagged s b) # readListPrec :: ReadPrec [Tagged s b] #
Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods readsPrec :: Int -> ReadS (CofreeT f w a) # readList :: ReadS [CofreeT f w a] # readPrec :: ReadPrec (CofreeT f w a) # readListPrec :: ReadPrec [CofreeT f w a] #
(Read a, Read (f b)) => Read (CofreeF f a b)
Instance details Defined in Control.Comonad.Trans.Cofree Methods readsPrec :: Int -> ReadS (CofreeF f a b) # readList :: ReadS [CofreeF f a b] # readPrec :: ReadPrec (CofreeF f a b) # readListPrec :: ReadPrec [CofreeF f a b] #
Read (p (Fix p a) a) => Read (Fix p a)
Instance details Defined in Data.Bifunctor.Fix Methods readsPrec :: Int -> ReadS (Fix p a) # readList :: ReadS [Fix p a] # readPrec :: ReadPrec (Fix p a) # readListPrec :: ReadPrec [Fix p a] #
(Read1 f, Read1 m, Read a) => Read (FreeT f m a)
Instance details Defined in Control.Monad.Trans.Free Methods readsPrec :: Int -> ReadS (FreeT f m a) # readList :: ReadS [FreeT f m a] # readPrec :: ReadPrec (FreeT f m a) # readListPrec :: ReadPrec [FreeT f m a] #
(Read a, Read (f b)) => Read (FreeF f a b)
Instance details Defined in Control.Monad.Trans.Free Methods readsPrec :: Int -> ReadS (FreeF f a b) # readList :: ReadS [FreeF f a b] # readPrec :: ReadPrec (FreeF f a b) # readListPrec :: ReadPrec [FreeF f a b] #
Read (p a a) => Read (Join p a)
Instance details Defined in Data.Bifunctor.Join Methods readsPrec :: Int -> ReadS (Join p a) # readList :: ReadS [Join p a] # readPrec :: ReadPrec (Join p a) # readListPrec :: ReadPrec [Join p a] #
Read (f a) => Read (CZippy f a)
Instance details Defined in Control.Subcategory.Zip Methods readsPrec :: Int -> ReadS (CZippy f a) # readList :: ReadS [CZippy f a] # readPrec :: ReadPrec (CZippy f a) # readListPrec :: ReadPrec [CZippy f a] #
Read c => Read (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (K1 i c p) # readList :: ReadS [K1 i c p] # readPrec :: ReadPrec (K1 i c p) # readListPrec :: ReadPrec [K1 i c p] #
(Read (f p), Read (g p)) => Read ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :+: g) p) # readList :: ReadS [(f :+: g) p] # readPrec :: ReadPrec ((f :+: g) p) # readListPrec :: ReadPrec [(f :+: g) p] #
(Read (f p), Read (g p)) => Read ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :: g) p) # readList :: ReadS [(f :: g) p] # readPrec :: ReadPrec ((f :: g) p) # readListPrec :: ReadPrec [(f :: g) p] #
(Read a, Read b, Read c, Read d) => Read (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d) # readList :: ReadS [(a, b, c, d)] # readPrec :: ReadPrec (a, b, c, d) # readListPrec :: ReadPrec [(a, b, c, d)] #
(Read1 f, Read1 g, Read a) => Read (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods readsPrec :: Int -> ReadS (Product f g a) # readList :: ReadS [Product f g a] # readPrec :: ReadPrec (Product f g a) # readListPrec :: ReadPrec [Product f g a] #
(Read1 f, Read1 g, Read a) => Read (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods readsPrec :: Int -> ReadS (Sum f g a) # readList :: ReadS [Sum f g a] # readPrec :: ReadPrec (Sum f g a) # readListPrec :: ReadPrec [Sum f g a] #
a ~~ b => Read (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~~: b) # readList :: ReadS [a :~~: b] # readPrec :: ReadPrec (a :~~: b) # readListPrec :: ReadPrec [a :~~: b] #
Read (f p) => Read (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (M1 i c f p) # readList :: ReadS [M1 i c f p] # readPrec :: ReadPrec (M1 i c f p) # readListPrec :: ReadPrec [M1 i c f p] #
Read (f (g p)) => Read ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :.: g) p) # readList :: ReadS [(f :.: g) p] # readPrec :: ReadPrec ((f :.: g) p) # readListPrec :: ReadPrec [(f :.: g) p] #
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e) # readList :: ReadS [(a, b, c, d, e)] # readPrec :: ReadPrec (a, b, c, d, e) # readListPrec :: ReadPrec [(a, b, c, d, e)] #
(Read1 f, Read1 g, Read a) => Read (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods readsPrec :: Int -> ReadS (Compose f g a) # readList :: ReadS [Compose f g a] # readPrec :: ReadPrec (Compose f g a) # readListPrec :: ReadPrec [Compose f g a] #
Read (f a) => Read (Clown f a b)
Instance details Defined in Data.Bifunctor.Clown Methods readsPrec :: Int -> ReadS (Clown f a b) # readList :: ReadS [Clown f a b] # readPrec :: ReadPrec (Clown f a b) # readListPrec :: ReadPrec [Clown f a b] #
Read (p b a) => Read (Flip p a b)
Instance details Defined in Data.Bifunctor.Flip Methods readsPrec :: Int -> ReadS (Flip p a b) # readList :: ReadS [Flip p a b] # readPrec :: ReadPrec (Flip p a b) # readListPrec :: ReadPrec [Flip p a b] #
Read (g b) => Read (Joker g a b)
Instance details Defined in Data.Bifunctor.Joker Methods readsPrec :: Int -> ReadS (Joker g a b) # readList :: ReadS [Joker g a b] # readPrec :: ReadPrec (Joker g a b) # readListPrec :: ReadPrec [Joker g a b] #
Read (p a b) => Read (WrappedBifunctor p a b)
Instance details Defined in Data.Bifunctor.Wrapped Methods readsPrec :: Int -> ReadS (WrappedBifunctor p a b) # readList :: ReadS [WrappedBifunctor p a b] # readPrec :: ReadPrec (WrappedBifunctor p a b) # readListPrec :: ReadPrec [WrappedBifunctor p a b] #
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f) # readList :: ReadS [(a, b, c, d, e, f)] # readPrec :: ReadPrec (a, b, c, d, e, f) # readListPrec :: ReadPrec [(a, b, c, d, e, f)] #
(Read (f a b), Read (g a b)) => Read (Product f g a b)
Instance details Defined in Data.Bifunctor.Product Methods readsPrec :: Int -> ReadS (Product f g a b) # readList :: ReadS [Product f g a b] # readPrec :: ReadPrec (Product f g a b) # readListPrec :: ReadPrec [Product f g a b] #
(Read (p a b), Read (q a b)) => Read (Sum p q a b)
Instance details Defined in Data.Bifunctor.Sum Methods readsPrec :: Int -> ReadS (Sum p q a b) # readList :: ReadS [Sum p q a b] # readPrec :: ReadPrec (Sum p q a b) # readListPrec :: ReadPrec [Sum p q a b] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) # readList :: ReadS [(a, b, c, d, e, f, g)] # readPrec :: ReadPrec (a, b, c, d, e, f, g) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] #
Read (f (p a b)) => Read (Tannen f p a b)
Instance details Defined in Data.Bifunctor.Tannen Methods readsPrec :: Int -> ReadS (Tannen f p a b) # readList :: ReadS [Tannen f p a b] # readPrec :: ReadPrec (Tannen f p a b) # readListPrec :: ReadPrec [Tannen f p a b] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) # readList :: ReadS [(a, b, c, d, e, f, g, h)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) # readList :: ReadS [(a, b, c, d, e, f, g, h, i)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] #
Read (p (f a) (g b)) => Read (Biff p f g a b)
Instance details Defined in Data.Bifunctor.Biff Methods readsPrec :: Int -> ReadS (Biff p f g a b) # readList :: ReadS [Biff p f g a b] # readPrec :: ReadPrec (Biff p f g a b) # readListPrec :: ReadPrec [Biff p f g a b] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

class (Num a, Ord a) => Real a where #

Methods

toRational :: a -> Rational #

the rational equivalent of its real argument with full precision

Instances

Instances details

Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Real Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int8 -> Rational #
Real Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int16 -> Rational #
Real Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int32 -> Rational #
Real Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int64 -> Rational #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Real Word	Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational #
Real Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word8 -> Rational #
Real Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word16 -> Rational #
Real Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word32 -> Rational #
Real Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word64 -> Rational #
Real CDev
Instance details Defined in System.Posix.Types Methods toRational :: CDev -> Rational #
Real CIno
Instance details Defined in System.Posix.Types Methods toRational :: CIno -> Rational #
Real CMode
Instance details Defined in System.Posix.Types Methods toRational :: CMode -> Rational #
Real COff
Instance details Defined in System.Posix.Types Methods toRational :: COff -> Rational #
Real CPid
Instance details Defined in System.Posix.Types Methods toRational :: CPid -> Rational #
Real CSsize
Instance details Defined in System.Posix.Types Methods toRational :: CSsize -> Rational #
Real CGid
Instance details Defined in System.Posix.Types Methods toRational :: CGid -> Rational #
Real CNlink
Instance details Defined in System.Posix.Types Methods toRational :: CNlink -> Rational #
Real CUid
Instance details Defined in System.Posix.Types Methods toRational :: CUid -> Rational #
Real CCc
Instance details Defined in System.Posix.Types Methods toRational :: CCc -> Rational #
Real CSpeed
Instance details Defined in System.Posix.Types Methods toRational :: CSpeed -> Rational #
Real CTcflag
Instance details Defined in System.Posix.Types Methods toRational :: CTcflag -> Rational #
Real CRLim
Instance details Defined in System.Posix.Types Methods toRational :: CRLim -> Rational #
Real CBlkSize
Instance details Defined in System.Posix.Types Methods toRational :: CBlkSize -> Rational #
Real CBlkCnt
Instance details Defined in System.Posix.Types Methods toRational :: CBlkCnt -> Rational #
Real CClockId
Instance details Defined in System.Posix.Types Methods toRational :: CClockId -> Rational #
Real CFsBlkCnt
Instance details Defined in System.Posix.Types Methods toRational :: CFsBlkCnt -> Rational #
Real CFsFilCnt
Instance details Defined in System.Posix.Types Methods toRational :: CFsFilCnt -> Rational #
Real CId
Instance details Defined in System.Posix.Types Methods toRational :: CId -> Rational #
Real CKey
Instance details Defined in System.Posix.Types Methods toRational :: CKey -> Rational #
Real CSocklen
Instance details Defined in System.Posix.Types Methods toRational :: CSocklen -> Rational #
Real CNfds
Instance details Defined in System.Posix.Types Methods toRational :: CNfds -> Rational #
Real Fd
Instance details Defined in System.Posix.Types Methods toRational :: Fd -> Rational #
Real CChar
Instance details Defined in Foreign.C.Types Methods toRational :: CChar -> Rational #
Real CSChar
Instance details Defined in Foreign.C.Types Methods toRational :: CSChar -> Rational #
Real CUChar
Instance details Defined in Foreign.C.Types Methods toRational :: CUChar -> Rational #
Real CShort
Instance details Defined in Foreign.C.Types Methods toRational :: CShort -> Rational #
Real CUShort
Instance details Defined in Foreign.C.Types Methods toRational :: CUShort -> Rational #
Real CInt
Instance details Defined in Foreign.C.Types Methods toRational :: CInt -> Rational #
Real CUInt
Instance details Defined in Foreign.C.Types Methods toRational :: CUInt -> Rational #
Real CLong
Instance details Defined in Foreign.C.Types Methods toRational :: CLong -> Rational #
Real CULong
Instance details Defined in Foreign.C.Types Methods toRational :: CULong -> Rational #
Real CLLong
Instance details Defined in Foreign.C.Types Methods toRational :: CLLong -> Rational #
Real CULLong
Instance details Defined in Foreign.C.Types Methods toRational :: CULLong -> Rational #
Real CBool
Instance details Defined in Foreign.C.Types Methods toRational :: CBool -> Rational #
Real CFloat
Instance details Defined in Foreign.C.Types Methods toRational :: CFloat -> Rational #
Real CDouble
Instance details Defined in Foreign.C.Types Methods toRational :: CDouble -> Rational #
Real CPtrdiff
Instance details Defined in Foreign.C.Types Methods toRational :: CPtrdiff -> Rational #
Real CSize
Instance details Defined in Foreign.C.Types Methods toRational :: CSize -> Rational #
Real CWchar
Instance details Defined in Foreign.C.Types Methods toRational :: CWchar -> Rational #
Real CSigAtomic
Instance details Defined in Foreign.C.Types Methods toRational :: CSigAtomic -> Rational #
Real CClock
Instance details Defined in Foreign.C.Types Methods toRational :: CClock -> Rational #
Real CTime
Instance details Defined in Foreign.C.Types Methods toRational :: CTime -> Rational #
Real CUSeconds
Instance details Defined in Foreign.C.Types Methods toRational :: CUSeconds -> Rational #
Real CSUSeconds
Instance details Defined in Foreign.C.Types Methods toRational :: CSUSeconds -> Rational #
Real CIntPtr
Instance details Defined in Foreign.C.Types Methods toRational :: CIntPtr -> Rational #
Real CUIntPtr
Instance details Defined in Foreign.C.Types Methods toRational :: CUIntPtr -> Rational #
Real CIntMax
Instance details Defined in Foreign.C.Types Methods toRational :: CIntMax -> Rational #
Real CUIntMax
Instance details Defined in Foreign.C.Types Methods toRational :: CUIntMax -> Rational #
Integral a => Real (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Ratio a -> Rational #
Real a => Real (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods toRational :: WrapFractional a -> Rational #
Real a => Real (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods toRational :: WrapIntegral a -> Rational #
Real a => Real (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods toRational :: Down a -> Rational #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
Real r => Real (Scalar r)
Instance details Defined in Algebra.Scalar Methods toRational :: Scalar r -> Rational #
HasResolution a => Real (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods toRational :: Fixed a -> Rational #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #
Real a => Real (Tagged s a)
Instance details Defined in Data.Tagged Methods toRational :: Tagged s a -> Rational #

class (RealFrac a, Floating a) => RealFloat a where #

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer #

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int #

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) #

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a #

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int #

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a #

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool #

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool #

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool #

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a #

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

Instances details

RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
RealFloat CFloat
Instance details Defined in Foreign.C.Types Methods floatRadix :: CFloat -> Integer # floatDigits :: CFloat -> Int # floatRange :: CFloat -> (Int, Int) # decodeFloat :: CFloat -> (Integer, Int) # encodeFloat :: Integer -> Int -> CFloat # exponent :: CFloat -> Int # significand :: CFloat -> CFloat # scaleFloat :: Int -> CFloat -> CFloat # isNaN :: CFloat -> Bool # isInfinite :: CFloat -> Bool # isDenormalized :: CFloat -> Bool # isNegativeZero :: CFloat -> Bool # isIEEE :: CFloat -> Bool # atan2 :: CFloat -> CFloat -> CFloat #
RealFloat CDouble
Instance details Defined in Foreign.C.Types Methods floatRadix :: CDouble -> Integer # floatDigits :: CDouble -> Int # floatRange :: CDouble -> (Int, Int) # decodeFloat :: CDouble -> (Integer, Int) # encodeFloat :: Integer -> Int -> CDouble # exponent :: CDouble -> Int # significand :: CDouble -> CDouble # scaleFloat :: Int -> CDouble -> CDouble # isNaN :: CDouble -> Bool # isInfinite :: CDouble -> Bool # isDenormalized :: CDouble -> Bool # isNegativeZero :: CDouble -> Bool # isIEEE :: CDouble -> Bool # atan2 :: CDouble -> CDouble -> CDouble #
RealFloat a => RealFloat (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods floatRadix :: Down a -> Integer # floatDigits :: Down a -> Int # floatRange :: Down a -> (Int, Int) # decodeFloat :: Down a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Down a # exponent :: Down a -> Int # significand :: Down a -> Down a # scaleFloat :: Int -> Down a -> Down a # isNaN :: Down a -> Bool # isInfinite :: Down a -> Bool # isDenormalized :: Down a -> Bool # isNegativeZero :: Down a -> Bool # isIEEE :: Down a -> Bool # atan2 :: Down a -> Down a -> Down a #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods floatRadix :: Identity a -> Integer # floatDigits :: Identity a -> Int # floatRange :: Identity a -> (Int, Int) # decodeFloat :: Identity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Identity a # exponent :: Identity a -> Int # significand :: Identity a -> Identity a # scaleFloat :: Int -> Identity a -> Identity a # isNaN :: Identity a -> Bool # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # isIEEE :: Identity a -> Bool # atan2 :: Identity a -> Identity a -> Identity a #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #
RealFloat a => RealFloat (Tagged s a)
Instance details Defined in Data.Tagged Methods floatRadix :: Tagged s a -> Integer # floatDigits :: Tagged s a -> Int # floatRange :: Tagged s a -> (Int, Int) # decodeFloat :: Tagged s a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Tagged s a # exponent :: Tagged s a -> Int # significand :: Tagged s a -> Tagged s a # scaleFloat :: Int -> Tagged s a -> Tagged s a # isNaN :: Tagged s a -> Bool # isInfinite :: Tagged s a -> Bool # isDenormalized :: Tagged s a -> Bool # isNegativeZero :: Tagged s a -> Bool # isIEEE :: Tagged s a -> Bool # atan2 :: Tagged s a -> Tagged s a -> Tagged s a #

class (Real a, Fractional a) => RealFrac a where #

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) #

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

n is an integral number with the same sign as x; and
f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b #

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b #

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b #

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b #

floor x returns the greatest integer not greater than x

Instances

Instances details

RealFrac CFloat
Instance details Defined in Foreign.C.Types Methods properFraction :: Integral b => CFloat -> (b, CFloat) # truncate :: Integral b => CFloat -> b # round :: Integral b => CFloat -> b # ceiling :: Integral b => CFloat -> b # floor :: Integral b => CFloat -> b #
RealFrac CDouble
Instance details Defined in Foreign.C.Types Methods properFraction :: Integral b => CDouble -> (b, CDouble) # truncate :: Integral b => CDouble -> b # round :: Integral b => CDouble -> b # ceiling :: Integral b => CDouble -> b # floor :: Integral b => CDouble -> b #
Integral a => RealFrac (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods properFraction :: Integral b => Ratio a -> (b, Ratio a) # truncate :: Integral b => Ratio a -> b # round :: Integral b => Ratio a -> b # ceiling :: Integral b => Ratio a -> b # floor :: Integral b => Ratio a -> b #
RealFrac a => RealFrac (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods properFraction :: Integral b => Down a -> (b, Down a) # truncate :: Integral b => Down a -> b # round :: Integral b => Down a -> b # ceiling :: Integral b => Down a -> b # floor :: Integral b => Down a -> b #
RealFrac a => RealFrac (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods properFraction :: Integral b => Identity a -> (b, Identity a) # truncate :: Integral b => Identity a -> b # round :: Integral b => Identity a -> b # ceiling :: Integral b => Identity a -> b # floor :: Integral b => Identity a -> b #
HasResolution a => RealFrac (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods properFraction :: Integral b => Fixed a -> (b, Fixed a) # truncate :: Integral b => Fixed a -> b # round :: Integral b => Fixed a -> b # ceiling :: Integral b => Fixed a -> b # floor :: Integral b => Fixed a -> b #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #
RealFrac a => RealFrac (Tagged s a)
Instance details Defined in Data.Tagged Methods properFraction :: Integral b => Tagged s a -> (b, Tagged s a) # truncate :: Integral b => Tagged s a -> b # round :: Integral b => Tagged s a -> b # ceiling :: Integral b => Tagged s a -> b # floor :: Integral b => Tagged s a -> b #

class Show a where #

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec #

Arguments

:: Int	the operator precedence of the enclosing context (a number from `0` to `11`). Function application has precedence `10`.
-> a	the value to be converted to a `String`
-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

(x,"") is an element of (readsPrec d (showsPrec d x "")).

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String #

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS #

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Instances details

Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
Show Char	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS # show :: Char -> String # showList :: [Char] -> ShowS #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
Show Int8	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int8 -> ShowS # show :: Int8 -> String # showList :: [Int8] -> ShowS #
Show Int16	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int16 -> ShowS # show :: Int16 -> String # showList :: [Int16] -> ShowS #
Show Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int32 -> ShowS # show :: Int32 -> String # showList :: [Int32] -> ShowS #
Show Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int64 -> ShowS # show :: Int64 -> String # showList :: [Int64] -> ShowS #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
Show Word	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS # show :: Word -> String # showList :: [Word] -> ShowS #
Show Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word8 -> ShowS # show :: Word8 -> String # showList :: [Word8] -> ShowS #
Show Word16	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word16 -> ShowS # show :: Word16 -> String # showList :: [Word16] -> ShowS #
Show Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word32 -> ShowS # show :: Word32 -> String # showList :: [Word32] -> ShowS #
Show Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word64 -> ShowS # show :: Word64 -> String # showList :: [Word64] -> ShowS #
Show RuntimeRep	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> RuntimeRep -> ShowS # show :: RuntimeRep -> String # showList :: [RuntimeRep] -> ShowS #
Show VecCount	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecCount -> ShowS # show :: VecCount -> String # showList :: [VecCount] -> ShowS #
Show VecElem	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecElem -> ShowS # show :: VecElem -> String # showList :: [VecElem] -> ShowS #
Show CallStack	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> CallStack -> ShowS # show :: CallStack -> String # showList :: [CallStack] -> ShowS #
Show SomeTypeRep	Since: base-4.10.0.0
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> SomeTypeRep -> ShowS # show :: SomeTypeRep -> String # showList :: [SomeTypeRep] -> ShowS #
Show Exp
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Exp -> ShowS # show :: Exp -> String # showList :: [Exp] -> ShowS #
Show Match
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Match -> ShowS # show :: Match -> String # showList :: [Match] -> ShowS #
Show Clause
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Clause -> ShowS # show :: Clause -> String # showList :: [Clause] -> ShowS #
Show Pat
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Pat -> ShowS # show :: Pat -> String # showList :: [Pat] -> ShowS #
Show Type
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Type -> ShowS # show :: Type -> String # showList :: [Type] -> ShowS #
Show Dec
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Dec -> ShowS # show :: Dec -> String # showList :: [Dec] -> ShowS #
Show Name
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Name -> ShowS # show :: Name -> String # showList :: [Name] -> ShowS #
Show FunDep
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> FunDep -> ShowS # show :: FunDep -> String # showList :: [FunDep] -> ShowS #
Show InjectivityAnn
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> InjectivityAnn -> ShowS # show :: InjectivityAnn -> String # showList :: [InjectivityAnn] -> ShowS #
Show Overlap
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Overlap -> ShowS # show :: Overlap -> String # showList :: [Overlap] -> ShowS #
Show ()	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> () -> ShowS # show :: () -> String # showList :: [()] -> ShowS #
Show TyCon	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TyCon -> ShowS # show :: TyCon -> String # showList :: [TyCon] -> ShowS #
Show Module	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Module -> ShowS # show :: Module -> String # showList :: [Module] -> ShowS #
Show TrName	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TrName -> ShowS # show :: TrName -> String # showList :: [TrName] -> ShowS #
Show KindRep
Instance details Defined in GHC.Show Methods showsPrec :: Int -> KindRep -> ShowS # show :: KindRep -> String # showList :: [KindRep] -> ShowS #
Show TypeLitSort	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TypeLitSort -> ShowS # show :: TypeLitSort -> String # showList :: [TypeLitSort] -> ShowS #
Show IntSet
Instance details Defined in Data.IntSet.Internal Methods showsPrec :: Int -> IntSet -> ShowS # show :: IntSet -> String # showList :: [IntSet] -> ShowS #
Show ByteString
Instance details Defined in Data.ByteString.Internal Methods showsPrec :: Int -> ByteString -> ShowS # show :: ByteString -> String # showList :: [ByteString] -> ShowS #
Show SomeException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods showsPrec :: Int -> SomeException -> ShowS # show :: SomeException -> String # showList :: [SomeException] -> ShowS #
Show IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOException -> ShowS # show :: IOException -> String # showList :: [IOException] -> ShowS #
Show IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOErrorType -> ShowS # show :: IOErrorType -> String # showList :: [IOErrorType] -> ShowS #
Show Handle	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> Handle -> ShowS # show :: Handle -> String # showList :: [Handle] -> ShowS #
Show Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods showsPrec :: Int -> Void -> ShowS # show :: Void -> String # showList :: [Void] -> ShowS #
Show Version	Since: base-2.1
Instance details Defined in Data.Version Methods showsPrec :: Int -> Version -> ShowS # show :: Version -> String # showList :: [Version] -> ShowS #
Show PatternMatchFail	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> PatternMatchFail -> ShowS # show :: PatternMatchFail -> String # showList :: [PatternMatchFail] -> ShowS #
Show RecSelError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> RecSelError -> ShowS # show :: RecSelError -> String # showList :: [RecSelError] -> ShowS #
Show RecConError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> RecConError -> ShowS # show :: RecConError -> String # showList :: [RecConError] -> ShowS #
Show RecUpdError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> RecUpdError -> ShowS # show :: RecUpdError -> String # showList :: [RecUpdError] -> ShowS #
Show NoMethodError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> NoMethodError -> ShowS # show :: NoMethodError -> String # showList :: [NoMethodError] -> ShowS #
Show TypeError	Since: base-4.9.0.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> TypeError -> ShowS # show :: TypeError -> String # showList :: [TypeError] -> ShowS #
Show NonTermination	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> NonTermination -> ShowS # show :: NonTermination -> String # showList :: [NonTermination] -> ShowS #
Show NestedAtomically	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods showsPrec :: Int -> NestedAtomically -> ShowS # show :: NestedAtomically -> String # showList :: [NestedAtomically] -> ShowS #
Show ThreadId	Since: base-4.2.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> ThreadId -> ShowS # show :: ThreadId -> String # showList :: [ThreadId] -> ShowS #
Show BlockReason	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> BlockReason -> ShowS # show :: BlockReason -> String # showList :: [BlockReason] -> ShowS #
Show ThreadStatus	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods showsPrec :: Int -> ThreadStatus -> ShowS # show :: ThreadStatus -> String # showList :: [ThreadStatus] -> ShowS #
Show CDev
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CDev -> ShowS # show :: CDev -> String # showList :: [CDev] -> ShowS #
Show CIno
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CIno -> ShowS # show :: CIno -> String # showList :: [CIno] -> ShowS #
Show CMode
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CMode -> ShowS # show :: CMode -> String # showList :: [CMode] -> ShowS #
Show COff
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> COff -> ShowS # show :: COff -> String # showList :: [COff] -> ShowS #
Show CPid
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CPid -> ShowS # show :: CPid -> String # showList :: [CPid] -> ShowS #
Show CSsize
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CSsize -> ShowS # show :: CSsize -> String # showList :: [CSsize] -> ShowS #
Show CGid
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CGid -> ShowS # show :: CGid -> String # showList :: [CGid] -> ShowS #
Show CNlink
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CNlink -> ShowS # show :: CNlink -> String # showList :: [CNlink] -> ShowS #
Show CUid
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CUid -> ShowS # show :: CUid -> String # showList :: [CUid] -> ShowS #
Show CCc
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CCc -> ShowS # show :: CCc -> String # showList :: [CCc] -> ShowS #
Show CSpeed
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CSpeed -> ShowS # show :: CSpeed -> String # showList :: [CSpeed] -> ShowS #
Show CTcflag
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CTcflag -> ShowS # show :: CTcflag -> String # showList :: [CTcflag] -> ShowS #
Show CRLim
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CRLim -> ShowS # show :: CRLim -> String # showList :: [CRLim] -> ShowS #
Show CBlkSize
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CBlkSize -> ShowS # show :: CBlkSize -> String # showList :: [CBlkSize] -> ShowS #
Show CBlkCnt
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CBlkCnt -> ShowS # show :: CBlkCnt -> String # showList :: [CBlkCnt] -> ShowS #
Show CClockId
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CClockId -> ShowS # show :: CClockId -> String # showList :: [CClockId] -> ShowS #
Show CFsBlkCnt
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CFsBlkCnt -> ShowS # show :: CFsBlkCnt -> String # showList :: [CFsBlkCnt] -> ShowS #
Show CFsFilCnt
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CFsFilCnt -> ShowS # show :: CFsFilCnt -> String # showList :: [CFsFilCnt] -> ShowS #
Show CId
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CId -> ShowS # show :: CId -> String # showList :: [CId] -> ShowS #
Show CKey
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CKey -> ShowS # show :: CKey -> String # showList :: [CKey] -> ShowS #
Show CTimer
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CTimer -> ShowS # show :: CTimer -> String # showList :: [CTimer] -> ShowS #
Show CSocklen
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CSocklen -> ShowS # show :: CSocklen -> String # showList :: [CSocklen] -> ShowS #
Show CNfds
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> CNfds -> ShowS # show :: CNfds -> String # showList :: [CNfds] -> ShowS #
Show Fd
Instance details Defined in System.Posix.Types Methods showsPrec :: Int -> Fd -> ShowS # show :: Fd -> String # showList :: [Fd] -> ShowS #
Show BlockedIndefinitelyOnMVar	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnMVar -> ShowS # show :: BlockedIndefinitelyOnMVar -> String # showList :: [BlockedIndefinitelyOnMVar] -> ShowS #
Show BlockedIndefinitelyOnSTM	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnSTM -> ShowS # show :: BlockedIndefinitelyOnSTM -> String # showList :: [BlockedIndefinitelyOnSTM] -> ShowS #
Show Deadlock	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> Deadlock -> ShowS # show :: Deadlock -> String # showList :: [Deadlock] -> ShowS #
Show AllocationLimitExceeded	Since: base-4.7.1.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AllocationLimitExceeded -> ShowS # show :: AllocationLimitExceeded -> String # showList :: [AllocationLimitExceeded] -> ShowS #
Show CompactionFailed	Since: base-4.10.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> CompactionFailed -> ShowS # show :: CompactionFailed -> String # showList :: [CompactionFailed] -> ShowS #
Show AssertionFailed	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AssertionFailed -> ShowS # show :: AssertionFailed -> String # showList :: [AssertionFailed] -> ShowS #
Show SomeAsyncException	Since: base-4.7.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> SomeAsyncException -> ShowS # show :: SomeAsyncException -> String # showList :: [SomeAsyncException] -> ShowS #
Show AsyncException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AsyncException -> ShowS # show :: AsyncException -> String # showList :: [AsyncException] -> ShowS #
Show ArrayException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ArrayException -> ShowS # show :: ArrayException -> String # showList :: [ArrayException] -> ShowS #
Show FixIOException	Since: base-4.11.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> FixIOException -> ShowS # show :: FixIOException -> String # showList :: [FixIOException] -> ShowS #
Show ExitCode
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ExitCode -> ShowS # show :: ExitCode -> String # showList :: [ExitCode] -> ShowS #
Show HandleType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> HandleType -> ShowS # show :: HandleType -> String # showList :: [HandleType] -> ShowS #
Show BufferMode	Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> BufferMode -> ShowS # show :: BufferMode -> String # showList :: [BufferMode] -> ShowS #
Show Newline	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> Newline -> ShowS # show :: Newline -> String # showList :: [Newline] -> ShowS #
Show NewlineMode	Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> NewlineMode -> ShowS # show :: NewlineMode -> String # showList :: [NewlineMode] -> ShowS #
Show MaskingState	Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods showsPrec :: Int -> MaskingState -> ShowS # show :: MaskingState -> String # showList :: [MaskingState] -> ShowS #
Show ErrorCall	Since: base-4.0.0.0
Instance details Defined in GHC.Exception Methods showsPrec :: Int -> ErrorCall -> ShowS # show :: ErrorCall -> String # showList :: [ErrorCall] -> ShowS #
Show ArithException	Since: base-4.0.0.0
Instance details Defined in GHC.Exception.Type Methods showsPrec :: Int -> ArithException -> ShowS # show :: ArithException -> String # showList :: [ArithException] -> ShowS #
Show All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Show Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Show Fixity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Fixity -> ShowS # show :: Fixity -> String # showList :: [Fixity] -> ShowS #
Show Associativity	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Associativity -> ShowS # show :: Associativity -> String # showList :: [Associativity] -> ShowS #
Show SourceUnpackedness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> SourceUnpackedness -> ShowS # show :: SourceUnpackedness -> String # showList :: [SourceUnpackedness] -> ShowS #
Show SourceStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> SourceStrictness -> ShowS # show :: SourceStrictness -> String # showList :: [SourceStrictness] -> ShowS #
Show DecidedStrictness	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> DecidedStrictness -> ShowS # show :: DecidedStrictness -> String # showList :: [DecidedStrictness] -> ShowS #
Show SomeSymbol	Since: base-4.7.0.0
Instance details Defined in GHC.TypeLits Methods showsPrec :: Int -> SomeSymbol -> ShowS # show :: SomeSymbol -> String # showList :: [SomeSymbol] -> ShowS #
Show SomeNat	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods showsPrec :: Int -> SomeNat -> ShowS # show :: SomeNat -> String # showList :: [SomeNat] -> ShowS #
Show CChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CChar -> ShowS # show :: CChar -> String # showList :: [CChar] -> ShowS #
Show CSChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSChar -> ShowS # show :: CSChar -> String # showList :: [CSChar] -> ShowS #
Show CUChar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUChar -> ShowS # show :: CUChar -> String # showList :: [CUChar] -> ShowS #
Show CShort
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CShort -> ShowS # show :: CShort -> String # showList :: [CShort] -> ShowS #
Show CUShort
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUShort -> ShowS # show :: CUShort -> String # showList :: [CUShort] -> ShowS #
Show CInt
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CInt -> ShowS # show :: CInt -> String # showList :: [CInt] -> ShowS #
Show CUInt
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUInt -> ShowS # show :: CUInt -> String # showList :: [CUInt] -> ShowS #
Show CLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CLong -> ShowS # show :: CLong -> String # showList :: [CLong] -> ShowS #
Show CULong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CULong -> ShowS # show :: CULong -> String # showList :: [CULong] -> ShowS #
Show CLLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CLLong -> ShowS # show :: CLLong -> String # showList :: [CLLong] -> ShowS #
Show CULLong
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CULLong -> ShowS # show :: CULLong -> String # showList :: [CULLong] -> ShowS #
Show CBool
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CBool -> ShowS # show :: CBool -> String # showList :: [CBool] -> ShowS #
Show CFloat
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CFloat -> ShowS # show :: CFloat -> String # showList :: [CFloat] -> ShowS #
Show CDouble
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CDouble -> ShowS # show :: CDouble -> String # showList :: [CDouble] -> ShowS #
Show CPtrdiff
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CPtrdiff -> ShowS # show :: CPtrdiff -> String # showList :: [CPtrdiff] -> ShowS #
Show CSize
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSize -> ShowS # show :: CSize -> String # showList :: [CSize] -> ShowS #
Show CWchar
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CWchar -> ShowS # show :: CWchar -> String # showList :: [CWchar] -> ShowS #
Show CSigAtomic
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSigAtomic -> ShowS # show :: CSigAtomic -> String # showList :: [CSigAtomic] -> ShowS #
Show CClock
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CClock -> ShowS # show :: CClock -> String # showList :: [CClock] -> ShowS #
Show CTime
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CTime -> ShowS # show :: CTime -> String # showList :: [CTime] -> ShowS #
Show CUSeconds
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUSeconds -> ShowS # show :: CUSeconds -> String # showList :: [CUSeconds] -> ShowS #
Show CSUSeconds
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CSUSeconds -> ShowS # show :: CSUSeconds -> String # showList :: [CSUSeconds] -> ShowS #
Show CIntPtr
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CIntPtr -> ShowS # show :: CIntPtr -> String # showList :: [CIntPtr] -> ShowS #
Show CUIntPtr
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUIntPtr -> ShowS # show :: CUIntPtr -> String # showList :: [CUIntPtr] -> ShowS #
Show CIntMax
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CIntMax -> ShowS # show :: CIntMax -> String # showList :: [CIntMax] -> ShowS #
Show CUIntMax
Instance details Defined in Foreign.C.Types Methods showsPrec :: Int -> CUIntMax -> ShowS # show :: CUIntMax -> String # showList :: [CUIntMax] -> ShowS #
Show Fingerprint	Since: base-4.7.0.0
Instance details Defined in GHC.Fingerprint.Type Methods showsPrec :: Int -> Fingerprint -> ShowS # show :: Fingerprint -> String # showList :: [Fingerprint] -> ShowS #
Show Lexeme	Since: base-2.1
Instance details Defined in Text.Read.Lex Methods showsPrec :: Int -> Lexeme -> ShowS # show :: Lexeme -> String # showList :: [Lexeme] -> ShowS #
Show Number	Since: base-4.6.0.0
Instance details Defined in Text.Read.Lex Methods showsPrec :: Int -> Number -> ShowS # show :: Number -> String # showList :: [Number] -> ShowS #
Show GeneralCategory	Since: base-2.1
Instance details Defined in GHC.Unicode Methods showsPrec :: Int -> GeneralCategory -> ShowS # show :: GeneralCategory -> String # showList :: [GeneralCategory] -> ShowS #
Show SrcLoc	Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> SrcLoc -> ShowS # show :: SrcLoc -> String # showList :: [SrcLoc] -> ShowS #
Show ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods showsPrec :: Int -> ShortByteString -> ShowS # show :: ShortByteString -> String # showList :: [ShortByteString] -> ShowS #
Show ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods showsPrec :: Int -> ByteString -> ShowS # show :: ByteString -> String # showList :: [ByteString] -> ShowS #
Show Extension
Instance details Defined in GHC.LanguageExtensions.Type Methods showsPrec :: Int -> Extension -> ShowS # show :: Extension -> String # showList :: [Extension] -> ShowS #
Show ForeignSrcLang
Instance details Defined in GHC.ForeignSrcLang.Type Methods showsPrec :: Int -> ForeignSrcLang -> ShowS # show :: ForeignSrcLang -> String # showList :: [ForeignSrcLang] -> ShowS #
Show Lex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Lex -> ShowS # show :: Lex -> String # showList :: [Lex] -> ShowS #
Show Revlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Revlex -> ShowS # show :: Revlex -> String # showList :: [Revlex] -> ShowS #
Show Grevlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Grevlex -> ShowS # show :: Grevlex -> String # showList :: [Grevlex] -> ShowS #
Show Grlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Grlex -> ShowS # show :: Grlex -> String # showList :: [Grlex] -> ShowS #
Show SomeSNat
Instance details Defined in Data.Type.Natural Methods showsPrec :: Int -> SomeSNat -> ShowS # show :: SomeSNat -> String # showList :: [SomeSNat] -> ShowS #
Show Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods showsPrec :: Int -> Doc -> ShowS # show :: Doc -> String # showList :: [Doc] -> ShowS #
Show TextDetails
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> TextDetails -> ShowS # show :: TextDetails -> String # showList :: [TextDetails] -> ShowS #
Show Style
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> Style -> ShowS # show :: Style -> String # showList :: [Style] -> ShowS #
Show Mode
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> Mode -> ShowS # show :: Mode -> String # showList :: [Mode] -> ShowS #
Show ModName
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> ModName -> ShowS # show :: ModName -> String # showList :: [ModName] -> ShowS #
Show PkgName
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> PkgName -> ShowS # show :: PkgName -> String # showList :: [PkgName] -> ShowS #
Show Module
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Module -> ShowS # show :: Module -> String # showList :: [Module] -> ShowS #
Show OccName
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> OccName -> ShowS # show :: OccName -> String # showList :: [OccName] -> ShowS #
Show NameFlavour
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> NameFlavour -> ShowS # show :: NameFlavour -> String # showList :: [NameFlavour] -> ShowS #
Show NameSpace
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> NameSpace -> ShowS # show :: NameSpace -> String # showList :: [NameSpace] -> ShowS #
Show Loc
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Loc -> ShowS # show :: Loc -> String # showList :: [Loc] -> ShowS #
Show Info
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Info -> ShowS # show :: Info -> String # showList :: [Info] -> ShowS #
Show ModuleInfo
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> ModuleInfo -> ShowS # show :: ModuleInfo -> String # showList :: [ModuleInfo] -> ShowS #
Show Fixity
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Fixity -> ShowS # show :: Fixity -> String # showList :: [Fixity] -> ShowS #
Show FixityDirection
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> FixityDirection -> ShowS # show :: FixityDirection -> String # showList :: [FixityDirection] -> ShowS #
Show Lit
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Lit -> ShowS # show :: Lit -> String # showList :: [Lit] -> ShowS #
Show Bytes
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Bytes -> ShowS # show :: Bytes -> String # showList :: [Bytes] -> ShowS #
Show Body
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Body -> ShowS # show :: Body -> String # showList :: [Body] -> ShowS #
Show Guard
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Guard -> ShowS # show :: Guard -> String # showList :: [Guard] -> ShowS #
Show Stmt
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Stmt -> ShowS # show :: Stmt -> String # showList :: [Stmt] -> ShowS #
Show Range
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Range -> ShowS # show :: Range -> String # showList :: [Range] -> ShowS #
Show DerivClause
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> DerivClause -> ShowS # show :: DerivClause -> String # showList :: [DerivClause] -> ShowS #
Show DerivStrategy
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> DerivStrategy -> ShowS # show :: DerivStrategy -> String # showList :: [DerivStrategy] -> ShowS #
Show TypeFamilyHead
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> TypeFamilyHead -> ShowS # show :: TypeFamilyHead -> String # showList :: [TypeFamilyHead] -> ShowS #
Show TySynEqn
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> TySynEqn -> ShowS # show :: TySynEqn -> String # showList :: [TySynEqn] -> ShowS #
Show Foreign
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Foreign -> ShowS # show :: Foreign -> String # showList :: [Foreign] -> ShowS #
Show Callconv
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Callconv -> ShowS # show :: Callconv -> String # showList :: [Callconv] -> ShowS #
Show Safety
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Safety -> ShowS # show :: Safety -> String # showList :: [Safety] -> ShowS #
Show Pragma
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Pragma -> ShowS # show :: Pragma -> String # showList :: [Pragma] -> ShowS #
Show Inline
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Inline -> ShowS # show :: Inline -> String # showList :: [Inline] -> ShowS #
Show RuleMatch
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> RuleMatch -> ShowS # show :: RuleMatch -> String # showList :: [RuleMatch] -> ShowS #
Show Phases
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Phases -> ShowS # show :: Phases -> String # showList :: [Phases] -> ShowS #
Show RuleBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> RuleBndr -> ShowS # show :: RuleBndr -> String # showList :: [RuleBndr] -> ShowS #
Show AnnTarget
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> AnnTarget -> ShowS # show :: AnnTarget -> String # showList :: [AnnTarget] -> ShowS #
Show SourceUnpackedness
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> SourceUnpackedness -> ShowS # show :: SourceUnpackedness -> String # showList :: [SourceUnpackedness] -> ShowS #
Show SourceStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> SourceStrictness -> ShowS # show :: SourceStrictness -> String # showList :: [SourceStrictness] -> ShowS #
Show DecidedStrictness
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> DecidedStrictness -> ShowS # show :: DecidedStrictness -> String # showList :: [DecidedStrictness] -> ShowS #
Show Con
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Con -> ShowS # show :: Con -> String # showList :: [Con] -> ShowS #
Show Bang
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Bang -> ShowS # show :: Bang -> String # showList :: [Bang] -> ShowS #
Show PatSynDir
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> PatSynDir -> ShowS # show :: PatSynDir -> String # showList :: [PatSynDir] -> ShowS #
Show PatSynArgs
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> PatSynArgs -> ShowS # show :: PatSynArgs -> String # showList :: [PatSynArgs] -> ShowS #
Show TyVarBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> TyVarBndr -> ShowS # show :: TyVarBndr -> String # showList :: [TyVarBndr] -> ShowS #
Show FamilyResultSig
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> FamilyResultSig -> ShowS # show :: FamilyResultSig -> String # showList :: [FamilyResultSig] -> ShowS #
Show TyLit
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> TyLit -> ShowS # show :: TyLit -> String # showList :: [TyLit] -> ShowS #
Show Role
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> Role -> ShowS # show :: Role -> String # showList :: [Role] -> ShowS #
Show AnnLookup
Instance details Defined in Language.Haskell.TH.Syntax Methods showsPrec :: Int -> AnnLookup -> ShowS # show :: AnnLookup -> String # showList :: [AnnLookup] -> ShowS #
Show Decoding
Instance details Defined in Data.Text.Encoding Methods showsPrec :: Int -> Decoding -> ShowS # show :: Decoding -> String # showList :: [Decoding] -> ShowS #
Show WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> WrapOrdering -> ShowS # show :: WrapOrdering -> String # showList :: [WrapOrdering] -> ShowS #
Show ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods showsPrec :: Int -> ByteArray -> ShowS # show :: ByteArray -> String # showList :: [ByteArray] -> ShowS #
Show DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods showsPrec :: Int -> DefName -> ShowS # show :: DefName -> String # showList :: [DefName] -> ShowS #
Show ConstructorInfo
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> ConstructorInfo -> ShowS # show :: ConstructorInfo -> String # showList :: [ConstructorInfo] -> ShowS #
Show DatatypeInfo
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> DatatypeInfo -> ShowS # show :: DatatypeInfo -> String # showList :: [DatatypeInfo] -> ShowS #
Show StdGen
Instance details Defined in System.Random.Internal Methods showsPrec :: Int -> StdGen -> ShowS # show :: StdGen -> String # showList :: [StdGen] -> ShowS #
Show ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods showsPrec :: Int -> ComplexBasis -> ShowS # show :: ComplexBasis -> String # showList :: [ComplexBasis] -> ShowS #
Show DType
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DType -> ShowS # show :: DType -> String # showList :: [DType] -> ShowS #
Show DLetDec
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DLetDec -> ShowS # show :: DLetDec -> String # showList :: [DLetDec] -> ShowS #
Show DTyVarBndr
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DTyVarBndr -> ShowS # show :: DTyVarBndr -> String # showList :: [DTyVarBndr] -> ShowS #
Show DCon
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DCon -> ShowS # show :: DCon -> String # showList :: [DCon] -> ShowS #
Show DClause
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DClause -> ShowS # show :: DClause -> String # showList :: [DClause] -> ShowS #
Show DExp
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DExp -> ShowS # show :: DExp -> String # showList :: [DExp] -> ShowS #
Show DTypeFamilyHead
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DTypeFamilyHead -> ShowS # show :: DTypeFamilyHead -> String # showList :: [DTypeFamilyHead] -> ShowS #
Show ConstructorVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> ConstructorVariant -> ShowS # show :: ConstructorVariant -> String # showList :: [ConstructorVariant] -> ShowS #
Show DatatypeVariant
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> DatatypeVariant -> ShowS # show :: DatatypeVariant -> String # showList :: [DatatypeVariant] -> ShowS #
Show FieldStrictness
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> FieldStrictness -> ShowS # show :: FieldStrictness -> String # showList :: [FieldStrictness] -> ShowS #
Show Strictness
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> Strictness -> ShowS # show :: Strictness -> String # showList :: [Strictness] -> ShowS #
Show Unpackedness
Instance details Defined in Language.Haskell.TH.Datatype Methods showsPrec :: Int -> Unpackedness -> ShowS # show :: Unpackedness -> String # showList :: [Unpackedness] -> ShowS #
Show Specificity
Instance details Defined in Language.Haskell.TH.Datatype.TyVarBndr Methods showsPrec :: Int -> Specificity -> ShowS # show :: Specificity -> String # showList :: [Specificity] -> ShowS #
Show DConFields
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DConFields -> ShowS # show :: DConFields -> String # showList :: [DConFields] -> ShowS #
Show DDec
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DDec -> ShowS # show :: DDec -> String # showList :: [DDec] -> ShowS #
Show DDerivClause
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DDerivClause -> ShowS # show :: DDerivClause -> String # showList :: [DDerivClause] -> ShowS #
Show DDerivStrategy
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DDerivStrategy -> ShowS # show :: DDerivStrategy -> String # showList :: [DDerivStrategy] -> ShowS #
Show DFamilyResultSig
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DFamilyResultSig -> ShowS # show :: DFamilyResultSig -> String # showList :: [DFamilyResultSig] -> ShowS #
Show DForeign
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DForeign -> ShowS # show :: DForeign -> String # showList :: [DForeign] -> ShowS #
Show DInfo
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DInfo -> ShowS # show :: DInfo -> String # showList :: [DInfo] -> ShowS #
Show DMatch
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DMatch -> ShowS # show :: DMatch -> String # showList :: [DMatch] -> ShowS #
Show DPat
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DPat -> ShowS # show :: DPat -> String # showList :: [DPat] -> ShowS #
Show DPatSynDir
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DPatSynDir -> ShowS # show :: DPatSynDir -> String # showList :: [DPatSynDir] -> ShowS #
Show DPragma
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DPragma -> ShowS # show :: DPragma -> String # showList :: [DPragma] -> ShowS #
Show DRuleBndr
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DRuleBndr -> ShowS # show :: DRuleBndr -> String # showList :: [DRuleBndr] -> ShowS #
Show DTySynEqn
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> DTySynEqn -> ShowS # show :: DTySynEqn -> String # showList :: [DTySynEqn] -> ShowS #
Show NewOrData
Instance details Defined in Language.Haskell.TH.Desugar.AST Methods showsPrec :: Int -> NewOrData -> ShowS # show :: NewOrData -> String # showList :: [NewOrData] -> ShowS #
Show DFunArgs
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods showsPrec :: Int -> DFunArgs -> ShowS # show :: DFunArgs -> String # showList :: [DFunArgs] -> ShowS #
Show DTypeArg
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods showsPrec :: Int -> DTypeArg -> ShowS # show :: DTypeArg -> String # showList :: [DTypeArg] -> ShowS #
Show DVisFunArg
Instance details Defined in Language.Haskell.TH.Desugar.Core Methods showsPrec :: Int -> DVisFunArg -> ShowS # show :: DVisFunArg -> String # showList :: [DVisFunArg] -> ShowS #
Show CodePoint
Instance details Defined in Data.Text.Encoding Methods showsPrec :: Int -> CodePoint -> ShowS # show :: CodePoint -> String # showList :: [CodePoint] -> ShowS #
Show DecoderState
Instance details Defined in Data.Text.Encoding Methods showsPrec :: Int -> DecoderState -> ShowS # show :: DecoderState -> String # showList :: [DecoderState] -> ShowS #
Show GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> GradedStrategy -> ShowS # show :: GradedStrategy -> String # showList :: [GradedStrategy] -> ShowS #
Show GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> GrevlexStrategy -> ShowS # show :: GrevlexStrategy -> String # showList :: [GrevlexStrategy] -> ShowS #
Show NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> NormalStrategy -> ShowS # show :: NormalStrategy -> String # showList :: [NormalStrategy] -> ShowS #
Show BothBottom
Instance details Defined in Data.Unamb Methods showsPrec :: Int -> BothBottom -> ShowS # show :: BothBottom -> String # showList :: [BothBottom] -> ShowS #
Show DontBother
Instance details Defined in Data.Unamb Methods showsPrec :: Int -> DontBother -> ShowS # show :: DontBother -> String # showList :: [DontBother] -> ShowS #
Show a => Show [a]	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> [a] -> ShowS # show :: [a] -> String # showList :: [[a]] -> ShowS #
Show a => Show (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS # show :: Maybe a -> String # showList :: [Maybe a] -> ShowS #
Show a => Show (Ratio a)	Since: base-2.0.1
Instance details Defined in GHC.Real Methods showsPrec :: Int -> Ratio a -> ShowS # show :: Ratio a -> String # showList :: [Ratio a] -> ShowS #
Show (Ptr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods showsPrec :: Int -> Ptr a -> ShowS # show :: Ptr a -> String # showList :: [Ptr a] -> ShowS #
Show (FunPtr a)	Since: base-2.1
Instance details Defined in GHC.Ptr Methods showsPrec :: Int -> FunPtr a -> ShowS # show :: FunPtr a -> String # showList :: [FunPtr a] -> ShowS #
Show p => Show (Par1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Par1 p -> ShowS # show :: Par1 p -> String # showList :: [Par1 p] -> ShowS #
Show a => Show (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapNum a -> ShowS # show :: WrapNum a -> String # showList :: [WrapNum a] -> ShowS #
Show a => Show (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapFractional a -> ShowS # show :: WrapFractional a -> String # showList :: [WrapFractional a] -> ShowS #
Show a => Show (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapIntegral a -> ShowS # show :: WrapIntegral a -> String # showList :: [WrapIntegral a] -> ShowS #
Show a => Show (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapAlgebra a -> ShowS # show :: WrapAlgebra a -> String # showList :: [WrapAlgebra a] -> ShowS #
Show a => Show (Add a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> Add a -> ShowS # show :: Add a -> String # showList :: [Add a] -> ShowS #
Show a => Show (Mult a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> Mult a -> ShowS # show :: Mult a -> String # showList :: [Mult a] -> ShowS #
(Eq d, Show d, Unital d) => Show (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods showsPrec :: Int -> Fraction d -> ShowS # show :: Fraction d -> String # showList :: [Fraction d] -> ShowS #
Show a => Show (Vector a)
Instance details Defined in Data.Vector Methods showsPrec :: Int -> Vector a -> ShowS # show :: Vector a -> String # showList :: [Vector a] -> ShowS #
Show a => Show (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods showsPrec :: Int -> HashSet a -> ShowS # show :: HashSet a -> String # showList :: [HashSet a] -> ShowS #
Show a => Show (Set a)
Instance details Defined in Data.Set.Internal Methods showsPrec :: Int -> Set a -> ShowS # show :: Set a -> String # showList :: [Set a] -> ShowS #
Show a => Show (Seq a)
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> Seq a -> ShowS # show :: Seq a -> String # showList :: [Seq a] -> ShowS #
Show a => Show (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods showsPrec :: Int -> IntMap a -> ShowS # show :: IntMap a -> String # showList :: [IntMap a] -> ShowS #
Show a => Show (Down a)	This instance would be equivalent to the derived instances of the `Down` newtype if the `getDown` field were removed Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods showsPrec :: Int -> Down a -> ShowS # show :: Down a -> String # showList :: [Down a] -> ShowS #
Show a => Show (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Show a => Show (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Min a -> ShowS # show :: Min a -> String # showList :: [Min a] -> ShowS #
Show a => Show (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Max a -> ShowS # show :: Max a -> String # showList :: [Max a] -> ShowS #
Show a => Show (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Show a => Show (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Show m => Show (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS # show :: WrappedMonoid m -> String # showList :: [WrappedMonoid m] -> ShowS #
Show a => Show (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Option a -> ShowS # show :: Option a -> String # showList :: [Option a] -> ShowS #
Show a => Show (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods showsPrec :: Int -> ZipList a -> ShowS # show :: ZipList a -> String # showList :: [ZipList a] -> ShowS #
Show a => Show (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
Show a => Show (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Show a => Show (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Show a => Show (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Show a => Show (NonEmpty a)	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> NonEmpty a -> ShowS # show :: NonEmpty a -> String # showList :: [NonEmpty a] -> ShowS #
Show a => Show (Tree a)
Instance details Defined in Data.Tree Methods showsPrec :: Int -> Tree a -> ShowS # show :: Tree a -> String # showList :: [Tree a] -> ShowS #
Show a => Show (ViewL a)
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewL a -> ShowS # show :: ViewL a -> String # showList :: [ViewL a] -> ShowS #
Show a => Show (ViewR a)
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> ViewR a -> ShowS # show :: ViewR a -> String # showList :: [ViewR a] -> ShowS #
KnownNat n => Show (Ordinal n)
Instance details Defined in Data.Type.Ordinal Methods showsPrec :: Int -> Ordinal n -> ShowS # show :: Ordinal n -> String # showList :: [Ordinal n] -> ShowS #
Show r => Show (Ideal r)
Instance details Defined in Algebra.Ring.Ideal Methods showsPrec :: Int -> Ideal r -> ShowS # show :: Ideal r -> String # showList :: [Ideal r] -> ShowS #
Show ord => Show (Graded ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Graded ord -> ShowS # show :: Graded ord -> String # showList :: [Graded ord] -> ShowS #
Show (IsTrue b)
Instance details Defined in Proof.Propositional Methods showsPrec :: Int -> IsTrue b -> ShowS # show :: IsTrue b -> String # showList :: [IsTrue b] -> ShowS #
Show (SOrdering ord)
Instance details Defined in Data.Type.Natural.Core Methods showsPrec :: Int -> SOrdering ord -> ShowS # show :: SOrdering ord -> String # showList :: [SOrdering ord] -> ShowS #
Show (SBool ord)
Instance details Defined in Data.Type.Natural.Core Methods showsPrec :: Int -> SBool ord -> ShowS # show :: SBool ord -> String # showList :: [SBool ord] -> ShowS #
Show (SNat n)
Instance details Defined in Data.Type.Natural.Core Methods showsPrec :: Int -> SNat n -> ShowS # show :: SNat n -> String # showList :: [SNat n] -> ShowS #
Show r => Show (Scalar r)
Instance details Defined in Algebra.Scalar Methods showsPrec :: Int -> Scalar r -> ShowS # show :: Scalar r -> String # showList :: [Scalar r] -> ShowS #
Show (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> Doc a -> ShowS # show :: Doc a -> String # showList :: [Doc a] -> ShowS #
Show a => Show (AnnotDetails a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> AnnotDetails a -> ShowS # show :: AnnotDetails a -> String # showList :: [AnnotDetails a] -> ShowS #
Show a => Show (Span a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods showsPrec :: Int -> Span a -> ShowS # show :: Span a -> String # showList :: [Span a] -> ShowS #
Show a => Show (Complex a)
Instance details Defined in Numeric.Algebra.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
(Show a, Prim a) => Show (Vector a)
Instance details Defined in Data.Vector.Primitive Methods showsPrec :: Int -> Vector a -> ShowS # show :: Vector a -> String # showList :: [Vector a] -> ShowS #
(Show a, Storable a) => Show (Vector a)
Instance details Defined in Data.Vector.Storable Methods showsPrec :: Int -> Vector a -> ShowS # show :: Vector a -> String # showList :: [Vector a] -> ShowS #
Show a => Show (Array a)
Instance details Defined in Data.Primitive.Array Methods showsPrec :: Int -> Array a -> ShowS # show :: Array a -> String # showList :: [Array a] -> ShowS #
(Show a, Prim a) => Show (PrimArray a)
Instance details Defined in Data.Primitive.PrimArray Methods showsPrec :: Int -> PrimArray a -> ShowS # show :: PrimArray a -> String # showList :: [PrimArray a] -> ShowS #
Show a => Show (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods showsPrec :: Int -> SmallArray a -> ShowS # show :: SmallArray a -> String # showList :: [SmallArray a] -> ShowS #
Show a => Show (Hashed a)
Instance details Defined in Data.Hashable.Class Methods showsPrec :: Int -> Hashed a -> ShowS # show :: Hashed a -> String # showList :: [Hashed a] -> ShowS #
Show g => Show (StateGen g)
Instance details Defined in System.Random.Internal Methods showsPrec :: Int -> StateGen g -> ShowS # show :: StateGen g -> String # showList :: [StateGen g] -> ShowS #
Show g => Show (AtomicGen g)
Instance details Defined in System.Random.Stateful Methods showsPrec :: Int -> AtomicGen g -> ShowS # show :: AtomicGen g -> String # showList :: [AtomicGen g] -> ShowS #
Show g => Show (IOGen g)
Instance details Defined in System.Random.Stateful Methods showsPrec :: Int -> IOGen g -> ShowS # show :: IOGen g -> String # showList :: [IOGen g] -> ShowS #
Show g => Show (STGen g)
Instance details Defined in System.Random.Stateful Methods showsPrec :: Int -> STGen g -> ShowS # show :: STGen g -> String # showList :: [STGen g] -> ShowS #
Show s => Show (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> SugarStrategy s -> ShowS # show :: SugarStrategy s -> String # showList :: [SugarStrategy s] -> ShowS #
(CoeffRing r, PrettyCoeff r) => Show (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods showsPrec :: Int -> Unipol r -> ShowS # show :: Unipol r -> String # showList :: [Unipol r] -> ShowS #
Show a => Show (Heap a)
Instance details Defined in Data.Heap Methods showsPrec :: Int -> Heap a -> ShowS # show :: Heap a -> String # showList :: [Heap a] -> ShowS #
Show a => Show (Forest a)
Instance details Defined in Data.Heap Methods showsPrec :: Int -> Forest a -> ShowS # show :: Forest a -> String # showList :: [Forest a] -> ShowS #
Show a => Show (Tree a)
Instance details Defined in Data.Heap Methods showsPrec :: Int -> Tree a -> ShowS # show :: Tree a -> String # showList :: [Tree a] -> ShowS #
Show (HVecView xs)
Instance details Defined in Proof.Equational Methods showsPrec :: Int -> HVecView xs -> ShowS # show :: HVecView xs -> String # showList :: [HVecView xs] -> ShowS #
Show a => Show (Matrix a)
Instance details Defined in Data.Matrix Methods showsPrec :: Int -> Matrix a -> ShowS # show :: Matrix a -> String # showList :: [Matrix a] -> ShowS #
(Show a, Show b) => Show (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS # show :: Either a b -> String # showList :: [Either a b] -> ShowS #
Show (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> V1 p -> ShowS # show :: V1 p -> String # showList :: [V1 p] -> ShowS #
Show (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> U1 p -> ShowS # show :: U1 p -> String # showList :: [U1 p] -> ShowS #
Show (TypeRep a)
Instance details Defined in Data.Typeable.Internal Methods showsPrec :: Int -> TypeRep a -> ShowS # show :: TypeRep a -> String # showList :: [TypeRep a] -> ShowS #
(Show a, Show b) => Show (a, b)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b) -> ShowS # show :: (a, b) -> String # showList :: [(a, b)] -> ShowS #
(Show k, Show v) => Show (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods showsPrec :: Int -> HashMap k v -> ShowS # show :: HashMap k v -> String # showList :: [HashMap k v] -> ShowS #
(Show k, Show a) => Show (Map k a)
Instance details Defined in Data.Map.Internal Methods showsPrec :: Int -> Map k a -> ShowS # show :: Map k a -> String # showList :: [Map k a] -> ShowS #
Show (ST s a)	Since: base-2.1
Instance details Defined in GHC.ST Methods showsPrec :: Int -> ST s a -> ShowS # show :: ST s a -> String # showList :: [ST s a] -> ShowS #
(Ix ix, Show ix, Show e, IArray UArray e) => Show (UArray ix e)
Instance details Defined in Data.Array.Base Methods showsPrec :: Int -> UArray ix e -> ShowS # show :: UArray ix e -> String # showList :: [UArray ix e] -> ShowS #
(Ix a, Show a, Show b) => Show (Array a b)	Since: base-2.1
Instance details Defined in GHC.Arr Methods showsPrec :: Int -> Array a b -> ShowS # show :: Array a b -> String # showList :: [Array a b] -> ShowS #
HasResolution a => Show (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods showsPrec :: Int -> Fixed a -> ShowS # show :: Fixed a -> String # showList :: [Fixed a] -> ShowS #
(Show a, Show b) => Show (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Arg a b -> ShowS # show :: Arg a b -> String # showList :: [Arg a b] -> ShowS #
Show (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods showsPrec :: Int -> Proxy s -> ShowS # show :: Proxy s -> String # showList :: [Proxy s] -> ShowS #
(Show1 m, Show a) => Show (MaybeT m a)
Instance details Defined in Control.Monad.Trans.Maybe Methods showsPrec :: Int -> MaybeT m a -> ShowS # show :: MaybeT m a -> String # showList :: [MaybeT m a] -> ShowS #
(Show1 m, Show a) => Show (ListT m a)
Instance details Defined in Control.Monad.Trans.List Methods showsPrec :: Int -> ListT m a -> ShowS # show :: ListT m a -> String # showList :: [ListT m a] -> ShowS #
(Show i, Show a) => Show (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods showsPrec :: Int -> Level i a -> ShowS # show :: Level i a -> String # showList :: [Level i a] -> ShowS #
Show (f a) => Show (SomeSized f a)
Instance details Defined in Data.Sized Methods showsPrec :: Int -> SomeSized f a -> ShowS # show :: SomeSized f a -> String # showList :: [SomeSized f a] -> ShowS #
(Show a, Show b) => Show (These a b)
Instance details Defined in Data.These Methods showsPrec :: Int -> These a b -> ShowS # show :: These a b -> String # showList :: [These a b] -> ShowS #
Show (a :<: b)
Instance details Defined in Data.Type.Natural.Lemma.Order Methods showsPrec :: Int -> (a :<: b) -> ShowS # show :: (a :<: b) -> String # showList :: [a :<: b] -> ShowS #
ShowSing (Maybe a) => Show (SFirst z)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> SFirst z -> ShowS # show :: SFirst z -> String # showList :: [SFirst z] -> ShowS #
ShowSing (Maybe a) => Show (SLast z)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> SLast z -> ShowS # show :: SLast z -> String # showList :: [SLast z] -> ShowS #
(Show1 w, Show a) => Show (CoiterT w a)
Instance details Defined in Control.Comonad.Trans.Coiter Methods showsPrec :: Int -> CoiterT w a -> ShowS # show :: CoiterT w a -> String # showList :: [CoiterT w a] -> ShowS #
(Show1 m, Show a) => Show (IterT m a)
Instance details Defined in Control.Monad.Trans.Iter Methods showsPrec :: Int -> IterT m a -> ShowS # show :: IterT m a -> String # showList :: [IterT m a] -> ShowS #
(Show1 f, Show a) => Show (Cofree f a)
Instance details Defined in Control.Comonad.Cofree Methods showsPrec :: Int -> Cofree f a -> ShowS # show :: Cofree f a -> String # showList :: [Cofree f a] -> ShowS #
(Show1 f, Show a) => Show (Free f a)
Instance details Defined in Control.Monad.Free Methods showsPrec :: Int -> Free f a -> ShowS # show :: Free f a -> String # showList :: [Free f a] -> ShowS #
Show (f a) => Show (Yoneda f a)
Instance details Defined in Data.Functor.Yoneda Methods showsPrec :: Int -> Yoneda f a -> ShowS # show :: Yoneda f a -> String # showList :: [Yoneda f a] -> ShowS #
(Show p, Show a) => Show (Entry p a)
Instance details Defined in Data.Heap Methods showsPrec :: Int -> Entry p a -> ShowS # show :: Entry p a -> String # showList :: [Entry p a] -> ShowS #
(PrettyCoeff (Coefficient poly), IsOrderedPolynomial poly, Wraps vars poly, SingI vars) => Show (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods showsPrec :: Int -> LabPolynomial poly vars -> ShowS # show :: LabPolynomial poly vars -> String # showList :: [LabPolynomial poly vars] -> ShowS #
Show (f p) => Show (Rec1 f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> Rec1 f p -> ShowS # show :: Rec1 f p -> String # showList :: [Rec1 f p] -> ShowS #
Show (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Char p -> ShowS # show :: URec Char p -> String # showList :: [URec Char p] -> ShowS #
Show (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Show (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Show (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Word p -> ShowS # show :: URec Word p -> String # showList :: [URec Word p] -> ShowS #
(Show a, Show b, Show c) => Show (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c) -> ShowS # show :: (a, b, c) -> String # showList :: [(a, b, c)] -> ShowS #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
Show (f a) => Show (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS # show :: Ap f a -> String # showList :: [Ap f a] -> ShowS #
Show (f a) => Show (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS # show :: Alt f a -> String # showList :: [Alt f a] -> ShowS #
Show (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~: b) -> ShowS # show :: (a :~: b) -> String # showList :: [a :~: b] -> ShowS #
(Show e, Show1 m, Show a) => Show (ExceptT e m a)
Instance details Defined in Control.Monad.Trans.Except Methods showsPrec :: Int -> ExceptT e m a -> ShowS # show :: ExceptT e m a -> String # showList :: [ExceptT e m a] -> ShowS #
KnownNat n => Show (OrderedMonomial ord n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> OrderedMonomial ord n -> ShowS # show :: OrderedMonomial ord n -> String # showList :: [OrderedMonomial ord n] -> ShowS #
(Show1 f, Show a) => Show (IdentityT f a)
Instance details Defined in Control.Monad.Trans.Identity Methods showsPrec :: Int -> IdentityT f a -> ShowS # show :: IdentityT f a -> String # showList :: [IdentityT f a] -> ShowS #
(Show e, Show1 m, Show a) => Show (ErrorT e m a)
Instance details Defined in Control.Monad.Trans.Error Methods showsPrec :: Int -> ErrorT e m a -> ShowS # show :: ErrorT e m a -> String # showList :: [ErrorT e m a] -> ShowS #
(Show w, Show1 m, Show a) => Show (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods showsPrec :: Int -> WriterT w m a -> ShowS # show :: WriterT w m a -> String # showList :: [WriterT w m a] -> ShowS #
(Show w, Show1 m, Show a) => Show (WriterT w m a)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods showsPrec :: Int -> WriterT w m a -> ShowS # show :: WriterT w m a -> String # showList :: [WriterT w m a] -> ShowS #
(Show1 f, Show a) => Show (Reverse f a)
Instance details Defined in Data.Functor.Reverse Methods showsPrec :: Int -> Reverse f a -> ShowS # show :: Reverse f a -> String # showList :: [Reverse f a] -> ShowS #
Show a => Show (Constant a b)
Instance details Defined in Data.Functor.Constant Methods showsPrec :: Int -> Constant a b -> ShowS # show :: Constant a b -> String # showList :: [Constant a b] -> ShowS #
(Show1 f, Show a) => Show (Backwards f a)
Instance details Defined in Control.Applicative.Backwards Methods showsPrec :: Int -> Backwards f a -> ShowS # show :: Backwards f a -> String # showList :: [Backwards f a] -> ShowS #
Show (f a) => Show (Sized f n a)
Instance details Defined in Data.Sized.Internal Methods showsPrec :: Int -> Sized f n a -> ShowS # show :: Sized f n a -> String # showList :: [Sized f n a] -> ShowS #
Show (f a) => Show (Flipped f a n)
Instance details Defined in Data.Sized.Flipped Methods showsPrec :: Int -> Flipped f a n -> ShowS # show :: Flipped f a n -> String # showList :: [Flipped f a n] -> ShowS #
(ShowSing a, ShowSing b) => Show (SArg z)
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> SArg z -> ShowS # show :: SArg z -> String # showList :: [SArg z] -> ShowS #
Show (SProxy z)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods showsPrec :: Int -> SProxy z -> ShowS # show :: SProxy z -> String # showList :: [SProxy z] -> ShowS #
Show (f a) => Show (CApp f a)
Instance details Defined in Control.Subcategory.Applicative Methods showsPrec :: Int -> CApp f a -> ShowS # show :: CApp f a -> String # showList :: [CApp f a] -> ShowS #
(r ~ Coefficient poly, IsOrderedPolynomial poly, SingI (Replicate n 1), KnownNat n, CoeffRing r, IsMonomialOrder n order, PrettyCoeff r) => Show (PadPolyL n order poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods showsPrec :: Int -> PadPolyL n order poly -> ShowS # show :: PadPolyL n order poly -> String # showList :: [PadPolyL n order poly] -> ShowS #
Show b => Show (Tagged s b)
Instance details Defined in Data.Tagged Methods showsPrec :: Int -> Tagged s b -> ShowS # show :: Tagged s b -> String # showList :: [Tagged s b] -> ShowS #
Show (w (CofreeF f a (CofreeT f w a))) => Show (CofreeT f w a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods showsPrec :: Int -> CofreeT f w a -> ShowS # show :: CofreeT f w a -> String # showList :: [CofreeT f w a] -> ShowS #
(Show a, Show (f b)) => Show (CofreeF f a b)
Instance details Defined in Control.Comonad.Trans.Cofree Methods showsPrec :: Int -> CofreeF f a b -> ShowS # show :: CofreeF f a b -> String # showList :: [CofreeF f a b] -> ShowS #
Show (p (Fix p a) a) => Show (Fix p a)
Instance details Defined in Data.Bifunctor.Fix Methods showsPrec :: Int -> Fix p a -> ShowS # show :: Fix p a -> String # showList :: [Fix p a] -> ShowS #
(Show1 f, Show1 m, Show a) => Show (FreeT f m a)
Instance details Defined in Control.Monad.Trans.Free Methods showsPrec :: Int -> FreeT f m a -> ShowS # show :: FreeT f m a -> String # showList :: [FreeT f m a] -> ShowS #
(Show a, Show (f b)) => Show (FreeF f a b)
Instance details Defined in Control.Monad.Trans.Free Methods showsPrec :: Int -> FreeF f a b -> ShowS # show :: FreeF f a b -> String # showList :: [FreeF f a b] -> ShowS #
Show (p a a) => Show (Join p a)
Instance details Defined in Data.Bifunctor.Join Methods showsPrec :: Int -> Join p a -> ShowS # show :: Join p a -> String # showList :: [Join p a] -> ShowS #
Show (f a) => Show (CZippy f a)
Instance details Defined in Control.Subcategory.Zip Methods showsPrec :: Int -> CZippy f a -> ShowS # show :: CZippy f a -> String # showList :: [CZippy f a] -> ShowS #
Show poly => Show (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods showsPrec :: Int -> Quotient poly ideal -> ShowS # show :: Quotient poly ideal -> String # showList :: [Quotient poly ideal] -> ShowS #
Show c => Show (K1 i c p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> K1 i c p -> ShowS # show :: K1 i c p -> String # showList :: [K1 i c p] -> ShowS #
(Show (f p), Show (g p)) => Show ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :+: g) p -> ShowS # show :: (f :+: g) p -> String # showList :: [(f :+: g) p] -> ShowS #
(Show (f p), Show (g p)) => Show ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :: g) p -> ShowS # show :: (f :: g) p -> String # showList :: [(f :*: g) p] -> ShowS #
(Show a, Show b, Show c, Show d) => Show (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d) -> ShowS # show :: (a, b, c, d) -> String # showList :: [(a, b, c, d)] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods showsPrec :: Int -> Product f g a -> ShowS # show :: Product f g a -> String # showList :: [Product f g a] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods showsPrec :: Int -> Sum f g a -> ShowS # show :: Sum f g a -> String # showList :: [Sum f g a] -> ShowS #
Show (a :~~: b)	Since: base-4.10.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~~: b) -> ShowS # show :: (a :~~: b) -> String # showList :: [a :~~: b] -> ShowS #
(Show i, Show a) => Show (Magma i t b a)
Instance details Defined in Control.Lens.Internal.Magma Methods showsPrec :: Int -> Magma i t b a -> ShowS # show :: Magma i t b a -> String # showList :: [Magma i t b a] -> ShowS #
(KnownNat n, CoeffRing r, IsMonomialOrder n order, PrettyCoeff r) => Show (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods showsPrec :: Int -> OrderedPolynomial r order n -> ShowS # show :: OrderedPolynomial r order n -> String # showList :: [OrderedPolynomial r order n] -> ShowS #
Show (f p) => Show (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> M1 i c f p -> ShowS # show :: M1 i c f p -> String # showList :: [M1 i c f p] -> ShowS #
Show (f (g p)) => Show ((f :.: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :.: g) p -> ShowS # show :: (f :.: g) p -> String # showList :: [(f :.: g) p] -> ShowS #
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e) -> ShowS # show :: (a, b, c, d, e) -> String # showList :: [(a, b, c, d, e)] -> ShowS #
(Show1 f, Show1 g, Show a) => Show (Compose f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods showsPrec :: Int -> Compose f g a -> ShowS # show :: Compose f g a -> String # showList :: [Compose f g a] -> ShowS #
Show (f a) => Show (Clown f a b)
Instance details Defined in Data.Bifunctor.Clown Methods showsPrec :: Int -> Clown f a b -> ShowS # show :: Clown f a b -> String # showList :: [Clown f a b] -> ShowS #
Show (p b a) => Show (Flip p a b)
Instance details Defined in Data.Bifunctor.Flip Methods showsPrec :: Int -> Flip p a b -> ShowS # show :: Flip p a b -> String # showList :: [Flip p a b] -> ShowS #
Show (g b) => Show (Joker g a b)
Instance details Defined in Data.Bifunctor.Joker Methods showsPrec :: Int -> Joker g a b -> ShowS # show :: Joker g a b -> String # showList :: [Joker g a b] -> ShowS #
Show (p a b) => Show (WrappedBifunctor p a b)
Instance details Defined in Data.Bifunctor.Wrapped Methods showsPrec :: Int -> WrappedBifunctor p a b -> ShowS # show :: WrappedBifunctor p a b -> String # showList :: [WrappedBifunctor p a b] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS # show :: (a, b, c, d, e, f) -> String # showList :: [(a, b, c, d, e, f)] -> ShowS #
(Show (f a b), Show (g a b)) => Show (Product f g a b)
Instance details Defined in Data.Bifunctor.Product Methods showsPrec :: Int -> Product f g a b -> ShowS # show :: Product f g a b -> String # showList :: [Product f g a b] -> ShowS #
(Show (p a b), Show (q a b)) => Show (Sum p q a b)
Instance details Defined in Data.Bifunctor.Sum Methods showsPrec :: Int -> Sum p q a b -> ShowS # show :: Sum p q a b -> String # showList :: [Sum p q a b] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS # show :: (a, b, c, d, e, f, g) -> String # showList :: [(a, b, c, d, e, f, g)] -> ShowS #
Show (f (p a b)) => Show (Tannen f p a b)
Instance details Defined in Data.Bifunctor.Tannen Methods showsPrec :: Int -> Tannen f p a b -> ShowS # show :: Tannen f p a b -> String # showList :: [Tannen f p a b] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS # show :: (a, b, c, d, e, f, g, h) -> String # showList :: [(a, b, c, d, e, f, g, h)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS # show :: (a, b, c, d, e, f, g, h, i) -> String # showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS #
Show (p (f a) (g b)) => Show (Biff p f g a b)
Instance details Defined in Data.Bifunctor.Biff Methods showsPrec :: Int -> Biff p f g a b -> ShowS # show :: Biff p f g a b -> String # showList :: [Biff p f g a b] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS #
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS #

class Typeable (a :: k) #

The class Typeable allows a concrete representation of a type to be calculated.

Minimal complete definition

typeRep#

class Monad m => MonadFail (m :: Type -> Type) where #

When a value is bound in do-notation, the pattern on the left hand side of <- might not match. In this case, this class provides a function to recover.

A Monad without a MonadFail instance may only be used in conjunction with pattern that always match, such as newtypes, tuples, data types with only a single data constructor, and irrefutable patterns (~pat).

Instances of MonadFail should satisfy the following law: fail s should be a left zero for >>=,

fail s >>= f  =  fail s

If your Monad is also MonadPlus, a popular definition is

fail _ = mzero

Since: base-4.9.0.0

Methods

fail :: String -> m a #

Instances

Instances details

MonadFail []	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> [a] #
MonadFail Maybe	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> Maybe a #
MonadFail IO	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> IO a #
MonadFail Q
Instance details Defined in Language.Haskell.TH.Syntax Methods fail :: String -> Q a #
MonadFail Vector
Instance details Defined in Data.Vector Methods fail :: String -> Vector a #
MonadFail ReadPrec	Since: base-4.9.0.0
Instance details Defined in Text.ParserCombinators.ReadPrec Methods fail :: String -> ReadPrec a #
MonadFail ReadP	Since: base-4.9.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fail :: String -> ReadP a #
MonadFail P	Since: base-4.9.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fail :: String -> P a #
MonadFail Array
Instance details Defined in Data.Primitive.Array Methods fail :: String -> Array a #
MonadFail SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods fail :: String -> SmallArray a #
MonadFail (ST s)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods fail :: String -> ST s a #
MonadFail (ST s)	Since: base-4.10
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fail :: String -> ST s a #
Monad m => MonadFail (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods fail :: String -> MaybeT m a #
Monad m => MonadFail (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods fail :: String -> CatchT m a #
Monad m => MonadFail (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods fail :: String -> ListT m a #
MonadFail f => MonadFail (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods fail :: String -> WrapFunctor f a #
Monad m => MonadFail (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods fail :: String -> IterT m a #
MonadFail f => MonadFail (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fail :: String -> Ap f a #
MonadFail m => MonadFail (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods fail :: String -> ExceptT e m a #
MonadFail m => MonadFail (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods fail :: String -> IdentityT m a #
(Monad m, Error e) => MonadFail (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods fail :: String -> ErrorT e m a #
MonadFail m => MonadFail (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fail :: String -> ReaderT r m a #
MonadFail m => MonadFail (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods fail :: String -> StateT s m a #
MonadFail m => MonadFail (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fail :: String -> StateT s m a #
(Monoid w, MonadFail m) => MonadFail (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fail :: String -> WriterT w m a #
(Monoid w, MonadFail m) => MonadFail (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fail :: String -> WriterT w m a #
MonadFail m => MonadFail (Reverse m)
Instance details Defined in Data.Functor.Reverse Methods fail :: String -> Reverse m a #
(Functor f, MonadFail m) => MonadFail (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods fail :: String -> FreeT f m a #
MonadFail m => MonadFail (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods fail :: String -> RandT g m a #
MonadFail m => MonadFail (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods fail :: String -> RandT g m a #
MonadFail m => MonadFail (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods fail :: String -> ContT r m a #
(Monoid w, MonadFail m) => MonadFail (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods fail :: String -> RWST r w s m a #
(Monoid w, MonadFail m) => MonadFail (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods fail :: String -> RWST r w s m a #

class IsString a where #

Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).

Methods

fromString :: String -> a #

Instances

Instances details

IsString ByteString	Beware: `fromString` truncates multi-byte characters to octets. e.g. "枯朶に烏のとまりけり秋の暮" becomes �6k�nh~�Q��n�
Instance details Defined in Data.ByteString.Internal Methods fromString :: String -> ByteString #
IsString ShortByteString	Beware: `fromString` truncates multi-byte characters to octets. e.g. "枯朶に烏のとまりけり秋の暮" becomes �6k�nh~�Q��n�
Instance details Defined in Data.ByteString.Short.Internal Methods fromString :: String -> ShortByteString #
IsString ByteString	Beware: `fromString` truncates multi-byte characters to octets. e.g. "枯朶に烏のとまりけり秋の暮" becomes �6k�nh~�Q��n�
Instance details Defined in Data.ByteString.Lazy.Internal Methods fromString :: String -> ByteString #
IsString Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods fromString :: String -> Doc #
a ~ Char => IsString [a]	`(a ~ Char)` context was introduced in `4.9.0.0` Since: base-2.1
Instance details Defined in Data.String Methods fromString :: String -> [a] #
a ~ Char => IsString (Seq a)	Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods fromString :: String -> Seq a #
IsString a => IsString (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.String Methods fromString :: String -> Identity a #
IsString (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fromString :: String -> Doc a #
(IsString a, Hashable a) => IsString (Hashed a)
Instance details Defined in Data.Hashable.Class Methods fromString :: String -> Hashed a #
IsString a => IsString (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.String Methods fromString :: String -> Const a b #
IsString a => IsString (Tagged s a)
Instance details Defined in Data.Tagged Methods fromString :: String -> Tagged s a #

class Functor f => Applicative (f :: Type -> Type) where #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity

pure id <*> v = v

Composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

Homomorphism

pure f <*> pure x = pure (f x)

Interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = (id <$ u) <*> v
```
```
u <* v = liftA2 const u v
```

As a consequence of these laws, the Functor instance for f will satisfy

```
fmap f x = pure f <*> x
```

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

```
pure = return
```

m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

```
(*>) = (>>)
```

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 #

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Using ApplicativeDo: 'fs <*> as' can be understood as the do expression

do f <- fs
   a <- as
   pure (f a)

liftA2 :: (a -> b -> c) -> f a -> f b -> f c #

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
   b <- bs
   pure (f a b)

(*>) :: f a -> f b -> f b infixl 4 #

Sequence actions, discarding the value of the first argument.

'as *> bs' can be understood as the do expression

do as
   bs

This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form

do _ <- as
   b <- bs
   pure b

(<*) :: f a -> f b -> f a infixl 4 #

Sequence actions, discarding the value of the second argument.

Using ApplicativeDo: 'as <* bs' can be understood as the do expression

do a <- as
   bs
   pure a

Instances

Instances details

Applicative []	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] # (<>) :: [a -> b] -> [a] -> [b] # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] # (>) :: [a] -> [b] -> [b] # (<*) :: [a] -> [b] -> [a] #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Applicative Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Par1 a # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b # liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c # (>) :: Par1 a -> Par1 b -> Par1 b # (<*) :: Par1 a -> Par1 b -> Par1 a #
Applicative Q
Instance details Defined in Language.Haskell.TH.Syntax Methods pure :: a -> Q a # (<>) :: Q (a -> b) -> Q a -> Q b # liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c # (>) :: Q a -> Q b -> Q b # (<*) :: Q a -> Q b -> Q a #
Applicative Vector
Instance details Defined in Data.Vector Methods pure :: a -> Vector a # (<>) :: Vector (a -> b) -> Vector a -> Vector b # liftA2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c # (>) :: Vector a -> Vector b -> Vector b # (<*) :: Vector a -> Vector b -> Vector a #
Applicative Seq	Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods pure :: a -> Seq a # (<>) :: Seq (a -> b) -> Seq a -> Seq b # liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # (>) :: Seq a -> Seq b -> Seq b # (<*) :: Seq a -> Seq b -> Seq a #
Applicative Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a # (<>) :: Down (a -> b) -> Down a -> Down b # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c # (>) :: Down a -> Down b -> Down b # (<*) :: Down a -> Down b -> Down a #
Applicative Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Applicative Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a # (<>) :: Min (a -> b) -> Min a -> Min b # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c # (>) :: Min a -> Min b -> Min b # (<*) :: Min a -> Min b -> Min a #
Applicative Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a # (<>) :: Max (a -> b) -> Max a -> Max b # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c # (>) :: Max a -> Max b -> Max b # (<*) :: Max a -> Max b -> Max a #
Applicative First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Option a # (<>) :: Option (a -> b) -> Option a -> Option b # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c # (>) :: Option a -> Option b -> Option b # (<*) :: Option a -> Option b -> Option a #
Applicative ZipList	f <$> ZipList xs1 <> ... <> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c # (>) :: ZipList a -> ZipList b -> ZipList b # (<*) :: ZipList a -> ZipList b -> ZipList a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Applicative STM	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods pure :: a -> STM a # (<>) :: STM (a -> b) -> STM a -> STM b # liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c # (>) :: STM a -> STM b -> STM b # (<*) :: STM a -> STM b -> STM a #
Applicative First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Applicative ReadPrec	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadPrec Methods pure :: a -> ReadPrec a # (<>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b # liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c # (>) :: ReadPrec a -> ReadPrec b -> ReadPrec b # (<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a #
Applicative ReadP	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a # (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c # (>) :: ReadP a -> ReadP b -> ReadP b # (<*) :: ReadP a -> ReadP b -> ReadP a #
Applicative NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a #
Applicative Tree
Instance details Defined in Data.Tree Methods pure :: a -> Tree a # (<>) :: Tree (a -> b) -> Tree a -> Tree b # liftA2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c # (>) :: Tree a -> Tree b -> Tree b # (<*) :: Tree a -> Tree b -> Tree a #
Applicative Id
Instance details Defined in Data.Vector.Fusion.Util Methods pure :: a -> Id a # (<>) :: Id (a -> b) -> Id a -> Id b # liftA2 :: (a -> b -> c) -> Id a -> Id b -> Id c # (>) :: Id a -> Id b -> Id b # (<*) :: Id a -> Id b -> Id a #
Applicative Complex
Instance details Defined in Numeric.Algebra.Complex Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Applicative P	Since: base-4.5.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> P a # (<>) :: P (a -> b) -> P a -> P b # liftA2 :: (a -> b -> c) -> P a -> P b -> P c # (>) :: P a -> P b -> P b # (<*) :: P a -> P b -> P a #
Applicative Box
Instance details Defined in Data.Vector.Fusion.Util Methods pure :: a -> Box a # (<>) :: Box (a -> b) -> Box a -> Box b # liftA2 :: (a -> b -> c) -> Box a -> Box b -> Box c # (>) :: Box a -> Box b -> Box b # (<*) :: Box a -> Box b -> Box a #
Applicative Array
Instance details Defined in Data.Primitive.Array Methods pure :: a -> Array a # (<>) :: Array (a -> b) -> Array a -> Array b # liftA2 :: (a -> b -> c) -> Array a -> Array b -> Array c # (>) :: Array a -> Array b -> Array b # (<*) :: Array a -> Array b -> Array a #
Applicative SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods pure :: a -> SmallArray a # (<>) :: SmallArray (a -> b) -> SmallArray a -> SmallArray b # liftA2 :: (a -> b -> c) -> SmallArray a -> SmallArray b -> SmallArray c # (>) :: SmallArray a -> SmallArray b -> SmallArray b # (<*) :: SmallArray a -> SmallArray b -> SmallArray a #
Applicative Matrix
Instance details Defined in Data.Matrix Methods pure :: a -> Matrix a # (<>) :: Matrix (a -> b) -> Matrix a -> Matrix b # liftA2 :: (a -> b -> c) -> Matrix a -> Matrix b -> Matrix c # (>) :: Matrix a -> Matrix b -> Matrix b # (<*) :: Matrix a -> Matrix b -> Matrix a #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Applicative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Monoid a => Applicative ((,) a)	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <> ("world!", 2002) ("hello world!",2017) Since: base-2.1*
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) # (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b) # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) # (>) :: (a, a0) -> (a, b) -> (a, b) # (<*) :: (a, a0) -> (a, b) -> (a, a0) #
Applicative (Covector r)
Instance details Defined in Numeric.Covector Methods pure :: a -> Covector r a # (<>) :: Covector r (a -> b) -> Covector r a -> Covector r b # liftA2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c # (>) :: Covector r a -> Covector r b -> Covector r b # (<*) :: Covector r a -> Covector r b -> Covector r a #
Applicative (ST s)	Since: base-4.4.0.0
Instance details Defined in GHC.ST Methods pure :: a -> ST s a # (<>) :: ST s (a -> b) -> ST s a -> ST s b # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c # (>) :: ST s a -> ST s b -> ST s b # (<*) :: ST s a -> ST s b -> ST s a #
Applicative (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods pure :: a -> ST s a # (<>) :: ST s (a -> b) -> ST s a -> ST s b # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c # (>) :: ST s a -> ST s b -> ST s b # (<*) :: ST s a -> ST s b -> ST s a #
Monad m => Applicative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #
Arrow a => Applicative (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 #
Applicative (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
(Functor m, Monad m) => Applicative (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods pure :: a -> MaybeT m a # (<>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b # liftA2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c # (>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # (<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #
Monad m => Applicative (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods pure :: a -> CatchT m a # (<>) :: CatchT m (a -> b) -> CatchT m a -> CatchT m b # liftA2 :: (a -> b -> c) -> CatchT m a -> CatchT m b -> CatchT m c # (>) :: CatchT m a -> CatchT m b -> CatchT m b # (<*) :: CatchT m a -> CatchT m b -> CatchT m a #
Applicative m => Applicative (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods pure :: a -> ListT m a # (<>) :: ListT m (a -> b) -> ListT m a -> ListT m b # liftA2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c # (>) :: ListT m a -> ListT m b -> ListT m b # (<*) :: ListT m a -> ListT m b -> ListT m a #
Applicative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a #
Applicative (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Applicative f => Applicative (WrappedPoly f)
Instance details Defined in Data.MonoTraversable Methods pure :: a -> WrappedPoly f a # (<>) :: WrappedPoly f (a -> b) -> WrappedPoly f a -> WrappedPoly f b # liftA2 :: (a -> b -> c) -> WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f c # (>) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f b # (<*) :: WrappedPoly f a -> WrappedPoly f b -> WrappedPoly f a #
Semigroup a => Applicative (These a)
Instance details Defined in Data.These Methods pure :: a0 -> These a a0 # (<>) :: These a (a0 -> b) -> These a a0 -> These a b # liftA2 :: (a0 -> b -> c) -> These a a0 -> These a b -> These a c # (>) :: These a a0 -> These a b -> These a b # (<*) :: These a a0 -> These a b -> These a a0 #
Applicative f => Applicative (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods pure :: a -> WrapFunctor f a # (<>) :: WrapFunctor f (a -> b) -> WrapFunctor f a -> WrapFunctor f b # liftA2 :: (a -> b -> c) -> WrapFunctor f a -> WrapFunctor f b -> WrapFunctor f c # (>) :: WrapFunctor f a -> WrapFunctor f b -> WrapFunctor f b # (<*) :: WrapFunctor f a -> WrapFunctor f b -> WrapFunctor f a #
Applicative (Alt f)
Instance details Defined in Control.Alternative.Free Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: Alt f a -> Alt f b -> Alt f b # (<*) :: Alt f a -> Alt f b -> Alt f a #
Applicative (AltF f)
Instance details Defined in Control.Alternative.Free Methods pure :: a -> AltF f a # (<>) :: AltF f (a -> b) -> AltF f a -> AltF f b # liftA2 :: (a -> b -> c) -> AltF f a -> AltF f b -> AltF f c # (>) :: AltF f a -> AltF f b -> AltF f b # (<*) :: AltF f a -> AltF f b -> AltF f a #
Monad m => Applicative (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods pure :: a -> IterT m a # (<>) :: IterT m (a -> b) -> IterT m a -> IterT m b # liftA2 :: (a -> b -> c) -> IterT m a -> IterT m b -> IterT m c # (>) :: IterT m a -> IterT m b -> IterT m b # (<*) :: IterT m a -> IterT m b -> IterT m a #
Apply f => Applicative (MaybeApply f)
Instance details Defined in Data.Functor.Bind.Class Methods pure :: a -> MaybeApply f a # (<>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b # liftA2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c # (>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b # (<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a #
Applicative f => Applicative (WrappedApplicative f)
Instance details Defined in Data.Functor.Bind.Class Methods pure :: a -> WrappedApplicative f a # (<>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # liftA2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c # (>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b # (<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a #
Applicative f => Applicative (Indexing f)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a -> Indexing f a # (<>) :: Indexing f (a -> b) -> Indexing f a -> Indexing f b # liftA2 :: (a -> b -> c) -> Indexing f a -> Indexing f b -> Indexing f c # (>) :: Indexing f a -> Indexing f b -> Indexing f b # (<*) :: Indexing f a -> Indexing f b -> Indexing f a #
Representable f => Applicative (Co f)
Instance details Defined in Data.Functor.Rep Methods pure :: a -> Co f a # (<>) :: Co f (a -> b) -> Co f a -> Co f b # liftA2 :: (a -> b -> c) -> Co f a -> Co f b -> Co f c # (>) :: Co f a -> Co f b -> Co f b # (<*) :: Co f a -> Co f b -> Co f a #
Alternative f => Applicative (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods pure :: a -> Cofree f a # (<>) :: Cofree f (a -> b) -> Cofree f a -> Cofree f b # liftA2 :: (a -> b -> c) -> Cofree f a -> Cofree f b -> Cofree f c # (>) :: Cofree f a -> Cofree f b -> Cofree f b # (<*) :: Cofree f a -> Cofree f b -> Cofree f a #
Functor f => Applicative (Free f)
Instance details Defined in Control.Monad.Free Methods pure :: a -> Free f a # (<>) :: Free f (a -> b) -> Free f a -> Free f b # liftA2 :: (a -> b -> c) -> Free f a -> Free f b -> Free f c # (>) :: Free f a -> Free f b -> Free f b # (<*) :: Free f a -> Free f b -> Free f a #
Applicative f => Applicative (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods pure :: a -> Yoneda f a # (<>) :: Yoneda f (a -> b) -> Yoneda f a -> Yoneda f b # liftA2 :: (a -> b -> c) -> Yoneda f a -> Yoneda f b -> Yoneda f c # (>) :: Yoneda f a -> Yoneda f b -> Yoneda f b # (<*) :: Yoneda f a -> Yoneda f b -> Yoneda f a #
Applicative (StateL s)
Instance details Defined in Data.Key Methods pure :: a -> StateL s a # (<>) :: StateL s (a -> b) -> StateL s a -> StateL s b # liftA2 :: (a -> b -> c) -> StateL s a -> StateL s b -> StateL s c # (>) :: StateL s a -> StateL s b -> StateL s b # (<*) :: StateL s a -> StateL s b -> StateL s a #
Applicative (StateR s)
Instance details Defined in Data.Key Methods pure :: a -> StateR s a # (<>) :: StateR s (a -> b) -> StateR s a -> StateR s b # liftA2 :: (a -> b -> c) -> StateR s a -> StateR s b -> StateR s c # (>) :: StateR s a -> StateR s b -> StateR s b # (<*) :: StateR s a -> StateR s b -> StateR s a #
Applicative f => Applicative (Indexing64 f)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a -> Indexing64 f a # (<>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b # liftA2 :: (a -> b -> c) -> Indexing64 f a -> Indexing64 f b -> Indexing64 f c # (>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b # (<*) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a #
Applicative f => Applicative (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #
(Monoid a, Monoid b) => Applicative ((,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, a0) # (<>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) # liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) # (>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) # (<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) #
Arrow a => Applicative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Applicative m => Applicative (Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> Kleisli m a a0 # (<>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c # (>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Applicative f => Applicative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a # (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c # (>) :: Ap f a -> Ap f b -> Ap f b # (<*) :: Ap f a -> Ap f b -> Ap f a #
Applicative f => Applicative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: Alt f a -> Alt f b -> Alt f b # (<*) :: Alt f a -> Alt f b -> Alt f a #
(Applicative f, Monad f) => Applicative (WhenMissing f x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a #
(Functor m, Monad m) => Applicative (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a # (<>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c # (>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #
Applicative m => Applicative (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a # (<>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c # (>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a #
(Functor m, Monad m) => Applicative (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a # (<>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c # (>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #
Applicative m => Applicative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # (>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
Applicative f => Applicative (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods pure :: a -> Reverse f a # (<>) :: Reverse f (a -> b) -> Reverse f a -> Reverse f b # liftA2 :: (a -> b -> c) -> Reverse f a -> Reverse f b -> Reverse f c # (>) :: Reverse f a -> Reverse f b -> Reverse f b # (<*) :: Reverse f a -> Reverse f b -> Reverse f a #
Monoid a => Applicative (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods pure :: a0 -> Constant a a0 # (<>) :: Constant a (a0 -> b) -> Constant a a0 -> Constant a b # liftA2 :: (a0 -> b -> c) -> Constant a a0 -> Constant a b -> Constant a c # (>) :: Constant a a0 -> Constant a b -> Constant a b # (<*) :: Constant a a0 -> Constant a b -> Constant a a0 #
Applicative f => Applicative (Backwards f)	Apply `f`-actions in the reverse order.
Instance details Defined in Control.Applicative.Backwards Methods pure :: a -> Backwards f a # (<>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b # liftA2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c # (>) :: Backwards f a -> Backwards f b -> Backwards f b # (<*) :: Backwards f a -> Backwards f b -> Backwards f a #
Applicative (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a0 -> Indexed i a a0 # (<>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # liftA2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c # (>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 #
Applicative f => Applicative (CAlt f)
Instance details Defined in Control.Subcategory.Alternative Methods pure :: a -> CAlt f a # (<>) :: CAlt f (a -> b) -> CAlt f a -> CAlt f b # liftA2 :: (a -> b -> c) -> CAlt f a -> CAlt f b -> CAlt f c # (>) :: CAlt f a -> CAlt f b -> CAlt f b # (<*) :: CAlt f a -> CAlt f b -> CAlt f a #
Applicative f => Applicative (CApp f)
Instance details Defined in Control.Subcategory.Applicative Methods pure :: a -> CApp f a # (<>) :: CApp f (a -> b) -> CApp f a -> CApp f b # liftA2 :: (a -> b -> c) -> CApp f a -> CApp f b -> CApp f c # (>) :: CApp f a -> CApp f b -> CApp f b # (<*) :: CApp f a -> CApp f b -> CApp f a #
Applicative (Tagged s)
Instance details Defined in Data.Tagged Methods pure :: a -> Tagged s a # (<>) :: Tagged s (a -> b) -> Tagged s a -> Tagged s b # liftA2 :: (a -> b -> c) -> Tagged s a -> Tagged s b -> Tagged s c # (>) :: Tagged s a -> Tagged s b -> Tagged s b # (<*) :: Tagged s a -> Tagged s b -> Tagged s a #
Applicative g => Applicative (ApT f g)
Instance details Defined in Control.Applicative.Trans.Free Methods pure :: a -> ApT f g a # (<>) :: ApT f g (a -> b) -> ApT f g a -> ApT f g b # liftA2 :: (a -> b -> c) -> ApT f g a -> ApT f g b -> ApT f g c # (>) :: ApT f g a -> ApT f g b -> ApT f g b # (<*) :: ApT f g a -> ApT f g b -> ApT f g a #
Applicative g => Applicative (ApF f g)
Instance details Defined in Control.Applicative.Trans.Free Methods pure :: a -> ApF f g a # (<>) :: ApF f g (a -> b) -> ApF f g a -> ApF f g b # liftA2 :: (a -> b -> c) -> ApF f g a -> ApF f g b -> ApF f g c # (>) :: ApF f g a -> ApF f g b -> ApF f g b # (<*) :: ApF f g a -> ApF f g b -> ApF f g a #
(Alternative f, Applicative w) => Applicative (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods pure :: a -> CofreeT f w a # (<>) :: CofreeT f w (a -> b) -> CofreeT f w a -> CofreeT f w b # liftA2 :: (a -> b -> c) -> CofreeT f w a -> CofreeT f w b -> CofreeT f w c # (>) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w b # (<*) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w a #
Biapplicative p => Applicative (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods pure :: a -> Fix p a # (<>) :: Fix p (a -> b) -> Fix p a -> Fix p b # liftA2 :: (a -> b -> c) -> Fix p a -> Fix p b -> Fix p c # (>) :: Fix p a -> Fix p b -> Fix p b # (<*) :: Fix p a -> Fix p b -> Fix p a #
(Functor f, Monad m) => Applicative (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods pure :: a -> FreeT f m a # (<>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b # liftA2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c # (>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # (<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a #
Biapplicative p => Applicative (Join p)
Instance details Defined in Data.Bifunctor.Join Methods pure :: a -> Join p a # (<>) :: Join p (a -> b) -> Join p a -> Join p b # liftA2 :: (a -> b -> c) -> Join p a -> Join p b -> Join p c # (>) :: Join p a -> Join p b -> Join p b # (<*) :: Join p a -> Join p b -> Join p a #
Applicative f => Applicative (Static f a)
Instance details Defined in Data.Semigroupoid.Static Methods pure :: a0 -> Static f a a0 # (<>) :: Static f a (a0 -> b) -> Static f a a0 -> Static f a b # liftA2 :: (a0 -> b -> c) -> Static f a a0 -> Static f a b -> Static f a c # (>) :: Static f a a0 -> Static f a b -> Static f a b # (<*) :: Static f a a0 -> Static f a b -> Static f a a0 #
Applicative w => Applicative (TracedT m w)
Instance details Defined in Control.Comonad.Trans.Traced Methods pure :: a -> TracedT m w a # (<>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b # liftA2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c # (>) :: TracedT m w a -> TracedT m w b -> TracedT m w b # (<*) :: TracedT m w a -> TracedT m w b -> TracedT m w a #
Monad m => Applicative (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods pure :: a -> RandT g m a # (<>) :: RandT g m (a -> b) -> RandT g m a -> RandT g m b # liftA2 :: (a -> b -> c) -> RandT g m a -> RandT g m b -> RandT g m c # (>) :: RandT g m a -> RandT g m b -> RandT g m b # (<*) :: RandT g m a -> RandT g m b -> RandT g m a #
Monad m => Applicative (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods pure :: a -> RandT g m a # (<>) :: RandT g m (a -> b) -> RandT g m a -> RandT g m b # liftA2 :: (a -> b -> c) -> RandT g m a -> RandT g m b -> RandT g m c # (>) :: RandT g m a -> RandT g m b -> RandT g m b # (<*) :: RandT g m a -> RandT g m b -> RandT g m a #
(Applicative f, Applicative g) => Applicative (Day f g)
Instance details Defined in Data.Functor.Day Methods pure :: a -> Day f g a # (<>) :: Day f g (a -> b) -> Day f g a -> Day f g b # liftA2 :: (a -> b -> c) -> Day f g a -> Day f g b -> Day f g c # (>) :: Day f g a -> Day f g b -> Day f g b # (<*) :: Day f g a -> Day f g b -> Day f g a #
(Applicative (Rep p), Representable p) => Applicative (Prep p)
Instance details Defined in Data.Profunctor.Rep Methods pure :: a -> Prep p a # (<>) :: Prep p (a -> b) -> Prep p a -> Prep p b # liftA2 :: (a -> b -> c) -> Prep p a -> Prep p b -> Prep p c # (>) :: Prep p a -> Prep p b -> Prep p b # (<*) :: Prep p a -> Prep p b -> Prep p a #
Applicative (Mag a b)
Instance details Defined in Data.Biapplicative Methods pure :: a0 -> Mag a b a0 # (<>) :: Mag a b (a0 -> b0) -> Mag a b a0 -> Mag a b b0 # liftA2 :: (a0 -> b0 -> c) -> Mag a b a0 -> Mag a b b0 -> Mag a b c # (>) :: Mag a b a0 -> Mag a b b0 -> Mag a b b0 # (<*) :: Mag a b a0 -> Mag a b b0 -> Mag a b a0 #
Applicative (Flows i b)
Instance details Defined in Control.Lens.Internal.Level Methods pure :: a -> Flows i b a # (<>) :: Flows i b (a -> b0) -> Flows i b a -> Flows i b b0 # liftA2 :: (a -> b0 -> c) -> Flows i b a -> Flows i b b0 -> Flows i b c # (>) :: Flows i b a -> Flows i b b0 -> Flows i b b0 # (<*) :: Flows i b a -> Flows i b b0 -> Flows i b a #
Applicative (Mafic a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> Mafic a b a0 # (<>) :: Mafic a b (a0 -> b0) -> Mafic a b a0 -> Mafic a b b0 # liftA2 :: (a0 -> b0 -> c) -> Mafic a b a0 -> Mafic a b b0 -> Mafic a b c # (>) :: Mafic a b a0 -> Mafic a b b0 -> Mafic a b b0 # (<*) :: Mafic a b a0 -> Mafic a b b0 -> Mafic a b a0 #
Monoid m => Applicative (Holes t m)
Instance details Defined in Control.Lens.Traversal Methods pure :: a -> Holes t m a # (<>) :: Holes t m (a -> b) -> Holes t m a -> Holes t m b # liftA2 :: (a -> b -> c) -> Holes t m a -> Holes t m b -> Holes t m c # (>) :: Holes t m a -> Holes t m b -> Holes t m b # (<*) :: Holes t m a -> Holes t m b -> Holes t m a #
Applicative ((->) r :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> r -> a # (<>) :: (r -> (a -> b)) -> (r -> a) -> r -> b # liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c # (>) :: (r -> a) -> (r -> b) -> r -> b # (<*) :: (r -> a) -> (r -> b) -> r -> a #
Monoid c => Applicative (K1 i c :: Type -> Type)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> K1 i c a # (<>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b # liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 # (>) :: K1 i c a -> K1 i c b -> K1 i c b # (<*) :: K1 i c a -> K1 i c b -> K1 i c a #
(Applicative f, Applicative g) => Applicative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a #
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, c, a0) # (<>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) # (>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
(Monad f, Applicative f) => Applicative (WhenMatched f x y)	Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a #
(Applicative f, Monad f) => Applicative (WhenMissing f k x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))` . Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a #
Applicative (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods pure :: a -> ContT r m a # (<>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b # liftA2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c # (>) :: ContT r m a -> ContT r m b -> ContT r m b # (<*) :: ContT r m a -> ContT r m b -> ContT r m a #
Applicative (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> Bazaar p a b a0 # (<>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # liftA2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c # (>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<*) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Applicative (Costar f a)
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Costar f a a0 # (<>) :: Costar f a (a0 -> b) -> Costar f a a0 -> Costar f a b # liftA2 :: (a0 -> b -> c) -> Costar f a a0 -> Costar f a b -> Costar f a c # (>) :: Costar f a a0 -> Costar f a b -> Costar f a b # (<*) :: Costar f a a0 -> Costar f a b -> Costar f a a0 #
Applicative f => Applicative (Star f a)
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Star f a a0 # (<>) :: Star f a (a0 -> b) -> Star f a a0 -> Star f a b # liftA2 :: (a0 -> b -> c) -> Star f a a0 -> Star f a b -> Star f a c # (>) :: Star f a a0 -> Star f a b -> Star f a b # (<*) :: Star f a a0 -> Star f a b -> Star f a a0 #
Applicative (Molten i a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> Molten i a b a0 # (<>) :: Molten i a b (a0 -> b0) -> Molten i a b a0 -> Molten i a b b0 # liftA2 :: (a0 -> b0 -> c) -> Molten i a b a0 -> Molten i a b b0 -> Molten i a b c # (>) :: Molten i a b a0 -> Molten i a b b0 -> Molten i a b b0 # (<*) :: Molten i a b a0 -> Molten i a b b0 -> Molten i a b a0 #
Applicative f => Applicative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #
(Applicative f, Applicative g) => Applicative (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Applicative f, Applicative g) => Applicative (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a # (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c # (>) :: Compose f g a -> Compose f g b -> Compose f g b # (<*) :: Compose f g a -> Compose f g b -> Compose f g a #
(Monad f, Applicative f) => Applicative (WhenMatched f k x y)	Equivalent to `ReaderT k (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
Reifies s (ReifiedApplicative f) => Applicative (ReflectedApplicative f s)
Instance details Defined in Data.Reflection Methods pure :: a -> ReflectedApplicative f s a # (<>) :: ReflectedApplicative f s (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # liftA2 :: (a -> b -> c) -> ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s c # (>) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s b # (<*) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s a #
Applicative (TakingWhile p f a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> TakingWhile p f a b a0 # (<>) :: TakingWhile p f a b (a0 -> b0) -> TakingWhile p f a b a0 -> TakingWhile p f a b b0 # liftA2 :: (a0 -> b0 -> c) -> TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b c # (>) :: TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b b0 # (<*) :: TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
Applicative (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> BazaarT p g a b a0 # (<>) :: BazaarT p g a b (a0 -> b0) -> BazaarT p g a b a0 -> BazaarT p g a b b0 # liftA2 :: (a0 -> b0 -> c) -> BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b c # (>) :: BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b b0 # (<*) :: BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #

class Foldable (t :: Type -> Type) where #

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z

foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z

fold = foldMap id

length = getSum . foldMap (Sum . const  1)

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Methods

foldMap :: Monoid m => (a -> m) -> t a -> m #

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

foldr' :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure, but with strict application of the operator.

Since: base-4.6.0.0

foldl :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z `f` x1 in the above example) before applying them to the operator (e.g. to (`f` x2)). This results in a thunk chain $\mathcal{O}(n)$ elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl f z . toList

foldl' :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite list to a single, monolithic result (e.g. length).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

foldr1 :: (a -> a -> a) -> t a -> a #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

foldl1 :: (a -> a -> a) -> t a -> a #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

null :: t a -> Bool #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

length :: t a -> Int #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

elem :: Eq a => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

Since: base-4.8.0.0

maximum :: Ord a => t a -> a #

The largest element of a non-empty structure.

Since: base-4.8.0.0

minimum :: Ord a => t a -> a #

The least element of a non-empty structure.

Since: base-4.8.0.0

Instances

Instances details

Foldable []	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # toList :: [a] -> [a] # null :: [a] -> Bool # length :: [a] -> Int # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # minimum :: Ord a => [a] -> a # sum :: Num a => [a] -> a # product :: Num a => [a] -> a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Foldable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # toList :: Par1 a -> [a] # null :: Par1 a -> Bool # length :: Par1 a -> Int # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # minimum :: Ord a => Par1 a -> a # sum :: Num a => Par1 a -> a # product :: Num a => Par1 a -> a #
Foldable Vector
Instance details Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldMap' :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # toList :: Vector a -> [a] # null :: Vector a -> Bool # length :: Vector a -> Int # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # sum :: Num a => Vector a -> a # product :: Num a => Vector a -> a #
Foldable HashSet
Instance details Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # toList :: HashSet a -> [a] # null :: HashSet a -> Bool # length :: HashSet a -> Int # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # sum :: Num a => HashSet a -> a # product :: Num a => HashSet a -> a #
Foldable Set	Folds in order of increasing key.
Instance details Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # toList :: Set a -> [a] # null :: Set a -> Bool # length :: Set a -> Int # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # minimum :: Ord a => Set a -> a # sum :: Num a => Set a -> a # product :: Num a => Set a -> a #
Foldable Seq
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # toList :: Seq a -> [a] # null :: Seq a -> Bool # length :: Seq a -> Int # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # minimum :: Ord a => Seq a -> a # sum :: Num a => Seq a -> a # product :: Num a => Seq a -> a #
Foldable IntMap	Folds in order of increasing key.
Instance details Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # toList :: IntMap a -> [a] # null :: IntMap a -> Bool # length :: IntMap a -> Int # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # sum :: Num a => IntMap a -> a # product :: Num a => IntMap a -> a #
Foldable Down	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # toList :: Down a -> [a] # null :: Down a -> Bool # length :: Down a -> Int # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # minimum :: Ord a => Down a -> a # sum :: Num a => Down a -> a # product :: Num a => Down a -> a #
Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Foldable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # toList :: Min a -> [a] # null :: Min a -> Bool # length :: Min a -> Int # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # minimum :: Ord a => Min a -> a # sum :: Num a => Min a -> a # product :: Num a => Min a -> a #
Foldable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # toList :: Max a -> [a] # null :: Max a -> Bool # length :: Max a -> Int # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # minimum :: Ord a => Max a -> a # sum :: Num a => Max a -> a # product :: Num a => Max a -> a #
Foldable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldMap' :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # toList :: Option a -> [a] # null :: Option a -> Bool # length :: Option a -> Int # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # sum :: Num a => Option a -> a # product :: Num a => Option a -> a #
Foldable ZipList	Since: base-4.9.0.0
Instance details Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # toList :: ZipList a -> [a] # null :: ZipList a -> Bool # length :: ZipList a -> Int # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # sum :: Num a => ZipList a -> a # product :: Num a => ZipList a -> a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Foldable First	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Foldable Last	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Foldable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # toList :: NonEmpty a -> [a] # null :: NonEmpty a -> Bool # length :: NonEmpty a -> Int # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # sum :: Num a => NonEmpty a -> a # product :: Num a => NonEmpty a -> a #
Foldable Tree
Instance details Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # toList :: Tree a -> [a] # null :: Tree a -> Bool # length :: Tree a -> Int # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # minimum :: Ord a => Tree a -> a # sum :: Num a => Tree a -> a # product :: Num a => Tree a -> a #
Foldable FingerTree
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a #
Foldable Digit
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # toList :: Digit a -> [a] # null :: Digit a -> Bool # length :: Digit a -> Int # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # sum :: Num a => Digit a -> a # product :: Num a => Digit a -> a #
Foldable Node
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # toList :: Node a -> [a] # null :: Node a -> Bool # length :: Node a -> Int # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # minimum :: Ord a => Node a -> a # sum :: Num a => Node a -> a # product :: Num a => Node a -> a #
Foldable Elem
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # toList :: Elem a -> [a] # null :: Elem a -> Bool # length :: Elem a -> Int # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # minimum :: Ord a => Elem a -> a # sum :: Num a => Elem a -> a # product :: Num a => Elem a -> a #
Foldable ViewL
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # toList :: ViewL a -> [a] # null :: ViewL a -> Bool # length :: ViewL a -> Int # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # sum :: Num a => ViewL a -> a # product :: Num a => ViewL a -> a #
Foldable ViewR
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # toList :: ViewR a -> [a] # null :: ViewR a -> Bool # length :: ViewR a -> Int # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # sum :: Num a => ViewR a -> a # product :: Num a => ViewR a -> a #
Foldable Ideal
Instance details Defined in Algebra.Ring.Ideal Methods fold :: Monoid m => Ideal m -> m # foldMap :: Monoid m => (a -> m) -> Ideal a -> m # foldMap' :: Monoid m => (a -> m) -> Ideal a -> m # foldr :: (a -> b -> b) -> b -> Ideal a -> b # foldr' :: (a -> b -> b) -> b -> Ideal a -> b # foldl :: (b -> a -> b) -> b -> Ideal a -> b # foldl' :: (b -> a -> b) -> b -> Ideal a -> b # foldr1 :: (a -> a -> a) -> Ideal a -> a # foldl1 :: (a -> a -> a) -> Ideal a -> a # toList :: Ideal a -> [a] # null :: Ideal a -> Bool # length :: Ideal a -> Int # elem :: Eq a => a -> Ideal a -> Bool # maximum :: Ord a => Ideal a -> a # minimum :: Ord a => Ideal a -> a # sum :: Num a => Ideal a -> a # product :: Num a => Ideal a -> a #
Foldable Complex
Instance details Defined in Numeric.Algebra.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Foldable Array
Instance details Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> m # foldMap' :: Monoid m => (a -> m) -> Array a -> m # foldr :: (a -> b -> b) -> b -> Array a -> b # foldr' :: (a -> b -> b) -> b -> Array a -> b # foldl :: (b -> a -> b) -> b -> Array a -> b # foldl' :: (b -> a -> b) -> b -> Array a -> b # foldr1 :: (a -> a -> a) -> Array a -> a # foldl1 :: (a -> a -> a) -> Array a -> a # toList :: Array a -> [a] # null :: Array a -> Bool # length :: Array a -> Int # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # sum :: Num a => Array a -> a # product :: Num a => Array a -> a #
Foldable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m # foldMap' :: Monoid m => (a -> m) -> SmallArray a -> m # foldr :: (a -> b -> b) -> b -> SmallArray a -> b # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b # foldl :: (b -> a -> b) -> b -> SmallArray a -> b # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b # foldr1 :: (a -> a -> a) -> SmallArray a -> a # foldl1 :: (a -> a -> a) -> SmallArray a -> a # toList :: SmallArray a -> [a] # null :: SmallArray a -> Bool # length :: SmallArray a -> Int # elem :: Eq a => a -> SmallArray a -> Bool # maximum :: Ord a => SmallArray a -> a # minimum :: Ord a => SmallArray a -> a # sum :: Num a => SmallArray a -> a # product :: Num a => SmallArray a -> a #
Foldable Hashed
Instance details Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> m # foldMap :: Monoid m => (a -> m) -> Hashed a -> m # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m # foldr :: (a -> b -> b) -> b -> Hashed a -> b # foldr' :: (a -> b -> b) -> b -> Hashed a -> b # foldl :: (b -> a -> b) -> b -> Hashed a -> b # foldl' :: (b -> a -> b) -> b -> Hashed a -> b # foldr1 :: (a -> a -> a) -> Hashed a -> a # foldl1 :: (a -> a -> a) -> Hashed a -> a # toList :: Hashed a -> [a] # null :: Hashed a -> Bool # length :: Hashed a -> Int # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # sum :: Num a => Hashed a -> a # product :: Num a => Hashed a -> a #
Foldable Unipol Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods fold :: Monoid m => Unipol m -> m # foldMap :: Monoid m => (a -> m) -> Unipol a -> m # foldMap' :: Monoid m => (a -> m) -> Unipol a -> m # foldr :: (a -> b -> b) -> b -> Unipol a -> b # foldr' :: (a -> b -> b) -> b -> Unipol a -> b # foldl :: (b -> a -> b) -> b -> Unipol a -> b # foldl' :: (b -> a -> b) -> b -> Unipol a -> b # foldr1 :: (a -> a -> a) -> Unipol a -> a # foldl1 :: (a -> a -> a) -> Unipol a -> a # toList :: Unipol a -> [a] # null :: Unipol a -> Bool # length :: Unipol a -> Int # elem :: Eq a => a -> Unipol a -> Bool # maximum :: Ord a => Unipol a -> a # minimum :: Ord a => Unipol a -> a # sum :: Num a => Unipol a -> a # product :: Num a => Unipol a -> a #
Foldable Heap
Instance details Defined in Data.Heap Methods fold :: Monoid m => Heap m -> m # foldMap :: Monoid m => (a -> m) -> Heap a -> m # foldMap' :: Monoid m => (a -> m) -> Heap a -> m # foldr :: (a -> b -> b) -> b -> Heap a -> b # foldr' :: (a -> b -> b) -> b -> Heap a -> b # foldl :: (b -> a -> b) -> b -> Heap a -> b # foldl' :: (b -> a -> b) -> b -> Heap a -> b # foldr1 :: (a -> a -> a) -> Heap a -> a # foldl1 :: (a -> a -> a) -> Heap a -> a # toList :: Heap a -> [a] # null :: Heap a -> Bool # length :: Heap a -> Int # elem :: Eq a => a -> Heap a -> Bool # maximum :: Ord a => Heap a -> a # minimum :: Ord a => Heap a -> a # sum :: Num a => Heap a -> a # product :: Num a => Heap a -> a #
Foldable Forest
Instance details Defined in Data.Heap Methods fold :: Monoid m => Forest m -> m # foldMap :: Monoid m => (a -> m) -> Forest a -> m # foldMap' :: Monoid m => (a -> m) -> Forest a -> m # foldr :: (a -> b -> b) -> b -> Forest a -> b # foldr' :: (a -> b -> b) -> b -> Forest a -> b # foldl :: (b -> a -> b) -> b -> Forest a -> b # foldl' :: (b -> a -> b) -> b -> Forest a -> b # foldr1 :: (a -> a -> a) -> Forest a -> a # foldl1 :: (a -> a -> a) -> Forest a -> a # toList :: Forest a -> [a] # null :: Forest a -> Bool # length :: Forest a -> Int # elem :: Eq a => a -> Forest a -> Bool # maximum :: Ord a => Forest a -> a # minimum :: Ord a => Forest a -> a # sum :: Num a => Forest a -> a # product :: Num a => Forest a -> a #
Foldable Tree
Instance details Defined in Data.Heap Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # toList :: Tree a -> [a] # null :: Tree a -> Bool # length :: Tree a -> Int # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # minimum :: Ord a => Tree a -> a # sum :: Num a => Tree a -> a # product :: Num a => Tree a -> a #
Foldable Matrix
Instance details Defined in Data.Matrix Methods fold :: Monoid m => Matrix m -> m # foldMap :: Monoid m => (a -> m) -> Matrix a -> m # foldMap' :: Monoid m => (a -> m) -> Matrix a -> m # foldr :: (a -> b -> b) -> b -> Matrix a -> b # foldr' :: (a -> b -> b) -> b -> Matrix a -> b # foldl :: (b -> a -> b) -> b -> Matrix a -> b # foldl' :: (b -> a -> b) -> b -> Matrix a -> b # foldr1 :: (a -> a -> a) -> Matrix a -> a # foldl1 :: (a -> a -> a) -> Matrix a -> a # toList :: Matrix a -> [a] # null :: Matrix a -> Bool # length :: Matrix a -> Int # elem :: Eq a => a -> Matrix a -> Bool # maximum :: Ord a => Matrix a -> a # minimum :: Ord a => Matrix a -> a # sum :: Num a => Matrix a -> a # product :: Num a => Matrix a -> a #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Foldable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Foldable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # toList :: U1 a -> [a] # null :: U1 a -> Bool # length :: U1 a -> Int # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # minimum :: Ord a => U1 a -> a # sum :: Num a => U1 a -> a # product :: Num a => U1 a -> a #
Foldable (UAddr :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # toList :: UAddr a -> [a] # null :: UAddr a -> Bool # length :: UAddr a -> Int # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # sum :: Num a => UAddr a -> a # product :: Num a => UAddr a -> a #
Foldable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # toList :: UChar a -> [a] # null :: UChar a -> Bool # length :: UChar a -> Int # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # sum :: Num a => UChar a -> a # product :: Num a => UChar a -> a #
Foldable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # toList :: UDouble a -> [a] # null :: UDouble a -> Bool # length :: UDouble a -> Int # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # sum :: Num a => UDouble a -> a # product :: Num a => UDouble a -> a #
Foldable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # toList :: UFloat a -> [a] # null :: UFloat a -> Bool # length :: UFloat a -> Int # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # sum :: Num a => UFloat a -> a # product :: Num a => UFloat a -> a #
Foldable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # toList :: UInt a -> [a] # null :: UInt a -> Bool # length :: UInt a -> Int # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # minimum :: Ord a => UInt a -> a # sum :: Num a => UInt a -> a # product :: Num a => UInt a -> a #
Foldable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # toList :: UWord a -> [a] # null :: UWord a -> Bool # length :: UWord a -> Int # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # sum :: Num a => UWord a -> a # product :: Num a => UWord a -> a #
Foldable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # toList :: (a, a0) -> [a0] # null :: (a, a0) -> Bool # length :: (a, a0) -> Int # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # sum :: Num a0 => (a, a0) -> a0 # product :: Num a0 => (a, a0) -> a0 #
Foldable (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # null :: HashMap k a -> Bool # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # sum :: Num a => HashMap k a -> a # product :: Num a => HashMap k a -> a #
Foldable (Map k)	Folds in order of increasing key.
Instance details Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # toList :: Map k a -> [a] # null :: Map k a -> Bool # length :: Map k a -> Int # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # sum :: Num a => Map k a -> a # product :: Num a => Map k a -> a #
Foldable (Array i)	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # toList :: Array i a -> [a] # null :: Array i a -> Bool # length :: Array i a -> Int # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # sum :: Num a => Array i a -> a # product :: Num a => Array i a -> a #
Foldable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # toList :: Arg a a0 -> [a0] # null :: Arg a a0 -> Bool # length :: Arg a a0 -> Int # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # sum :: Num a0 => Arg a a0 -> a0 # product :: Num a0 => Arg a a0 -> a0 #
Foldable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # toList :: Proxy a -> [a] # null :: Proxy a -> Bool # length :: Proxy a -> Int # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # sum :: Num a => Proxy a -> a # product :: Num a => Proxy a -> a #
Foldable f => Foldable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b # foldr1 :: (a -> a -> a) -> MaybeT f a -> a # foldl1 :: (a -> a -> a) -> MaybeT f a -> a # toList :: MaybeT f a -> [a] # null :: MaybeT f a -> Bool # length :: MaybeT f a -> Int # elem :: Eq a => a -> MaybeT f a -> Bool # maximum :: Ord a => MaybeT f a -> a # minimum :: Ord a => MaybeT f a -> a # sum :: Num a => MaybeT f a -> a # product :: Num a => MaybeT f a -> a #
Foldable m => Foldable (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods fold :: Monoid m0 => CatchT m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> CatchT m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> CatchT m a -> m0 # foldr :: (a -> b -> b) -> b -> CatchT m a -> b # foldr' :: (a -> b -> b) -> b -> CatchT m a -> b # foldl :: (b -> a -> b) -> b -> CatchT m a -> b # foldl' :: (b -> a -> b) -> b -> CatchT m a -> b # foldr1 :: (a -> a -> a) -> CatchT m a -> a # foldl1 :: (a -> a -> a) -> CatchT m a -> a # toList :: CatchT m a -> [a] # null :: CatchT m a -> Bool # length :: CatchT m a -> Int # elem :: Eq a => a -> CatchT m a -> Bool # maximum :: Ord a => CatchT m a -> a # minimum :: Ord a => CatchT m a -> a # sum :: Num a => CatchT m a -> a # product :: Num a => CatchT m a -> a #
Foldable f => Foldable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods fold :: Monoid m => ListT f m -> m # foldMap :: Monoid m => (a -> m) -> ListT f a -> m # foldMap' :: Monoid m => (a -> m) -> ListT f a -> m # foldr :: (a -> b -> b) -> b -> ListT f a -> b # foldr' :: (a -> b -> b) -> b -> ListT f a -> b # foldl :: (b -> a -> b) -> b -> ListT f a -> b # foldl' :: (b -> a -> b) -> b -> ListT f a -> b # foldr1 :: (a -> a -> a) -> ListT f a -> a # foldl1 :: (a -> a -> a) -> ListT f a -> a # toList :: ListT f a -> [a] # null :: ListT f a -> Bool # length :: ListT f a -> Int # elem :: Eq a => a -> ListT f a -> Bool # maximum :: Ord a => ListT f a -> a # minimum :: Ord a => ListT f a -> a # sum :: Num a => ListT f a -> a # product :: Num a => ListT f a -> a #
Foldable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldMap' :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # toList :: Level i a -> [a] # null :: Level i a -> Bool # length :: Level i a -> Int # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # sum :: Num a => Level i a -> a # product :: Num a => Level i a -> a #
MonoFoldable mono => Foldable (WrappedMono mono)
Instance details Defined in Data.MonoTraversable Methods fold :: Monoid m => WrappedMono mono m -> m # foldMap :: Monoid m => (a -> m) -> WrappedMono mono a -> m # foldMap' :: Monoid m => (a -> m) -> WrappedMono mono a -> m # foldr :: (a -> b -> b) -> b -> WrappedMono mono a -> b # foldr' :: (a -> b -> b) -> b -> WrappedMono mono a -> b # foldl :: (b -> a -> b) -> b -> WrappedMono mono a -> b # foldl' :: (b -> a -> b) -> b -> WrappedMono mono a -> b # foldr1 :: (a -> a -> a) -> WrappedMono mono a -> a # foldl1 :: (a -> a -> a) -> WrappedMono mono a -> a # toList :: WrappedMono mono a -> [a] # null :: WrappedMono mono a -> Bool # length :: WrappedMono mono a -> Int # elem :: Eq a => a -> WrappedMono mono a -> Bool # maximum :: Ord a => WrappedMono mono a -> a # minimum :: Ord a => WrappedMono mono a -> a # sum :: Num a => WrappedMono mono a -> a # product :: Num a => WrappedMono mono a -> a #
Foldable f => Foldable (WrappedPoly f)
Instance details Defined in Data.MonoTraversable Methods fold :: Monoid m => WrappedPoly f m -> m # foldMap :: Monoid m => (a -> m) -> WrappedPoly f a -> m # foldMap' :: Monoid m => (a -> m) -> WrappedPoly f a -> m # foldr :: (a -> b -> b) -> b -> WrappedPoly f a -> b # foldr' :: (a -> b -> b) -> b -> WrappedPoly f a -> b # foldl :: (b -> a -> b) -> b -> WrappedPoly f a -> b # foldl' :: (b -> a -> b) -> b -> WrappedPoly f a -> b # foldr1 :: (a -> a -> a) -> WrappedPoly f a -> a # foldl1 :: (a -> a -> a) -> WrappedPoly f a -> a # toList :: WrappedPoly f a -> [a] # null :: WrappedPoly f a -> Bool # length :: WrappedPoly f a -> Int # elem :: Eq a => a -> WrappedPoly f a -> Bool # maximum :: Ord a => WrappedPoly f a -> a # minimum :: Ord a => WrappedPoly f a -> a # sum :: Num a => WrappedPoly f a -> a # product :: Num a => WrappedPoly f a -> a #
Foldable (These a)
Instance details Defined in Data.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # null :: These a a0 -> Bool # length :: These a a0 -> Int # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # sum :: Num a0 => These a a0 -> a0 # product :: Num a0 => These a a0 -> a0 #
Foldable f => Foldable (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods fold :: Monoid m => WrapFunctor f m -> m # foldMap :: Monoid m => (a -> m) -> WrapFunctor f a -> m # foldMap' :: Monoid m => (a -> m) -> WrapFunctor f a -> m # foldr :: (a -> b -> b) -> b -> WrapFunctor f a -> b # foldr' :: (a -> b -> b) -> b -> WrapFunctor f a -> b # foldl :: (b -> a -> b) -> b -> WrapFunctor f a -> b # foldl' :: (b -> a -> b) -> b -> WrapFunctor f a -> b # foldr1 :: (a -> a -> a) -> WrapFunctor f a -> a # foldl1 :: (a -> a -> a) -> WrapFunctor f a -> a # toList :: WrapFunctor f a -> [a] # null :: WrapFunctor f a -> Bool # length :: WrapFunctor f a -> Int # elem :: Eq a => a -> WrapFunctor f a -> Bool # maximum :: Ord a => WrapFunctor f a -> a # minimum :: Ord a => WrapFunctor f a -> a # sum :: Num a => WrapFunctor f a -> a # product :: Num a => WrapFunctor f a -> a #
Foldable w => Foldable (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods fold :: Monoid m => CoiterT w m -> m # foldMap :: Monoid m => (a -> m) -> CoiterT w a -> m # foldMap' :: Monoid m => (a -> m) -> CoiterT w a -> m # foldr :: (a -> b -> b) -> b -> CoiterT w a -> b # foldr' :: (a -> b -> b) -> b -> CoiterT w a -> b # foldl :: (b -> a -> b) -> b -> CoiterT w a -> b # foldl' :: (b -> a -> b) -> b -> CoiterT w a -> b # foldr1 :: (a -> a -> a) -> CoiterT w a -> a # foldl1 :: (a -> a -> a) -> CoiterT w a -> a # toList :: CoiterT w a -> [a] # null :: CoiterT w a -> Bool # length :: CoiterT w a -> Int # elem :: Eq a => a -> CoiterT w a -> Bool # maximum :: Ord a => CoiterT w a -> a # minimum :: Ord a => CoiterT w a -> a # sum :: Num a => CoiterT w a -> a # product :: Num a => CoiterT w a -> a #
Foldable m => Foldable (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods fold :: Monoid m0 => IterT m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> IterT m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> IterT m a -> m0 # foldr :: (a -> b -> b) -> b -> IterT m a -> b # foldr' :: (a -> b -> b) -> b -> IterT m a -> b # foldl :: (b -> a -> b) -> b -> IterT m a -> b # foldl' :: (b -> a -> b) -> b -> IterT m a -> b # foldr1 :: (a -> a -> a) -> IterT m a -> a # foldl1 :: (a -> a -> a) -> IterT m a -> a # toList :: IterT m a -> [a] # null :: IterT m a -> Bool # length :: IterT m a -> Int # elem :: Eq a => a -> IterT m a -> Bool # maximum :: Ord a => IterT m a -> a # minimum :: Ord a => IterT m a -> a # sum :: Num a => IterT m a -> a # product :: Num a => IterT m a -> a #
Foldable f => Foldable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods fold :: Monoid m => Cofree f m -> m # foldMap :: Monoid m => (a -> m) -> Cofree f a -> m # foldMap' :: Monoid m => (a -> m) -> Cofree f a -> m # foldr :: (a -> b -> b) -> b -> Cofree f a -> b # foldr' :: (a -> b -> b) -> b -> Cofree f a -> b # foldl :: (b -> a -> b) -> b -> Cofree f a -> b # foldl' :: (b -> a -> b) -> b -> Cofree f a -> b # foldr1 :: (a -> a -> a) -> Cofree f a -> a # foldl1 :: (a -> a -> a) -> Cofree f a -> a # toList :: Cofree f a -> [a] # null :: Cofree f a -> Bool # length :: Cofree f a -> Int # elem :: Eq a => a -> Cofree f a -> Bool # maximum :: Ord a => Cofree f a -> a # minimum :: Ord a => Cofree f a -> a # sum :: Num a => Cofree f a -> a # product :: Num a => Cofree f a -> a #
Foldable f => Foldable (Free f)
Instance details Defined in Control.Monad.Free Methods fold :: Monoid m => Free f m -> m # foldMap :: Monoid m => (a -> m) -> Free f a -> m # foldMap' :: Monoid m => (a -> m) -> Free f a -> m # foldr :: (a -> b -> b) -> b -> Free f a -> b # foldr' :: (a -> b -> b) -> b -> Free f a -> b # foldl :: (b -> a -> b) -> b -> Free f a -> b # foldl' :: (b -> a -> b) -> b -> Free f a -> b # foldr1 :: (a -> a -> a) -> Free f a -> a # foldl1 :: (a -> a -> a) -> Free f a -> a # toList :: Free f a -> [a] # null :: Free f a -> Bool # length :: Free f a -> Int # elem :: Eq a => a -> Free f a -> Bool # maximum :: Ord a => Free f a -> a # minimum :: Ord a => Free f a -> a # sum :: Num a => Free f a -> a # product :: Num a => Free f a -> a #
Foldable f => Foldable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods fold :: Monoid m => Yoneda f m -> m # foldMap :: Monoid m => (a -> m) -> Yoneda f a -> m # foldMap' :: Monoid m => (a -> m) -> Yoneda f a -> m # foldr :: (a -> b -> b) -> b -> Yoneda f a -> b # foldr' :: (a -> b -> b) -> b -> Yoneda f a -> b # foldl :: (b -> a -> b) -> b -> Yoneda f a -> b # foldl' :: (b -> a -> b) -> b -> Yoneda f a -> b # foldr1 :: (a -> a -> a) -> Yoneda f a -> a # foldl1 :: (a -> a -> a) -> Yoneda f a -> a # toList :: Yoneda f a -> [a] # null :: Yoneda f a -> Bool # length :: Yoneda f a -> Int # elem :: Eq a => a -> Yoneda f a -> Bool # maximum :: Ord a => Yoneda f a -> a # minimum :: Ord a => Yoneda f a -> a # sum :: Num a => Yoneda f a -> a # product :: Num a => Yoneda f a -> a #
Foldable (Entry p)
Instance details Defined in Data.Heap Methods fold :: Monoid m => Entry p m -> m # foldMap :: Monoid m => (a -> m) -> Entry p a -> m # foldMap' :: Monoid m => (a -> m) -> Entry p a -> m # foldr :: (a -> b -> b) -> b -> Entry p a -> b # foldr' :: (a -> b -> b) -> b -> Entry p a -> b # foldl :: (b -> a -> b) -> b -> Entry p a -> b # foldl' :: (b -> a -> b) -> b -> Entry p a -> b # foldr1 :: (a -> a -> a) -> Entry p a -> a # foldl1 :: (a -> a -> a) -> Entry p a -> a # toList :: Entry p a -> [a] # null :: Entry p a -> Bool # length :: Entry p a -> Int # elem :: Eq a => a -> Entry p a -> Bool # maximum :: Ord a => Entry p a -> a # minimum :: Ord a => Entry p a -> a # sum :: Num a => Entry p a -> a # product :: Num a => Entry p a -> a #
Foldable f => Foldable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # toList :: Rec1 f a -> [a] # null :: Rec1 f a -> Bool # length :: Rec1 f a -> Int # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # sum :: Num a => Rec1 f a -> a # product :: Num a => Rec1 f a -> a #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Foldable f => Foldable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # toList :: Ap f a -> [a] # null :: Ap f a -> Bool # length :: Ap f a -> Int # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # sum :: Num a => Ap f a -> a # product :: Num a => Ap f a -> a #
Foldable f => Foldable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # toList :: Alt f a -> [a] # null :: Alt f a -> Bool # length :: Alt f a -> Int # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # sum :: Num a => Alt f a -> a # product :: Num a => Alt f a -> a #
Foldable f => Foldable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a # toList :: ExceptT e f a -> [a] # null :: ExceptT e f a -> Bool # length :: ExceptT e f a -> Int # elem :: Eq a => a -> ExceptT e f a -> Bool # maximum :: Ord a => ExceptT e f a -> a # minimum :: Ord a => ExceptT e f a -> a # sum :: Num a => ExceptT e f a -> a # product :: Num a => ExceptT e f a -> a #
Foldable f => Foldable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b # foldr1 :: (a -> a -> a) -> IdentityT f a -> a # foldl1 :: (a -> a -> a) -> IdentityT f a -> a # toList :: IdentityT f a -> [a] # null :: IdentityT f a -> Bool # length :: IdentityT f a -> Int # elem :: Eq a => a -> IdentityT f a -> Bool # maximum :: Ord a => IdentityT f a -> a # minimum :: Ord a => IdentityT f a -> a # sum :: Num a => IdentityT f a -> a # product :: Num a => IdentityT f a -> a #
Foldable f => Foldable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # sum :: Num a => ErrorT e f a -> a # product :: Num a => ErrorT e f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b # foldr1 :: (a -> a -> a) -> WriterT w f a -> a # foldl1 :: (a -> a -> a) -> WriterT w f a -> a # toList :: WriterT w f a -> [a] # null :: WriterT w f a -> Bool # length :: WriterT w f a -> Int # elem :: Eq a => a -> WriterT w f a -> Bool # maximum :: Ord a => WriterT w f a -> a # minimum :: Ord a => WriterT w f a -> a # sum :: Num a => WriterT w f a -> a # product :: Num a => WriterT w f a -> a #
Foldable f => Foldable (Reverse f)	Fold from right to left.
Instance details Defined in Data.Functor.Reverse Methods fold :: Monoid m => Reverse f m -> m # foldMap :: Monoid m => (a -> m) -> Reverse f a -> m # foldMap' :: Monoid m => (a -> m) -> Reverse f a -> m # foldr :: (a -> b -> b) -> b -> Reverse f a -> b # foldr' :: (a -> b -> b) -> b -> Reverse f a -> b # foldl :: (b -> a -> b) -> b -> Reverse f a -> b # foldl' :: (b -> a -> b) -> b -> Reverse f a -> b # foldr1 :: (a -> a -> a) -> Reverse f a -> a # foldl1 :: (a -> a -> a) -> Reverse f a -> a # toList :: Reverse f a -> [a] # null :: Reverse f a -> Bool # length :: Reverse f a -> Int # elem :: Eq a => a -> Reverse f a -> Bool # maximum :: Ord a => Reverse f a -> a # minimum :: Ord a => Reverse f a -> a # sum :: Num a => Reverse f a -> a # product :: Num a => Reverse f a -> a #
Foldable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods fold :: Monoid m => Constant a m -> m # foldMap :: Monoid m => (a0 -> m) -> Constant a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Constant a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Constant a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Constant a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Constant a a0 -> a0 # toList :: Constant a a0 -> [a0] # null :: Constant a a0 -> Bool # length :: Constant a a0 -> Int # elem :: Eq a0 => a0 -> Constant a a0 -> Bool # maximum :: Ord a0 => Constant a a0 -> a0 # minimum :: Ord a0 => Constant a a0 -> a0 # sum :: Num a0 => Constant a a0 -> a0 # product :: Num a0 => Constant a a0 -> a0 #
Foldable f => Foldable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods fold :: Monoid m => Backwards f m -> m # foldMap :: Monoid m => (a -> m) -> Backwards f a -> m # foldMap' :: Monoid m => (a -> m) -> Backwards f a -> m # foldr :: (a -> b -> b) -> b -> Backwards f a -> b # foldr' :: (a -> b -> b) -> b -> Backwards f a -> b # foldl :: (b -> a -> b) -> b -> Backwards f a -> b # foldl' :: (b -> a -> b) -> b -> Backwards f a -> b # foldr1 :: (a -> a -> a) -> Backwards f a -> a # foldl1 :: (a -> a -> a) -> Backwards f a -> a # toList :: Backwards f a -> [a] # null :: Backwards f a -> Bool # length :: Backwards f a -> Int # elem :: Eq a => a -> Backwards f a -> Bool # maximum :: Ord a => Backwards f a -> a # minimum :: Ord a => Backwards f a -> a # sum :: Num a => Backwards f a -> a # product :: Num a => Backwards f a -> a #
Foldable f => Foldable (Sized f n)
Instance details Defined in Data.Sized.Internal Methods fold :: Monoid m => Sized f n m -> m # foldMap :: Monoid m => (a -> m) -> Sized f n a -> m # foldMap' :: Monoid m => (a -> m) -> Sized f n a -> m # foldr :: (a -> b -> b) -> b -> Sized f n a -> b # foldr' :: (a -> b -> b) -> b -> Sized f n a -> b # foldl :: (b -> a -> b) -> b -> Sized f n a -> b # foldl' :: (b -> a -> b) -> b -> Sized f n a -> b # foldr1 :: (a -> a -> a) -> Sized f n a -> a # foldl1 :: (a -> a -> a) -> Sized f n a -> a # toList :: Sized f n a -> [a] # null :: Sized f n a -> Bool # length :: Sized f n a -> Int # elem :: Eq a => a -> Sized f n a -> Bool # maximum :: Ord a => Sized f n a -> a # minimum :: Ord a => Sized f n a -> a # sum :: Num a => Sized f n a -> a # product :: Num a => Sized f n a -> a #
Foldable (Tagged s)
Instance details Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m # foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m # foldr :: (a -> b -> b) -> b -> Tagged s a -> b # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b # foldl :: (b -> a -> b) -> b -> Tagged s a -> b # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b # foldr1 :: (a -> a -> a) -> Tagged s a -> a # foldl1 :: (a -> a -> a) -> Tagged s a -> a # toList :: Tagged s a -> [a] # null :: Tagged s a -> Bool # length :: Tagged s a -> Int # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # sum :: Num a => Tagged s a -> a # product :: Num a => Tagged s a -> a #
(Foldable f, Foldable w) => Foldable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeT f w m -> m # foldMap :: Monoid m => (a -> m) -> CofreeT f w a -> m # foldMap' :: Monoid m => (a -> m) -> CofreeT f w a -> m # foldr :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldr' :: (a -> b -> b) -> b -> CofreeT f w a -> b # foldl :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldl' :: (b -> a -> b) -> b -> CofreeT f w a -> b # foldr1 :: (a -> a -> a) -> CofreeT f w a -> a # foldl1 :: (a -> a -> a) -> CofreeT f w a -> a # toList :: CofreeT f w a -> [a] # null :: CofreeT f w a -> Bool # length :: CofreeT f w a -> Int # elem :: Eq a => a -> CofreeT f w a -> Bool # maximum :: Ord a => CofreeT f w a -> a # minimum :: Ord a => CofreeT f w a -> a # sum :: Num a => CofreeT f w a -> a # product :: Num a => CofreeT f w a -> a #
Foldable f => Foldable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods fold :: Monoid m => CofreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0 # toList :: CofreeF f a a0 -> [a0] # null :: CofreeF f a a0 -> Bool # length :: CofreeF f a a0 -> Int # elem :: Eq a0 => a0 -> CofreeF f a a0 -> Bool # maximum :: Ord a0 => CofreeF f a a0 -> a0 # minimum :: Ord a0 => CofreeF f a a0 -> a0 # sum :: Num a0 => CofreeF f a a0 -> a0 # product :: Num a0 => CofreeF f a a0 -> a0 #
Bifoldable p => Foldable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods fold :: Monoid m => Fix p m -> m # foldMap :: Monoid m => (a -> m) -> Fix p a -> m # foldMap' :: Monoid m => (a -> m) -> Fix p a -> m # foldr :: (a -> b -> b) -> b -> Fix p a -> b # foldr' :: (a -> b -> b) -> b -> Fix p a -> b # foldl :: (b -> a -> b) -> b -> Fix p a -> b # foldl' :: (b -> a -> b) -> b -> Fix p a -> b # foldr1 :: (a -> a -> a) -> Fix p a -> a # foldl1 :: (a -> a -> a) -> Fix p a -> a # toList :: Fix p a -> [a] # null :: Fix p a -> Bool # length :: Fix p a -> Int # elem :: Eq a => a -> Fix p a -> Bool # maximum :: Ord a => Fix p a -> a # minimum :: Ord a => Fix p a -> a # sum :: Num a => Fix p a -> a # product :: Num a => Fix p a -> a #
(Foldable m, Foldable f) => Foldable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods fold :: Monoid m0 => FreeT f m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldr :: (a -> b -> b) -> b -> FreeT f m a -> b # foldr' :: (a -> b -> b) -> b -> FreeT f m a -> b # foldl :: (b -> a -> b) -> b -> FreeT f m a -> b # foldl' :: (b -> a -> b) -> b -> FreeT f m a -> b # foldr1 :: (a -> a -> a) -> FreeT f m a -> a # foldl1 :: (a -> a -> a) -> FreeT f m a -> a # toList :: FreeT f m a -> [a] # null :: FreeT f m a -> Bool # length :: FreeT f m a -> Int # elem :: Eq a => a -> FreeT f m a -> Bool # maximum :: Ord a => FreeT f m a -> a # minimum :: Ord a => FreeT f m a -> a # sum :: Num a => FreeT f m a -> a # product :: Num a => FreeT f m a -> a #
Foldable f => Foldable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods fold :: Monoid m => FreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # toList :: FreeF f a a0 -> [a0] # null :: FreeF f a a0 -> Bool # length :: FreeF f a a0 -> Int # elem :: Eq a0 => a0 -> FreeF f a a0 -> Bool # maximum :: Ord a0 => FreeF f a a0 -> a0 # minimum :: Ord a0 => FreeF f a a0 -> a0 # sum :: Num a0 => FreeF f a a0 -> a0 # product :: Num a0 => FreeF f a a0 -> a0 #
Bifoldable p => Foldable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods fold :: Monoid m => Join p m -> m # foldMap :: Monoid m => (a -> m) -> Join p a -> m # foldMap' :: Monoid m => (a -> m) -> Join p a -> m # foldr :: (a -> b -> b) -> b -> Join p a -> b # foldr' :: (a -> b -> b) -> b -> Join p a -> b # foldl :: (b -> a -> b) -> b -> Join p a -> b # foldl' :: (b -> a -> b) -> b -> Join p a -> b # foldr1 :: (a -> a -> a) -> Join p a -> a # foldl1 :: (a -> a -> a) -> Join p a -> a # toList :: Join p a -> [a] # null :: Join p a -> Bool # length :: Join p a -> Int # elem :: Eq a => a -> Join p a -> Bool # maximum :: Ord a => Join p a -> a # minimum :: Ord a => Join p a -> a # sum :: Num a => Join p a -> a # product :: Num a => Join p a -> a #
Foldable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # toList :: K1 i c a -> [a] # null :: K1 i c a -> Bool # length :: K1 i c a -> Int # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # sum :: Num a => K1 i c a -> a # product :: Num a => K1 i c a -> a #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
(Foldable f, Foldable g) => Foldable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :*: g) a -> a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # toList :: Sum f g a -> [a] # null :: Sum f g a -> Bool # length :: Sum f g a -> Int # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # sum :: Num a => Sum f g a -> a # product :: Num a => Sum f g a -> a #
Foldable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fold :: Monoid m => Magma i t b m -> m # foldMap :: Monoid m => (a -> m) -> Magma i t b a -> m # foldMap' :: Monoid m => (a -> m) -> Magma i t b a -> m # foldr :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldr' :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldl :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldl' :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldr1 :: (a -> a -> a) -> Magma i t b a -> a # foldl1 :: (a -> a -> a) -> Magma i t b a -> a # toList :: Magma i t b a -> [a] # null :: Magma i t b a -> Bool # length :: Magma i t b a -> Int # elem :: Eq a => a -> Magma i t b a -> Bool # maximum :: Ord a => Magma i t b a -> a # minimum :: Ord a => Magma i t b a -> a # sum :: Num a => Magma i t b a -> a # product :: Num a => Magma i t b a -> a #
Foldable (Forget r a :: Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods fold :: Monoid m => Forget r a m -> m # foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 # toList :: Forget r a a0 -> [a0] # null :: Forget r a a0 -> Bool # length :: Forget r a a0 -> Int # elem :: Eq a0 => a0 -> Forget r a a0 -> Bool # maximum :: Ord a0 => Forget r a a0 -> a0 # minimum :: Ord a0 => Forget r a a0 -> a0 # sum :: Num a0 => Forget r a a0 -> a0 # product :: Num a0 => Forget r a a0 -> a0 #
Foldable f => Foldable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # toList :: M1 i c f a -> [a] # null :: M1 i c f a -> Bool # length :: M1 i c f a -> Int # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # sum :: Num a => M1 i c f a -> a # product :: Num a => M1 i c f a -> a #
(Foldable f, Foldable g) => Foldable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # null :: (f :.: g) a -> Bool # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # sum :: Num a => (f :.: g) a -> a # product :: Num a => (f :.: g) a -> a #
(Foldable f, Foldable g) => Foldable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # sum :: Num a => Compose f g a -> a # product :: Num a => Compose f g a -> a #
Foldable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods fold :: Monoid m => Clown f a m -> m # foldMap :: Monoid m => (a0 -> m) -> Clown f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Clown f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Clown f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Clown f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Clown f a a0 -> a0 # toList :: Clown f a a0 -> [a0] # null :: Clown f a a0 -> Bool # length :: Clown f a a0 -> Int # elem :: Eq a0 => a0 -> Clown f a a0 -> Bool # maximum :: Ord a0 => Clown f a a0 -> a0 # minimum :: Ord a0 => Clown f a a0 -> a0 # sum :: Num a0 => Clown f a a0 -> a0 # product :: Num a0 => Clown f a a0 -> a0 #
Bifoldable p => Foldable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods fold :: Monoid m => Flip p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Flip p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Flip p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Flip p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Flip p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Flip p a a0 -> a0 # toList :: Flip p a a0 -> [a0] # null :: Flip p a a0 -> Bool # length :: Flip p a a0 -> Int # elem :: Eq a0 => a0 -> Flip p a a0 -> Bool # maximum :: Ord a0 => Flip p a a0 -> a0 # minimum :: Ord a0 => Flip p a a0 -> a0 # sum :: Num a0 => Flip p a a0 -> a0 # product :: Num a0 => Flip p a a0 -> a0 #
Foldable g => Foldable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods fold :: Monoid m => Joker g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Joker g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Joker g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Joker g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Joker g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Joker g a a0 -> a0 # toList :: Joker g a a0 -> [a0] # null :: Joker g a a0 -> Bool # length :: Joker g a a0 -> Int # elem :: Eq a0 => a0 -> Joker g a a0 -> Bool # maximum :: Ord a0 => Joker g a a0 -> a0 # minimum :: Ord a0 => Joker g a a0 -> a0 # sum :: Num a0 => Joker g a a0 -> a0 # product :: Num a0 => Joker g a a0 -> a0 #
Bifoldable p => Foldable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods fold :: Monoid m => WrappedBifunctor p a m -> m # foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0 # toList :: WrappedBifunctor p a a0 -> [a0] # null :: WrappedBifunctor p a a0 -> Bool # length :: WrappedBifunctor p a a0 -> Int # elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool # maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0 # sum :: Num a0 => WrappedBifunctor p a a0 -> a0 # product :: Num a0 => WrappedBifunctor p a a0 -> a0 #
(Foldable f, Bifoldable p) => Foldable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods fold :: Monoid m => Tannen f p a m -> m # foldMap :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Tannen f p a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Tannen f p a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Tannen f p a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Tannen f p a a0 -> a0 # toList :: Tannen f p a a0 -> [a0] # null :: Tannen f p a a0 -> Bool # length :: Tannen f p a a0 -> Int # elem :: Eq a0 => a0 -> Tannen f p a a0 -> Bool # maximum :: Ord a0 => Tannen f p a a0 -> a0 # minimum :: Ord a0 => Tannen f p a a0 -> a0 # sum :: Num a0 => Tannen f p a a0 -> a0 # product :: Num a0 => Tannen f p a a0 -> a0 #
(Bifoldable p, Foldable g) => Foldable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods fold :: Monoid m => Biff p f g a m -> m # foldMap :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Biff p f g a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Biff p f g a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Biff p f g a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Biff p f g a a0 -> a0 # toList :: Biff p f g a a0 -> [a0] # null :: Biff p f g a a0 -> Bool # length :: Biff p f g a a0 -> Int # elem :: Eq a0 => a0 -> Biff p f g a a0 -> Bool # maximum :: Ord a0 => Biff p f g a a0 -> a0 # minimum :: Ord a0 => Biff p f g a a0 -> a0 # sum :: Num a0 => Biff p f g a a0 -> a0 # product :: Num a0 => Biff p f g a a0 -> a0 #

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

Naturality: t . traverse f = traverse (t . f) for every applicative transformation t
Identity: traverse Identity = Identity
Composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

Naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
Identity: sequenceA . fmap Identity = Identity
Composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

t (pure x) = pure x
t (f <*> x) = t f <*> t x

and the identity functor Identity and composition functors Compose are from Data.Functor.Identity and Data.Functor.Compose.

A result of the naturality law is a purity law for traverse

traverse pure = pure

(The naturality law is implied by parametricity and thus so is the purity law [1, p15].)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

References: [1] The Essence of the Iterator Pattern, Jeremy Gibbons and Bruno C. d. S. Oliveira

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

sequenceA :: Applicative f => t (f a) -> f (t a) #

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

mapM :: Monad m => (a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

sequence :: Monad m => t (m a) -> m (t a) #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Instances

Instances details

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable IntMap	Traverses in order of increasing key.
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable Ideal
Instance details Defined in Algebra.Ring.Ideal Methods traverse :: Applicative f => (a -> f b) -> Ideal a -> f (Ideal b) # sequenceA :: Applicative f => Ideal (f a) -> f (Ideal a) # mapM :: Monad m => (a -> m b) -> Ideal a -> m (Ideal b) # sequence :: Monad m => Ideal (m a) -> m (Ideal a) #
Traversable Complex
Instance details Defined in Numeric.Algebra.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Matrix
Instance details Defined in Data.Matrix Methods traverse :: Applicative f => (a -> f b) -> Matrix a -> f (Matrix b) # sequenceA :: Applicative f => Matrix (f a) -> f (Matrix a) # mapM :: Monad m => (a -> m b) -> Matrix a -> m (Matrix b) # sequence :: Monad m => Matrix (m a) -> m (Matrix a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable (UAddr :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UAddr a -> f (UAddr b) # sequenceA :: Applicative f => UAddr (f a) -> f (UAddr a) # mapM :: Monad m => (a -> m b) -> UAddr a -> m (UAddr b) # sequence :: Monad m => UAddr (m a) -> m (UAddr a) #
Traversable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) # sequenceA :: Applicative f => UChar (f a) -> f (UChar a) # mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) # sequence :: Monad m => UChar (m a) -> m (UChar a) #
Traversable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) # sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) # mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) # sequence :: Monad m => UDouble (m a) -> m (UDouble a) #
Traversable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) # sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) # mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) # sequence :: Monad m => UFloat (m a) -> m (UFloat a) #
Traversable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) # sequenceA :: Applicative f => UInt (f a) -> f (UInt a) # mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) # sequence :: Monad m => UInt (m a) -> m (UInt a) #
Traversable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) # sequenceA :: Applicative f => UWord (f a) -> f (UWord a) # mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) # sequence :: Monad m => UWord (m a) -> m (UWord a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable (Map k)	Traverses in order of increasing key.
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
(Monad m, Traversable m) => Traversable (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods traverse :: Applicative f => (a -> f b) -> CatchT m a -> f (CatchT m b) # sequenceA :: Applicative f => CatchT m (f a) -> f (CatchT m a) # mapM :: Monad m0 => (a -> m0 b) -> CatchT m a -> m0 (CatchT m b) # sequence :: Monad m0 => CatchT m (m0 a) -> m0 (CatchT m a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Traversable (These a)
Instance details Defined in Data.These Methods traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b) # sequenceA :: Applicative f => These a (f a0) -> f (These a a0) # mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b) # sequence :: Monad m => These a (m a0) -> m (These a a0) #
Traversable f => Traversable (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods traverse :: Applicative f0 => (a -> f0 b) -> WrapFunctor f a -> f0 (WrapFunctor f b) # sequenceA :: Applicative f0 => WrapFunctor f (f0 a) -> f0 (WrapFunctor f a) # mapM :: Monad m => (a -> m b) -> WrapFunctor f a -> m (WrapFunctor f b) # sequence :: Monad m => WrapFunctor f (m a) -> m (WrapFunctor f a) #
Traversable w => Traversable (CoiterT w)
Instance details Defined in Control.Comonad.Trans.Coiter Methods traverse :: Applicative f => (a -> f b) -> CoiterT w a -> f (CoiterT w b) # sequenceA :: Applicative f => CoiterT w (f a) -> f (CoiterT w a) # mapM :: Monad m => (a -> m b) -> CoiterT w a -> m (CoiterT w b) # sequence :: Monad m => CoiterT w (m a) -> m (CoiterT w a) #
(Monad m, Traversable m) => Traversable (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods traverse :: Applicative f => (a -> f b) -> IterT m a -> f (IterT m b) # sequenceA :: Applicative f => IterT m (f a) -> f (IterT m a) # mapM :: Monad m0 => (a -> m0 b) -> IterT m a -> m0 (IterT m b) # sequence :: Monad m0 => IterT m (m0 a) -> m0 (IterT m a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
Traversable (Entry p)
Instance details Defined in Data.Heap Methods traverse :: Applicative f => (a -> f b) -> Entry p a -> f (Entry p b) # sequenceA :: Applicative f => Entry p (f a) -> f (Entry p a) # mapM :: Monad m => (a -> m b) -> Entry p a -> m (Entry p b) # sequence :: Monad m => Entry p (m a) -> m (Entry p a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (Reverse f)	Traverse from right to left.
Instance details Defined in Data.Functor.Reverse Methods traverse :: Applicative f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequenceA :: Applicative f0 => Reverse f (f0 a) -> f0 (Reverse f a) # mapM :: Monad m => (a -> m b) -> Reverse f a -> m (Reverse f b) # sequence :: Monad m => Reverse f (m a) -> m (Reverse f a) #
Traversable (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods traverse :: Applicative f => (a0 -> f b) -> Constant a a0 -> f (Constant a b) # sequenceA :: Applicative f => Constant a (f a0) -> f (Constant a a0) # mapM :: Monad m => (a0 -> m b) -> Constant a a0 -> m (Constant a b) # sequence :: Monad m => Constant a (m a0) -> m (Constant a a0) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable f => Traversable (Sized f n)
Instance details Defined in Data.Sized.Internal Methods traverse :: Applicative f0 => (a -> f0 b) -> Sized f n a -> f0 (Sized f n b) # sequenceA :: Applicative f0 => Sized f n (f0 a) -> f0 (Sized f n a) # mapM :: Monad m => (a -> m b) -> Sized f n a -> m (Sized f n b) # sequence :: Monad m => Sized f n (m a) -> m (Sized f n a) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable (Forget r a :: Type -> Type)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
Traversable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

class IsLabel (x :: Symbol) a where #

Methods

fromLabel :: a #

Instances

Instances details

Unital r => IsLabel "x" (Unipol r) Source #	By this instance, you can use `#x` for the unique variable of `Unipol r`.
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods fromLabel :: Unipol r #
(KnownSymbol symb, SingI vars, UniqueList vars, IsPolynomial poly, Wraps vars poly, Elem symb vars ~ 'True) => IsLabel symb (LabPolynomial poly vars) Source #	This instance allows something like `#x :: LabPolynomial (OrderedPolynomial Integer Grevlex 3) '["x", "y", "z"]`.
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromLabel :: LabPolynomial poly vars #

(<>) :: Semigroup a => a -> a -> a infixr 6 #

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

class Semigroup a => Monoid a where #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity: x <> mempty = x
Left identity: mempty <> x = x
Associativity: x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation: mconcat = foldr (<>) mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a #

Identity of mappend

>>> "Hello world" <> mempty
"Hello world"

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a #

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Instances details

Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid ByteString
Instance details Defined in Data.ByteString.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods mempty :: ShortByteString # mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid PluginRecompile
Instance details Defined in Plugins Methods mempty :: PluginRecompile # mappend :: PluginRecompile -> PluginRecompile -> PluginRecompile # mconcat :: [PluginRecompile] -> PluginRecompile #
Monoid Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods mempty :: WrapOrdering # mappend :: WrapOrdering -> WrapOrdering -> WrapOrdering # mconcat :: [WrapOrdering] -> WrapOrdering #
Monoid ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods mempty :: ByteArray # mappend :: ByteArray -> ByteArray -> ByteArray # mconcat :: [ByteArray] -> ByteArray #
Monoid PromDPatInfos
Instance details Defined in Data.Singletons.Syntax Methods mempty :: PromDPatInfos # mappend :: PromDPatInfos -> PromDPatInfos -> PromDPatInfos # mconcat :: [PromDPatInfos] -> PromDPatInfos #
Monoid ULetDecEnv
Instance details Defined in Data.Singletons.Syntax Methods mempty :: ULetDecEnv # mappend :: ULetDecEnv -> ULetDecEnv -> ULetDecEnv # mconcat :: [ULetDecEnv] -> ULetDecEnv #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid p => Monoid (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p # mappend :: Par1 p -> Par1 p -> Par1 p # mconcat :: [Par1 p] -> Par1 p #
Monoidal a => Monoid (Add a)
Instance details Defined in AlgebraicPrelude Methods mempty :: Add a # mappend :: Add a -> Add a -> Add a # mconcat :: [Add a] -> Add a #
Unital a => Monoid (Mult a)
Instance details Defined in AlgebraicPrelude Methods mempty :: Mult a # mappend :: Mult a -> Mult a -> Mult a # mconcat :: [Mult a] -> Mult a #
Monoid (Vector a)
Instance details Defined in Data.Vector Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
(Hashable a, Eq a) => Monoid (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid (Seq a)
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
Monoid (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
Monoid (Predicate a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a # mappend :: Predicate a -> Predicate a -> Predicate a # mconcat :: [Predicate a] -> Predicate a #
Monoid (Comparison a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a #
Monoid (Equivalence a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Semigroup a => Monoid (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Monoid (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Prim a => Monoid (Vector a)
Instance details Defined in Data.Vector.Primitive Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Monoid (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #
Monoid (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #
Storable a => Monoid (Vector a)
Instance details Defined in Data.Vector.Storable Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Monoid (Array a)
Instance details Defined in Data.Primitive.Array Methods mempty :: Array a # mappend :: Array a -> Array a -> Array a # mconcat :: [Array a] -> Array a #
Monoid (PrimArray a)
Instance details Defined in Data.Primitive.PrimArray Methods mempty :: PrimArray a # mappend :: PrimArray a -> PrimArray a -> PrimArray a # mconcat :: [PrimArray a] -> PrimArray a #
Monoid (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a #
Monoid (MergeSet a)
Instance details Defined in Data.Set.Internal Methods mempty :: MergeSet a # mappend :: MergeSet a -> MergeSet a -> MergeSet a # mconcat :: [MergeSet a] -> MergeSet a #
Monoid (Heap a)
Instance details Defined in Data.Heap Methods mempty :: Heap a # mappend :: Heap a -> Heap a -> Heap a # mconcat :: [Heap a] -> Heap a #
Monoid a => Monoid (Matrix a)
Instance details Defined in Data.Matrix Methods mempty :: Matrix a # mappend :: Matrix a -> Matrix a -> Matrix a # mconcat :: [Matrix a] -> Matrix a #
Ord a => Monoid (Max a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
Ord a => Monoid (Min a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
(Eq k, Hashable k) => Monoid (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods mempty :: HashMap k v # mappend :: HashMap k v -> HashMap k v -> HashMap k v # mconcat :: [HashMap k v] -> HashMap k v #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
Monoid a => Monoid (ST s a)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a # mappend :: ST s a -> ST s a -> ST s a # mconcat :: [ST s a] -> ST s a #
Monoid a => Monoid (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b # mappend :: Op a b -> Op a b -> Op a b # mconcat :: [Op a b] -> Op a b #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Monad m => Monoid (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #
Applicative f => Monoid (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #
Monoid (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
Monoid (Alt f a)
Instance details Defined in Control.Alternative.Free Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
(Monad m, Semigroup a, Monoid a) => Monoid (IterT m a)
Instance details Defined in Control.Monad.Trans.Iter Methods mempty :: IterT m a # mappend :: IterT m a -> IterT m a -> IterT m a # mconcat :: [IterT m a] -> IterT m a #
Monoid (f a) => Monoid (Indexing f a)
Instance details Defined in Control.Lens.Internal.Indexed Methods mempty :: Indexing f a # mappend :: Indexing f a -> Indexing f a -> Indexing f a # mconcat :: [Indexing f a] -> Indexing f a #
(Contravariant f, Applicative f) => Monoid (Folding f a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Folding f a # mappend :: Folding f a -> Folding f a -> Folding f a # mconcat :: [Folding f a] -> Folding f a #
(Apply f, Applicative f) => Monoid (TraversedF a f)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: TraversedF a f # mappend :: TraversedF a f -> TraversedF a f -> TraversedF a f # mconcat :: [TraversedF a f] -> TraversedF a f #
Monoid (Deepening i a)
Instance details Defined in Control.Lens.Internal.Level Methods mempty :: Deepening i a # mappend :: Deepening i a -> Deepening i a -> Deepening i a # mconcat :: [Deepening i a] -> Deepening i a #
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p # mconcat :: [Rec1 f p] -> Rec1 f p #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Monoid a => Monoid (Constant a b)
Instance details Defined in Data.Functor.Constant Methods mempty :: Constant a b # mappend :: Constant a b -> Constant a b -> Constant a b # mconcat :: [Constant a b] -> Constant a b #
Monoid (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a #
Reifies s (ReifiedMonoid a) => Monoid (ReflectedMonoid a s)
Instance details Defined in Data.Reflection Methods mempty :: ReflectedMonoid a s # mappend :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # mconcat :: [ReflectedMonoid a s] -> ReflectedMonoid a s #
(Dom f a, CAlternative f) => Monoid (CAlt f a)
Instance details Defined in Control.Subcategory.Alternative Methods mempty :: CAlt f a # mappend :: CAlt f a -> CAlt f a -> CAlt f a # mconcat :: [CAlt f a] -> CAlt f a #
Monoid mono => Monoid (WrapMono mono b)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods mempty :: WrapMono mono b # mappend :: WrapMono mono b -> WrapMono mono b -> WrapMono mono b # mconcat :: [WrapMono mono b] -> WrapMono mono b #
(Dom f a, CPointed f, CApplicative f, Monoid a, Dom f (a, a)) => Monoid (CApp f a)
Instance details Defined in Control.Subcategory.Applicative Methods mempty :: CApp f a # mappend :: CApp f a -> CApp f a -> CApp f a # mconcat :: [CApp f a] -> CApp f a #
(Semigroup a, Monoid a) => Monoid (Tagged s a)
Instance details Defined in Data.Tagged Methods mempty :: Tagged s a # mappend :: Tagged s a -> Tagged s a -> Tagged s a # mconcat :: [Tagged s a] -> Tagged s a #
(CRepeat f, Dom f a, Monoid a) => Monoid (CZippy f a)
Instance details Defined in Control.Subcategory.Zip Methods mempty :: CZippy f a # mappend :: CZippy f a -> CZippy f a -> CZippy f a # mconcat :: [CZippy f a] -> CZippy f a #
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p # mappend :: K1 i c p -> K1 i c p -> K1 i c p # mconcat :: [K1 i c p] -> K1 i c p #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p # mconcat :: [(f :: g) p] -> (f :: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
Monoid r => Monoid (Forget r a b)
Instance details Defined in Data.Profunctor.Types Methods mempty :: Forget r a b # mappend :: Forget r a b -> Forget r a b -> Forget r a b # mconcat :: [Forget r a b] -> Forget r a b #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p # mconcat :: [M1 i c f p] -> M1 i c f p #
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # mconcat :: [(f :.: g) p] -> (f :.: g) p #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #
Contravariant g => Monoid (BazaarT p g a b t)
Instance details Defined in Control.Lens.Internal.Bazaar Methods mempty :: BazaarT p g a b t # mappend :: BazaarT p g a b t -> BazaarT p g a b t -> BazaarT p g a b t # mconcat :: [BazaarT p g a b t] -> BazaarT p g a b t #

data Bool #

Constructors

False
True

Instances

Instances details

Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
Ix Bool	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Bool, Bool) -> [Bool] # index :: (Bool, Bool) -> Bool -> Int # unsafeIndex :: (Bool, Bool) -> Bool -> Int # inRange :: (Bool, Bool) -> Bool -> Bool # rangeSize :: (Bool, Bool) -> Int # unsafeRangeSize :: (Bool, Bool) -> Int #
Generic Bool	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep Bool :: Type -> Type # Methods from :: Bool -> Rep Bool x # to :: Rep Bool x -> Bool #
ZeroProductSemiring Bool
Instance details Defined in Numeric.Semiring.ZeroProduct
OrderedRig Bool
Instance details Defined in Numeric.Rig.Ordered
Rig Bool
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Bool #
Characteristic Bool
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Bool -> Natural #
LocallyFiniteOrder Bool
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Bool -> Bool -> [Bool] rangeSize :: Bool -> Bool -> Natural moebiusInversion :: Ring r => Bool -> Bool -> r
AdditiveOrder Bool
Instance details Defined in Numeric.Order.Additive
DecidableZero Bool
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Bool -> Bool #
DecidableUnits Bool
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Bool -> Maybe Bool # isUnit :: Bool -> Bool # (^?) :: Integral n => Bool -> n -> Maybe Bool #
DecidableAssociates Bool
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Bool -> Bool -> Bool #
Unital Bool
Instance details Defined in Numeric.Algebra.Unital Methods one :: Bool # pow :: Bool -> Natural -> Bool # productWith :: Foldable f => (a -> Bool) -> f a -> Bool #
TriviallyInvolutive Bool
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Bool
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Bool
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Bool -> Bool #
Band Bool
Instance details Defined in Numeric.Algebra.Idempotent
Factorable Bool
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: (Bool -> Bool -> r) -> Bool -> NonEmpty r #
Commutative Bool
Instance details Defined in Numeric.Algebra.Commutative
Semiring Bool
Instance details Defined in Numeric.Algebra.Class
Multiplicative Bool
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Bool -> Bool -> Bool # pow1p :: Bool -> Natural -> Bool # productWith1 :: Foldable1 f => (a -> Bool) -> f a -> Bool #
Monoidal Bool
Instance details Defined in Numeric.Algebra.Class Methods zero :: Bool # sinnum :: Natural -> Bool -> Bool # sumWith :: Foldable f => (a -> Bool) -> f a -> Bool #
Partitionable Bool
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: (Bool -> Bool -> r) -> Bool -> NonEmpty r #
Idempotent Bool
Instance details Defined in Numeric.Additive.Class
Additive Bool
Instance details Defined in Numeric.Additive.Class Methods (+) :: Bool -> Bool -> Bool # sinnum1p :: Natural -> Bool -> Bool # sumWith1 :: Foldable1 f => (a -> Bool) -> f a -> Bool #
Abelian Bool
Instance details Defined in Numeric.Additive.Class
Unbox Bool
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Bool
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Bool -> Int # hash :: Bool -> Int #
Storable Bool	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Bool -> Int # alignment :: Bool -> Int # peekElemOff :: Ptr Bool -> Int -> IO Bool # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () # peekByteOff :: Ptr b -> Int -> IO Bool # pokeByteOff :: Ptr b -> Int -> Bool -> IO () # peek :: Ptr Bool -> IO Bool # poke :: Ptr Bool -> Bool -> IO () #
Bits Bool	Interpret `Bool` as 1-bit bit-field Since: base-4.7.0.0
Instance details Defined in Data.Bits Methods (.&.) :: Bool -> Bool -> Bool # (.\|.) :: Bool -> Bool -> Bool # xor :: Bool -> Bool -> Bool # complement :: Bool -> Bool # shift :: Bool -> Int -> Bool # rotate :: Bool -> Int -> Bool # zeroBits :: Bool # bit :: Int -> Bool # setBit :: Bool -> Int -> Bool # clearBit :: Bool -> Int -> Bool # complementBit :: Bool -> Int -> Bool # testBit :: Bool -> Int -> Bool # bitSizeMaybe :: Bool -> Maybe Int # bitSize :: Bool -> Int # isSigned :: Bool -> Bool # shiftL :: Bool -> Int -> Bool # unsafeShiftL :: Bool -> Int -> Bool # shiftR :: Bool -> Int -> Bool # unsafeShiftR :: Bool -> Int -> Bool # rotateL :: Bool -> Int -> Bool # rotateR :: Bool -> Int -> Bool # popCount :: Bool -> Int #
FiniteBits Bool	Since: base-4.7.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Bool -> Int # countLeadingZeros :: Bool -> Int # countTrailingZeros :: Bool -> Int #
NFData Bool
Instance details Defined in Control.DeepSeq Methods rnf :: Bool -> () #
SBounded Bool
Instance details Defined in Data.Singletons.Prelude.Enum Methods sMinBound :: Sing MinBoundSym0 sMaxBound :: Sing MaxBoundSym0
SEnum Bool
Instance details Defined in Data.Singletons.Prelude.Enum Methods sSucc :: forall (t :: Bool). Sing t -> Sing (Apply SuccSym0 t) sPred :: forall (t :: Bool). Sing t -> Sing (Apply PredSym0 t) sToEnum :: forall (t :: Nat). Sing t -> Sing (Apply ToEnumSym0 t) sFromEnum :: forall (t :: Bool). Sing t -> Sing (Apply FromEnumSym0 t) sEnumFromTo :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply EnumFromToSym0 t1) t2) sEnumFromThenTo :: forall (t1 :: Bool) (t2 :: Bool) (t3 :: Bool). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply EnumFromThenToSym0 t1) t2) t3)
SEq Bool
Instance details Defined in Data.Singletons.Prelude.Eq Methods (%==) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a == b) (%/=) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a /= b)
SOrd Bool
Instance details Defined in Data.Singletons.Prelude.Ord Methods sCompare :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply CompareSym0 t1) t2) (%<) :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2) (%<=) :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<=@#@$) t1) t2) (%>) :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%>=) :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>=@#@$) t1) t2) sMax :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply MaxSym0 t1) t2) sMin :: forall (t1 :: Bool) (t2 :: Bool). Sing t1 -> Sing t2 -> Sing (Apply (Apply MinSym0 t1) t2)
PEnum Bool
Instance details Defined in Data.Singletons.Prelude.Enum Associated Types type Succ arg :: a type Pred arg :: a type ToEnum arg :: a type FromEnum arg :: Nat type EnumFromTo arg arg1 :: [a] type EnumFromThenTo arg arg1 arg2 :: [a]
PEq Bool
Instance details Defined in Data.Singletons.Prelude.Eq Associated Types type x == y :: Bool type x /= y :: Bool
POrd Bool
Instance details Defined in Data.Singletons.Prelude.Ord Associated Types type Compare arg arg1 :: Ordering type arg < arg1 :: Bool type arg <= arg1 :: Bool type arg > arg1 :: Bool type arg >= arg1 :: Bool type Max arg arg1 :: a type Min arg arg1 :: a
PShow Bool
Instance details Defined in Data.Singletons.Prelude.Show Associated Types type ShowsPrec arg arg1 arg2 :: Symbol type Show_ arg :: Symbol type ShowList arg arg1 :: Symbol
SShow Bool
Instance details Defined in Data.Singletons.Prelude.Show Methods sShowsPrec :: forall (t1 :: Nat) (t2 :: Bool) (t3 :: Symbol). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply ShowsPrecSym0 t1) t2) t3) sShow_ :: forall (t :: Bool). Sing t -> Sing (Apply Show_Sym0 t) sShowList :: forall (t1 :: [Bool]) (t2 :: Symbol). Sing t1 -> Sing t2 -> Sing (Apply (Apply ShowListSym0 t1) t2)
PBounded Bool
Instance details Defined in Data.Singletons.Prelude.Enum Associated Types type MinBound :: a type MaxBound :: a
SingKind Bool	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep Bool Methods fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool
Uniform Bool
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Bool
UniformRange Bool
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Bool, Bool) -> g -> m Bool
Lift Bool
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Bool -> Q Exp # liftTyped :: Bool -> Q (TExp Bool) #
Rig r => Quadrance r Bool
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Bool -> r #
RightModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Bool -> Natural -> Bool #
LeftModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Bool -> Bool #
IArray UArray Bool
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Bool -> (i, i) # numElements :: Ix i => UArray i Bool -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Bool)] -> UArray i Bool unsafeAt :: Ix i => UArray i Bool -> Int -> Bool unsafeReplace :: Ix i => UArray i Bool -> [(Int, Bool)] -> UArray i Bool unsafeAccum :: Ix i => (Bool -> e' -> Bool) -> UArray i Bool -> [(Int, e')] -> UArray i Bool unsafeAccumArray :: Ix i => (Bool -> e' -> Bool) -> Bool -> (i, i) -> [(Int, e')] -> UArray i Bool
TestCoercion SBool
Instance details Defined in Data.Singletons.Prelude.Instances Methods testCoercion :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (Coercion a b) #
TestEquality SBool
Instance details Defined in Data.Singletons.Prelude.Instances Methods testEquality :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (a :~: b) #
MVector MVector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Bool -> Int basicUnsafeSlice :: Int -> Int -> MVector s Bool -> MVector s Bool basicOverlaps :: MVector s Bool -> MVector s Bool -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Bool) basicInitialize :: PrimMonad m => MVector (PrimState m) Bool -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Bool -> m (MVector (PrimState m) Bool) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m Bool basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Bool -> Int -> Bool -> m () basicClear :: PrimMonad m => MVector (PrimState m) Bool -> m () basicSet :: PrimMonad m => MVector (PrimState m) Bool -> Bool -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m (MVector (PrimState m) Bool)
Vector Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Bool -> m (Vector Bool) basicUnsafeThaw :: PrimMonad m => Vector Bool -> m (Mutable Vector (PrimState m) Bool) basicLength :: Vector Bool -> Int basicUnsafeSlice :: Int -> Int -> Vector Bool -> Vector Bool basicUnsafeIndexM :: Monad m => Vector Bool -> Int -> m Bool basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Bool -> Vector Bool -> m () elemseq :: Vector Bool -> Bool -> b -> b
SingI 'False	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'False
SingI 'True	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'True
MArray (STUArray s) Bool (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Bool -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Bool -> ST s Int newArray :: Ix i => (i, i) -> Bool -> ST s (STUArray s i Bool) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) unsafeRead :: Ix i => STUArray s i Bool -> Int -> ST s Bool unsafeWrite :: Ix i => STUArray s i Bool -> Int -> Bool -> ST s ()
SingI NotSym0
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing NotSym0 #
SingI (&&@#@$)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (&&@#@$) #
SingI (\|\|@#@$)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) #
SingI (<=?@#@$)
Instance details Defined in Data.Singletons.TypeLits.Internal Methods sing :: Sing (<=?@#@$) #
SingI AllSym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing AllSym0 #
SingI All_Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation Methods sing :: Sing All_Sym0 #
SingI AnySym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing AnySym0 #
SingI Any_Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation Methods sing :: Sing Any_Sym0 #
SingI ShowParenSym0
Instance details Defined in Data.Singletons.Prelude.Show Methods sing :: Sing ShowParenSym0 #
SingI AndSym0
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing AndSym0 #
SingI OrSym0
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing OrSym0 #
SingI GetAllSym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing GetAllSym0 #
SingI GetAnySym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing GetAnySym0 #
SuppressUnusedWarnings NotSym0
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings FromEnum_6989586621680204253Sym0
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings AllSym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings All_Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings AnySym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Any_Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (&&@#@$)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (\|\|@#@$)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621679849009Sym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ShowParenSym0
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings AndSym0
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings OrSym0
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ToEnum_6989586621680204240Sym0
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ShowsPrec_6989586621680654062Sym0
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (<=?@#@$)
Instance details Defined in Data.Singletons.TypeLits.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings GetAllSym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings GetAnySym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SingI x => SingI ((&&@#@$$) x :: TyFun Bool Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((&&@#@$$) x) #
SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) #
SingI x => SingI ((<=?@#@$$) x :: TyFun Nat Bool -> Type)
Instance details Defined in Data.Singletons.TypeLits.Internal Methods sing :: Sing ((<=?@#@$$) x) #
SAlternative f => SingI (GuardSym0 :: TyFun Bool (f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sing :: Sing GuardSym0 #
SApplicative f => SingI (WhenSym0 :: TyFun Bool (f () ~> f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sing :: Sing WhenSym0 #
SApplicative f => SingI (UnlessSym0 :: TyFun Bool (f () ~> f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods sing :: Sing UnlessSym0 #
SingI (ListnullSym0 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListnullSym0 #
SEq a => SingI (ListisPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListisPrefixOfSym0 #
SingI (NullSym0 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing NullSym0 #
SEq a => SingI (IsSuffixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing IsSuffixOfSym0 #
SEq a => SingI (IsPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing IsPrefixOfSym0 #
SEq a => SingI (IsInfixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing IsInfixOfSym0 #
SingI (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing IsNothingSym0 #
SingI (IsJustSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing IsJustSym0 #
SEq a => SingI (ListelemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListelemSym0 #
SFoldable t => SingI (OrSym0 :: TyFun (t Bool) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing OrSym0 #
SFoldable t => SingI (AndSym0 :: TyFun (t Bool) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing AndSym0 #
SEq a => SingI ((==@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods sing :: Sing (==@#@$) #
SEq a => SingI ((/=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods sing :: Sing (/=@#@$) #
SingI (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing Bool_Sym0 #
SEq a => SingI (NotElemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing NotElemSym0 #
SEq a => SingI (ElemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing ElemSym0 #
SOrd a => SingI ((>@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (>@#@$) #
SOrd a => SingI ((>=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (>=@#@$) #
SOrd a => SingI ((<@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (<@#@$) #
SOrd a => SingI ((<=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (<=@#@$) #
SingI (ListtakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListtakeWhileSym0 #
SingI (ListspanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListspanSym0 #
SingI (ListpartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListpartitionSym0 #
SingI (ListnubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListnubBySym0 #
SingI (ListfilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListfilterSym0 #
SingI (ListdropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListdropWhileSym0 #
SingI (UntilSym0 :: TyFun (a ~> Bool) ((a ~> a) ~> (a ~> a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Base Methods sing :: Sing UntilSym0 #
SingI (UnionBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing UnionBySym0 #
SingI (TakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing TakeWhileSym0 #
SingI (SpanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing SpanSym0 #
SingI (SelectSym0 :: TyFun (a ~> Bool) (a ~> (([a], [a]) ~> ([a], [a]))) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing SelectSym0 #
SingI (PartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing PartitionSym0 #
SingI (NubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing NubBySym0 #
SingI (IntersectBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing IntersectBySym0 #
SingI (GroupBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [[a]]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing GroupBySym0 #
SingI (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FindSym0 #
SingI (FindIndicesSym0 :: TyFun (a ~> Bool) ([a] ~> [Nat]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FindIndicesSym0 #
SingI (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FindIndexSym0 #
SingI (FilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FilterSym0 #
SingI (Elem_bySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> Bool)) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing Elem_bySym0 #
SingI (DropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing DropWhileSym0 #
SingI (DropWhileEndSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing DropWhileEndSym0 #
SingI (DeleteFirstsBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing DeleteFirstsBySym0 #
SingI (DeleteBySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing DeleteBySym0 #
SingI (BreakSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing BreakSym0 #
SingI (AnySym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing AnySym0 #
SingI (AllSym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing AllSym0 #
SuppressUnusedWarnings ((&&@#@$$) a6989586621679816034 :: TyFun Bool Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679816336 :: TyFun Bool Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GuardSym0 :: TyFun Bool (f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ShowsPrec_6989586621680654062Sym1 a6989586621680654072 :: TyFun Bool (Symbol ~> Symbol) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (WhenSym0 :: TyFun Bool (f () ~> f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (UnlessSym0 :: TyFun Bool (f () ~> f ()) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListnullSym0 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListisPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823265Sym0 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NullSym0 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsSuffixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsInfixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsJustSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((<=?@#@$$) a6989586621679910752 :: TyFun Nat Bool -> Type)
Instance details Defined in Data.Singletons.TypeLits.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListelemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (OrSym0 :: TyFun (t Bool) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814130Scrutinee_6989586621680814072Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814106Scrutinee_6989586621680814070Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823889Sym0 :: TyFun a (Product a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823714Sym0 :: TyFun a (Sum a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823539Sym0 :: TyFun a (Dual a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823507Sym0 :: TyFun a (Proxy a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823131Sym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AndSym0 :: TyFun (t Bool) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DefaultEqSym0 :: TyFun k (k ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((==@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((/=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NotElemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemSym0 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837495Sym0 :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837479Sym0 :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837463Sym0 :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837447Sym0 :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837536Scrutinee_6989586621679837364Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837520Scrutinee_6989586621679837362Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837439Scrutinee_6989586621679837352Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837435Scrutinee_6989586621679837350Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((>@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((>=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((<@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((<=@#@$) :: TyFun a (a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680787270Scrutinee_6989586621680786675Sym0 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621681012558Sym0 :: TyFun a (Identity a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Identity Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621681012674Sym0 :: TyFun (Identity a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Identity Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823671Sym0 :: TyFun (Dual a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823846Sym0 :: TyFun (Sum a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680824021Sym0 :: TyFun (Product a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListtakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListspanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListpartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListnubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListfilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListdropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (UntilSym0 :: TyFun (a ~> Bool) ((a ~> a) ~> (a ~> a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Base Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (UnionBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (SpanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (SelectSym0 :: TyFun (a ~> Bool) (a ~> (([a], [a]) ~> ([a], [a]))) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (PartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379530ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379530YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379530X_6989586621680379531Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379495ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379495YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379495X_6989586621680379496Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IntersectBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GroupBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [[a]]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindIndicesSym0 :: TyFun (a ~> Bool) ([a] ~> [Nat]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_bySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> Bool)) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DropWhileEndSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DeleteFirstsBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DeleteBySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (BreakSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AnySym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AllSym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
(SEq a, SingI d) => SingI (ListisPrefixOfSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing (ListisPrefixOfSym1 d) #
(SEq a, SingI d) => SingI (ListelemSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing (ListelemSym1 d) #
(SEq a, SingI d) => SingI (NotElemSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (NotElemSym1 d) #
(SEq a, SingI d) => SingI (IsSuffixOfSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (IsSuffixOfSym1 d) #
(SEq a, SingI d) => SingI (IsPrefixOfSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (IsPrefixOfSym1 d) #
(SEq a, SingI d) => SingI (IsInfixOfSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (IsInfixOfSym1 d) #
(SEq a, SingI d) => SingI (ElemSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (ElemSym1 d) #
SingI d => SingI (AnySym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (AnySym1 d) #
SingI d => SingI (AllSym1 d :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (AllSym1 d) #
SingI (IsRightSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsRightSym0 #
SingI (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsLeftSym0 #
(SFoldable t, SEq a) => SingI (NotElemSym0 :: TyFun a (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing NotElemSym0 #
(SFoldable t, SEq a) => SingI (ElemSym0 :: TyFun a (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing ElemSym0 #
(SEq a, SingI x) => SingI ((==@#@$$) x :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods sing :: Sing ((==@#@$$) x) #
(SEq a, SingI x) => SingI ((/=@#@$$) x :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods sing :: Sing ((/=@#@$$) x) #
SingI d => SingI (Bool_Sym1 d :: TyFun a (Bool ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym1 d) #
SingI d => SingI (Elem_bySym1 d :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (Elem_bySym1 d) #
(SOrd a, SingI d) => SingI ((>@#@$$) d :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ((>@#@$$) d) #
(SOrd a, SingI d) => SingI ((>=@#@$$) d :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ((>=@#@$$) d) #
(SOrd a, SingI d) => SingI ((<@#@$$) d :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ((<@#@$$) d) #
(SOrd a, SingI d) => SingI ((<=@#@$$) d :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ((<=@#@$$) d) #
SFoldable t => SingI (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing FindSym0 #
SFoldable t => SingI (AnySym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing AnySym0 #
SFoldable t => SingI (AllSym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing AllSym0 #
SMonadPlus m => SingI (MfilterSym0 :: TyFun (a ~> Bool) (m a ~> m a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods sing :: Sing MfilterSym0 #
SApplicative m => SingI (FilterMSym0 :: TyFun (a ~> m Bool) ([a] ~> m [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods sing :: Sing FilterMSym0 #
SuppressUnusedWarnings (ListisPrefixOfSym1 a6989586621680749515 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListelemSym1 a6989586621680749443 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823131Sym1 a6989586621680823140 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NotElemSym1 a6989586621680380013 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsSuffixOfSym1 a6989586621680380036 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsPrefixOfSym1 a6989586621680380043 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsInfixOfSym1 a6989586621680380029 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemSym1 a6989586621680380021 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AnySym1 a6989586621680380238 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AllSym1 a6989586621680380246 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NotElemSym0 :: TyFun a (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814130Scrutinee_6989586621680814072Sym1 x6989586621680814125 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814106Scrutinee_6989586621680814070Sym1 x6989586621680814101 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823021Sym0 :: TyFun a (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemSym0 :: TyFun a (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DefaultEqSym1 a6989586621679819423 :: TyFun k Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((==@#@$$) a6989586621679819417 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((/=@#@$$) a6989586621679819420 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Eq Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Bool_Sym1 a6989586621679815230 :: TyFun a (Bool ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379318Scrutinee_6989586621680375763Sym0 :: TyFun k1 (TyFun k Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_bySym1 a6989586621680379249 :: TyFun a ([a] ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837495Sym1 a6989586621679837500 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837479Sym1 a6989586621679837484 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837463Sym1 a6989586621679837468 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679837447Sym1 a6989586621679837452 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837536Scrutinee_6989586621679837364Sym1 x6989586621679837534 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837520Scrutinee_6989586621679837362Sym1 x6989586621679837518 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837439Scrutinee_6989586621679837352Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837435Scrutinee_6989586621679837350Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((>@#@$$) a6989586621679837407 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((>=@#@$$) a6989586621679837412 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((<@#@$$) a6989586621679837397 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ((<=@#@$$) a6989586621679837402 :: TyFun a Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681203603Sym0 :: TyFun (Arg a b) (Arg a b ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621681012558Sym1 a6989586621681012563 :: TyFun (Identity a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Identity Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823539Sym1 a6989586621680823548 :: TyFun (Dual a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823714Sym1 a6989586621680823723 :: TyFun (Sum a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823889Sym1 a6989586621680823898 :: TyFun (Product a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823507Sym1 a6989586621680823512 :: TyFun (Proxy a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823500Sym0 :: TyFun (Proxy a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680787214Sym0 :: TyFun (Proxy s) (Proxy s ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680822554Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (First a) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AnySym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AllSym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679990284GoSym0 :: TyFun (k1 ~> Bool) (TyFun (k1 ~> k1) (TyFun k2 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Base Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379397ZsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379397YsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379397X_6989586621680379398Sym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] ([a], [a]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379263NubBy'Sym0 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k (TyFun [k1] ([k1] ~> [k1]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680379558Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (TyFun [a] [a] -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MfilterSym0 :: TyFun (a ~> Bool) (m a ~> m a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FilterMSym0 :: TyFun (a ~> m Bool) ([a] ~> m [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
(SingI d1, SingI d2) => SingI (Bool_Sym2 d1 d2 :: TyFun Bool a -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym2 d1 d2) #
(SingI d1, SingI d2) => SingI (Elem_bySym2 d1 d2 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (Elem_bySym2 d1 d2) #
SFoldable t => SingI (NullSym0 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing NullSym0 #
(SFoldable t, SEq a, SingI d) => SingI (NotElemSym1 d :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing (NotElemSym1 d) #
(SFoldable t, SEq a, SingI d) => SingI (ElemSym1 d :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing (ElemSym1 d) #
(SFoldable t, SingI d) => SingI (AnySym1 d :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing (AnySym1 d) #
(SFoldable t, SingI d) => SingI (AllSym1 d :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing (AllSym1 d) #
SuppressUnusedWarnings (Bool_Sym2 a6989586621679815230 a6989586621679815231 :: TyFun Bool a -> Type)
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_bySym2 a6989586621680379249 a6989586621680379250 :: TyFun [a] Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680822985Sym0 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NullSym0 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (NotElemSym1 a6989586621680822568 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680822993Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Elem_6989586621680823021Sym1 a6989586621680823030 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemSym1 a6989586621680822821 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AnySym1 a6989586621680822626 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (AllSym1 a6989586621680822617 :: TyFun (t a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379562Scrutinee_6989586621680375741Sym0 :: TyFun k1 (TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379474Scrutinee_6989586621680375747Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379461Scrutinee_6989586621680375749Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379384Scrutinee_6989586621680375759Sym0 :: TyFun k1 (TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379318Scrutinee_6989586621680375763Sym1 n6989586621680379316 :: TyFun k Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379299Scrutinee_6989586621680375765Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379286Scrutinee_6989586621680375767Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379270Scrutinee_6989586621680375769Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501422Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681203603Sym1 a6989586621681203608 :: TyFun (Arg a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680787214Sym1 a6989586621680787219 :: TyFun (Proxy s) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501419Sym0 :: TyFun (k2 ~> f Bool) (TyFun k3 (TyFun k2 (f [k2] ~> f [k2]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501257Sym0 :: TyFun (k1 ~> Bool) (TyFun k (TyFun k1 (m k1) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379562Scrutinee_6989586621680375741Sym1 x6989586621680379560 :: TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680822993Sym1 a_69895866216808229876989586621680822992 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180970Scrutinee_6989586621680180778Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379474Scrutinee_6989586621680375747Sym1 n6989586621680379471 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379461Scrutinee_6989586621680375749Sym1 n6989586621680379458 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379384Scrutinee_6989586621680375759Sym1 key6989586621680379380 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379299Scrutinee_6989586621680375765Sym1 x6989586621680379296 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379286Scrutinee_6989586621680375767Sym1 x6989586621680379283 :: TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379270Scrutinee_6989586621680375769Sym1 y6989586621680379267 :: TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501422Sym1 x6989586621681501421 :: TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379286Scrutinee_6989586621680375767Sym2 x6989586621680379283 xs6989586621680379284 :: TyFun [k1] (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379270Scrutinee_6989586621680375769Sym2 y6989586621680379267 ys6989586621680379268 :: TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680822993Sym2 a_69895866216808229876989586621680822992 arg_69895866216808223796989586621680822995 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180970Scrutinee_6989586621680180778Sym1 x6989586621680180969 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379474Scrutinee_6989586621680375747Sym2 n6989586621680379471 x6989586621680379472 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379461Scrutinee_6989586621680375749Sym2 n6989586621680379458 x6989586621680379459 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379384Scrutinee_6989586621680375759Sym2 key6989586621680379380 x6989586621680379381 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379299Scrutinee_6989586621680375765Sym2 x6989586621680379296 xs6989586621680379297 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501422Sym2 x6989586621681501421 p6989586621681501417 :: TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379562Scrutinee_6989586621680375741Sym2 x6989586621680379560 xs6989586621680379561 :: TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680379611Sym0 :: TyFun (b ~> (a ~> Bool)) (TyFun k1 (TyFun k2 (TyFun a (TyFun [a] (TyFun b (m b) -> Type) -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621681501422Sym3 x6989586621681501421 p6989586621681501417 a_69895866216815014106989586621681501418 :: TyFun Bool ([k1] ~> [k1]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180970Scrutinee_6989586621680180778Sym2 x6989586621680180969 x06989586621680180964 :: TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym1 x16989586621680180911 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym1 x16989586621680180874 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379562Scrutinee_6989586621680375741Sym3 x6989586621680379560 xs6989586621680379561 p6989586621680379556 :: TyFun k Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379384Scrutinee_6989586621680375759Sym3 key6989586621680379380 x6989586621680379381 y6989586621680379382 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379286Scrutinee_6989586621680375767Sym3 x6989586621680379283 xs6989586621680379284 ls6989586621680379285 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379270Scrutinee_6989586621680375769Sym3 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180970Scrutinee_6989586621680180778Sym3 x6989586621680180969 x06989586621680180964 y6989586621680180965 :: TyFun k3 (TyFun k4 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym2 x16989586621680180911 x26989586621680180912 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym2 x16989586621680180874 x26989586621680180875 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379270Scrutinee_6989586621680375769Sym4 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 eq6989586621680379261 :: TyFun k3 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180970Scrutinee_6989586621680180778Sym4 x6989586621680180969 x06989586621680180964 y6989586621680180965 arg_69895866216801807746989586621680180960 :: TyFun k4 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym3 x16989586621680180911 x26989586621680180912 y6989586621680180913 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym3 x16989586621680180874 x26989586621680180875 y6989586621680180876 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym4 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym4 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180916Scrutinee_6989586621680180792Sym5 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 arg_69895866216801807886989586621680180907 :: TyFun k5 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680180879Scrutinee_6989586621680180802Sym5 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 arg_69895866216801807986989586621680180870 :: TyFun k5 Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
type Rep Bool
Instance details Defined in GHC.Generics type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))
type Sing
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SBool
type Demote Bool
Instance details Defined in Data.Singletons.Prelude.Instances type Demote Bool = Bool
newtype Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Bool = V_Bool (Vector Word8)
type MaxBound
Instance details Defined in Data.Singletons.Prelude.Enum type MaxBound = MaxBound_6989586621680176877Sym0
type MinBound
Instance details Defined in Data.Singletons.Prelude.Enum type MinBound = MinBound_6989586621680176874Sym0
type DemoteRep Bool
Instance details Defined in GHC.Generics type DemoteRep Bool = Bool
data Sing (a :: Bool)
Instance details Defined in GHC.Generics data Sing (a :: Bool) where STrue :: Sing 'True SFalse :: Sing 'False
newtype MVector s Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Bool = MV_Bool (MVector s Word8)
type FromEnum (a :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type FromEnum (a :: Bool) = Apply FromEnum_6989586621680204253Sym0 a
type Pred (arg :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type Pred (arg :: Bool) = Apply (Pred_6989586621680181017Sym0 :: TyFun Bool Bool -> Type) arg
type Succ (arg :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type Succ (arg :: Bool) = Apply (Succ_6989586621680181004Sym0 :: TyFun Bool Bool -> Type) arg
type ToEnum a
Instance details Defined in Data.Singletons.Prelude.Enum type ToEnum a = Apply ToEnum_6989586621680204240Sym0 a
type Show_ (arg :: Bool)
Instance details Defined in Data.Singletons.Prelude.Show type Show_ (arg :: Bool) = Apply (Show__6989586621680636786Sym0 :: TyFun Bool Symbol -> Type) arg
type EnumFromTo (arg1 :: Bool) (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type EnumFromTo (arg1 :: Bool) (arg2 :: Bool) = Apply (Apply (EnumFromTo_6989586621680181027Sym0 :: TyFun Bool (Bool ~> [Bool]) -> Type) arg1) arg2
type (x :: Bool) /= (y :: Bool)
Instance details Defined in Data.Singletons.Prelude.Eq type (x :: Bool) /= (y :: Bool) = Not (x == y)
type (a :: Bool) == (b :: Bool)
Instance details Defined in Data.Singletons.Prelude.Eq type (a :: Bool) == (b :: Bool) = Equals_6989586621679820689 a b
type Max (arg1 :: Bool) (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Max (arg1 :: Bool) (arg2 :: Bool) = Apply (Apply (Max_6989586621679837511Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type Min (arg1 :: Bool) (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Min (arg1 :: Bool) (arg2 :: Bool) = Apply (Apply (Min_6989586621679837527Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type Compare (a1 :: Bool) (a2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Compare (a1 :: Bool) (a2 :: Bool) = Apply (Apply Compare_6989586621679849009Sym0 a1) a2
type (arg1 :: Bool) <= (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Bool) <= (arg2 :: Bool) = Apply (Apply (TFHelper_6989586621679837463Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type (arg1 :: Bool) < (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Bool) < (arg2 :: Bool) = Apply (Apply (TFHelper_6989586621679837447Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type (arg1 :: Bool) >= (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Bool) >= (arg2 :: Bool) = Apply (Apply (TFHelper_6989586621679837495Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type (arg1 :: Bool) > (arg2 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Bool) > (arg2 :: Bool) = Apply (Apply (TFHelper_6989586621679837479Sym0 :: TyFun Bool (Bool ~> Bool) -> Type) arg1) arg2
type ShowList (arg1 :: [Bool]) arg2
Instance details Defined in Data.Singletons.Prelude.Show type ShowList (arg1 :: [Bool]) arg2 = Apply (Apply (ShowList_6989586621680636794Sym0 :: TyFun [Bool] (Symbol ~> Symbol) -> Type) arg1) arg2
type Apply NotSym0 (a6989586621679816617 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply NotSym0 (a6989586621679816617 :: Bool) = NotSym1 a6989586621679816617
type Apply FromEnum_6989586621680204253Sym0 (a6989586621680204257 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply FromEnum_6989586621680204253Sym0 (a6989586621680204257 :: Bool) = FromEnum_6989586621680204253Sym1 a6989586621680204257
type Apply AllSym0 (a6989586621680250074 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply AllSym0 (a6989586621680250074 :: Bool) = AllSym1 a6989586621680250074
type Apply All_Sym0 (a6989586621680362895 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation type Apply All_Sym0 (a6989586621680362895 :: Bool) = All_Sym1 a6989586621680362895
type Apply AnySym0 (a6989586621680250091 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply AnySym0 (a6989586621680250091 :: Bool) = AnySym1 a6989586621680250091
type Apply Any_Sym0 (a6989586621680362889 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal.Disambiguation type Apply Any_Sym0 (a6989586621680362889 :: Bool) = Any_Sym1 a6989586621680362889
type Apply ToEnum_6989586621680204240Sym0 (a6989586621680204244 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply ToEnum_6989586621680204240Sym0 (a6989586621680204244 :: Nat) = ToEnum_6989586621680204240Sym1 a6989586621680204244
type Apply GetAllSym0 (a6989586621680250077 :: All)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply GetAllSym0 (a6989586621680250077 :: All) = GetAllSym1 a6989586621680250077
type Apply GetAnySym0 (a6989586621680250094 :: Any)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply GetAnySym0 (a6989586621680250094 :: Any) = GetAnySym1 a6989586621680250094
type EnumFromThenTo (arg1 :: Bool) (arg2 :: Bool) (arg3 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Enum type EnumFromThenTo (arg1 :: Bool) (arg2 :: Bool) (arg3 :: Bool) = Apply (Apply (Apply (EnumFromThenTo_6989586621680181039Sym0 :: TyFun Bool (Bool ~> (Bool ~> [Bool])) -> Type) arg1) arg2) arg3
type ShowsPrec a1 (a2 :: Bool) a3
Instance details Defined in Data.Singletons.Prelude.Show type ShowsPrec a1 (a2 :: Bool) a3 = Apply (Apply (Apply ShowsPrec_6989586621680654062Sym0 a1) a2) a3
type Apply ((&&@#@$$) a6989586621679816034 :: TyFun Bool Bool -> Type) (a6989586621679816035 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((&&@#@$$) a6989586621679816034 :: TyFun Bool Bool -> Type) (a6989586621679816035 :: Bool) = a6989586621679816034 &&@#@$$$ a6989586621679816035
type Apply ((\|\|@#@$$) a6989586621679816336 :: TyFun Bool Bool -> Type) (a6989586621679816337 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679816336 :: TyFun Bool Bool -> Type) (a6989586621679816337 :: Bool) = a6989586621679816336 \|\|@#@$$$ a6989586621679816337
type Apply (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type) (a6989586621679849015 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type) (a6989586621679849015 :: Bool) = Compare_6989586621679849009Sym2 a6989586621679849014 a6989586621679849015
type Apply ((<=?@#@$$) a6989586621679910752 :: TyFun Nat Bool -> Type) (a6989586621679910753 :: Nat)
Instance details Defined in Data.Singletons.TypeLits.Internal type Apply ((<=?@#@$$) a6989586621679910752 :: TyFun Nat Bool -> Type) (a6989586621679910753 :: Nat) = a6989586621679910752 <=?@#@$$$ a6989586621679910753
type Apply (Let6989586621680787270Scrutinee_6989586621680786675Sym0 :: TyFun k1 Bool -> Type) (n6989586621680787269 :: k1)
Instance details Defined in Data.Singletons.Prelude.Proxy type Apply (Let6989586621680787270Scrutinee_6989586621680786675Sym0 :: TyFun k1 Bool -> Type) (n6989586621680787269 :: k1) = Let6989586621680787270Scrutinee_6989586621680786675Sym1 n6989586621680787269
type Apply (TFHelper_6989586621679837463Sym1 a6989586621679837468 :: TyFun a Bool -> Type) (a6989586621679837469 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837463Sym1 a6989586621679837468 :: TyFun a Bool -> Type) (a6989586621679837469 :: a) = TFHelper_6989586621679837463Sym2 a6989586621679837468 a6989586621679837469
type Apply (TFHelper_6989586621679837447Sym1 a6989586621679837452 :: TyFun a Bool -> Type) (a6989586621679837453 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837447Sym1 a6989586621679837452 :: TyFun a Bool -> Type) (a6989586621679837453 :: a) = TFHelper_6989586621679837447Sym2 a6989586621679837452 a6989586621679837453
type Apply (TFHelper_6989586621679837495Sym1 a6989586621679837500 :: TyFun a Bool -> Type) (a6989586621679837501 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837495Sym1 a6989586621679837500 :: TyFun a Bool -> Type) (a6989586621679837501 :: a) = TFHelper_6989586621679837495Sym2 a6989586621679837500 a6989586621679837501
type Apply (TFHelper_6989586621679837479Sym1 a6989586621679837484 :: TyFun a Bool -> Type) (a6989586621679837485 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837479Sym1 a6989586621679837484 :: TyFun a Bool -> Type) (a6989586621679837485 :: a) = TFHelper_6989586621679837479Sym2 a6989586621679837484 a6989586621679837485
type Apply ((==@#@$$) a6989586621679819417 :: TyFun a Bool -> Type) (a6989586621679819418 :: a)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply ((==@#@$$) a6989586621679819417 :: TyFun a Bool -> Type) (a6989586621679819418 :: a) = a6989586621679819417 ==@#@$$$ a6989586621679819418
type Apply (Let6989586621680814106Scrutinee_6989586621680814070Sym1 x6989586621680814101 :: TyFun k1 Bool -> Type) (y6989586621680814102 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814106Scrutinee_6989586621680814070Sym1 x6989586621680814101 :: TyFun k1 Bool -> Type) (y6989586621680814102 :: k1) = Let6989586621680814106Scrutinee_6989586621680814070Sym2 x6989586621680814101 y6989586621680814102
type Apply (Let6989586621680814130Scrutinee_6989586621680814072Sym1 x6989586621680814125 :: TyFun k1 Bool -> Type) (y6989586621680814126 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814130Scrutinee_6989586621680814072Sym1 x6989586621680814125 :: TyFun k1 Bool -> Type) (y6989586621680814126 :: k1) = Let6989586621680814130Scrutinee_6989586621680814072Sym2 x6989586621680814125 y6989586621680814126
type Apply ((/=@#@$$) a6989586621679819420 :: TyFun a Bool -> Type) (a6989586621679819421 :: a)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply ((/=@#@$$) a6989586621679819420 :: TyFun a Bool -> Type) (a6989586621679819421 :: a) = a6989586621679819420 /=@#@$$$ a6989586621679819421
type Apply (DefaultEqSym1 a6989586621679819423 :: TyFun k Bool -> Type) (a6989586621679819424 :: k)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply (DefaultEqSym1 a6989586621679819423 :: TyFun k Bool -> Type) (a6989586621679819424 :: k) = DefaultEqSym2 a6989586621679819423 a6989586621679819424
type Apply (Let6989586621679837435Scrutinee_6989586621679837350Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type) (y6989586621679837434 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837435Scrutinee_6989586621679837350Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type) (y6989586621679837434 :: k1) = Let6989586621679837435Scrutinee_6989586621679837350Sym2 x6989586621679837433 y6989586621679837434
type Apply ((<=@#@$$) a6989586621679837402 :: TyFun a Bool -> Type) (a6989586621679837403 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((<=@#@$$) a6989586621679837402 :: TyFun a Bool -> Type) (a6989586621679837403 :: a) = a6989586621679837402 <=@#@$$$ a6989586621679837403
type Apply ((>=@#@$$) a6989586621679837412 :: TyFun a Bool -> Type) (a6989586621679837413 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((>=@#@$$) a6989586621679837412 :: TyFun a Bool -> Type) (a6989586621679837413 :: a) = a6989586621679837412 >=@#@$$$ a6989586621679837413
type Apply ((>@#@$$) a6989586621679837407 :: TyFun a Bool -> Type) (a6989586621679837408 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((>@#@$$) a6989586621679837407 :: TyFun a Bool -> Type) (a6989586621679837408 :: a) = a6989586621679837407 >@#@$$$ a6989586621679837408
type Apply (Let6989586621679837536Scrutinee_6989586621679837364Sym1 x6989586621679837534 :: TyFun k1 Bool -> Type) (y6989586621679837535 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837536Scrutinee_6989586621679837364Sym1 x6989586621679837534 :: TyFun k1 Bool -> Type) (y6989586621679837535 :: k1) = Let6989586621679837536Scrutinee_6989586621679837364Sym2 x6989586621679837534 y6989586621679837535
type Apply (Let6989586621679837520Scrutinee_6989586621679837362Sym1 x6989586621679837518 :: TyFun k1 Bool -> Type) (y6989586621679837519 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837520Scrutinee_6989586621679837362Sym1 x6989586621679837518 :: TyFun k1 Bool -> Type) (y6989586621679837519 :: k1) = Let6989586621679837520Scrutinee_6989586621679837362Sym2 x6989586621679837518 y6989586621679837519
type Apply (Let6989586621679837439Scrutinee_6989586621679837352Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type) (y6989586621679837434 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837439Scrutinee_6989586621679837352Sym1 x6989586621679837433 :: TyFun k1 Bool -> Type) (y6989586621679837434 :: k1) = Let6989586621679837439Scrutinee_6989586621679837352Sym2 x6989586621679837433 y6989586621679837434
type Apply ((<@#@$$) a6989586621679837397 :: TyFun a Bool -> Type) (a6989586621679837398 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((<@#@$$) a6989586621679837397 :: TyFun a Bool -> Type) (a6989586621679837398 :: a) = a6989586621679837397 <@#@$$$ a6989586621679837398
type Apply (Bool_Sym2 a6989586621679815230 a6989586621679815231 :: TyFun Bool a -> Type) (a6989586621679815232 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym2 a6989586621679815230 a6989586621679815231 :: TyFun Bool a -> Type) (a6989586621679815232 :: Bool) = Bool_Sym3 a6989586621679815230 a6989586621679815231 a6989586621679815232
type Apply (Let6989586621680379318Scrutinee_6989586621680375763Sym1 n6989586621680379316 :: TyFun k Bool -> Type) (x6989586621680379317 :: k)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379318Scrutinee_6989586621680375763Sym1 n6989586621680379316 :: TyFun k Bool -> Type) (x6989586621680379317 :: k) = Let6989586621680379318Scrutinee_6989586621680375763Sym2 n6989586621680379316 x6989586621680379317
type Apply (Lambda_6989586621680822993Sym2 a_69895866216808229876989586621680822992 arg_69895866216808223796989586621680822995 :: TyFun k3 Bool -> Type) (arg_69895866216808223816989586621680822996 :: k3)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Lambda_6989586621680822993Sym2 a_69895866216808229876989586621680822992 arg_69895866216808223796989586621680822995 :: TyFun k3 Bool -> Type) (arg_69895866216808223816989586621680822996 :: k3) = Lambda_6989586621680822993Sym3 a_69895866216808229876989586621680822992 arg_69895866216808223796989586621680822995 arg_69895866216808223816989586621680822996
type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym2 x6989586621680379296 xs6989586621680379297 :: TyFun k3 Bool -> Type) (n6989586621680379298 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym2 x6989586621680379296 xs6989586621680379297 :: TyFun k3 Bool -> Type) (n6989586621680379298 :: k3) = Let6989586621680379299Scrutinee_6989586621680375765Sym3 x6989586621680379296 xs6989586621680379297 n6989586621680379298
type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym2 n6989586621680379458 x6989586621680379459 :: TyFun k3 Bool -> Type) (xs6989586621680379460 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym2 n6989586621680379458 x6989586621680379459 :: TyFun k3 Bool -> Type) (xs6989586621680379460 :: k3) = Let6989586621680379461Scrutinee_6989586621680375749Sym3 n6989586621680379458 x6989586621680379459 xs6989586621680379460
type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym2 n6989586621680379471 x6989586621680379472 :: TyFun k3 Bool -> Type) (xs6989586621680379473 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym2 n6989586621680379471 x6989586621680379472 :: TyFun k3 Bool -> Type) (xs6989586621680379473 :: k3) = Let6989586621680379474Scrutinee_6989586621680375747Sym3 n6989586621680379471 x6989586621680379472 xs6989586621680379473
type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym3 key6989586621680379380 x6989586621680379381 y6989586621680379382 :: TyFun k3 Bool -> Type) (xys6989586621680379383 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym3 key6989586621680379380 x6989586621680379381 y6989586621680379382 :: TyFun k3 Bool -> Type) (xys6989586621680379383 :: k3) = Let6989586621680379384Scrutinee_6989586621680375759Sym4 key6989586621680379380 x6989586621680379381 y6989586621680379382 xys6989586621680379383
type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym3 x6989586621680379283 xs6989586621680379284 ls6989586621680379285 :: TyFun k3 Bool -> Type) (l6989586621680379278 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym3 x6989586621680379283 xs6989586621680379284 ls6989586621680379285 :: TyFun k3 Bool -> Type) (l6989586621680379278 :: k3) = Let6989586621680379286Scrutinee_6989586621680375767Sym4 x6989586621680379283 xs6989586621680379284 ls6989586621680379285 l6989586621680379278
type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym3 x6989586621680379560 xs6989586621680379561 p6989586621680379556 :: TyFun k Bool -> Type) (a_69895866216803795496989586621680379557 :: k)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym3 x6989586621680379560 xs6989586621680379561 p6989586621680379556 :: TyFun k Bool -> Type) (a_69895866216803795496989586621680379557 :: k) = Let6989586621680379562Scrutinee_6989586621680375741Sym4 x6989586621680379560 xs6989586621680379561 p6989586621680379556 a_69895866216803795496989586621680379557
type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym4 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 eq6989586621680379261 :: TyFun k3 Bool -> Type) (l6989586621680379262 :: k3)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym4 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 eq6989586621680379261 :: TyFun k3 Bool -> Type) (l6989586621680379262 :: k3) = Let6989586621680379270Scrutinee_6989586621680375769Sym5 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 eq6989586621680379261 l6989586621680379262
type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym4 x6989586621680180969 x06989586621680180964 y6989586621680180965 arg_69895866216801807746989586621680180960 :: TyFun k4 Bool -> Type) (arg_69895866216801807766989586621680180961 :: k4)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym4 x6989586621680180969 x06989586621680180964 y6989586621680180965 arg_69895866216801807746989586621680180960 :: TyFun k4 Bool -> Type) (arg_69895866216801807766989586621680180961 :: k4) = Let6989586621680180970Scrutinee_6989586621680180778Sym5 x6989586621680180969 x06989586621680180964 y6989586621680180965 arg_69895866216801807746989586621680180960 arg_69895866216801807766989586621680180961
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym5 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 arg_69895866216801807986989586621680180870 :: TyFun k5 Bool -> Type) (arg_69895866216801808006989586621680180871 :: k5)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym5 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 arg_69895866216801807986989586621680180870 :: TyFun k5 Bool -> Type) (arg_69895866216801808006989586621680180871 :: k5) = Let6989586621680180879Scrutinee_6989586621680180802Sym6 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 arg_69895866216801807986989586621680180870 arg_69895866216801808006989586621680180871
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym5 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 arg_69895866216801807886989586621680180907 :: TyFun k5 Bool -> Type) (arg_69895866216801807906989586621680180908 :: k5)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym5 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 arg_69895866216801807886989586621680180907 :: TyFun k5 Bool -> Type) (arg_69895866216801807906989586621680180908 :: k5) = Let6989586621680180916Scrutinee_6989586621680180792Sym6 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 arg_69895866216801807886989586621680180907 arg_69895866216801807906989586621680180908
type Apply (GuardSym0 :: TyFun Bool (f ()) -> Type) (a6989586621680011717 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (GuardSym0 :: TyFun Bool (f ()) -> Type) (a6989586621680011717 :: Bool) = GuardSym1 a6989586621680011717 :: f ()
type Apply (&&@#@$) (a6989586621679816034 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (&&@#@$) (a6989586621679816034 :: Bool) = (&&@#@$$) a6989586621679816034
type Apply (\|\|@#@$) (a6989586621679816336 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679816336 :: Bool) = (\|\|@#@$$) a6989586621679816336
type Apply Compare_6989586621679849009Sym0 (a6989586621679849014 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply Compare_6989586621679849009Sym0 (a6989586621679849014 :: Bool) = Compare_6989586621679849009Sym1 a6989586621679849014
type Apply ShowParenSym0 (a6989586621680636699 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Show type Apply ShowParenSym0 (a6989586621680636699 :: Bool) = ShowParenSym1 a6989586621680636699
type Apply ShowsPrec_6989586621680654062Sym0 (a6989586621680654072 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Show type Apply ShowsPrec_6989586621680654062Sym0 (a6989586621680654072 :: Nat) = ShowsPrec_6989586621680654062Sym1 a6989586621680654072
type Apply (<=?@#@$) (a6989586621679910752 :: Nat)
Instance details Defined in Data.Singletons.TypeLits.Internal type Apply (<=?@#@$) (a6989586621679910752 :: Nat) = (<=?@#@$$) a6989586621679910752
type Apply (ShowsPrec_6989586621680654062Sym1 a6989586621680654072 :: TyFun Bool (Symbol ~> Symbol) -> Type) (a6989586621680654073 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680654062Sym1 a6989586621680654072 :: TyFun Bool (Symbol ~> Symbol) -> Type) (a6989586621680654073 :: Bool) = ShowsPrec_6989586621680654062Sym2 a6989586621680654072 a6989586621680654073
type Apply (WhenSym0 :: TyFun Bool (f () ~> f ()) -> Type) (a6989586621680011861 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (WhenSym0 :: TyFun Bool (f () ~> f ()) -> Type) (a6989586621680011861 :: Bool) = WhenSym1 a6989586621680011861 :: TyFun (f ()) (f ()) -> Type
type Apply (UnlessSym0 :: TyFun Bool (f () ~> f ()) -> Type) (a6989586621681501282 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (UnlessSym0 :: TyFun Bool (f () ~> f ()) -> Type) (a6989586621681501282 :: Bool) = UnlessSym1 a6989586621681501282 :: TyFun (f ()) (f ()) -> Type
type Apply (TFHelper_6989586621679837463Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837468 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837463Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837468 :: a) = TFHelper_6989586621679837463Sym1 a6989586621679837468
type Apply (TFHelper_6989586621679837447Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837452 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837447Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837452 :: a) = TFHelper_6989586621679837447Sym1 a6989586621679837452
type Apply (TFHelper_6989586621679837495Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837500 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837495Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837500 :: a) = TFHelper_6989586621679837495Sym1 a6989586621679837500
type Apply (TFHelper_6989586621679837479Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837484 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (TFHelper_6989586621679837479Sym0 :: TyFun a (a ~> Bool) -> Type) (a6989586621679837484 :: a) = TFHelper_6989586621679837479Sym1 a6989586621679837484
type Apply ((==@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679819417 :: a)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply ((==@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679819417 :: a) = (==@#@$$) a6989586621679819417
type Apply (Elem_6989586621680823131Sym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680823140 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823131Sym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680823140 :: a) = Elem_6989586621680823131Sym1 a6989586621680823140
type Apply (ListelemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680749443 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListelemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680749443 :: a) = ListelemSym1 a6989586621680749443
type Apply (ElemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680380021 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (ElemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680380021 :: a) = ElemSym1 a6989586621680380021
type Apply (Let6989586621680814106Scrutinee_6989586621680814070Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621680814101 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814106Scrutinee_6989586621680814070Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621680814101 :: k1) = Let6989586621680814106Scrutinee_6989586621680814070Sym1 x6989586621680814101
type Apply (Let6989586621680814130Scrutinee_6989586621680814072Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621680814125 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814130Scrutinee_6989586621680814072Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621680814125 :: k1) = Let6989586621680814130Scrutinee_6989586621680814072Sym1 x6989586621680814125
type Apply (Elem_6989586621680823507Sym0 :: TyFun a (Proxy a ~> Bool) -> Type) (a6989586621680823512 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823507Sym0 :: TyFun a (Proxy a ~> Bool) -> Type) (a6989586621680823512 :: a) = Elem_6989586621680823507Sym1 a6989586621680823512
type Apply (Elem_6989586621680823539Sym0 :: TyFun a (Dual a ~> Bool) -> Type) (a6989586621680823548 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823539Sym0 :: TyFun a (Dual a ~> Bool) -> Type) (a6989586621680823548 :: a) = Elem_6989586621680823539Sym1 a6989586621680823548
type Apply (Elem_6989586621680823714Sym0 :: TyFun a (Sum a ~> Bool) -> Type) (a6989586621680823723 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823714Sym0 :: TyFun a (Sum a ~> Bool) -> Type) (a6989586621680823723 :: a) = Elem_6989586621680823714Sym1 a6989586621680823723
type Apply (Elem_6989586621680823889Sym0 :: TyFun a (Product a ~> Bool) -> Type) (a6989586621680823898 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823889Sym0 :: TyFun a (Product a ~> Bool) -> Type) (a6989586621680823898 :: a) = Elem_6989586621680823889Sym1 a6989586621680823898
type Apply ((/=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679819420 :: a)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply ((/=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679819420 :: a) = (/=@#@$$) a6989586621679819420
type Apply (DefaultEqSym0 :: TyFun k (k ~> Bool) -> Type) (a6989586621679819423 :: k)
Instance details Defined in Data.Singletons.Prelude.Eq type Apply (DefaultEqSym0 :: TyFun k (k ~> Bool) -> Type) (a6989586621679819423 :: k) = DefaultEqSym1 a6989586621679819423
type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679815230 :: a)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679815230 :: a) = Bool_Sym1 a6989586621679815230
type Apply (NotElemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680380013 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (NotElemSym0 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680380013 :: a) = NotElemSym1 a6989586621680380013
type Apply (Let6989586621679837435Scrutinee_6989586621679837350Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837433 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837435Scrutinee_6989586621679837350Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837433 :: k1) = Let6989586621679837435Scrutinee_6989586621679837350Sym1 x6989586621679837433
type Apply ((<=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837402 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((<=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837402 :: a) = (<=@#@$$) a6989586621679837402
type Apply ((>=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837412 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((>=@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837412 :: a) = (>=@#@$$) a6989586621679837412
type Apply ((>@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837407 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((>@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837407 :: a) = (>@#@$$) a6989586621679837407
type Apply (Let6989586621679837536Scrutinee_6989586621679837364Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837534 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837536Scrutinee_6989586621679837364Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837534 :: k1) = Let6989586621679837536Scrutinee_6989586621679837364Sym1 x6989586621679837534
type Apply (Let6989586621679837520Scrutinee_6989586621679837362Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837518 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837520Scrutinee_6989586621679837362Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837518 :: k1) = Let6989586621679837520Scrutinee_6989586621679837362Sym1 x6989586621679837518
type Apply (Let6989586621679837439Scrutinee_6989586621679837352Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837433 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837439Scrutinee_6989586621679837352Sym0 :: TyFun k1 (TyFun k1 Bool -> Type) -> Type) (x6989586621679837433 :: k1) = Let6989586621679837439Scrutinee_6989586621679837352Sym1 x6989586621679837433
type Apply ((<@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837397 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ((<@#@$) :: TyFun a (a ~> Bool) -> Type) (a6989586621679837397 :: a) = (<@#@$$) a6989586621679837397
type Apply (Elem_6989586621681012558Sym0 :: TyFun a (Identity a ~> Bool) -> Type) (a6989586621681012563 :: a)
Instance details Defined in Data.Singletons.Prelude.Identity type Apply (Elem_6989586621681012558Sym0 :: TyFun a (Identity a ~> Bool) -> Type) (a6989586621681012563 :: a) = Elem_6989586621681012558Sym1 a6989586621681012563
type Apply (Elem_6989586621680823021Sym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680823030 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823021Sym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680823030 :: a) = Elem_6989586621680823021Sym1 a6989586621680823030 :: TyFun (t a) Bool -> Type
type Apply (ElemSym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680822821 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (ElemSym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680822821 :: a) = ElemSym1 a6989586621680822821 :: TyFun (t a) Bool -> Type
type Apply (NotElemSym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680822568 :: a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (NotElemSym0 :: TyFun a (t a ~> Bool) -> Type) (a6989586621680822568 :: a) = NotElemSym1 a6989586621680822568 :: TyFun (t a) Bool -> Type
type Apply (Bool_Sym1 a6989586621679815230 :: TyFun a (Bool ~> a) -> Type) (a6989586621679815231 :: a)
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym1 a6989586621679815230 :: TyFun a (Bool ~> a) -> Type) (a6989586621679815231 :: a) = Bool_Sym2 a6989586621679815230 a6989586621679815231
type Apply (Let6989586621680379318Scrutinee_6989586621680375763Sym0 :: TyFun k1 (TyFun k Bool -> Type) -> Type) (n6989586621680379316 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379318Scrutinee_6989586621680375763Sym0 :: TyFun k1 (TyFun k Bool -> Type) -> Type) (n6989586621680379316 :: k1) = Let6989586621680379318Scrutinee_6989586621680375763Sym1 n6989586621680379316 :: TyFun k Bool -> Type
type Apply (Elem_bySym1 a6989586621680379249 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680379250 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Elem_bySym1 a6989586621680379249 :: TyFun a ([a] ~> Bool) -> Type) (a6989586621680379250 :: a) = Elem_bySym2 a6989586621680379249 a6989586621680379250
type Apply (Lambda_6989586621680822993Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (a_69895866216808229876989586621680822992 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Lambda_6989586621680822993Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (a_69895866216808229876989586621680822992 :: k1) = Lambda_6989586621680822993Sym1 a_69895866216808229876989586621680822992 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (x6989586621680379296 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (x6989586621680379296 :: k1) = Let6989586621680379299Scrutinee_6989586621680375765Sym1 x6989586621680379296 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym0 :: TyFun k1 (TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (key6989586621680379380 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym0 :: TyFun k1 (TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (key6989586621680379380 :: k1) = Let6989586621680379384Scrutinee_6989586621680375759Sym1 key6989586621680379380 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (n6989586621680379458 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (n6989586621680379458 :: k1) = Let6989586621680379461Scrutinee_6989586621680375749Sym1 n6989586621680379458 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (n6989586621680379471 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (n6989586621680379471 :: k1) = Let6989586621680379474Scrutinee_6989586621680375747Sym1 n6989586621680379471 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (y6989586621680379267 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (y6989586621680379267 :: k1) = Let6989586621680379270Scrutinee_6989586621680375769Sym1 y6989586621680379267 :: TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (x6989586621680379283 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym0 :: TyFun k1 (TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (x6989586621680379283 :: k1) = Let6989586621680379286Scrutinee_6989586621680375767Sym1 x6989586621680379283 :: TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym0 :: TyFun k1 (TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type) -> Type) (x6989586621680379560 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym0 :: TyFun k1 (TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type) -> Type) (x6989586621680379560 :: k1) = Let6989586621680379562Scrutinee_6989586621680375741Sym1 x6989586621680379560 :: TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type
type Apply (Lambda_6989586621681501422Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type) -> Type) (x6989586621681501421 :: k1)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501422Sym0 :: TyFun k1 (TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type) -> Type) (x6989586621681501421 :: k1) = Lambda_6989586621681501422Sym1 x6989586621681501421 :: TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type
type Apply (Lambda_6989586621680822993Sym1 a_69895866216808229876989586621680822992 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (arg_69895866216808223796989586621680822995 :: k2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Lambda_6989586621680822993Sym1 a_69895866216808229876989586621680822992 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (arg_69895866216808223796989586621680822995 :: k2) = Lambda_6989586621680822993Sym2 a_69895866216808229876989586621680822992 arg_69895866216808223796989586621680822995 :: TyFun k3 Bool -> Type
type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x6989586621680180969 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x6989586621680180969 :: k1) = Let6989586621680180970Scrutinee_6989586621680180778Sym1 x6989586621680180969 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym1 x6989586621680379296 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (xs6989586621680379297 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379299Scrutinee_6989586621680375765Sym1 x6989586621680379296 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (xs6989586621680379297 :: k2) = Let6989586621680379299Scrutinee_6989586621680375765Sym2 x6989586621680379296 xs6989586621680379297 :: TyFun k3 Bool -> Type
type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym1 key6989586621680379380 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (x6989586621680379381 :: k1)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym1 key6989586621680379380 :: TyFun k1 (TyFun k2 (TyFun k3 Bool -> Type) -> Type) -> Type) (x6989586621680379381 :: k1) = Let6989586621680379384Scrutinee_6989586621680375759Sym2 key6989586621680379380 x6989586621680379381 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym1 n6989586621680379458 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (x6989586621680379459 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379461Scrutinee_6989586621680375749Sym1 n6989586621680379458 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (x6989586621680379459 :: k2) = Let6989586621680379461Scrutinee_6989586621680375749Sym2 n6989586621680379458 x6989586621680379459 :: TyFun k3 Bool -> Type
type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym1 n6989586621680379471 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (x6989586621680379472 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379474Scrutinee_6989586621680375747Sym1 n6989586621680379471 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (x6989586621680379472 :: k2) = Let6989586621680379474Scrutinee_6989586621680375747Sym2 n6989586621680379471 x6989586621680379472 :: TyFun k3 Bool -> Type
type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym1 y6989586621680379267 :: TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (ys6989586621680379268 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym1 y6989586621680379267 :: TyFun k2 (TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) -> Type) (ys6989586621680379268 :: k2) = Let6989586621680379270Scrutinee_6989586621680375769Sym2 y6989586621680379267 ys6989586621680379268 :: TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym1 x6989586621680379283 :: TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type) (xs6989586621680379284 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym1 x6989586621680379283 :: TyFun k2 (TyFun [k1] (TyFun k3 Bool -> Type) -> Type) -> Type) (xs6989586621680379284 :: k2) = Let6989586621680379286Scrutinee_6989586621680375767Sym2 x6989586621680379283 xs6989586621680379284 :: TyFun [k1] (TyFun k3 Bool -> Type) -> Type
type Apply (Lambda_6989586621681501422Sym1 x6989586621681501421 :: TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type) (p6989586621681501417 :: k2)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501422Sym1 x6989586621681501421 :: TyFun k2 (TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) -> Type) (p6989586621681501417 :: k2) = Lambda_6989586621681501422Sym2 x6989586621681501421 p6989586621681501417 :: TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (x16989586621680180874 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (x16989586621680180874 :: k1) = Let6989586621680180879Scrutinee_6989586621680180802Sym1 x16989586621680180874 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (x16989586621680180911 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym0 :: TyFun k1 (TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (x16989586621680180911 :: k1) = Let6989586621680180916Scrutinee_6989586621680180792Sym1 x16989586621680180911 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym1 x6989586621680180969 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type) (x06989586621680180964 :: k2)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym1 x6989586621680180969 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) -> Type) (x06989586621680180964 :: k2) = Let6989586621680180970Scrutinee_6989586621680180778Sym2 x6989586621680180969 x06989586621680180964 :: TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym2 key6989586621680379380 x6989586621680379381 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (y6989586621680379382 :: k2)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379384Scrutinee_6989586621680375759Sym2 key6989586621680379380 x6989586621680379381 :: TyFun k2 (TyFun k3 Bool -> Type) -> Type) (y6989586621680379382 :: k2) = Let6989586621680379384Scrutinee_6989586621680375759Sym3 key6989586621680379380 x6989586621680379381 y6989586621680379382 :: TyFun k3 Bool -> Type
type Apply (Lambda_6989586621681501422Sym2 x6989586621681501421 p6989586621681501417 :: TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) (a_69895866216815014106989586621681501418 :: k3)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501422Sym2 x6989586621681501421 p6989586621681501417 :: TyFun k3 (TyFun Bool ([k1] ~> [k1]) -> Type) -> Type) (a_69895866216815014106989586621681501418 :: k3) = Lambda_6989586621681501422Sym3 x6989586621681501421 p6989586621681501417 a_69895866216815014106989586621681501418
type Apply (Lambda_6989586621681501422Sym3 x6989586621681501421 p6989586621681501417 a_69895866216815014106989586621681501418 :: TyFun Bool ([k1] ~> [k1]) -> Type) (flg6989586621681501424 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501422Sym3 x6989586621681501421 p6989586621681501417 a_69895866216815014106989586621681501418 :: TyFun Bool ([k1] ~> [k1]) -> Type) (flg6989586621681501424 :: Bool) = Lambda_6989586621681501422Sym4 x6989586621681501421 p6989586621681501417 a_69895866216815014106989586621681501418 flg6989586621681501424
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym1 x16989586621680180874 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x26989586621680180875 :: k2)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym1 x16989586621680180874 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x26989586621680180875 :: k2) = Let6989586621680180879Scrutinee_6989586621680180802Sym2 x16989586621680180874 x26989586621680180875 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym1 x16989586621680180911 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x26989586621680180912 :: k2)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym1 x16989586621680180911 :: TyFun k2 (TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) -> Type) (x26989586621680180912 :: k2) = Let6989586621680180916Scrutinee_6989586621680180792Sym2 x16989586621680180911 x26989586621680180912 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym2 x6989586621680180969 x06989586621680180964 :: TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) (y6989586621680180965 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym2 x6989586621680180969 x06989586621680180964 :: TyFun k1 (TyFun k3 (TyFun k4 Bool -> Type) -> Type) -> Type) (y6989586621680180965 :: k1) = Let6989586621680180970Scrutinee_6989586621680180778Sym3 x6989586621680180969 x06989586621680180964 y6989586621680180965 :: TyFun k3 (TyFun k4 Bool -> Type) -> Type
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym2 x16989586621680180874 x26989586621680180875 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) (y6989586621680180876 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym2 x16989586621680180874 x26989586621680180875 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) (y6989586621680180876 :: k1) = Let6989586621680180879Scrutinee_6989586621680180802Sym3 x16989586621680180874 x26989586621680180875 y6989586621680180876 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym2 x16989586621680180911 x26989586621680180912 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) (y6989586621680180913 :: k1)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym2 x16989586621680180911 x26989586621680180912 :: TyFun k1 (TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) -> Type) (y6989586621680180913 :: k1) = Let6989586621680180916Scrutinee_6989586621680180792Sym3 x16989586621680180911 x26989586621680180912 y6989586621680180913 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type
type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym3 x6989586621680180969 x06989586621680180964 y6989586621680180965 :: TyFun k3 (TyFun k4 Bool -> Type) -> Type) (arg_69895866216801807746989586621680180960 :: k3)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180970Scrutinee_6989586621680180778Sym3 x6989586621680180969 x06989586621680180964 y6989586621680180965 :: TyFun k3 (TyFun k4 Bool -> Type) -> Type) (arg_69895866216801807746989586621680180960 :: k3) = Let6989586621680180970Scrutinee_6989586621680180778Sym4 x6989586621680180969 x06989586621680180964 y6989586621680180965 arg_69895866216801807746989586621680180960 :: TyFun k4 Bool -> Type
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym3 x16989586621680180874 x26989586621680180875 y6989586621680180876 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) (arg_69895866216801807966989586621680180869 :: k3)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym3 x16989586621680180874 x26989586621680180875 y6989586621680180876 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) (arg_69895866216801807966989586621680180869 :: k3) = Let6989586621680180879Scrutinee_6989586621680180802Sym4 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym3 x16989586621680180911 x26989586621680180912 y6989586621680180913 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) (arg_69895866216801807866989586621680180906 :: k3)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym3 x16989586621680180911 x26989586621680180912 y6989586621680180913 :: TyFun k3 (TyFun k4 (TyFun k5 Bool -> Type) -> Type) -> Type) (arg_69895866216801807866989586621680180906 :: k3) = Let6989586621680180916Scrutinee_6989586621680180792Sym4 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type
type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym4 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type) (arg_69895866216801807986989586621680180870 :: k4)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180879Scrutinee_6989586621680180802Sym4 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type) (arg_69895866216801807986989586621680180870 :: k4) = Let6989586621680180879Scrutinee_6989586621680180802Sym5 x16989586621680180874 x26989586621680180875 y6989586621680180876 arg_69895866216801807966989586621680180869 arg_69895866216801807986989586621680180870 :: TyFun k5 Bool -> Type
type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym4 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type) (arg_69895866216801807886989586621680180907 :: k4)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply (Let6989586621680180916Scrutinee_6989586621680180792Sym4 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 :: TyFun k4 (TyFun k5 Bool -> Type) -> Type) (arg_69895866216801807886989586621680180907 :: k4) = Let6989586621680180916Scrutinee_6989586621680180792Sym5 x16989586621680180911 x26989586621680180912 y6989586621680180913 arg_69895866216801807866989586621680180906 arg_69895866216801807886989586621680180907 :: TyFun k5 Bool -> Type
type Apply AndSym0 (a6989586621680380258 :: [Bool])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply AndSym0 (a6989586621680380258 :: [Bool]) = AndSym1 a6989586621680380258
type Apply OrSym0 (a6989586621680380253 :: [Bool])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply OrSym0 (a6989586621680380253 :: [Bool]) = OrSym1 a6989586621680380253
type Apply (ListnullSym0 :: TyFun [a] Bool -> Type) (a6989586621680749352 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListnullSym0 :: TyFun [a] Bool -> Type) (a6989586621680749352 :: [a]) = ListnullSym1 a6989586621680749352
type Apply (Null_6989586621680823265Sym0 :: TyFun [a] Bool -> Type) (a6989586621680823271 :: [a])
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823265Sym0 :: TyFun [a] Bool -> Type) (a6989586621680823271 :: [a]) = Null_6989586621680823265Sym1 a6989586621680823271
type Apply (NullSym0 :: TyFun [a] Bool -> Type) (a6989586621680380431 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (NullSym0 :: TyFun [a] Bool -> Type) (a6989586621680380431 :: [a]) = NullSym1 a6989586621680380431
type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959464 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959464 :: Maybe a) = IsNothingSym1 a6989586621679959464
type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959467 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959467 :: Maybe a) = IsJustSym1 a6989586621679959467
type Apply (AndSym0 :: TyFun (t Bool) Bool -> Type) (a6989586621680822640 :: t Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (AndSym0 :: TyFun (t Bool) Bool -> Type) (a6989586621680822640 :: t Bool) = AndSym1 a6989586621680822640
type Apply (OrSym0 :: TyFun (t Bool) Bool -> Type) (a6989586621680822634 :: t Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (OrSym0 :: TyFun (t Bool) Bool -> Type) (a6989586621680822634 :: t Bool) = OrSym1 a6989586621680822634
type Apply (Null_6989586621681012674Sym0 :: TyFun (Identity a) Bool -> Type) (a6989586621681012678 :: Identity a)
Instance details Defined in Data.Singletons.Prelude.Identity type Apply (Null_6989586621681012674Sym0 :: TyFun (Identity a) Bool -> Type) (a6989586621681012678 :: Identity a) = Null_6989586621681012674Sym1 a6989586621681012678
type Apply (Null_6989586621680823671Sym0 :: TyFun (Dual a) Bool -> Type) (a6989586621680823675 :: Dual a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823671Sym0 :: TyFun (Dual a) Bool -> Type) (a6989586621680823675 :: Dual a) = Null_6989586621680823671Sym1 a6989586621680823675
type Apply (Null_6989586621680823846Sym0 :: TyFun (Sum a) Bool -> Type) (a6989586621680823850 :: Sum a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823846Sym0 :: TyFun (Sum a) Bool -> Type) (a6989586621680823850 :: Sum a) = Null_6989586621680823846Sym1 a6989586621680823850
type Apply (Null_6989586621680824021Sym0 :: TyFun (Product a) Bool -> Type) (a6989586621680824025 :: Product a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680824021Sym0 :: TyFun (Product a) Bool -> Type) (a6989586621680824025 :: Product a) = Null_6989586621680824021Sym1 a6989586621680824025
type Apply (Elem_6989586621680823131Sym1 a6989586621680823140 :: TyFun [a] Bool -> Type) (a6989586621680823141 :: [a])
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823131Sym1 a6989586621680823140 :: TyFun [a] Bool -> Type) (a6989586621680823141 :: [a]) = Elem_6989586621680823131Sym2 a6989586621680823140 a6989586621680823141
type Apply (ListelemSym1 a6989586621680749443 :: TyFun [a] Bool -> Type) (a6989586621680749444 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListelemSym1 a6989586621680749443 :: TyFun [a] Bool -> Type) (a6989586621680749444 :: [a]) = ListelemSym2 a6989586621680749443 a6989586621680749444
type Apply (ElemSym1 a6989586621680380021 :: TyFun [a] Bool -> Type) (a6989586621680380022 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (ElemSym1 a6989586621680380021 :: TyFun [a] Bool -> Type) (a6989586621680380022 :: [a]) = ElemSym2 a6989586621680380021 a6989586621680380022
type Apply (ListisPrefixOfSym1 a6989586621680749515 :: TyFun [a] Bool -> Type) (a6989586621680749516 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListisPrefixOfSym1 a6989586621680749515 :: TyFun [a] Bool -> Type) (a6989586621680749516 :: [a]) = ListisPrefixOfSym2 a6989586621680749515 a6989586621680749516
type Apply (NotElemSym1 a6989586621680380013 :: TyFun [a] Bool -> Type) (a6989586621680380014 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (NotElemSym1 a6989586621680380013 :: TyFun [a] Bool -> Type) (a6989586621680380014 :: [a]) = NotElemSym2 a6989586621680380013 a6989586621680380014
type Apply (IsPrefixOfSym1 a6989586621680380043 :: TyFun [a] Bool -> Type) (a6989586621680380044 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsPrefixOfSym1 a6989586621680380043 :: TyFun [a] Bool -> Type) (a6989586621680380044 :: [a]) = IsPrefixOfSym2 a6989586621680380043 a6989586621680380044
type Apply (AnySym1 a6989586621680380238 :: TyFun [a] Bool -> Type) (a6989586621680380239 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (AnySym1 a6989586621680380238 :: TyFun [a] Bool -> Type) (a6989586621680380239 :: [a]) = AnySym2 a6989586621680380238 a6989586621680380239
type Apply (IsInfixOfSym1 a6989586621680380029 :: TyFun [a] Bool -> Type) (a6989586621680380030 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsInfixOfSym1 a6989586621680380029 :: TyFun [a] Bool -> Type) (a6989586621680380030 :: [a]) = IsInfixOfSym2 a6989586621680380029 a6989586621680380030
type Apply (AllSym1 a6989586621680380246 :: TyFun [a] Bool -> Type) (a6989586621680380247 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (AllSym1 a6989586621680380246 :: TyFun [a] Bool -> Type) (a6989586621680380247 :: [a]) = AllSym2 a6989586621680380246 a6989586621680380247
type Apply (IsSuffixOfSym1 a6989586621680380036 :: TyFun [a] Bool -> Type) (a6989586621680380037 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsSuffixOfSym1 a6989586621680380036 :: TyFun [a] Bool -> Type) (a6989586621680380037 :: [a]) = IsSuffixOfSym2 a6989586621680380036 a6989586621680380037
type Apply (Elem_6989586621681012558Sym1 a6989586621681012563 :: TyFun (Identity a) Bool -> Type) (a6989586621681012564 :: Identity a)
Instance details Defined in Data.Singletons.Prelude.Identity type Apply (Elem_6989586621681012558Sym1 a6989586621681012563 :: TyFun (Identity a) Bool -> Type) (a6989586621681012564 :: Identity a) = Elem_6989586621681012558Sym2 a6989586621681012563 a6989586621681012564
type Apply (Elem_6989586621680823539Sym1 a6989586621680823548 :: TyFun (Dual a) Bool -> Type) (a6989586621680823549 :: Dual a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823539Sym1 a6989586621680823548 :: TyFun (Dual a) Bool -> Type) (a6989586621680823549 :: Dual a) = Elem_6989586621680823539Sym2 a6989586621680823548 a6989586621680823549
type Apply (Elem_6989586621680823714Sym1 a6989586621680823723 :: TyFun (Sum a) Bool -> Type) (a6989586621680823724 :: Sum a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823714Sym1 a6989586621680823723 :: TyFun (Sum a) Bool -> Type) (a6989586621680823724 :: Sum a) = Elem_6989586621680823714Sym2 a6989586621680823723 a6989586621680823724
type Apply (Elem_6989586621680823889Sym1 a6989586621680823898 :: TyFun (Product a) Bool -> Type) (a6989586621680823899 :: Product a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823889Sym1 a6989586621680823898 :: TyFun (Product a) Bool -> Type) (a6989586621680823899 :: Product a) = Elem_6989586621680823889Sym2 a6989586621680823898 a6989586621680823899
type Apply (Elem_bySym2 a6989586621680379249 a6989586621680379250 :: TyFun [a] Bool -> Type) (a6989586621680379251 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Elem_bySym2 a6989586621680379249 a6989586621680379250 :: TyFun [a] Bool -> Type) (a6989586621680379251 :: [a]) = Elem_bySym3 a6989586621680379249 a6989586621680379250 a6989586621680379251
type Apply (Elem_6989586621680823021Sym1 a6989586621680823030 :: TyFun (t a) Bool -> Type) (a6989586621680823031 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823021Sym1 a6989586621680823030 :: TyFun (t a) Bool -> Type) (a6989586621680823031 :: t a) = Elem_6989586621680823021Sym2 a6989586621680823030 a6989586621680823031
type Apply (Null_6989586621680822985Sym0 :: TyFun (t a) Bool -> Type) (a6989586621680822991 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680822985Sym0 :: TyFun (t a) Bool -> Type) (a6989586621680822991 :: t a) = Null_6989586621680822985Sym1 a6989586621680822991
type Apply (AnySym1 a6989586621680822626 :: TyFun (t a) Bool -> Type) (a6989586621680822627 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (AnySym1 a6989586621680822626 :: TyFun (t a) Bool -> Type) (a6989586621680822627 :: t a) = AnySym2 a6989586621680822626 a6989586621680822627
type Apply (ElemSym1 a6989586621680822821 :: TyFun (t a) Bool -> Type) (a6989586621680822822 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (ElemSym1 a6989586621680822821 :: TyFun (t a) Bool -> Type) (a6989586621680822822 :: t a) = ElemSym2 a6989586621680822821 a6989586621680822822
type Apply (NotElemSym1 a6989586621680822568 :: TyFun (t a) Bool -> Type) (a6989586621680822569 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (NotElemSym1 a6989586621680822568 :: TyFun (t a) Bool -> Type) (a6989586621680822569 :: t a) = NotElemSym2 a6989586621680822568 a6989586621680822569
type Apply (NullSym0 :: TyFun (t a) Bool -> Type) (a6989586621680822814 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (NullSym0 :: TyFun (t a) Bool -> Type) (a6989586621680822814 :: t a) = NullSym1 a6989586621680822814
type Apply (AllSym1 a6989586621680822617 :: TyFun (t a) Bool -> Type) (a6989586621680822618 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (AllSym1 a6989586621680822617 :: TyFun (t a) Bool -> Type) (a6989586621680822618 :: t a) = AllSym2 a6989586621680822617 a6989586621680822618
type Apply (ListisPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680749515 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListisPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680749515 :: [a]) = ListisPrefixOfSym1 a6989586621680749515
type Apply (IsPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380043 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsPrefixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380043 :: [a]) = IsPrefixOfSym1 a6989586621680380043
type Apply (IsInfixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380029 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsInfixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380029 :: [a]) = IsInfixOfSym1 a6989586621680380029
type Apply (IsSuffixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380036 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IsSuffixOfSym0 :: TyFun [a] ([a] ~> Bool) -> Type) (a6989586621680380036 :: [a]) = IsSuffixOfSym1 a6989586621680380036
type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym1 x6989586621680379560 :: TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type) (xs6989586621680379561 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym1 x6989586621680379560 :: TyFun [a] (TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) -> Type) (xs6989586621680379561 :: [a]) = Let6989586621680379562Scrutinee_6989586621680375741Sym2 x6989586621680379560 xs6989586621680379561 :: TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type
type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym2 y6989586621680379267 ys6989586621680379268 :: TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) (xs6989586621680379269 :: [k1])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym2 y6989586621680379267 ys6989586621680379268 :: TyFun [k1] (TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) -> Type) (xs6989586621680379269 :: [k1]) = Let6989586621680379270Scrutinee_6989586621680375769Sym3 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type
type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym2 x6989586621680379283 xs6989586621680379284 :: TyFun [k1] (TyFun k3 Bool -> Type) -> Type) (ls6989586621680379285 :: [k1])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379286Scrutinee_6989586621680375767Sym2 x6989586621680379283 xs6989586621680379284 :: TyFun [k1] (TyFun k3 Bool -> Type) -> Type) (ls6989586621680379285 :: [k1]) = Let6989586621680379286Scrutinee_6989586621680375767Sym3 x6989586621680379283 xs6989586621680379284 ls6989586621680379285 :: TyFun k3 Bool -> Type
type Apply (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type) (a6989586621680823432 :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type) (a6989586621680823432 :: Either a1 a2) = Null_6989586621680823426Sym1 a6989586621680823432
type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804040 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804040 :: Either a b) = IsRightSym1 a6989586621680804040
type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804043 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804043 :: Either a b) = IsLeftSym1 a6989586621680804043
type Apply (Elem_6989586621680823507Sym1 a6989586621680823512 :: TyFun (Proxy a) Bool -> Type) (a6989586621680823513 :: Proxy a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Elem_6989586621680823507Sym1 a6989586621680823512 :: TyFun (Proxy a) Bool -> Type) (a6989586621680823513 :: Proxy a) = Elem_6989586621680823507Sym2 a6989586621680823512 a6989586621680823513
type Apply (Null_6989586621680823500Sym0 :: TyFun (Proxy a) Bool -> Type) (a6989586621680823504 :: Proxy a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823500Sym0 :: TyFun (Proxy a) Bool -> Type) (a6989586621680823504 :: Proxy a) = Null_6989586621680823500Sym1 a6989586621680823504
type Apply (TFHelper_6989586621681203603Sym1 a6989586621681203608 :: TyFun (Arg a b) Bool -> Type) (a6989586621681203609 :: Arg a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup type Apply (TFHelper_6989586621681203603Sym1 a6989586621681203608 :: TyFun (Arg a b) Bool -> Type) (a6989586621681203609 :: Arg a b) = TFHelper_6989586621681203603Sym2 a6989586621681203608 a6989586621681203609
type Apply (TFHelper_6989586621680787214Sym1 a6989586621680787219 :: TyFun (Proxy s) Bool -> Type) (a6989586621680787220 :: Proxy s)
Instance details Defined in Data.Singletons.Prelude.Proxy type Apply (TFHelper_6989586621680787214Sym1 a6989586621680787219 :: TyFun (Proxy s) Bool -> Type) (a6989586621680787220 :: Proxy s) = TFHelper_6989586621680787214Sym2 a6989586621680787219 a6989586621680787220
type Apply (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type) (a6989586621680379652 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type) (a6989586621680379652 :: a ~> Bool) = FindIndexSym1 a6989586621680379652
type Apply (FindIndicesSym0 :: TyFun (a ~> Bool) ([a] ~> [Nat]) -> Type) (a6989586621680379629 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindIndicesSym0 :: TyFun (a ~> Bool) ([a] ~> [Nat]) -> Type) (a6989586621680379629 :: a ~> Bool) = FindIndicesSym1 a6989586621680379629
type Apply (FilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379686 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379686 :: a ~> Bool) = FilterSym1 a6989586621680379686
type Apply (ListnubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type) (a6989586621680749477 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListnubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type) (a6989586621680749477 :: a ~> (a ~> Bool)) = ListnubBySym1 a6989586621680749477
type Apply (ListpartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680749537 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListpartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680749537 :: a ~> Bool) = ListpartitionSym1 a6989586621680749537
type Apply (ListfilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749548 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListfilterSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749548 :: a ~> Bool) = ListfilterSym1 a6989586621680749548
type Apply (ListspanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680749559 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListspanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680749559 :: a ~> Bool) = ListspanSym1 a6989586621680749559
type Apply (ListdropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749570 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListdropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749570 :: a ~> Bool) = ListdropWhileSym1 a6989586621680749570
type Apply (ListtakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749581 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListtakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680749581 :: a ~> Bool) = ListtakeWhileSym1 a6989586621680749581
type Apply (UntilSym0 :: TyFun (a ~> Bool) ((a ~> a) ~> (a ~> a)) -> Type) (a6989586621679990278 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Base type Apply (UntilSym0 :: TyFun (a ~> Bool) ((a ~> a) ~> (a ~> a)) -> Type) (a6989586621679990278 :: a ~> Bool) = UntilSym1 a6989586621679990278
type Apply (Elem_bySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> Bool)) -> Type) (a6989586621680379249 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Elem_bySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> Bool)) -> Type) (a6989586621680379249 :: a ~> (a ~> Bool)) = Elem_bySym1 a6989586621680379249
type Apply (NubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type) (a6989586621680379259 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (NubBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [a]) -> Type) (a6989586621680379259 :: a ~> (a ~> Bool)) = NubBySym1 a6989586621680379259
type Apply (SelectSym0 :: TyFun (a ~> Bool) (a ~> (([a], [a]) ~> ([a], [a]))) -> Type) (a6989586621680379355 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (SelectSym0 :: TyFun (a ~> Bool) (a ~> (([a], [a]) ~> ([a], [a]))) -> Type) (a6989586621680379355 :: a ~> Bool) = SelectSym1 a6989586621680379355
type Apply (PartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379370 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (PartitionSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379370 :: a ~> Bool) = PartitionSym1 a6989586621680379370
type Apply (BreakSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379482 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (BreakSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379482 :: a ~> Bool) = BreakSym1 a6989586621680379482
type Apply (Let6989586621680379495YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379495YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool) = Let6989586621680379495YsSym1 p6989586621680379486
type Apply (Let6989586621680379495ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379495ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool) = Let6989586621680379495ZsSym1 p6989586621680379486
type Apply (Let6989586621680379495X_6989586621680379496Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379495X_6989586621680379496Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type) (p6989586621680379486 :: k ~> Bool) = Let6989586621680379495X_6989586621680379496Sym1 p6989586621680379486
type Apply (SpanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379517 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (SpanSym0 :: TyFun (a ~> Bool) ([a] ~> ([a], [a])) -> Type) (a6989586621680379517 :: a ~> Bool) = SpanSym1 a6989586621680379517
type Apply (Let6989586621680379530YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379530YsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool) = Let6989586621680379530YsSym1 p6989586621680379521
type Apply (Let6989586621680379530ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379530ZsSym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] [k] -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool) = Let6989586621680379530ZsSym1 p6989586621680379521
type Apply (Let6989586621680379530X_6989586621680379531Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379530X_6989586621680379531Sym0 :: TyFun (k ~> Bool) (TyFun k (TyFun [k] ([k], [k]) -> Type) -> Type) -> Type) (p6989586621680379521 :: k ~> Bool) = Let6989586621680379530X_6989586621680379531Sym1 p6989586621680379521
type Apply (GroupBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [[a]]) -> Type) (a6989586621680379392 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (GroupBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> [[a]]) -> Type) (a6989586621680379392 :: a ~> (a ~> Bool)) = GroupBySym1 a6989586621680379392
type Apply (DropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379571 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (DropWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379571 :: a ~> Bool) = DropWhileSym1 a6989586621680379571
type Apply (TakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379586 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (TakeWhileSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379586 :: a ~> Bool) = TakeWhileSym1 a6989586621680379586
type Apply (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type) (a6989586621680379679 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type) (a6989586621680379679 :: a ~> Bool) = FindSym1 a6989586621680379679
type Apply (DeleteBySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> [a])) -> Type) (a6989586621680379785 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (DeleteBySym0 :: TyFun (a ~> (a ~> Bool)) (a ~> ([a] ~> [a])) -> Type) (a6989586621680379785 :: a ~> (a ~> Bool)) = DeleteBySym1 a6989586621680379785
type Apply (DeleteFirstsBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379775 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (DeleteFirstsBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379775 :: a ~> (a ~> Bool)) = DeleteFirstsBySym1 a6989586621680379775
type Apply (UnionBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379239 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (UnionBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379239 :: a ~> (a ~> Bool)) = UnionBySym1 a6989586621680379239
type Apply (AnySym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type) (a6989586621680380238 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (AnySym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type) (a6989586621680380238 :: a ~> Bool) = AnySym1 a6989586621680380238
type Apply (IntersectBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379600 :: a ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (IntersectBySym0 :: TyFun (a ~> (a ~> Bool)) ([a] ~> ([a] ~> [a])) -> Type) (a6989586621680379600 :: a ~> (a ~> Bool)) = IntersectBySym1 a6989586621680379600
type Apply (AllSym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type) (a6989586621680380246 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (AllSym0 :: TyFun (a ~> Bool) ([a] ~> Bool) -> Type) (a6989586621680380246 :: a ~> Bool) = AllSym1 a6989586621680380246
type Apply (DropWhileEndSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379554 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (DropWhileEndSym0 :: TyFun (a ~> Bool) ([a] ~> [a]) -> Type) (a6989586621680379554 :: a ~> Bool) = DropWhileEndSym1 a6989586621680379554
type Apply (TFHelper_6989586621681203603Sym0 :: TyFun (Arg a b) (Arg a b ~> Bool) -> Type) (a6989586621681203608 :: Arg a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup type Apply (TFHelper_6989586621681203603Sym0 :: TyFun (Arg a b) (Arg a b ~> Bool) -> Type) (a6989586621681203608 :: Arg a b) = TFHelper_6989586621681203603Sym1 a6989586621681203608
type Apply (TFHelper_6989586621680787214Sym0 :: TyFun (Proxy s) (Proxy s ~> Bool) -> Type) (a6989586621680787219 :: Proxy s)
Instance details Defined in Data.Singletons.Prelude.Proxy type Apply (TFHelper_6989586621680787214Sym0 :: TyFun (Proxy s) (Proxy s ~> Bool) -> Type) (a6989586621680787219 :: Proxy s) = TFHelper_6989586621680787214Sym1 a6989586621680787219
type Apply (Lambda_6989586621680822554Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (First a) -> Type) -> Type) -> Type) (p6989586621680822552 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Lambda_6989586621680822554Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (First a) -> Type) -> Type) -> Type) (p6989586621680822552 :: a ~> Bool) = Lambda_6989586621680822554Sym1 p6989586621680822552 :: TyFun k (TyFun a (First a) -> Type) -> Type
type Apply (AnySym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type) (a6989586621680822626 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (AnySym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type) (a6989586621680822626 :: a ~> Bool) = AnySym1 a6989586621680822626 :: TyFun (t a) Bool -> Type
type Apply (AllSym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type) (a6989586621680822617 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (AllSym0 :: TyFun (a ~> Bool) (t a ~> Bool) -> Type) (a6989586621680822617 :: a ~> Bool) = AllSym1 a6989586621680822617 :: TyFun (t a) Bool -> Type
type Apply (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type) (a6989586621680822550 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type) (a6989586621680822550 :: a ~> Bool) = FindSym1 a6989586621680822550 :: TyFun (t a) (Maybe a) -> Type
type Apply (Let6989586621679990284GoSym0 :: TyFun (k1 ~> Bool) (TyFun (k1 ~> k1) (TyFun k2 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (p6989586621679990281 :: k1 ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Base type Apply (Let6989586621679990284GoSym0 :: TyFun (k1 ~> Bool) (TyFun (k1 ~> k1) (TyFun k2 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (p6989586621679990281 :: k1 ~> Bool) = Let6989586621679990284GoSym1 p6989586621679990281 :: TyFun (k1 ~> k1) (TyFun k2 (TyFun k1 k1 -> Type) -> Type) -> Type
type Apply (Let6989586621680379263NubBy'Sym0 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k (TyFun [k1] ([k1] ~> [k1]) -> Type) -> Type) -> Type) (eq6989586621680379261 :: k1 ~> (k1 ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379263NubBy'Sym0 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k (TyFun [k1] ([k1] ~> [k1]) -> Type) -> Type) -> Type) (eq6989586621680379261 :: k1 ~> (k1 ~> Bool)) = Let6989586621680379263NubBy'Sym1 eq6989586621680379261 :: TyFun k (TyFun [k1] ([k1] ~> [k1]) -> Type) -> Type
type Apply (Let6989586621680379397YsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379397YsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool)) = Let6989586621680379397YsSym1 eq6989586621680379394
type Apply (Let6989586621680379397ZsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379397ZsSym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] [a] -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool)) = Let6989586621680379397ZsSym1 eq6989586621680379394
type Apply (Let6989586621680379397X_6989586621680379398Sym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] ([a], [a]) -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379397X_6989586621680379398Sym0 :: TyFun (k1 ~> (a ~> Bool)) (TyFun k1 (TyFun [a] ([a], [a]) -> Type) -> Type) -> Type) (eq6989586621680379394 :: k1 ~> (a ~> Bool)) = Let6989586621680379397X_6989586621680379398Sym1 eq6989586621680379394
type Apply (Lambda_6989586621680379558Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (TyFun [a] [a] -> Type) -> Type) -> Type) -> Type) (p6989586621680379556 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Lambda_6989586621680379558Sym0 :: TyFun (a ~> Bool) (TyFun k (TyFun a (TyFun [a] [a] -> Type) -> Type) -> Type) -> Type) (p6989586621680379556 :: a ~> Bool) = Lambda_6989586621680379558Sym1 p6989586621680379556 :: TyFun k (TyFun a (TyFun [a] [a] -> Type) -> Type) -> Type
type Apply (MfilterSym0 :: TyFun (a ~> Bool) (m a ~> m a) -> Type) (a6989586621681501253 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (MfilterSym0 :: TyFun (a ~> Bool) (m a ~> m a) -> Type) (a6989586621681501253 :: a ~> Bool) = MfilterSym1 a6989586621681501253 :: TyFun (m a) (m a) -> Type
type Apply (FilterMSym0 :: TyFun (a ~> m Bool) ([a] ~> m [a]) -> Type) (a6989586621681501415 :: a ~> m Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (FilterMSym0 :: TyFun (a ~> m Bool) ([a] ~> m [a]) -> Type) (a6989586621681501415 :: a ~> m Bool) = FilterMSym1 a6989586621681501415
type Apply (Lambda_6989586621681501257Sym0 :: TyFun (k1 ~> Bool) (TyFun k (TyFun k1 (m k1) -> Type) -> Type) -> Type) (p6989586621681501255 :: k1 ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501257Sym0 :: TyFun (k1 ~> Bool) (TyFun k (TyFun k1 (m k1) -> Type) -> Type) -> Type) (p6989586621681501255 :: k1 ~> Bool) = Lambda_6989586621681501257Sym1 p6989586621681501255 :: TyFun k (TyFun k1 (m k1) -> Type) -> Type
type Apply (Lambda_6989586621681501419Sym0 :: TyFun (k2 ~> f Bool) (TyFun k3 (TyFun k2 (f [k2] ~> f [k2]) -> Type) -> Type) -> Type) (p6989586621681501417 :: k2 ~> f Bool)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (Lambda_6989586621681501419Sym0 :: TyFun (k2 ~> f Bool) (TyFun k3 (TyFun k2 (f [k2] ~> f [k2]) -> Type) -> Type) -> Type) (p6989586621681501417 :: k2 ~> f Bool) = Lambda_6989586621681501419Sym1 p6989586621681501417 :: TyFun k3 (TyFun k2 (f [k2] ~> f [k2]) -> Type) -> Type
type Apply (Lambda_6989586621680379611Sym0 :: TyFun (b ~> (a ~> Bool)) (TyFun k1 (TyFun k2 (TyFun a (TyFun [a] (TyFun b (m b) -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (eq6989586621680379603 :: b ~> (a ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Lambda_6989586621680379611Sym0 :: TyFun (b ~> (a ~> Bool)) (TyFun k1 (TyFun k2 (TyFun a (TyFun [a] (TyFun b (m b) -> Type) -> Type) -> Type) -> Type) -> Type) -> Type) (eq6989586621680379603 :: b ~> (a ~> Bool)) = Lambda_6989586621680379611Sym1 eq6989586621680379603 :: TyFun k1 (TyFun k2 (TyFun a (TyFun [a] (TyFun b (m b) -> Type) -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym2 x6989586621680379560 xs6989586621680379561 :: TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) (p6989586621680379556 :: k1 ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379562Scrutinee_6989586621680375741Sym2 x6989586621680379560 xs6989586621680379561 :: TyFun (k1 ~> Bool) (TyFun k Bool -> Type) -> Type) (p6989586621680379556 :: k1 ~> Bool) = Let6989586621680379562Scrutinee_6989586621680375741Sym3 x6989586621680379560 xs6989586621680379561 p6989586621680379556 :: TyFun k Bool -> Type
type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym3 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) (eq6989586621680379261 :: k1 ~> (k1 ~> Bool))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379270Scrutinee_6989586621680375769Sym3 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 :: TyFun (k1 ~> (k1 ~> Bool)) (TyFun k3 Bool -> Type) -> Type) (eq6989586621680379261 :: k1 ~> (k1 ~> Bool)) = Let6989586621680379270Scrutinee_6989586621680375769Sym4 y6989586621680379267 ys6989586621680379268 xs6989586621680379269 eq6989586621680379261 :: TyFun k3 Bool -> Type

data Char #

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).

Instances

Instances details

Bounded Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char # maxBound :: Char #
Enum Char	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char # pred :: Char -> Char # toEnum :: Int -> Char # fromEnum :: Char -> Int # enumFrom :: Char -> [Char] # enumFromThen :: Char -> Char -> [Char] # enumFromTo :: Char -> Char -> [Char] # enumFromThenTo :: Char -> Char -> Char -> [Char] #
Eq Char
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool # (/=) :: Char -> Char -> Bool #
Ord Char
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering # (<) :: Char -> Char -> Bool # (<=) :: Char -> Char -> Bool # (>) :: Char -> Char -> Bool # (>=) :: Char -> Char -> Bool # max :: Char -> Char -> Char # min :: Char -> Char -> Char #
Read Char	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char # readList :: ReadS [Char] # readPrec :: ReadPrec Char # readListPrec :: ReadPrec [Char] #
Show Char	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS # show :: Char -> String # showList :: [Char] -> ShowS #
Ix Char	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Char, Char) -> [Char] # index :: (Char, Char) -> Char -> Int # unsafeIndex :: (Char, Char) -> Char -> Int # inRange :: (Char, Char) -> Char -> Bool # rangeSize :: (Char, Char) -> Int # unsafeRangeSize :: (Char, Char) -> Int #
Unbox Char
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Char
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Char -> Int # hash :: Char -> Int #
Storable Char	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Char -> Int # alignment :: Char -> Int # peekElemOff :: Ptr Char -> Int -> IO Char # pokeElemOff :: Ptr Char -> Int -> Char -> IO () # peekByteOff :: Ptr b -> Int -> IO Char # pokeByteOff :: Ptr b -> Int -> Char -> IO () # peek :: Ptr Char -> IO Char # poke :: Ptr Char -> Char -> IO () #
NFData Char
Instance details Defined in Control.DeepSeq Methods rnf :: Char -> () #
ErrorList Char
Instance details Defined in Control.Monad.Trans.Error Methods listMsg :: String -> [Char] #
Prim Char
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Char -> Int# alignment# :: Char -> Int# indexByteArray# :: ByteArray# -> Int# -> Char readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Char #) writeByteArray# :: MutableByteArray# s -> Int# -> Char -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Char -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Char readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Char #) writeOffAddr# :: Addr# -> Int# -> Char -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Char -> State# s -> State# s
Uniform Char
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Char
UniformRange Char
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Char, Char) -> g -> m Char
Lift Char
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Char -> Q Exp # liftTyped :: Char -> Q (TExp Char) #
IArray UArray Char
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Char -> (i, i) # numElements :: Ix i => UArray i Char -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Char)] -> UArray i Char unsafeAt :: Ix i => UArray i Char -> Int -> Char unsafeReplace :: Ix i => UArray i Char -> [(Int, Char)] -> UArray i Char unsafeAccum :: Ix i => (Char -> e' -> Char) -> UArray i Char -> [(Int, e')] -> UArray i Char unsafeAccumArray :: Ix i => (Char -> e' -> Char) -> Char -> (i, i) -> [(Int, e')] -> UArray i Char
MVector MVector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Char -> Int basicUnsafeSlice :: Int -> Int -> MVector s Char -> MVector s Char basicOverlaps :: MVector s Char -> MVector s Char -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Char) basicInitialize :: PrimMonad m => MVector (PrimState m) Char -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Char -> m (MVector (PrimState m) Char) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Char -> Int -> m Char basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Char -> Int -> Char -> m () basicClear :: PrimMonad m => MVector (PrimState m) Char -> m () basicSet :: PrimMonad m => MVector (PrimState m) Char -> Char -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Char -> Int -> m (MVector (PrimState m) Char)
Vector Vector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Char -> m (Vector Char) basicUnsafeThaw :: PrimMonad m => Vector Char -> m (Mutable Vector (PrimState m) Char) basicLength :: Vector Char -> Int basicUnsafeSlice :: Int -> Int -> Vector Char -> Vector Char basicUnsafeIndexM :: Monad m => Vector Char -> Int -> m Char basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Char -> Vector Char -> m () elemseq :: Vector Char -> Char -> b -> b
KnownSymbol n => Reifies (n :: Symbol) String
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> String
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text)
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text)
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char)
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char)
Generic1 (URec Char :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Char) :: k -> Type # Methods from1 :: forall (a :: k0). URec Char a -> Rep1 (URec Char) a # to1 :: forall (a :: k0). Rep1 (URec Char) a -> URec Char a #
Foldable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # toList :: UChar a -> [a] # null :: UChar a -> Bool # length :: UChar a -> Int # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # sum :: Num a => UChar a -> a # product :: Num a => UChar a -> a #
Traversable (UChar :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UChar a -> f (UChar b) # sequenceA :: Applicative f => UChar (f a) -> f (UChar a) # mapM :: Monad m => (a -> m b) -> UChar a -> m (UChar b) # sequence :: Monad m => UChar (m a) -> m (UChar a) #
MArray (STUArray s) Char (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Char -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Char -> ST s Int newArray :: Ix i => (i, i) -> Char -> ST s (STUArray s i Char) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Char) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Char) unsafeRead :: Ix i => STUArray s i Char -> Int -> ST s Char unsafeWrite :: Ix i => STUArray s i Char -> Int -> Char -> ST s ()
Functor (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
CFoldable (URec Char :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (URec Char) a, Monoid w) => (a -> w) -> URec Char a -> w cfoldMap' :: (Dom (URec Char) a, Monoid m) => (a -> m) -> URec Char a -> m cfold :: (Dom (URec Char) w, Monoid w) => URec Char w -> w cfoldr :: Dom (URec Char) a => (a -> b -> b) -> b -> URec Char a -> b cfoldlM :: (Monad m, Dom (URec Char) b) => (a -> b -> m a) -> a -> URec Char b -> m a cfoldlM' :: (Monad m, Dom (URec Char) b) => (a -> b -> m a) -> a -> URec Char b -> m a cfoldrM :: (Monad m, Dom (URec Char) a) => (a -> b -> m b) -> b -> URec Char a -> m b cfoldrM' :: (Monad m, Dom (URec Char) a) => (a -> b -> m b) -> b -> URec Char a -> m b cfoldl :: Dom (URec Char) a => (b -> a -> b) -> b -> URec Char a -> b cfoldr' :: Dom (URec Char) a => (a -> b -> b) -> b -> URec Char a -> b cfoldl' :: Dom (URec Char) a => (b -> a -> b) -> b -> URec Char a -> b cbasicToList :: Dom (URec Char) a => URec Char a -> [a] cfoldr1 :: Dom (URec Char) a => (a -> a -> a) -> URec Char a -> a cfoldl1 :: Dom (URec Char) a => (a -> a -> a) -> URec Char a -> a cindex :: Dom (URec Char) a => URec Char a -> Int -> a cnull :: Dom (URec Char) a => URec Char a -> Bool clength :: Dom (URec Char) a => URec Char a -> Int cany :: Dom (URec Char) a => (a -> Bool) -> URec Char a -> Bool call :: Dom (URec Char) a => (a -> Bool) -> URec Char a -> Bool celem :: (Eq a, Dom (URec Char) a) => a -> URec Char a -> Bool cnotElem :: (Eq a, Dom (URec Char) a) => a -> URec Char a -> Bool cminimum :: (Ord a, Dom (URec Char) a) => URec Char a -> a cmaximum :: (Ord a, Dom (URec Char) a) => URec Char a -> a csum :: (Num a, Dom (URec Char) a) => URec Char a -> a cproduct :: (Num a, Dom (URec Char) a) => URec Char a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (URec Char) a, Dom g b) => (a -> g b) -> URec Char a -> g () ctraverse_ :: (Applicative g, Dom (URec Char) a) => (a -> g b) -> URec Char a -> g () clast :: Dom (URec Char) a => URec Char a -> a chead :: Dom (URec Char) a => URec Char a -> a cfind :: Dom (URec Char) a => (a -> Bool) -> URec Char a -> Maybe a cfindIndex :: Dom (URec Char) a => (a -> Bool) -> URec Char a -> Maybe Int cfindIndices :: Dom (URec Char) a => (a -> Bool) -> URec Char a -> [Int] celemIndex :: (Dom (URec Char) a, Eq a) => a -> URec Char a -> Maybe Int celemIndices :: (Dom (URec Char) a, Eq a) => a -> URec Char a -> [Int]
CFunctor (URec Char :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (URec Char) a, Dom (URec Char) b) => (a -> b) -> URec Char a -> URec Char b (<$:) :: (Dom (URec Char) a, Dom (URec Char) b) => a -> URec Char b -> URec Char a
CTraversable (URec Char :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (URec Char) a, Dom (URec Char) b, Applicative g) => (a -> g b) -> URec Char a -> g (URec Char b)
Constrained (URec Char :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (URec Char) a
SuppressUnusedWarnings (Fail_6989586621680156267Sym0 :: TyFun [Char] [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods suppressUnusedWarnings :: ()
SMonadFail m => SingI (FailSym0 :: TyFun [Char] (m a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods sing :: Sing FailSym0 #
SuppressUnusedWarnings (FailSym0 :: TyFun [Char] (m a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods suppressUnusedWarnings :: ()
Eq (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Char p -> URec Char p -> Bool # (/=) :: URec Char p -> URec Char p -> Bool #
Ord (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering # (<) :: URec Char p -> URec Char p -> Bool # (<=) :: URec Char p -> URec Char p -> Bool # (>) :: URec Char p -> URec Char p -> Bool # (>=) :: URec Char p -> URec Char p -> Bool # max :: URec Char p -> URec Char p -> URec Char p # min :: URec Char p -> URec Char p -> URec Char p #
Show (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Char p -> ShowS # show :: URec Char p -> String # showList :: [URec Char p] -> ShowS #
Generic (URec Char p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (URec Char p) :: Type -> Type # Methods from :: URec Char p -> Rep (URec Char p) x # to :: Rep (URec Char p) x -> URec Char p #
newtype Vector Char
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Char = V_Char (Vector Char)
data URec Char (p :: k)	Used for marking occurrences of `Char#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Char (p :: k) = UChar { uChar# :: Char# }
newtype MVector s Char
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Char = MV_Char (MVector s Char)
type Rep1 (URec Char :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (URec Char :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: k -> Type)))
type Apply (Fail_6989586621680156267Sym0 :: TyFun [Char] [a] -> Type) (a6989586621680156271 :: [Char])
Instance details Defined in Data.Singletons.Prelude.Monad.Fail type Apply (Fail_6989586621680156267Sym0 :: TyFun [Char] [a] -> Type) (a6989586621680156271 :: [Char]) = Fail_6989586621680156267Sym1 a6989586621680156271 :: [a]
type Apply (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type) (a6989586621680156265 :: [Char])
Instance details Defined in Data.Singletons.Prelude.Monad.Fail type Apply (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type) (a6989586621680156265 :: [Char]) = Fail_6989586621680156261Sym1 a6989586621680156265 :: Maybe a
type Apply (FailSym0 :: TyFun [Char] (m a) -> Type) (a6989586621680156259 :: [Char])
Instance details Defined in Data.Singletons.Prelude.Monad.Fail type Apply (FailSym0 :: TyFun [Char] (m a) -> Type) (a6989586621680156259 :: [Char]) = FailSym1 a6989586621680156259 :: m a
type Dom (URec Char :: Type -> Type) a
Instance details Defined in Control.Subcategory.Functor type Dom (URec Char :: Type -> Type) a = ()
type Rep (URec Char p)
Instance details Defined in GHC.Generics type Rep (URec Char p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UChar" 'PrefixI 'True) (S1 ('MetaSel ('Just "uChar#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UChar :: Type -> Type)))

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Instances details

Eq Double	Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Double)`False Also note that `Double`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Double)`True `>>>` `recip 0 == recip (-0 :: Double)`False
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
Unbox Double
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Double
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Double -> Int # hash :: Double -> Int #
Storable Double	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Double -> Int # alignment :: Double -> Int # peekElemOff :: Ptr Double -> Int -> IO Double # pokeElemOff :: Ptr Double -> Int -> Double -> IO () # peekByteOff :: Ptr b -> Int -> IO Double # pokeByteOff :: Ptr b -> Int -> Double -> IO () # peek :: Ptr Double -> IO Double # poke :: Ptr Double -> Double -> IO () #
NFData Double
Instance details Defined in Control.DeepSeq Methods rnf :: Double -> () #
Normed Double
Instance details Defined in Algebra.Normed Associated Types type Norm Double # Methods norm :: Double -> Norm Double # liftNorm :: Norm Double -> Double #
Prim Double
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Double -> Int# alignment# :: Double -> Int# indexByteArray# :: ByteArray# -> Int# -> Double readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Double #) writeByteArray# :: MutableByteArray# s -> Int# -> Double -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Double -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Double readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Double #) writeOffAddr# :: Addr# -> Int# -> Double -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Double -> State# s -> State# s
UniformRange Double
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Double, Double) -> g -> m Double
Lift Double
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Double -> Q Exp # liftTyped :: Double -> Q (TExp Double) #
IArray UArray Double
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Double -> (i, i) # numElements :: Ix i => UArray i Double -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Double)] -> UArray i Double unsafeAt :: Ix i => UArray i Double -> Int -> Double unsafeReplace :: Ix i => UArray i Double -> [(Int, Double)] -> UArray i Double unsafeAccum :: Ix i => (Double -> e' -> Double) -> UArray i Double -> [(Int, e')] -> UArray i Double unsafeAccumArray :: Ix i => (Double -> e' -> Double) -> Double -> (i, i) -> [(Int, e')] -> UArray i Double
MVector MVector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Double -> Int basicUnsafeSlice :: Int -> Int -> MVector s Double -> MVector s Double basicOverlaps :: MVector s Double -> MVector s Double -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Double) basicInitialize :: PrimMonad m => MVector (PrimState m) Double -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Double -> m (MVector (PrimState m) Double) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Double -> Int -> m Double basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Double -> Int -> Double -> m () basicClear :: PrimMonad m => MVector (PrimState m) Double -> m () basicSet :: PrimMonad m => MVector (PrimState m) Double -> Double -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Double -> Int -> m (MVector (PrimState m) Double)
Vector Vector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Double -> m (Vector Double) basicUnsafeThaw :: PrimMonad m => Vector Double -> m (Mutable Vector (PrimState m) Double) basicLength :: Vector Double -> Int basicUnsafeSlice :: Int -> Int -> Vector Double -> Vector Double basicUnsafeIndexM :: Monad m => Vector Double -> Int -> m Double basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Double -> Vector Double -> m () elemseq :: Vector Double -> Double -> b -> b
Generic1 (URec Double :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> Type # Methods from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a # to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #
Foldable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # toList :: UDouble a -> [a] # null :: UDouble a -> Bool # length :: UDouble a -> Int # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # sum :: Num a => UDouble a -> a # product :: Num a => UDouble a -> a #
Traversable (UDouble :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) # sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) # mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) # sequence :: Monad m => UDouble (m a) -> m (UDouble a) #
MArray (STUArray s) Double (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Double -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Double -> ST s Int newArray :: Ix i => (i, i) -> Double -> ST s (STUArray s i Double) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Double) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Double) unsafeRead :: Ix i => STUArray s i Double -> Int -> ST s Double unsafeWrite :: Ix i => STUArray s i Double -> Int -> Double -> ST s ()
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
CFoldable (URec Double :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (URec Double) a, Monoid w) => (a -> w) -> URec Double a -> w cfoldMap' :: (Dom (URec Double) a, Monoid m) => (a -> m) -> URec Double a -> m cfold :: (Dom (URec Double) w, Monoid w) => URec Double w -> w cfoldr :: Dom (URec Double) a => (a -> b -> b) -> b -> URec Double a -> b cfoldlM :: (Monad m, Dom (URec Double) b) => (a -> b -> m a) -> a -> URec Double b -> m a cfoldlM' :: (Monad m, Dom (URec Double) b) => (a -> b -> m a) -> a -> URec Double b -> m a cfoldrM :: (Monad m, Dom (URec Double) a) => (a -> b -> m b) -> b -> URec Double a -> m b cfoldrM' :: (Monad m, Dom (URec Double) a) => (a -> b -> m b) -> b -> URec Double a -> m b cfoldl :: Dom (URec Double) a => (b -> a -> b) -> b -> URec Double a -> b cfoldr' :: Dom (URec Double) a => (a -> b -> b) -> b -> URec Double a -> b cfoldl' :: Dom (URec Double) a => (b -> a -> b) -> b -> URec Double a -> b cbasicToList :: Dom (URec Double) a => URec Double a -> [a] cfoldr1 :: Dom (URec Double) a => (a -> a -> a) -> URec Double a -> a cfoldl1 :: Dom (URec Double) a => (a -> a -> a) -> URec Double a -> a cindex :: Dom (URec Double) a => URec Double a -> Int -> a cnull :: Dom (URec Double) a => URec Double a -> Bool clength :: Dom (URec Double) a => URec Double a -> Int cany :: Dom (URec Double) a => (a -> Bool) -> URec Double a -> Bool call :: Dom (URec Double) a => (a -> Bool) -> URec Double a -> Bool celem :: (Eq a, Dom (URec Double) a) => a -> URec Double a -> Bool cnotElem :: (Eq a, Dom (URec Double) a) => a -> URec Double a -> Bool cminimum :: (Ord a, Dom (URec Double) a) => URec Double a -> a cmaximum :: (Ord a, Dom (URec Double) a) => URec Double a -> a csum :: (Num a, Dom (URec Double) a) => URec Double a -> a cproduct :: (Num a, Dom (URec Double) a) => URec Double a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (URec Double) a, Dom g b) => (a -> g b) -> URec Double a -> g () ctraverse_ :: (Applicative g, Dom (URec Double) a) => (a -> g b) -> URec Double a -> g () clast :: Dom (URec Double) a => URec Double a -> a chead :: Dom (URec Double) a => URec Double a -> a cfind :: Dom (URec Double) a => (a -> Bool) -> URec Double a -> Maybe a cfindIndex :: Dom (URec Double) a => (a -> Bool) -> URec Double a -> Maybe Int cfindIndices :: Dom (URec Double) a => (a -> Bool) -> URec Double a -> [Int] celemIndex :: (Dom (URec Double) a, Eq a) => a -> URec Double a -> Maybe Int celemIndices :: (Dom (URec Double) a, Eq a) => a -> URec Double a -> [Int]
CFunctor (URec Double :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (URec Double) a, Dom (URec Double) b) => (a -> b) -> URec Double a -> URec Double b (<$:) :: (Dom (URec Double) a, Dom (URec Double) b) => a -> URec Double b -> URec Double a
CTraversable (URec Double :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (URec Double) a, Dom (URec Double) b, Applicative g) => (a -> g b) -> URec Double a -> g (URec Double b)
Constrained (URec Double :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (URec Double) a
Eq (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Ord (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Show (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Generic (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: Type -> Type # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
type Norm Double
Instance details Defined in Algebra.Normed type Norm Double = Double
newtype Vector Double
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Double = V_Double (Vector Double)
data URec Double (p :: k)	Used for marking occurrences of `Double#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Double (p :: k) = UDouble { uDouble# :: Double# }
newtype MVector s Double
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Double = MV_Double (MVector s Double)
type Rep1 (URec Double :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Dom (URec Double :: Type -> Type) a
Instance details Defined in Control.Subcategory.Functor type Dom (URec Double :: Type -> Type) a = ()
type Rep (URec Double p)
Instance details Defined in GHC.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Instances details

Eq Float	Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity. `>>>` `0/0 == (0/0 :: Float)`False Also note that `Float`'s `Eq` instance does not satisfy substitutivity: `>>>` `0 == (-0 :: Float)`True `>>>` `recip 0 == recip (-0 :: Float)`False
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
Unbox Float
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Float
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Float -> Int # hash :: Float -> Int #
Storable Float	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Float -> Int # alignment :: Float -> Int # peekElemOff :: Ptr Float -> Int -> IO Float # pokeElemOff :: Ptr Float -> Int -> Float -> IO () # peekByteOff :: Ptr b -> Int -> IO Float # pokeByteOff :: Ptr b -> Int -> Float -> IO () # peek :: Ptr Float -> IO Float # poke :: Ptr Float -> Float -> IO () #
NFData Float
Instance details Defined in Control.DeepSeq Methods rnf :: Float -> () #
Prim Float
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Float -> Int# alignment# :: Float -> Int# indexByteArray# :: ByteArray# -> Int# -> Float readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Float #) writeByteArray# :: MutableByteArray# s -> Int# -> Float -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Float -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Float readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Float #) writeOffAddr# :: Addr# -> Int# -> Float -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Float -> State# s -> State# s
UniformRange Float
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Float, Float) -> g -> m Float
Lift Float
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Float -> Q Exp # liftTyped :: Float -> Q (TExp Float) #
IArray UArray Float
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Float -> (i, i) # numElements :: Ix i => UArray i Float -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Float)] -> UArray i Float unsafeAt :: Ix i => UArray i Float -> Int -> Float unsafeReplace :: Ix i => UArray i Float -> [(Int, Float)] -> UArray i Float unsafeAccum :: Ix i => (Float -> e' -> Float) -> UArray i Float -> [(Int, e')] -> UArray i Float unsafeAccumArray :: Ix i => (Float -> e' -> Float) -> Float -> (i, i) -> [(Int, e')] -> UArray i Float
MVector MVector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Float -> Int basicUnsafeSlice :: Int -> Int -> MVector s Float -> MVector s Float basicOverlaps :: MVector s Float -> MVector s Float -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Float) basicInitialize :: PrimMonad m => MVector (PrimState m) Float -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Float -> m (MVector (PrimState m) Float) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Float -> Int -> m Float basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Float -> Int -> Float -> m () basicClear :: PrimMonad m => MVector (PrimState m) Float -> m () basicSet :: PrimMonad m => MVector (PrimState m) Float -> Float -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Float -> Int -> m (MVector (PrimState m) Float)
Vector Vector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Float -> m (Vector Float) basicUnsafeThaw :: PrimMonad m => Vector Float -> m (Mutable Vector (PrimState m) Float) basicLength :: Vector Float -> Int basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float basicUnsafeIndexM :: Monad m => Vector Float -> Int -> m Float basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Float -> Vector Float -> m () elemseq :: Vector Float -> Float -> b -> b
Generic1 (URec Float :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> Type # Methods from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a # to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a #
Foldable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # toList :: UFloat a -> [a] # null :: UFloat a -> Bool # length :: UFloat a -> Int # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # sum :: Num a => UFloat a -> a # product :: Num a => UFloat a -> a #
Traversable (UFloat :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) # sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) # mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) # sequence :: Monad m => UFloat (m a) -> m (UFloat a) #
MArray (STUArray s) Float (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Float -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Float -> ST s Int newArray :: Ix i => (i, i) -> Float -> ST s (STUArray s i Float) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Float) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Float) unsafeRead :: Ix i => STUArray s i Float -> Int -> ST s Float unsafeWrite :: Ix i => STUArray s i Float -> Int -> Float -> ST s ()
Functor (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
CFoldable (URec Float :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (URec Float) a, Monoid w) => (a -> w) -> URec Float a -> w cfoldMap' :: (Dom (URec Float) a, Monoid m) => (a -> m) -> URec Float a -> m cfold :: (Dom (URec Float) w, Monoid w) => URec Float w -> w cfoldr :: Dom (URec Float) a => (a -> b -> b) -> b -> URec Float a -> b cfoldlM :: (Monad m, Dom (URec Float) b) => (a -> b -> m a) -> a -> URec Float b -> m a cfoldlM' :: (Monad m, Dom (URec Float) b) => (a -> b -> m a) -> a -> URec Float b -> m a cfoldrM :: (Monad m, Dom (URec Float) a) => (a -> b -> m b) -> b -> URec Float a -> m b cfoldrM' :: (Monad m, Dom (URec Float) a) => (a -> b -> m b) -> b -> URec Float a -> m b cfoldl :: Dom (URec Float) a => (b -> a -> b) -> b -> URec Float a -> b cfoldr' :: Dom (URec Float) a => (a -> b -> b) -> b -> URec Float a -> b cfoldl' :: Dom (URec Float) a => (b -> a -> b) -> b -> URec Float a -> b cbasicToList :: Dom (URec Float) a => URec Float a -> [a] cfoldr1 :: Dom (URec Float) a => (a -> a -> a) -> URec Float a -> a cfoldl1 :: Dom (URec Float) a => (a -> a -> a) -> URec Float a -> a cindex :: Dom (URec Float) a => URec Float a -> Int -> a cnull :: Dom (URec Float) a => URec Float a -> Bool clength :: Dom (URec Float) a => URec Float a -> Int cany :: Dom (URec Float) a => (a -> Bool) -> URec Float a -> Bool call :: Dom (URec Float) a => (a -> Bool) -> URec Float a -> Bool celem :: (Eq a, Dom (URec Float) a) => a -> URec Float a -> Bool cnotElem :: (Eq a, Dom (URec Float) a) => a -> URec Float a -> Bool cminimum :: (Ord a, Dom (URec Float) a) => URec Float a -> a cmaximum :: (Ord a, Dom (URec Float) a) => URec Float a -> a csum :: (Num a, Dom (URec Float) a) => URec Float a -> a cproduct :: (Num a, Dom (URec Float) a) => URec Float a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (URec Float) a, Dom g b) => (a -> g b) -> URec Float a -> g () ctraverse_ :: (Applicative g, Dom (URec Float) a) => (a -> g b) -> URec Float a -> g () clast :: Dom (URec Float) a => URec Float a -> a chead :: Dom (URec Float) a => URec Float a -> a cfind :: Dom (URec Float) a => (a -> Bool) -> URec Float a -> Maybe a cfindIndex :: Dom (URec Float) a => (a -> Bool) -> URec Float a -> Maybe Int cfindIndices :: Dom (URec Float) a => (a -> Bool) -> URec Float a -> [Int] celemIndex :: (Dom (URec Float) a, Eq a) => a -> URec Float a -> Maybe Int celemIndices :: (Dom (URec Float) a, Eq a) => a -> URec Float a -> [Int]
CFunctor (URec Float :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (URec Float) a, Dom (URec Float) b) => (a -> b) -> URec Float a -> URec Float b (<$:) :: (Dom (URec Float) a, Dom (URec Float) b) => a -> URec Float b -> URec Float a
CTraversable (URec Float :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (URec Float) a, Dom (URec Float) b, Applicative g) => (a -> g b) -> URec Float a -> g (URec Float b)
Constrained (URec Float :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (URec Float) a
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Generic (URec Float p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: Type -> Type # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
newtype Vector Float
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Float = V_Float (Vector Float)
data URec Float (p :: k)	Used for marking occurrences of `Float#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Float (p :: k) = UFloat { uFloat# :: Float# }
newtype MVector s Float
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Float = MV_Float (MVector s Float)
type Rep1 (URec Float :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Dom (URec Float :: Type -> Type) a
Instance details Defined in Control.Subcategory.Functor type Dom (URec Float :: Type -> Type) a = ()
type Rep (URec Float p)
Instance details Defined in GHC.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Instances details

Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
Ix Int	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Int, Int) -> [Int] # index :: (Int, Int) -> Int -> Int # unsafeIndex :: (Int, Int) -> Int -> Int # inRange :: (Int, Int) -> Int -> Bool # rangeSize :: (Int, Int) -> Int # unsafeRangeSize :: (Int, Int) -> Int #
Ring Int
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int
Rig Int
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int #
Characteristic Int
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int -> Natural #
LocallyFiniteOrder Int
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int -> Int -> [Int] rangeSize :: Int -> Int -> Natural moebiusInversion :: Ring r => Int -> Int -> r
DecidableZero Int
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int -> Bool #
DecidableUnits Int
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int -> Maybe Int # isUnit :: Int -> Bool # (^?) :: Integral n => Int -> n -> Maybe Int #
DecidableAssociates Int
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int -> Int -> Bool #
Unital Int
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int # pow :: Int -> Natural -> Int # productWith :: Foldable f => (a -> Int) -> f a -> Int #
TriviallyInvolutive Int
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Int
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int -> Int #
Commutative Int
Instance details Defined in Numeric.Algebra.Commutative
Semiring Int
Instance details Defined in Numeric.Algebra.Class
Multiplicative Int
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int -> Int -> Int # pow1p :: Int -> Natural -> Int # productWith1 :: Foldable1 f => (a -> Int) -> f a -> Int #
Monoidal Int
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int # sinnum :: Natural -> Int -> Int # sumWith :: Foldable f => (a -> Int) -> f a -> Int #
Group Int
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int -> Int -> Int # negate :: Int -> Int # subtract :: Int -> Int -> Int # times :: Integral n => n -> Int -> Int #
Additive Int
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int -> Int -> Int # sinnum1p :: Natural -> Int -> Int # sumWith1 :: Foldable1 f => (a -> Int) -> f a -> Int #
Abelian Int
Instance details Defined in Numeric.Additive.Class
Unbox Int
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Int
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int -> Int # hash :: Int -> Int #
Storable Int	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int -> Int # alignment :: Int -> Int # peekElemOff :: Ptr Int -> Int -> IO Int # pokeElemOff :: Ptr Int -> Int -> Int -> IO () # peekByteOff :: Ptr b -> Int -> IO Int # pokeByteOff :: Ptr b -> Int -> Int -> IO () # peek :: Ptr Int -> IO Int # poke :: Ptr Int -> Int -> IO () #
Bits Int	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Int -> Int -> Int # (.\|.) :: Int -> Int -> Int # xor :: Int -> Int -> Int # complement :: Int -> Int # shift :: Int -> Int -> Int # rotate :: Int -> Int -> Int # zeroBits :: Int # bit :: Int -> Int # setBit :: Int -> Int -> Int # clearBit :: Int -> Int -> Int # complementBit :: Int -> Int -> Int # testBit :: Int -> Int -> Bool # bitSizeMaybe :: Int -> Maybe Int # bitSize :: Int -> Int # isSigned :: Int -> Bool # shiftL :: Int -> Int -> Int # unsafeShiftL :: Int -> Int -> Int # shiftR :: Int -> Int -> Int # unsafeShiftR :: Int -> Int -> Int # rotateL :: Int -> Int -> Int # rotateR :: Int -> Int -> Int # popCount :: Int -> Int #
FiniteBits Int	Since: base-4.6.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Int -> Int # countLeadingZeros :: Int -> Int # countTrailingZeros :: Int -> Int #
NFData Int
Instance details Defined in Control.DeepSeq Methods rnf :: Int -> () #
PrettyCoeff Int
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Int -> ShowSCoeff #
Normed Int
Instance details Defined in Algebra.Normed Associated Types type Norm Int # Methods norm :: Int -> Norm Int # liftNorm :: Norm Int -> Int #
Prim Int
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Int -> Int# alignment# :: Int -> Int# indexByteArray# :: ByteArray# -> Int# -> Int readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int #) writeByteArray# :: MutableByteArray# s -> Int# -> Int -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Int -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Int readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Int #) writeOffAddr# :: Addr# -> Int# -> Int -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Int -> State# s -> State# s
Uniform Int
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int
UniformRange Int
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Int, Int) -> g -> m Int
Lift Int
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Int -> Q Exp # liftTyped :: Int -> Q (TExp Int) #
Rig r => Quadrance r Int
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int -> r #
RightModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Integer -> Int #
RightModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Natural -> Int #
LeftModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int -> Int #
LeftModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int -> Int #
IArray UArray Int
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int -> (i, i) # numElements :: Ix i => UArray i Int -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int)] -> UArray i Int unsafeAt :: Ix i => UArray i Int -> Int -> Int unsafeReplace :: Ix i => UArray i Int -> [(Int, Int)] -> UArray i Int unsafeAccum :: Ix i => (Int -> e' -> Int) -> UArray i Int -> [(Int, e')] -> UArray i Int unsafeAccumArray :: Ix i => (Int -> e' -> Int) -> Int -> (i, i) -> [(Int, e')] -> UArray i Int
MVector MVector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int -> Int basicUnsafeSlice :: Int -> Int -> MVector s Int -> MVector s Int basicOverlaps :: MVector s Int -> MVector s Int -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int) basicInitialize :: PrimMonad m => MVector (PrimState m) Int -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Int -> m (MVector (PrimState m) Int) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int -> Int -> m Int basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int -> Int -> Int -> m () basicClear :: PrimMonad m => MVector (PrimState m) Int -> m () basicSet :: PrimMonad m => MVector (PrimState m) Int -> Int -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int -> Int -> m (MVector (PrimState m) Int)
Vector Vector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int -> m (Vector Int) basicUnsafeThaw :: PrimMonad m => Vector Int -> m (Mutable Vector (PrimState m) Int) basicLength :: Vector Int -> Int basicUnsafeSlice :: Int -> Int -> Vector Int -> Vector Int basicUnsafeIndexM :: Monad m => Vector Int -> Int -> m Int basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int -> Vector Int -> m () elemseq :: Vector Int -> Int -> b -> b
FoldableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> [a] -> m ifolded :: IndexedFold Int [a] a ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b ifoldl :: (Int -> b -> a -> b) -> b -> [a] -> b ifoldr' :: (Int -> a -> b -> b) -> b -> [a] -> b ifoldl' :: (Int -> b -> a -> b) -> b -> [a] -> b
FoldableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Vector a -> m ifolded :: IndexedFold Int (Vector a) a ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b ifoldl :: (Int -> b -> a -> b) -> b -> Vector a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> Vector a -> b
FoldableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Seq a -> m ifolded :: IndexedFold Int (Seq a) a ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> Seq a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> Seq a -> b
FoldableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> IntMap a -> m ifolded :: IndexedFold Int (IntMap a) a ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b ifoldl :: (Int -> b -> a -> b) -> b -> IntMap a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> IntMap a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b
FoldableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> ZipList a -> m ifolded :: IndexedFold Int (ZipList a) a ifoldr :: (Int -> a -> b -> b) -> b -> ZipList a -> b ifoldl :: (Int -> b -> a -> b) -> b -> ZipList a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> ZipList a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> ZipList a -> b
FoldableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> NonEmpty a -> m ifolded :: IndexedFold Int (NonEmpty a) a ifoldr :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b ifoldl :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b
FunctorWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> [a] -> [b] imapped :: IndexedSetter Int [a] [b] a b
FunctorWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Vector a -> Vector b imapped :: IndexedSetter Int (Vector a) (Vector b) a b
FunctorWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Seq a -> Seq b imapped :: IndexedSetter Int (Seq a) (Seq b) a b
FunctorWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> IntMap a -> IntMap b imapped :: IndexedSetter Int (IntMap a) (IntMap b) a b
FunctorWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> ZipList a -> ZipList b imapped :: IndexedSetter Int (ZipList a) (ZipList b) a b
FunctorWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> NonEmpty a -> NonEmpty b imapped :: IndexedSetter Int (NonEmpty a) (NonEmpty b) a b
TraversableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> [a] -> f [b] itraversed :: IndexedTraversal Int [a] [b] a b
TraversableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Vector a -> f (Vector b) itraversed :: IndexedTraversal Int (Vector a) (Vector b) a b
TraversableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) itraversed :: IndexedTraversal Int (Seq a) (Seq b) a b
TraversableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) itraversed :: IndexedTraversal Int (IntMap a) (IntMap b) a b
TraversableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> ZipList a -> f (ZipList b) itraversed :: IndexedTraversal Int (ZipList a) (ZipList b) a b
TraversableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b) itraversed :: IndexedTraversal Int (NonEmpty a) (NonEmpty b) a b
TraverseMax Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v
TraverseMin Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v
Generic1 (URec Int :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Int) :: k -> Type # Methods from1 :: forall (a :: k0). URec Int a -> Rep1 (URec Int) a # to1 :: forall (a :: k0). Rep1 (URec Int) a -> URec Int a #
Foldable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # toList :: UInt a -> [a] # null :: UInt a -> Bool # length :: UInt a -> Int # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # minimum :: Ord a => UInt a -> a # sum :: Num a => UInt a -> a # product :: Num a => UInt a -> a #
Traversable (UInt :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b) # sequenceA :: Applicative f => UInt (f a) -> f (UInt a) # mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b) # sequence :: Monad m => UInt (m a) -> m (UInt a) #
FoldableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([Int] -> a -> m) -> Tree a -> m ifolded :: IndexedFold [Int] (Tree a) a ifoldr :: ([Int] -> a -> b -> b) -> b -> Tree a -> b ifoldl :: ([Int] -> b -> a -> b) -> b -> Tree a -> b ifoldr' :: ([Int] -> a -> b -> b) -> b -> Tree a -> b ifoldl' :: ([Int] -> b -> a -> b) -> b -> Tree a -> b
FunctorWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods imap :: ([Int] -> a -> b) -> Tree a -> Tree b imapped :: IndexedSetter [Int] (Tree a) (Tree b) a b
TraversableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => ([Int] -> a -> f b) -> Tree a -> f (Tree b) itraversed :: IndexedTraversal [Int] (Tree a) (Tree b) a b
Bizarre (Indexed Int) Mafic
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed Int a (f b) -> Mafic a b t -> f t
Reifies Z Int
Instance details Defined in Data.Reflection Methods reflect :: proxy Z -> Int
MArray (STUArray s) Int (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int -> ST s Int newArray :: Ix i => (i, i) -> Int -> ST s (STUArray s i Int) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int) unsafeRead :: Ix i => STUArray s i Int -> Int -> ST s Int unsafeWrite :: Ix i => STUArray s i Int -> Int -> Int -> ST s ()
Reifies n Int => Reifies (D n :: Type) Int
Instance details Defined in Data.Reflection Methods reflect :: proxy (D n) -> Int
Reifies n Int => Reifies (PD n :: Type) Int
Instance details Defined in Data.Reflection Methods reflect :: proxy (PD n) -> Int
Reifies n Int => Reifies (SD n :: Type) Int
Instance details Defined in Data.Reflection Methods reflect :: proxy (SD n) -> Int
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
CFoldable (URec Int :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (URec Int) a, Monoid w) => (a -> w) -> URec Int a -> w cfoldMap' :: (Dom (URec Int) a, Monoid m) => (a -> m) -> URec Int a -> m cfold :: (Dom (URec Int) w, Monoid w) => URec Int w -> w cfoldr :: Dom (URec Int) a => (a -> b -> b) -> b -> URec Int a -> b cfoldlM :: (Monad m, Dom (URec Int) b) => (a -> b -> m a) -> a -> URec Int b -> m a cfoldlM' :: (Monad m, Dom (URec Int) b) => (a -> b -> m a) -> a -> URec Int b -> m a cfoldrM :: (Monad m, Dom (URec Int) a) => (a -> b -> m b) -> b -> URec Int a -> m b cfoldrM' :: (Monad m, Dom (URec Int) a) => (a -> b -> m b) -> b -> URec Int a -> m b cfoldl :: Dom (URec Int) a => (b -> a -> b) -> b -> URec Int a -> b cfoldr' :: Dom (URec Int) a => (a -> b -> b) -> b -> URec Int a -> b cfoldl' :: Dom (URec Int) a => (b -> a -> b) -> b -> URec Int a -> b cbasicToList :: Dom (URec Int) a => URec Int a -> [a] cfoldr1 :: Dom (URec Int) a => (a -> a -> a) -> URec Int a -> a cfoldl1 :: Dom (URec Int) a => (a -> a -> a) -> URec Int a -> a cindex :: Dom (URec Int) a => URec Int a -> Int -> a cnull :: Dom (URec Int) a => URec Int a -> Bool clength :: Dom (URec Int) a => URec Int a -> Int cany :: Dom (URec Int) a => (a -> Bool) -> URec Int a -> Bool call :: Dom (URec Int) a => (a -> Bool) -> URec Int a -> Bool celem :: (Eq a, Dom (URec Int) a) => a -> URec Int a -> Bool cnotElem :: (Eq a, Dom (URec Int) a) => a -> URec Int a -> Bool cminimum :: (Ord a, Dom (URec Int) a) => URec Int a -> a cmaximum :: (Ord a, Dom (URec Int) a) => URec Int a -> a csum :: (Num a, Dom (URec Int) a) => URec Int a -> a cproduct :: (Num a, Dom (URec Int) a) => URec Int a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (URec Int) a, Dom g b) => (a -> g b) -> URec Int a -> g () ctraverse_ :: (Applicative g, Dom (URec Int) a) => (a -> g b) -> URec Int a -> g () clast :: Dom (URec Int) a => URec Int a -> a chead :: Dom (URec Int) a => URec Int a -> a cfind :: Dom (URec Int) a => (a -> Bool) -> URec Int a -> Maybe a cfindIndex :: Dom (URec Int) a => (a -> Bool) -> URec Int a -> Maybe Int cfindIndices :: Dom (URec Int) a => (a -> Bool) -> URec Int a -> [Int] celemIndex :: (Dom (URec Int) a, Eq a) => a -> URec Int a -> Maybe Int celemIndices :: (Dom (URec Int) a, Eq a) => a -> URec Int a -> [Int]
CFunctor (URec Int :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (URec Int) a, Dom (URec Int) b) => (a -> b) -> URec Int a -> URec Int b (<$:) :: (Dom (URec Int) a, Dom (URec Int) b) => a -> URec Int b -> URec Int a
CTraversable (URec Int :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (URec Int) a, Dom (URec Int) b, Applicative g) => (a -> g b) -> URec Int a -> g (URec Int b)
Constrained (URec Int :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (URec Int) a
Eq (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Ord (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Show (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Generic (URec Int p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (URec Int p) :: Type -> Type # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
type Norm Int
Instance details Defined in Algebra.Normed type Norm Int = Int
newtype Vector Int
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int = V_Int (Vector Int)
data URec Int (p :: k)	Used for marking occurrences of `Int#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Int (p :: k) = UInt { uInt# :: Int# }
newtype MVector s Int
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int = MV_Int (MVector s Int)
type Rep1 (URec Int :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Dom (URec Int :: Type -> Type) a
Instance details Defined in Control.Subcategory.Functor type Dom (URec Int :: Type -> Type) a = ()
type Rep (URec Int p)
Instance details Defined in GHC.Generics type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Int32 #

32-bit signed integer type

Instances

Instances details

Bounded Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int32 # maxBound :: Int32 #
Enum Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int32 -> Int32 # pred :: Int32 -> Int32 # toEnum :: Int -> Int32 # fromEnum :: Int32 -> Int # enumFrom :: Int32 -> [Int32] # enumFromThen :: Int32 -> Int32 -> [Int32] # enumFromTo :: Int32 -> Int32 -> [Int32] # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] #
Eq Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int32 -> Int32 -> Bool # (/=) :: Int32 -> Int32 -> Bool #
Integral Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int32 -> Int32 -> Int32 # rem :: Int32 -> Int32 -> Int32 # div :: Int32 -> Int32 -> Int32 # mod :: Int32 -> Int32 -> Int32 # quotRem :: Int32 -> Int32 -> (Int32, Int32) # divMod :: Int32 -> Int32 -> (Int32, Int32) # toInteger :: Int32 -> Integer #
Num Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int32 -> Int32 -> Int32 # (-) :: Int32 -> Int32 -> Int32 # (*) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # abs :: Int32 -> Int32 # signum :: Int32 -> Int32 # fromInteger :: Integer -> Int32 #
Ord Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int32 -> Int32 -> Ordering # (<) :: Int32 -> Int32 -> Bool # (<=) :: Int32 -> Int32 -> Bool # (>) :: Int32 -> Int32 -> Bool # (>=) :: Int32 -> Int32 -> Bool # max :: Int32 -> Int32 -> Int32 # min :: Int32 -> Int32 -> Int32 #
Read Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int32 # readList :: ReadS [Int32] # readPrec :: ReadPrec Int32 # readListPrec :: ReadPrec [Int32] #
Real Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int32 -> Rational #
Show Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int32 -> ShowS # show :: Int32 -> String # showList :: [Int32] -> ShowS #
Ix Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods range :: (Int32, Int32) -> [Int32] # index :: (Int32, Int32) -> Int32 -> Int # unsafeIndex :: (Int32, Int32) -> Int32 -> Int # inRange :: (Int32, Int32) -> Int32 -> Bool # rangeSize :: (Int32, Int32) -> Int # unsafeRangeSize :: (Int32, Int32) -> Int #
Ring Int32
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int32
Rig Int32
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int32 #
Characteristic Int32
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int32 -> Natural #
LocallyFiniteOrder Int32
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int32 -> Int32 -> [Int32] rangeSize :: Int32 -> Int32 -> Natural moebiusInversion :: Ring r => Int32 -> Int32 -> r
DecidableZero Int32
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int32 -> Bool #
DecidableUnits Int32
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int32 -> Maybe Int32 # isUnit :: Int32 -> Bool # (^?) :: Integral n => Int32 -> n -> Maybe Int32 #
DecidableAssociates Int32
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int32 -> Int32 -> Bool #
Unital Int32
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int32 # pow :: Int32 -> Natural -> Int32 # productWith :: Foldable f => (a -> Int32) -> f a -> Int32 #
TriviallyInvolutive Int32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Int32
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int32 -> Int32 #
Commutative Int32
Instance details Defined in Numeric.Algebra.Commutative
Semiring Int32
Instance details Defined in Numeric.Algebra.Class
Multiplicative Int32
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int32 -> Int32 -> Int32 # pow1p :: Int32 -> Natural -> Int32 # productWith1 :: Foldable1 f => (a -> Int32) -> f a -> Int32 #
Monoidal Int32
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int32 # sinnum :: Natural -> Int32 -> Int32 # sumWith :: Foldable f => (a -> Int32) -> f a -> Int32 #
Group Int32
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # subtract :: Int32 -> Int32 -> Int32 # times :: Integral n => n -> Int32 -> Int32 #
Additive Int32
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int32 -> Int32 -> Int32 # sinnum1p :: Natural -> Int32 -> Int32 # sumWith1 :: Foldable1 f => (a -> Int32) -> f a -> Int32 #
Abelian Int32
Instance details Defined in Numeric.Additive.Class
Unbox Int32
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Int32
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int32 -> Int # hash :: Int32 -> Int #
Storable Int32	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int32 -> Int # alignment :: Int32 -> Int # peekElemOff :: Ptr Int32 -> Int -> IO Int32 # pokeElemOff :: Ptr Int32 -> Int -> Int32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int32 # pokeByteOff :: Ptr b -> Int -> Int32 -> IO () # peek :: Ptr Int32 -> IO Int32 # poke :: Ptr Int32 -> Int32 -> IO () #
Bits Int32	Since: base-2.1
Instance details Defined in GHC.Int Methods (.&.) :: Int32 -> Int32 -> Int32 # (.\|.) :: Int32 -> Int32 -> Int32 # xor :: Int32 -> Int32 -> Int32 # complement :: Int32 -> Int32 # shift :: Int32 -> Int -> Int32 # rotate :: Int32 -> Int -> Int32 # zeroBits :: Int32 # bit :: Int -> Int32 # setBit :: Int32 -> Int -> Int32 # clearBit :: Int32 -> Int -> Int32 # complementBit :: Int32 -> Int -> Int32 # testBit :: Int32 -> Int -> Bool # bitSizeMaybe :: Int32 -> Maybe Int # bitSize :: Int32 -> Int # isSigned :: Int32 -> Bool # shiftL :: Int32 -> Int -> Int32 # unsafeShiftL :: Int32 -> Int -> Int32 # shiftR :: Int32 -> Int -> Int32 # unsafeShiftR :: Int32 -> Int -> Int32 # rotateL :: Int32 -> Int -> Int32 # rotateR :: Int32 -> Int -> Int32 # popCount :: Int32 -> Int #
FiniteBits Int32	Since: base-4.6.0.0
Instance details Defined in GHC.Int Methods finiteBitSize :: Int32 -> Int # countLeadingZeros :: Int32 -> Int # countTrailingZeros :: Int32 -> Int #
NFData Int32
Instance details Defined in Control.DeepSeq Methods rnf :: Int32 -> () #
PrettyCoeff Int32
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Int32 -> ShowSCoeff #
Prim Int32
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Int32 -> Int# alignment# :: Int32 -> Int# indexByteArray# :: ByteArray# -> Int# -> Int32 readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int32 #) writeByteArray# :: MutableByteArray# s -> Int# -> Int32 -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Int32 -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Int32 readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Int32 #) writeOffAddr# :: Addr# -> Int# -> Int32 -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Int32 -> State# s -> State# s
Uniform Int32
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int32
UniformRange Int32
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Int32, Int32) -> g -> m Int32
Lift Int32
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Int32 -> Q Exp # liftTyped :: Int32 -> Q (TExp Int32) #
Rig r => Quadrance r Int32
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int32 -> r #
RightModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Integer -> Int32 #
RightModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Natural -> Int32 #
LeftModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int32 -> Int32 #
LeftModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int32 -> Int32 #
IArray UArray Int32
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int32 -> (i, i) # numElements :: Ix i => UArray i Int32 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int32)] -> UArray i Int32 unsafeAt :: Ix i => UArray i Int32 -> Int -> Int32 unsafeReplace :: Ix i => UArray i Int32 -> [(Int, Int32)] -> UArray i Int32 unsafeAccum :: Ix i => (Int32 -> e' -> Int32) -> UArray i Int32 -> [(Int, e')] -> UArray i Int32 unsafeAccumArray :: Ix i => (Int32 -> e' -> Int32) -> Int32 -> (i, i) -> [(Int, e')] -> UArray i Int32
MVector MVector Int32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int32 -> Int basicUnsafeSlice :: Int -> Int -> MVector s Int32 -> MVector s Int32 basicOverlaps :: MVector s Int32 -> MVector s Int32 -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int32) basicInitialize :: PrimMonad m => MVector (PrimState m) Int32 -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Int32 -> m (MVector (PrimState m) Int32) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> m Int32 basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> Int32 -> m () basicClear :: PrimMonad m => MVector (PrimState m) Int32 -> m () basicSet :: PrimMonad m => MVector (PrimState m) Int32 -> Int32 -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int32 -> MVector (PrimState m) Int32 -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int32 -> MVector (PrimState m) Int32 -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> m (MVector (PrimState m) Int32)
Vector Vector Int32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> m (Vector Int32) basicUnsafeThaw :: PrimMonad m => Vector Int32 -> m (Mutable Vector (PrimState m) Int32) basicLength :: Vector Int32 -> Int basicUnsafeSlice :: Int -> Int -> Vector Int32 -> Vector Int32 basicUnsafeIndexM :: Monad m => Vector Int32 -> Int -> m Int32 basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> Vector Int32 -> m () elemseq :: Vector Int32 -> Int32 -> b -> b
MArray (STUArray s) Int32 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int32 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int32 -> ST s Int newArray :: Ix i => (i, i) -> Int32 -> ST s (STUArray s i Int32) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int32) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int32) unsafeRead :: Ix i => STUArray s i Int32 -> Int -> ST s Int32 unsafeWrite :: Ix i => STUArray s i Int32 -> Int -> Int32 -> ST s ()
newtype Vector Int32
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int32 = V_Int32 (Vector Int32)
newtype MVector s Int32
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int32 = MV_Int32 (MVector s Int32)

data Int64 #

64-bit signed integer type

Instances

Instances details

Bounded Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods minBound :: Int64 # maxBound :: Int64 #
Enum Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods succ :: Int64 -> Int64 # pred :: Int64 -> Int64 # toEnum :: Int -> Int64 # fromEnum :: Int64 -> Int # enumFrom :: Int64 -> [Int64] # enumFromThen :: Int64 -> Int64 -> [Int64] # enumFromTo :: Int64 -> Int64 -> [Int64] # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] #
Eq Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (==) :: Int64 -> Int64 -> Bool # (/=) :: Int64 -> Int64 -> Bool #
Integral Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods quot :: Int64 -> Int64 -> Int64 # rem :: Int64 -> Int64 -> Int64 # div :: Int64 -> Int64 -> Int64 # mod :: Int64 -> Int64 -> Int64 # quotRem :: Int64 -> Int64 -> (Int64, Int64) # divMod :: Int64 -> Int64 -> (Int64, Int64) # toInteger :: Int64 -> Integer #
Num Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (+) :: Int64 -> Int64 -> Int64 # (-) :: Int64 -> Int64 -> Int64 # (*) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # abs :: Int64 -> Int64 # signum :: Int64 -> Int64 # fromInteger :: Integer -> Int64 #
Ord Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods compare :: Int64 -> Int64 -> Ordering # (<) :: Int64 -> Int64 -> Bool # (<=) :: Int64 -> Int64 -> Bool # (>) :: Int64 -> Int64 -> Bool # (>=) :: Int64 -> Int64 -> Bool # max :: Int64 -> Int64 -> Int64 # min :: Int64 -> Int64 -> Int64 #
Read Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods readsPrec :: Int -> ReadS Int64 # readList :: ReadS [Int64] # readPrec :: ReadPrec Int64 # readListPrec :: ReadPrec [Int64] #
Real Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods toRational :: Int64 -> Rational #
Show Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods showsPrec :: Int -> Int64 -> ShowS # show :: Int64 -> String # showList :: [Int64] -> ShowS #
Ix Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods range :: (Int64, Int64) -> [Int64] # index :: (Int64, Int64) -> Int64 -> Int # unsafeIndex :: (Int64, Int64) -> Int64 -> Int # inRange :: (Int64, Int64) -> Int64 -> Bool # rangeSize :: (Int64, Int64) -> Int # unsafeRangeSize :: (Int64, Int64) -> Int #
Ring Int64
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int64
Rig Int64
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int64 #
Characteristic Int64
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int64 -> Natural #
LocallyFiniteOrder Int64
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int64 -> Int64 -> [Int64] rangeSize :: Int64 -> Int64 -> Natural moebiusInversion :: Ring r => Int64 -> Int64 -> r
DecidableZero Int64
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int64 -> Bool #
DecidableUnits Int64
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int64 -> Maybe Int64 # isUnit :: Int64 -> Bool # (^?) :: Integral n => Int64 -> n -> Maybe Int64 #
DecidableAssociates Int64
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int64 -> Int64 -> Bool #
Unital Int64
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int64 # pow :: Int64 -> Natural -> Int64 # productWith :: Foldable f => (a -> Int64) -> f a -> Int64 #
TriviallyInvolutive Int64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Int64
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int64 -> Int64 #
Commutative Int64
Instance details Defined in Numeric.Algebra.Commutative
Semiring Int64
Instance details Defined in Numeric.Algebra.Class
Multiplicative Int64
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int64 -> Int64 -> Int64 # pow1p :: Int64 -> Natural -> Int64 # productWith1 :: Foldable1 f => (a -> Int64) -> f a -> Int64 #
Monoidal Int64
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int64 # sinnum :: Natural -> Int64 -> Int64 # sumWith :: Foldable f => (a -> Int64) -> f a -> Int64 #
Group Int64
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # subtract :: Int64 -> Int64 -> Int64 # times :: Integral n => n -> Int64 -> Int64 #
Additive Int64
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int64 -> Int64 -> Int64 # sinnum1p :: Natural -> Int64 -> Int64 # sumWith1 :: Foldable1 f => (a -> Int64) -> f a -> Int64 #
Abelian Int64
Instance details Defined in Numeric.Additive.Class
Unbox Int64
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Int64
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int64 -> Int # hash :: Int64 -> Int #
Storable Int64	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int64 -> Int # alignment :: Int64 -> Int # peekElemOff :: Ptr Int64 -> Int -> IO Int64 # pokeElemOff :: Ptr Int64 -> Int -> Int64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int64 # pokeByteOff :: Ptr b -> Int -> Int64 -> IO () # peek :: Ptr Int64 -> IO Int64 # poke :: Ptr Int64 -> Int64 -> IO () #
Bits Int64	Since: base-2.1
Instance details Defined in GHC.Int Methods (.&.) :: Int64 -> Int64 -> Int64 # (.\|.) :: Int64 -> Int64 -> Int64 # xor :: Int64 -> Int64 -> Int64 # complement :: Int64 -> Int64 # shift :: Int64 -> Int -> Int64 # rotate :: Int64 -> Int -> Int64 # zeroBits :: Int64 # bit :: Int -> Int64 # setBit :: Int64 -> Int -> Int64 # clearBit :: Int64 -> Int -> Int64 # complementBit :: Int64 -> Int -> Int64 # testBit :: Int64 -> Int -> Bool # bitSizeMaybe :: Int64 -> Maybe Int # bitSize :: Int64 -> Int # isSigned :: Int64 -> Bool # shiftL :: Int64 -> Int -> Int64 # unsafeShiftL :: Int64 -> Int -> Int64 # shiftR :: Int64 -> Int -> Int64 # unsafeShiftR :: Int64 -> Int -> Int64 # rotateL :: Int64 -> Int -> Int64 # rotateR :: Int64 -> Int -> Int64 # popCount :: Int64 -> Int #
FiniteBits Int64	Since: base-4.6.0.0
Instance details Defined in GHC.Int Methods finiteBitSize :: Int64 -> Int # countLeadingZeros :: Int64 -> Int # countTrailingZeros :: Int64 -> Int #
NFData Int64
Instance details Defined in Control.DeepSeq Methods rnf :: Int64 -> () #
PrettyCoeff Int64
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Int64 -> ShowSCoeff #
Prim Int64
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Int64 -> Int# alignment# :: Int64 -> Int# indexByteArray# :: ByteArray# -> Int# -> Int64 readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int64 #) writeByteArray# :: MutableByteArray# s -> Int# -> Int64 -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Int64 -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Int64 readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Int64 #) writeOffAddr# :: Addr# -> Int# -> Int64 -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Int64 -> State# s -> State# s
Uniform Int64
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int64
UniformRange Int64
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Int64, Int64) -> g -> m Int64
Lift Int64
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Int64 -> Q Exp # liftTyped :: Int64 -> Q (TExp Int64) #
Rig r => Quadrance r Int64
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int64 -> r #
RightModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Integer -> Int64 #
RightModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Natural -> Int64 #
LeftModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int64 -> Int64 #
LeftModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int64 -> Int64 #
IArray UArray Int64
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int64 -> (i, i) # numElements :: Ix i => UArray i Int64 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int64)] -> UArray i Int64 unsafeAt :: Ix i => UArray i Int64 -> Int -> Int64 unsafeReplace :: Ix i => UArray i Int64 -> [(Int, Int64)] -> UArray i Int64 unsafeAccum :: Ix i => (Int64 -> e' -> Int64) -> UArray i Int64 -> [(Int, e')] -> UArray i Int64 unsafeAccumArray :: Ix i => (Int64 -> e' -> Int64) -> Int64 -> (i, i) -> [(Int, e')] -> UArray i Int64
MVector MVector Int64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int64 -> Int basicUnsafeSlice :: Int -> Int -> MVector s Int64 -> MVector s Int64 basicOverlaps :: MVector s Int64 -> MVector s Int64 -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int64) basicInitialize :: PrimMonad m => MVector (PrimState m) Int64 -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Int64 -> m (MVector (PrimState m) Int64) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> m Int64 basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> Int64 -> m () basicClear :: PrimMonad m => MVector (PrimState m) Int64 -> m () basicSet :: PrimMonad m => MVector (PrimState m) Int64 -> Int64 -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int64 -> MVector (PrimState m) Int64 -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int64 -> MVector (PrimState m) Int64 -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> m (MVector (PrimState m) Int64)
Vector Vector Int64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> m (Vector Int64) basicUnsafeThaw :: PrimMonad m => Vector Int64 -> m (Mutable Vector (PrimState m) Int64) basicLength :: Vector Int64 -> Int basicUnsafeSlice :: Int -> Int -> Vector Int64 -> Vector Int64 basicUnsafeIndexM :: Monad m => Vector Int64 -> Int -> m Int64 basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> Vector Int64 -> m () elemseq :: Vector Int64 -> Int64 -> b -> b
MArray (STUArray s) Int64 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int64 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int64 -> ST s Int newArray :: Ix i => (i, i) -> Int64 -> ST s (STUArray s i Int64) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int64) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int64) unsafeRead :: Ix i => STUArray s i Int64 -> Int -> ST s Int64 unsafeWrite :: Ix i => STUArray s i Int64 -> Int -> Int64 -> ST s ()
newtype Vector Int64
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int64 = V_Int64 (Vector Int64)
newtype MVector s Int64
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int64 = MV_Int64 (MVector s Int64)

data Integer #

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

For more information about this type's representation, see the comments in its implementation.

Instances

Instances details

Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Ix Integer	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Integer, Integer) -> [Integer] # index :: (Integer, Integer) -> Integer -> Int # unsafeIndex :: (Integer, Integer) -> Integer -> Int # inRange :: (Integer, Integer) -> Integer -> Bool # rangeSize :: (Integer, Integer) -> Int # unsafeRangeSize :: (Integer, Integer) -> Int #
UFD Integer
Instance details Defined in Numeric.Domain.Internal
PID Integer
Instance details Defined in Numeric.Domain.Internal Methods egcd :: Integer -> Integer -> (Integer, Integer, Integer) #
GCDDomain Integer
Instance details Defined in Numeric.Domain.Internal Methods gcd :: Integer -> Integer -> Integer # reduceFraction :: Integer -> Integer -> (Integer, Integer) # lcm :: Integer -> Integer -> Integer #
IntegralDomain Integer
Instance details Defined in Numeric.Domain.Internal Methods divides :: Integer -> Integer -> Bool # maybeQuot :: Integer -> Integer -> Maybe Integer #
Euclidean Integer
Instance details Defined in Numeric.Domain.Internal Methods degree :: Integer -> Maybe Natural # divide :: Integer -> Integer -> (Integer, Integer) # quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer #
ZeroProductSemiring Integer
Instance details Defined in Numeric.Semiring.ZeroProduct
UnitNormalForm Integer
Instance details Defined in Numeric.Algebra.Unital.UnitNormalForm Methods splitUnit :: Integer -> (Integer, Integer) #
Ring Integer
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Integer
OrderedRig Integer
Instance details Defined in Numeric.Rig.Ordered
Rig Integer
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Integer #
Characteristic Integer
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Integer -> Natural #
LocallyFiniteOrder Integer
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Integer -> Integer -> [Integer] rangeSize :: Integer -> Integer -> Natural moebiusInversion :: Ring r => Integer -> Integer -> r
AdditiveOrder Integer
Instance details Defined in Numeric.Order.Additive
DecidableZero Integer
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Integer -> Bool #
DecidableUnits Integer
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Integer -> Maybe Integer # isUnit :: Integer -> Bool # (^?) :: Integral n => Integer -> n -> Maybe Integer #
DecidableAssociates Integer
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Integer -> Integer -> Bool #
Unital Integer
Instance details Defined in Numeric.Algebra.Unital Methods one :: Integer # pow :: Integer -> Natural -> Integer # productWith :: Foldable f => (a -> Integer) -> f a -> Integer #
TriviallyInvolutive Integer
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Integer
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Integer
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Integer -> Integer #
Commutative Integer
Instance details Defined in Numeric.Algebra.Commutative
Semiring Integer
Instance details Defined in Numeric.Algebra.Class
Multiplicative Integer
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Integer -> Integer -> Integer # pow1p :: Integer -> Natural -> Integer # productWith1 :: Foldable1 f => (a -> Integer) -> f a -> Integer #
Monoidal Integer
Instance details Defined in Numeric.Algebra.Class Methods zero :: Integer # sinnum :: Natural -> Integer -> Integer # sumWith :: Foldable f => (a -> Integer) -> f a -> Integer #
Group Integer
Instance details Defined in Numeric.Additive.Group Methods (-) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # subtract :: Integer -> Integer -> Integer # times :: Integral n => n -> Integer -> Integer #
Additive Integer
Instance details Defined in Numeric.Additive.Class Methods (+) :: Integer -> Integer -> Integer # sinnum1p :: Natural -> Integer -> Integer # sumWith1 :: Foldable1 f => (a -> Integer) -> f a -> Integer #
Abelian Integer
Instance details Defined in Numeric.Additive.Class
Hashable Integer
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Integer -> Int # hash :: Integer -> Int #
Bits Integer	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Integer -> Integer -> Integer # (.\|.) :: Integer -> Integer -> Integer # xor :: Integer -> Integer -> Integer # complement :: Integer -> Integer # shift :: Integer -> Int -> Integer # rotate :: Integer -> Int -> Integer # zeroBits :: Integer # bit :: Int -> Integer # setBit :: Integer -> Int -> Integer # clearBit :: Integer -> Int -> Integer # complementBit :: Integer -> Int -> Integer # testBit :: Integer -> Int -> Bool # bitSizeMaybe :: Integer -> Maybe Int # bitSize :: Integer -> Int # isSigned :: Integer -> Bool # shiftL :: Integer -> Int -> Integer # unsafeShiftL :: Integer -> Int -> Integer # shiftR :: Integer -> Int -> Integer # unsafeShiftR :: Integer -> Int -> Integer # rotateL :: Integer -> Int -> Integer # rotateR :: Integer -> Int -> Integer # popCount :: Integer -> Int #
NFData Integer
Instance details Defined in Control.DeepSeq Methods rnf :: Integer -> () #
PrettyCoeff Integer
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Integer -> ShowSCoeff #
Normed Integer
Instance details Defined in Algebra.Normed Associated Types type Norm Integer # Methods norm :: Integer -> Norm Integer # liftNorm :: Norm Integer -> Integer #
UniformRange Integer
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Integer, Integer) -> g -> m Integer
Lift Integer
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Integer -> Q Exp # liftTyped :: Integer -> Q (TExp Integer) #
Rig r => Quadrance r Integer
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Integer -> r #
RightModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Integer -> Int #
RightModule Integer Int8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int8 -> Integer -> Int8 #
RightModule Integer Int16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int16 -> Integer -> Int16 #
RightModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Integer -> Int32 #
RightModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Integer -> Int64 #
RightModule Integer Integer
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Integer -> Integer -> Integer #
RightModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Integer -> Word #
RightModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Integer -> Word8 #
RightModule Integer Word16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word16 -> Integer -> Word16 #
RightModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Integer -> Word32 #
RightModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Integer -> Word64 #
RightModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Integer -> Natural -> Integer #
LeftModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int -> Int #
LeftModule Integer Int8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int8 -> Int8 #
LeftModule Integer Int16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int16 -> Int16 #
LeftModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int32 -> Int32 #
LeftModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int64 -> Int64 #
LeftModule Integer Integer
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Integer -> Integer #
LeftModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word -> Word #
LeftModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word8 -> Word8 #
LeftModule Integer Word16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word16 -> Word16 #
LeftModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word32 -> Word32 #
LeftModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word64 -> Word64 #
LeftModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Integer -> Integer #
KnownNat n => Reifies (n :: Nat) Integer
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> Integer
Num a => RightModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Integer -> WrapNum a #
Num a => RightModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Integer -> WrapFractional a #
Num a => RightModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Integer -> WrapIntegral a #
RightModule Integer a => RightModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Integer -> WrapAlgebra a #
RightModule Integer a => RightModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Integer -> Add a #
GCDDomain d => RightModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Integer -> Fraction d #
RightModule Integer r => RightModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Integer -> Scalar r #
(DecidableZero r, RightModule Integer r) => RightModule Integer (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Integer -> Unipol r #
Num a => LeftModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapNum a -> WrapNum a #
Num a => LeftModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapFractional a -> WrapFractional a #
Num a => LeftModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapIntegral a -> WrapIntegral a #
LeftModule Integer a => LeftModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapAlgebra a -> WrapAlgebra a #
LeftModule Integer a => LeftModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> Add a -> Add a #
GCDDomain d => LeftModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Integer -> Fraction d -> Fraction d #
LeftModule Integer r => LeftModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Integer -> Scalar r -> Scalar r #
(DecidableZero r, LeftModule Integer r) => LeftModule Integer (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Integer -> Unipol r -> Unipol r #
(Wraps vars poly, RightModule Integer poly) => RightModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Integer -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule Integer poly) => LeftModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Integer -> LabPolynomial poly vars -> LabPolynomial poly vars #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Integer -> PadPolyL n ord poly #
Group poly => RightModule Integer (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Integer -> Quotient poly ideal #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> PadPolyL n ord poly -> PadPolyL n ord poly #
Group poly => LeftModule Integer (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Integer -> Quotient poly ideal -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Integer -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
PrettyCoeff (Fraction Integer)
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Fraction Integer -> ShowSCoeff #
type Norm Integer
Instance details Defined in Algebra.Normed type Norm Integer = Integer

data Natural #

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

Operations whose result would be negative throw (Underflow :: ArithException),

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: base-4.8.0.0

Instances

Instances details

Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Ix Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Ix Methods range :: (Natural, Natural) -> [Natural] # index :: (Natural, Natural) -> Natural -> Int # unsafeIndex :: (Natural, Natural) -> Natural -> Int # inRange :: (Natural, Natural) -> Natural -> Bool # rangeSize :: (Natural, Natural) -> Int # unsafeRangeSize :: (Natural, Natural) -> Int #
ZeroProductSemiring Natural
Instance details Defined in Numeric.Semiring.ZeroProduct
OrderedRig Natural
Instance details Defined in Numeric.Rig.Ordered
Rig Natural
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Natural #
Characteristic Natural
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Natural -> Natural #
LocallyFiniteOrder Natural
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Natural -> Natural -> [Natural] rangeSize :: Natural -> Natural -> Natural moebiusInversion :: Ring r => Natural -> Natural -> r
AdditiveOrder Natural
Instance details Defined in Numeric.Order.Additive
DecidableZero Natural
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Natural -> Bool #
DecidableUnits Natural
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Natural -> Maybe Natural # isUnit :: Natural -> Bool # (^?) :: Integral n => Natural -> n -> Maybe Natural #
DecidableAssociates Natural
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Natural -> Natural -> Bool #
Unital Natural
Instance details Defined in Numeric.Algebra.Unital Methods one :: Natural # pow :: Natural -> Natural -> Natural # productWith :: Foldable f => (a -> Natural) -> f a -> Natural #
TriviallyInvolutive Natural
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Natural
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Natural
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Natural -> Natural #
Commutative Natural
Instance details Defined in Numeric.Algebra.Commutative
Semiring Natural
Instance details Defined in Numeric.Algebra.Class
Multiplicative Natural
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Natural -> Natural -> Natural # pow1p :: Natural -> Natural -> Natural # productWith1 :: Foldable1 f => (a -> Natural) -> f a -> Natural #
Monoidal Natural
Instance details Defined in Numeric.Algebra.Class Methods zero :: Natural # sinnum :: Natural -> Natural -> Natural # sumWith :: Foldable f => (a -> Natural) -> f a -> Natural #
Partitionable Natural
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: (Natural -> Natural -> r) -> Natural -> NonEmpty r #
Additive Natural
Instance details Defined in Numeric.Additive.Class Methods (+) :: Natural -> Natural -> Natural # sinnum1p :: Natural -> Natural -> Natural # sumWith1 :: Foldable1 f => (a -> Natural) -> f a -> Natural #
Abelian Natural
Instance details Defined in Numeric.Additive.Class
Hashable Natural
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Natural -> Int # hash :: Natural -> Int #
Bits Natural	Since: base-4.8.0
Instance details Defined in Data.Bits Methods (.&.) :: Natural -> Natural -> Natural # (.\|.) :: Natural -> Natural -> Natural # xor :: Natural -> Natural -> Natural # complement :: Natural -> Natural # shift :: Natural -> Int -> Natural # rotate :: Natural -> Int -> Natural # zeroBits :: Natural # bit :: Int -> Natural # setBit :: Natural -> Int -> Natural # clearBit :: Natural -> Int -> Natural # complementBit :: Natural -> Int -> Natural # testBit :: Natural -> Int -> Bool # bitSizeMaybe :: Natural -> Maybe Int # bitSize :: Natural -> Int # isSigned :: Natural -> Bool # shiftL :: Natural -> Int -> Natural # unsafeShiftL :: Natural -> Int -> Natural # shiftR :: Natural -> Int -> Natural # unsafeShiftR :: Natural -> Int -> Natural # rotateL :: Natural -> Int -> Natural # rotateR :: Natural -> Int -> Natural # popCount :: Natural -> Int #
NFData Natural	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Natural -> () #
PrettyCoeff Natural
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Natural -> ShowSCoeff #
UniformRange Natural
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Natural, Natural) -> g -> m Natural
Lift Natural
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Natural -> Q Exp # liftTyped :: Natural -> Q (TExp Natural) #
Rig r => Quadrance r Natural
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Natural -> r #
RightModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Bool -> Natural -> Bool #
RightModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Natural -> Int #
RightModule Natural Int8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int8 -> Natural -> Int8 #
RightModule Natural Int16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int16 -> Natural -> Int16 #
RightModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Natural -> Int32 #
RightModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Natural -> Int64 #
RightModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Integer -> Natural -> Integer #
RightModule Natural Natural
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Natural -> Natural -> Natural #
RightModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Natural -> Word #
RightModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Natural -> Word8 #
RightModule Natural Word16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word16 -> Natural -> Word16 #
RightModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Natural -> Word32 #
RightModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Natural -> Word64 #
LeftModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Bool -> Bool #
LeftModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int -> Int #
LeftModule Natural Int8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int8 -> Int8 #
LeftModule Natural Int16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int16 -> Int16 #
LeftModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int32 -> Int32 #
LeftModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int64 -> Int64 #
LeftModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Integer -> Integer #
LeftModule Natural Natural
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Natural -> Natural #
LeftModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word -> Word #
LeftModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word8 -> Word8 #
LeftModule Natural Word16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word16 -> Word16 #
LeftModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word32 -> Word32 #
LeftModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word64 -> Word64 #
Num a => RightModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Natural -> WrapNum a #
Num a => RightModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Natural -> WrapFractional a #
Num a => RightModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Natural -> WrapIntegral a #
RightModule Natural a => RightModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Natural -> WrapAlgebra a #
RightModule Natural a => RightModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Natural -> Add a #
GCDDomain d => RightModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Natural -> Fraction d #
RightModule Natural r => RightModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Natural -> Scalar r #
(DecidableZero r, RightModule Natural r) => RightModule Natural (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Natural -> Unipol r #
Num a => LeftModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapNum a -> WrapNum a #
Num a => LeftModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapFractional a -> WrapFractional a #
Num a => LeftModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapIntegral a -> WrapIntegral a #
LeftModule Natural a => LeftModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapAlgebra a -> WrapAlgebra a #
LeftModule Natural a => LeftModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> Add a -> Add a #
GCDDomain d => LeftModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Natural -> Fraction d -> Fraction d #
LeftModule Natural r => LeftModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Natural -> Scalar r -> Scalar r #
(DecidableZero r, LeftModule Natural r) => LeftModule Natural (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Natural -> Unipol r -> Unipol r #
(Wraps vars poly, RightModule Natural poly) => RightModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule Natural poly) => LeftModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly #
Monoidal poly => RightModule Natural (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Natural -> Quotient poly ideal #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly #
Monoidal poly => LeftModule Natural (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Natural -> Quotient poly ideal -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n #

data Maybe a #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing
Just a

Instances

Instances details

Monad Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b # (>>) :: Maybe a -> Maybe b -> Maybe b # return :: a -> Maybe a #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
MonadFail Maybe	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> Maybe a #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Foldable Maybe	Since: base-2.1
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # toList :: Maybe a -> [a] # null :: Maybe a -> Bool # length :: Maybe a -> Int # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # sum :: Num a => Maybe a -> a # product :: Num a => Maybe a -> a #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
MonadPlus Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a # mplus :: Maybe a -> Maybe a -> Maybe a #
Eq1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #
Ord1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #
Read1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] #
Show1 Maybe	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #
Alternative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a # (<\|>) :: Maybe a -> Maybe a -> Maybe a # some :: Maybe a -> Maybe [a] # many :: Maybe a -> Maybe [a] #
NFData1 Maybe	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Maybe a -> () #
PFoldable Maybe
Instance details Defined in Data.Singletons.Prelude.Foldable Associated Types type Fold arg :: m type FoldMap arg arg1 :: m type Foldr arg arg1 arg2 :: b type Foldr' arg arg1 arg2 :: b type Foldl arg arg1 arg2 :: b type Foldl' arg arg1 arg2 :: b type Foldr1 arg arg1 :: a type Foldl1 arg arg1 :: a type ToList arg :: [a] type Null arg :: Bool type Length arg :: Nat type Elem arg arg1 :: Bool type Maximum arg :: a type Minimum arg :: a type Sum arg :: a type Product arg :: a
SFoldable Maybe
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sFold :: forall m (t1 :: Maybe m). SMonoid m => Sing t1 -> Sing (Apply FoldSym0 t1) sFoldMap :: forall a m (t1 :: a ~> m) (t2 :: Maybe a). SMonoid m => Sing t1 -> Sing t2 -> Sing (Apply (Apply FoldMapSym0 t1) t2) sFoldr :: forall a b (t1 :: a ~> (b ~> b)) (t2 :: b) (t3 :: Maybe a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldrSym0 t1) t2) t3) sFoldr' :: forall a b (t1 :: a ~> (b ~> b)) (t2 :: b) (t3 :: Maybe a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldr'Sym0 t1) t2) t3) sFoldl :: forall b a (t1 :: b ~> (a ~> b)) (t2 :: b) (t3 :: Maybe a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldlSym0 t1) t2) t3) sFoldl' :: forall b a (t1 :: b ~> (a ~> b)) (t2 :: b) (t3 :: Maybe a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldl'Sym0 t1) t2) t3) sFoldr1 :: forall a (t1 :: a ~> (a ~> a)) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldr1Sym0 t1) t2) sFoldl1 :: forall a (t1 :: a ~> (a ~> a)) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldl1Sym0 t1) t2) sToList :: forall a (t1 :: Maybe a). Sing t1 -> Sing (Apply ToListSym0 t1) sNull :: forall a (t1 :: Maybe a). Sing t1 -> Sing (Apply NullSym0 t1) sLength :: forall a (t1 :: Maybe a). Sing t1 -> Sing (Apply LengthSym0 t1) sElem :: forall a (t1 :: a) (t2 :: Maybe a). SEq a => Sing t1 -> Sing t2 -> Sing (Apply (Apply ElemSym0 t1) t2) sMaximum :: forall a (t1 :: Maybe a). SOrd a => Sing t1 -> Sing (Apply MaximumSym0 t1) sMinimum :: forall a (t1 :: Maybe a). SOrd a => Sing t1 -> Sing (Apply MinimumSym0 t1) sSum :: forall a (t1 :: Maybe a). SNum a => Sing t1 -> Sing (Apply SumSym0 t1) sProduct :: forall a (t1 :: Maybe a). SNum a => Sing t1 -> Sing (Apply ProductSym0 t1)
CFoldable Maybe
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom Maybe a, Monoid w) => (a -> w) -> Maybe a -> w cfoldMap' :: (Dom Maybe a, Monoid m) => (a -> m) -> Maybe a -> m cfold :: (Dom Maybe w, Monoid w) => Maybe w -> w cfoldr :: Dom Maybe a => (a -> b -> b) -> b -> Maybe a -> b cfoldlM :: (Monad m, Dom Maybe b) => (a -> b -> m a) -> a -> Maybe b -> m a cfoldlM' :: (Monad m, Dom Maybe b) => (a -> b -> m a) -> a -> Maybe b -> m a cfoldrM :: (Monad m, Dom Maybe a) => (a -> b -> m b) -> b -> Maybe a -> m b cfoldrM' :: (Monad m, Dom Maybe a) => (a -> b -> m b) -> b -> Maybe a -> m b cfoldl :: Dom Maybe a => (b -> a -> b) -> b -> Maybe a -> b cfoldr' :: Dom Maybe a => (a -> b -> b) -> b -> Maybe a -> b cfoldl' :: Dom Maybe a => (b -> a -> b) -> b -> Maybe a -> b cbasicToList :: Dom Maybe a => Maybe a -> [a] cfoldr1 :: Dom Maybe a => (a -> a -> a) -> Maybe a -> a cfoldl1 :: Dom Maybe a => (a -> a -> a) -> Maybe a -> a cindex :: Dom Maybe a => Maybe a -> Int -> a cnull :: Dom Maybe a => Maybe a -> Bool clength :: Dom Maybe a => Maybe a -> Int cany :: Dom Maybe a => (a -> Bool) -> Maybe a -> Bool call :: Dom Maybe a => (a -> Bool) -> Maybe a -> Bool celem :: (Eq a, Dom Maybe a) => a -> Maybe a -> Bool cnotElem :: (Eq a, Dom Maybe a) => a -> Maybe a -> Bool cminimum :: (Ord a, Dom Maybe a) => Maybe a -> a cmaximum :: (Ord a, Dom Maybe a) => Maybe a -> a csum :: (Num a, Dom Maybe a) => Maybe a -> a cproduct :: (Num a, Dom Maybe a) => Maybe a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom Maybe a, Dom g b) => (a -> g b) -> Maybe a -> g () ctraverse_ :: (Applicative g, Dom Maybe a) => (a -> g b) -> Maybe a -> g () clast :: Dom Maybe a => Maybe a -> a chead :: Dom Maybe a => Maybe a -> a cfind :: Dom Maybe a => (a -> Bool) -> Maybe a -> Maybe a cfindIndex :: Dom Maybe a => (a -> Bool) -> Maybe a -> Maybe Int cfindIndices :: Dom Maybe a => (a -> Bool) -> Maybe a -> [Int] celemIndex :: (Dom Maybe a, Eq a) => a -> Maybe a -> Maybe Int celemIndices :: (Dom Maybe a, Eq a) => a -> Maybe a -> [Int]
CZip Maybe
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom Maybe a, Dom Maybe b, Dom Maybe c) => (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c czip :: (Dom Maybe a, Dom Maybe b, Dom Maybe (a, b)) => Maybe a -> Maybe b -> Maybe (a, b)
CFunctor Maybe
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom Maybe a, Dom Maybe b) => (a -> b) -> Maybe a -> Maybe b (<$:) :: (Dom Maybe a, Dom Maybe b) => a -> Maybe b -> Maybe a
CPointed Maybe
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom Maybe a => a -> Maybe a
CRepeat Maybe
Instance details Defined in Control.Subcategory.Zip Methods crepeat :: Dom Maybe a => a -> Maybe a
CTraversable Maybe
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom Maybe a, Dom Maybe b, Applicative g) => (a -> g b) -> Maybe a -> g (Maybe b)
CUnzip Maybe
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom Maybe (a, b), Dom Maybe a, Dom Maybe b) => Maybe (a, b) -> (Maybe a, Maybe b) cunzipWith :: (Dom Maybe c, Dom Maybe a, Dom Maybe b) => (c -> (a, b)) -> Maybe c -> (Maybe a, Maybe b)
SMonadFail Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods sFail :: forall a (t :: [Char]). Sing t -> Sing (Apply FailSym0 t)
PFunctor Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Fmap arg arg1 :: f b type arg <$ arg1 :: f a
PMonad Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type arg >>= arg1 :: m b type arg >> arg1 :: m b type Return arg :: m a
SFunctor Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sFmap :: forall a b (t1 :: a ~> b) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply FmapSym0 t1) t2) (%<$) :: forall a b (t1 :: a) (t2 :: Maybe b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<$@#@$) t1) t2)
SMonad Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods (%>>=) :: forall a b (t1 :: Maybe a) (t2 :: a ~> Maybe b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>=@#@$) t1) t2) (%>>) :: forall a b (t1 :: Maybe a) (t2 :: Maybe b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>@#@$) t1) t2) sReturn :: forall a (t :: a). Sing t -> Sing (Apply ReturnSym0 t)
SMonadPlus Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sMzero :: Sing MzeroSym0 sMplus :: forall a (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MplusSym0 t1) t2)
PTraversable Maybe
Instance details Defined in Data.Singletons.Prelude.Traversable Associated Types type Traverse arg arg1 :: f (t b) type SequenceA arg :: f (t a) type MapM arg arg1 :: m (t b) type Sequence arg :: m (t a)
STraversable Maybe
Instance details Defined in Data.Singletons.Prelude.Traversable Methods sTraverse :: forall a (f :: Type -> Type) b (t1 :: a ~> f b) (t2 :: Maybe a). SApplicative f => Sing t1 -> Sing t2 -> Sing (Apply (Apply TraverseSym0 t1) t2) sSequenceA :: forall (f :: Type -> Type) a (t1 :: Maybe (f a)). SApplicative f => Sing t1 -> Sing (Apply SequenceASym0 t1) sMapM :: forall a (m :: Type -> Type) b (t1 :: a ~> m b) (t2 :: Maybe a). SMonad m => Sing t1 -> Sing t2 -> Sing (Apply (Apply MapMSym0 t1) t2) sSequence :: forall (m :: Type -> Type) a (t1 :: Maybe (m a)). SMonad m => Sing t1 -> Sing (Apply SequenceSym0 t1)
SApplicative Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sPure :: forall a (t :: a). Sing t -> Sing (Apply PureSym0 t) (%<>) :: forall a b (t1 :: Maybe (a ~> b)) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sLiftA2 :: forall a b c (t1 :: a ~> (b ~> c)) (t2 :: Maybe a) (t3 :: Maybe b). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply LiftA2Sym0 t1) t2) t3) (%>) :: forall a b (t1 :: Maybe a) (t2 :: Maybe b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%<) :: forall a b (t1 :: Maybe a) (t2 :: Maybe b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2)
PApplicative Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Pure arg :: f a type arg <> arg1 :: f b type LiftA2 arg arg1 arg2 :: f c type arg > arg1 :: f b type arg <* arg1 :: f a
SAlternative Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sEmpty :: Sing EmptySym0 (%<\|>) :: forall a (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<\|>@#@$) t1) t2)
Apply Maybe
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b (.>) :: Maybe a -> Maybe b -> Maybe b (<.) :: Maybe a -> Maybe b -> Maybe a liftF2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c
Bind Maybe
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Maybe a -> (a -> Maybe b) -> Maybe b join :: Maybe (Maybe a) -> Maybe a
FoldableWithKey Maybe
Instance details Defined in Data.Key Methods toKeyedList :: Maybe a -> [(Key Maybe, a)] foldMapWithKey :: Monoid m => (Key Maybe -> a -> m) -> Maybe a -> m foldrWithKey :: (Key Maybe -> a -> b -> b) -> b -> Maybe a -> b foldlWithKey :: (b -> Key Maybe -> a -> b) -> b -> Maybe a -> b
Indexable Maybe
Instance details Defined in Data.Key Methods index :: Maybe a -> Key Maybe -> a
Keyed Maybe
Instance details Defined in Data.Key Methods mapWithKey :: (Key Maybe -> a -> b) -> Maybe a -> Maybe b
Lookup Maybe
Instance details Defined in Data.Key Methods lookup :: Key Maybe -> Maybe a -> Maybe a
TraversableWithKey Maybe
Instance details Defined in Data.Key Methods traverseWithKey :: Applicative f => (Key Maybe -> a -> f b) -> Maybe a -> f (Maybe b) mapWithKeyM :: Monad m => (Key Maybe -> a -> m b) -> Maybe a -> m (Maybe b)
Zip Maybe
Instance details Defined in Data.Key Methods zipWith :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c zip :: Maybe a -> Maybe b -> Maybe (a, b) zap :: Maybe (a -> b) -> Maybe a -> Maybe b
ZipWithKey Maybe
Instance details Defined in Data.Key Methods zipWithKey :: (Key Maybe -> a -> b -> c) -> Maybe a -> Maybe b -> Maybe c zapWithKey :: Maybe (Key Maybe -> a -> b) -> Maybe a -> Maybe b
Constrained Maybe
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom Maybe a
Hashable1 Maybe
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Maybe a -> Int
FoldableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Maybe a -> m ifolded :: IndexedFold () (Maybe a) a ifoldr :: (() -> a -> b -> b) -> b -> Maybe a -> b ifoldl :: (() -> b -> a -> b) -> b -> Maybe a -> b ifoldr' :: (() -> a -> b -> b) -> b -> Maybe a -> b ifoldl' :: (() -> b -> a -> b) -> b -> Maybe a -> b
FunctorWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Maybe a -> Maybe b imapped :: IndexedSetter () (Maybe a) (Maybe b) a b
TraversableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Maybe a -> f (Maybe b) itraversed :: IndexedTraversal () (Maybe a) (Maybe b) a b
Lift a => Lift (Maybe a :: Type)
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Maybe a -> Q Exp # liftTyped :: Maybe a -> Q (TExp (Maybe a)) #
Eq a => Eq (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool # (/=) :: Maybe a -> Maybe a -> Bool #
Ord a => Ord (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering # (<) :: Maybe a -> Maybe a -> Bool # (<=) :: Maybe a -> Maybe a -> Bool # (>) :: Maybe a -> Maybe a -> Bool # (>=) :: Maybe a -> Maybe a -> Bool # max :: Maybe a -> Maybe a -> Maybe a # min :: Maybe a -> Maybe a -> Maybe a #
Read a => Read (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) # readList :: ReadS [Maybe a] # readPrec :: ReadPrec (Maybe a) # readListPrec :: ReadPrec [Maybe a] #
Show a => Show (Maybe a)	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS # show :: Maybe a -> String # showList :: [Maybe a] -> ShowS #
Generic (Maybe a)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (Maybe a) :: Type -> Type # Methods from :: Maybe a -> Rep (Maybe a) x # to :: Rep (Maybe a) x -> Maybe a #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Hashable a => Hashable (Maybe a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Maybe a -> Int # hash :: Maybe a -> Int #
NFData a => NFData (Maybe a)
Instance details Defined in Control.DeepSeq Methods rnf :: Maybe a -> () #
At (Maybe a)
Instance details Defined in Control.Lens.At Methods at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a)))
Ixed (Maybe a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a))
AsEmpty (Maybe a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Maybe a) ()
MonoFoldable (Maybe a)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Maybe a) -> m) -> Maybe a -> m ofoldr :: (Element (Maybe a) -> b -> b) -> b -> Maybe a -> b ofoldl' :: (a0 -> Element (Maybe a) -> a0) -> a0 -> Maybe a -> a0 otoList :: Maybe a -> [Element (Maybe a)] oall :: (Element (Maybe a) -> Bool) -> Maybe a -> Bool oany :: (Element (Maybe a) -> Bool) -> Maybe a -> Bool onull :: Maybe a -> Bool olength :: Maybe a -> Int olength64 :: Maybe a -> Int64 ocompareLength :: Integral i => Maybe a -> i -> Ordering otraverse_ :: Applicative f => (Element (Maybe a) -> f b) -> Maybe a -> f () ofor_ :: Applicative f => Maybe a -> (Element (Maybe a) -> f b) -> f () omapM_ :: Applicative m => (Element (Maybe a) -> m ()) -> Maybe a -> m () oforM_ :: Applicative m => Maybe a -> (Element (Maybe a) -> m ()) -> m () ofoldlM :: Monad m => (a0 -> Element (Maybe a) -> m a0) -> a0 -> Maybe a -> m a0 ofoldMap1Ex :: Semigroup m => (Element (Maybe a) -> m) -> Maybe a -> m ofoldr1Ex :: (Element (Maybe a) -> Element (Maybe a) -> Element (Maybe a)) -> Maybe a -> Element (Maybe a) ofoldl1Ex' :: (Element (Maybe a) -> Element (Maybe a) -> Element (Maybe a)) -> Maybe a -> Element (Maybe a) headEx :: Maybe a -> Element (Maybe a) lastEx :: Maybe a -> Element (Maybe a) unsafeHead :: Maybe a -> Element (Maybe a) unsafeLast :: Maybe a -> Element (Maybe a) maximumByEx :: (Element (Maybe a) -> Element (Maybe a) -> Ordering) -> Maybe a -> Element (Maybe a) minimumByEx :: (Element (Maybe a) -> Element (Maybe a) -> Ordering) -> Maybe a -> Element (Maybe a) oelem :: Element (Maybe a) -> Maybe a -> Bool onotElem :: Element (Maybe a) -> Maybe a -> Bool
MonoFunctor (Maybe a)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (Maybe a) -> Element (Maybe a)) -> Maybe a -> Maybe a
MonoPointed (Maybe a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (Maybe a) -> Maybe a
MonoTraversable (Maybe a)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (Maybe a) -> f (Element (Maybe a))) -> Maybe a -> f (Maybe a) omapM :: Applicative m => (Element (Maybe a) -> m (Element (Maybe a))) -> Maybe a -> m (Maybe a)
SEq a => SEq (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Eq Methods (%==) :: forall (a0 :: Maybe a) (b :: Maybe a). Sing a0 -> Sing b -> Sing (a0 == b) (%/=) :: forall (a0 :: Maybe a) (b :: Maybe a). Sing a0 -> Sing b -> Sing (a0 /= b)
SSemigroup a => SMonoid (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sMempty :: Sing MemptySym0 sMappend :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MappendSym0 t1) t2) sMconcat :: forall (t :: [Maybe a]). Sing t -> Sing (Apply MconcatSym0 t)
SSemigroup a => SSemigroup (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%<>) :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sSconcat :: forall (t :: NonEmpty (Maybe a)). Sing t -> Sing (Apply SconcatSym0 t)
SOrd a => SOrd (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sCompare :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply CompareSym0 t1) t2) (%<) :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2) (%<=) :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<=@#@$) t1) t2) (%>) :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%>=) :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>=@#@$) t1) t2) sMax :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MaxSym0 t1) t2) sMin :: forall (t1 :: Maybe a) (t2 :: Maybe a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MinSym0 t1) t2)
PSemigroup (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Associated Types type arg <> arg1 :: a type Sconcat arg :: a
PEq (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Eq Associated Types type x == y :: Bool type x /= y :: Bool
PMonoid (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monoid Associated Types type Mempty :: a type Mappend arg arg1 :: a type Mconcat arg :: a
POrd (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord Associated Types type Compare arg arg1 :: Ordering type arg < arg1 :: Bool type arg <= arg1 :: Bool type arg > arg1 :: Bool type arg >= arg1 :: Bool type Max arg arg1 :: a type Min arg arg1 :: a
PShow (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Show Associated Types type ShowsPrec arg arg1 arg2 :: Symbol type Show_ arg :: Symbol type ShowList arg arg1 :: Symbol
SShow a => SShow (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Show Methods sShowsPrec :: forall (t1 :: Nat) (t2 :: Maybe a) (t3 :: Symbol). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply ShowsPrecSym0 t1) t2) t3) sShow_ :: forall (t :: Maybe a). Sing t -> Sing (Apply Show_Sym0 t) sShowList :: forall (t1 :: [Maybe a]) (t2 :: Symbol). Sing t1 -> Sing t2 -> Sing (Apply (Apply ShowListSym0 t1) t2)
SingKind a => SingKind (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) Methods fromSing :: forall (a0 :: Maybe a). Sing a0 -> DemoteRep (Maybe a)
Generic1 Maybe	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 Maybe :: k -> Type # Methods from1 :: forall (a :: k). Maybe a -> Rep1 Maybe a # to1 :: forall (a :: k). Rep1 Maybe a -> Maybe a #
PMonadFail Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Associated Types type Fail arg :: m a
PMonadPlus Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Mzero :: m a type Mplus arg arg1 :: m a
PAlternative Maybe
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Empty :: f a type arg <\|> arg1 :: f a
SDecide a => TestCoercion (SMaybe :: Maybe a -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods testCoercion :: forall (a0 :: k) (b :: k). SMaybe a0 -> SMaybe b -> Maybe (Coercion a0 b) #
SDecide a => TestEquality (SMaybe :: Maybe a -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods testEquality :: forall (a0 :: k) (b :: k). SMaybe a0 -> SMaybe b -> Maybe (a0 :~: b) #
SingI ('Nothing :: Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'Nothing
Each (Maybe a) (Maybe b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Maybe a) (Maybe b) a b
SingI a2 => SingI ('Just a2 :: Maybe a1)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing ('Just a2)
SingI (CatMaybesSym0 :: TyFun [Maybe a] [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing CatMaybesSym0 #
SingI (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing ListToMaybeSym0 #
SingI (MaybeToListSym0 :: TyFun (Maybe a) [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing MaybeToListSym0 #
SingI (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing IsNothingSym0 #
SingI (IsJustSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing IsJustSym0 #
SingI (FromJustSym0 :: TyFun (Maybe a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing FromJustSym0 #
SingI (MinInternalSym0 :: TyFun (Maybe a) (MinInternal a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing MinInternalSym0 #
SingI (MaxInternalSym0 :: TyFun (Maybe a) (MaxInternal a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing MaxInternalSym0 #
SingI (OptionSym0 :: TyFun (Maybe a) (Option a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing OptionSym0 #
SingI (LastSym0 :: TyFun (Maybe a) (Last a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sing :: Sing LastSym0 #
SingI (FirstSym0 :: TyFun (Maybe a) (First a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sing :: Sing FirstSym0 #
SingI (FromMaybeSym0 :: TyFun a (Maybe a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing FromMaybeSym0 #
SEq a => SingI (ElemIndexSym0 :: TyFun a ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing ElemIndexSym0 #
SingI (JustSym0 :: TyFun a (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods sing :: Sing JustSym0 #
SingI (GetOptionSym0 :: TyFun (Option a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods sing :: Sing GetOptionSym0 #
SingI (GetFirstSym0 :: TyFun (First a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sing :: Sing GetFirstSym0 #
SingI (GetLastSym0 :: TyFun (Last a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sing :: Sing GetLastSym0 #
SingI (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FindSym0 #
SingI (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing FindIndexSym0 #
SingI (GetMaxInternalSym0 :: TyFun (MaxInternal a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing GetMaxInternalSym0 #
SingI (GetMinInternalSym0 :: TyFun (MinInternal a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing GetMinInternalSym0 #
SuppressUnusedWarnings (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Fail Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (CatMaybesSym0 :: TyFun [Maybe a] [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (StripPrefixSym0 :: TyFun [a] ([a] ~> Maybe [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073082Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MaybeToListSym0 :: TyFun (Maybe a) [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsJustSym0 :: TyFun (Maybe a) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FromJustSym0 :: TyFun (Maybe a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MinInternalSym0 :: TyFun (Maybe a) (MinInternal a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MaxInternalSym0 :: TyFun (Maybe a) (MaxInternal a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240831Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (OptionSym0 :: TyFun (Maybe a) (Option a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LastSym0 :: TyFun (Maybe a) (Last a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FirstSym0 :: TyFun (Maybe a) (First a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ShowsPrec_6989586621680653944Sym0 :: TyFun Nat (Maybe a ~> (Symbol ~> Symbol)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Pure_6989586621680072824Sym0 :: TyFun a (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680073091LSym0 :: TyFun k1 (Maybe k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FromMaybeSym0 :: TyFun a (Maybe a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemIndexSym0 :: TyFun a ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (JustSym0 :: TyFun a (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetOptionSym0 :: TyFun (Option a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetFirstSym0 :: TyFun (First a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetLastSym0 :: TyFun (Last a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetMaxInternalSym0 :: TyFun (MaxInternal a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetMinInternalSym0 :: TyFun (MinInternal a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SingI d => SingI (FindSym1 d :: TyFun [a] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (FindSym1 d) #
SingI d => SingI (FindIndexSym1 d :: TyFun [a] (Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (FindIndexSym1 d) #
(SEq a, SingI d) => SingI (ElemIndexSym1 d :: TyFun [a] (Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (ElemIndexSym1 d) #
SingI d => SingI (FromMaybeSym1 d :: TyFun (Maybe a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing (FromMaybeSym1 d) #
SingI (Maybe_Sym0 :: TyFun b ((a ~> b) ~> (Maybe a ~> b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing Maybe_Sym0 #
SEq a => SingI (LookupSym0 :: TyFun a ([(a, b)] ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing LookupSym0 #
SAlternative f => SingI (OptionalSym0 :: TyFun (f a) (f (Maybe a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Applicative Methods sing :: Sing OptionalSym0 #
SingI (MapMaybeSym0 :: TyFun (a ~> Maybe b) ([a] ~> [b]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing MapMaybeSym0 #
SFoldable t => SingI (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing FindSym0 #
SingI (UnfoldrSym0 :: TyFun (b ~> Maybe (a, b)) (b ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing UnfoldrSym0 #
SuppressUnusedWarnings (StripPrefixSym1 a6989586621680499001 :: TyFun [a] (Maybe [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym1 a6989586621680379679 :: TyFun [a] (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindIndexSym1 a6989586621680379652 :: TyFun [a] (Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ElemIndexSym1 a6989586621680379670 :: TyFun [a] (Maybe Nat) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ShowsPrec_6989586621680653944Sym1 a6989586621680653954 :: TyFun (Maybe a) (Symbol ~> Symbol) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073082Sym1 a6989586621680073087 :: TyFun (Maybe a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073006Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072995Sym0 :: TyFun (Maybe a) ((a ~> Maybe b) ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072861Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FromMaybeSym1 a6989586621679959450 :: TyFun (Maybe a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240831Sym1 a6989586621680240836 :: TyFun (Maybe a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072834Sym0 :: TyFun (Maybe (a ~> b)) (Maybe a ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072713Sym0 :: TyFun a (Maybe b ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Maybe_Sym0 :: TyFun b ((a ~> b) ~> (Maybe a ~> b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680823058MkJustSym0 :: TyFun k (TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680823043MkJustSym0 :: TyFun k (TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814127NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814127MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814103NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814103MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LookupSym0 :: TyFun a ([(a, b)] ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (OptionalSym0 :: TyFun (f a) (f (Maybe a)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Applicative Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680072701Sym0 :: TyFun (a ~> b) (Maybe a ~> Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MapMaybeSym0 :: TyFun (a ~> Maybe b) ([a] ~> [b]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823100Sym0 :: TyFun (a ~> (b ~> b)) (b ~> (Maybe a ~> b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldl_6989586621680823116Sym0 :: TyFun (b ~> (a ~> b)) (b ~> (Maybe a ~> b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FoldMap_6989586621680823084Sym0 :: TyFun (a ~> m) (Maybe a ~> m) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (UnfoldrSym0 :: TyFun (b ~> Maybe (a, b)) (b ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
(SEq a, SingI d) => SingI (LookupSym1 d :: TyFun [(a, b)] (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing (LookupSym1 d) #
(SFoldable t, SingI d) => SingI (FindSym1 d :: TyFun (t a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing (FindSym1 d) #
SingI d => SingI (Maybe_Sym1 d :: TyFun (a ~> b) (Maybe a ~> b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing (Maybe_Sym1 d) #
SuppressUnusedWarnings (LookupSym1 a6989586621680379377 :: TyFun [(a, b)] (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073006Sym1 a6989586621680073015 :: TyFun (Maybe b) (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072861Sym1 a6989586621680072866 :: TyFun (Maybe b) (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072834Sym1 a6989586621680072839 :: TyFun (Maybe a) (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072713Sym1 a6989586621680072718 :: TyFun (Maybe b) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680072701Sym1 a6989586621680072706 :: TyFun (Maybe a) (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FoldMap_6989586621680823084Sym1 a6989586621680823093 :: TyFun (Maybe a) m -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680823058MkJustSym1 a_69895866216808230526989586621680823057 :: TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680823043MkJustSym1 a_69895866216808230376989586621680823042 :: TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814127NSym1 x6989586621680814125 :: TyFun k1 (Maybe k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814127MSym1 x6989586621680814125 :: TyFun k (Maybe k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814103NSym1 x6989586621680814101 :: TyFun k1 (Maybe k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680814103MSym1 x6989586621680814101 :: TyFun k (Maybe k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823100Sym1 a6989586621680823106 :: TyFun b (Maybe a ~> b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldl_6989586621680823116Sym1 a6989586621680823122 :: TyFun b (Maybe a ~> b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FindSym1 a6989586621680822550 :: TyFun (t a) (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701132Sym0 :: TyFun k (TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701053Sym0 :: TyFun k (TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Traverse_6989586621681088303Sym0 :: TyFun (a ~> f b) (Maybe a ~> f (Maybe b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Traversable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072995Sym1 a6989586621680073000 :: TyFun (a ~> Maybe b) (Maybe b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LiftA2_6989586621680072847Sym0 :: TyFun (a ~> (b ~> c)) (Maybe a ~> (Maybe b ~> Maybe c)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Maybe_Sym1 a6989586621679957884 :: TyFun (a ~> b) (Maybe a ~> b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679959425RsSym0 :: TyFun (a ~> Maybe k1) (TyFun k (TyFun [a] [k1] -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822965MfSym0 :: TyFun (k2 ~> (k3 ~> k3)) (TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822944MfSym0 :: TyFun (k2 ~> (k3 ~> k2)) (TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
(SingI d1, SingI d2) => SingI (Maybe_Sym2 d1 d2 :: TyFun (Maybe a) b -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods sing :: Sing (Maybe_Sym2 d1 d2) #
SuppressUnusedWarnings (Traverse_6989586621681088303Sym1 a6989586621681088308 :: TyFun (Maybe a) (f (Maybe b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Traversable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LiftA2_6989586621680072847Sym1 a6989586621680072853 :: TyFun (Maybe a) (Maybe b ~> Maybe c) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Maybe_Sym2 a6989586621679957884 a6989586621679957885 :: TyFun (Maybe a) b -> Type)
Instance details Defined in Data.Singletons.Prelude.Maybe Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823100Sym2 a6989586621680823106 a6989586621680823107 :: TyFun (Maybe a) b -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldl_6989586621680823116Sym2 a6989586621680823122 a6989586621680823123 :: TyFun (Maybe a) b -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822965MfSym1 f6989586621680822963 :: TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822944MfSym1 f6989586621680822942 :: TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701132Sym1 a6989586621680701130 :: TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701053Sym1 a6989586621680701051 :: TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LiftA2_6989586621680072847Sym2 a6989586621680072853 a6989586621680072854 :: TyFun (Maybe b) (Maybe c) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822965MfSym2 f6989586621680822963 xs6989586621680822964 :: TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822944MfSym2 f6989586621680822942 xs6989586621680822943 :: TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701132Sym2 a6989586621680701130 k6989586621680701131 :: TyFun k1 (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Lambda_6989586621680701053Sym2 a6989586621680701051 k6989586621680701052 :: TyFun k1 (Maybe a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822944MfSym3 f6989586621680822942 xs6989586621680822943 a6989586621680822945 :: TyFun (Maybe k3) (Maybe k2) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822965MfSym3 f6989586621680822963 xs6989586621680822964 a6989586621680822966 :: TyFun k3 (Maybe k3) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
type Key Maybe
Instance details Defined in Data.Key type Key Maybe = ()
type Dom Maybe a
Instance details Defined in Control.Subcategory.Functor type Dom Maybe a = ()
type Length (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Length (arg :: Maybe a) = Apply (Length_6989586621680823002Sym0 :: TyFun (Maybe a) Nat -> Type) arg
type Maximum (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Maximum (arg :: Maybe a) = Apply (Maximum_6989586621680823035Sym0 :: TyFun (Maybe a) a -> Type) arg
type Minimum (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Minimum (arg :: Maybe a) = Apply (Minimum_6989586621680823050Sym0 :: TyFun (Maybe a) a -> Type) arg
type Null (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Null (arg :: Maybe a) = Apply (Null_6989586621680822985Sym0 :: TyFun (Maybe a) Bool -> Type) arg
type Product (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Product (arg :: Maybe a) = Apply (Product_6989586621680823074Sym0 :: TyFun (Maybe a) a -> Type) arg
type Sum (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Sum (arg :: Maybe a) = Apply (Sum_6989586621680823065Sym0 :: TyFun (Maybe a) a -> Type) arg
type Return (arg :: a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Return (arg :: a) = Apply (Return_6989586621680012055Sym0 :: TyFun a (Maybe a) -> Type) arg
type Pure (a :: k1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Pure (a :: k1) = Apply (Pure_6989586621680072824Sym0 :: TyFun k1 (Maybe k1) -> Type) a
type Fold (arg :: Maybe m)
Instance details Defined in Data.Singletons.Prelude.Foldable type Fold (arg :: Maybe m) = Apply (Fold_6989586621680822836Sym0 :: TyFun (Maybe m) m -> Type) arg
type ToList (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type ToList (arg :: Maybe a) = Apply (ToList_6989586621680822976Sym0 :: TyFun (Maybe a) [a] -> Type) arg
type Elem (arg1 :: a) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Elem (arg1 :: a) (arg2 :: Maybe a) = Apply (Apply (Elem_6989586621680823021Sym0 :: TyFun a (Maybe a ~> Bool) -> Type) arg1) arg2
type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a) = Apply (Apply (Foldl1_6989586621680822956Sym0 :: TyFun (a ~> (a ~> a)) (Maybe a ~> a) -> Type) arg1) arg2
type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr1 (arg1 :: a ~> (a ~> a)) (arg2 :: Maybe a) = Apply (Apply (Foldr1_6989586621680822935Sym0 :: TyFun (a ~> (a ~> a)) (Maybe a ~> a) -> Type) arg1) arg2
type Sequence (arg :: Maybe (m a))
Instance details Defined in Data.Singletons.Prelude.Traversable type Sequence (arg :: Maybe (m a)) = Apply (Sequence_6989586621681082098Sym0 :: TyFun (Maybe (m a)) (m (Maybe a)) -> Type) arg
type SequenceA (arg :: Maybe (f a))
Instance details Defined in Data.Singletons.Prelude.Traversable type SequenceA (arg :: Maybe (f a)) = Apply (SequenceA_6989586621681082074Sym0 :: TyFun (Maybe (f a)) (f (Maybe a)) -> Type) arg
type Fmap (a2 :: a1 ~> b) (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Fmap (a2 :: a1 ~> b) (a3 :: Maybe a1) = Apply (Apply (Fmap_6989586621680072701Sym0 :: TyFun (a1 ~> b) (Maybe a1 ~> Maybe b) -> Type) a2) a3
type (a2 :: Maybe a1) >> (a3 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Maybe a1) >> (a3 :: Maybe b) = Apply (Apply (TFHelper_6989586621680073006Sym0 :: TyFun (Maybe a1) (Maybe b ~> Maybe b) -> Type) a2) a3
type (a2 :: Maybe a1) >>= (a3 :: a1 ~> Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Maybe a1) >>= (a3 :: a1 ~> Maybe b) = Apply (Apply (TFHelper_6989586621680072995Sym0 :: TyFun (Maybe a1) ((a1 ~> Maybe b) ~> Maybe b) -> Type) a2) a3
type (a2 :: Maybe a1) *> (a3 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Maybe a1) *> (a3 :: Maybe b) = Apply (Apply (TFHelper_6989586621680072861Sym0 :: TyFun (Maybe a1) (Maybe b ~> Maybe b) -> Type) a2) a3
type (arg1 :: Maybe a) <* (arg2 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (arg1 :: Maybe a) <* (arg2 :: Maybe b) = Apply (Apply (TFHelper_6989586621680012010Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe a) -> Type) arg1) arg2
type (a2 :: Maybe (a1 ~> b)) <*> (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Maybe (a1 ~> b)) <*> (a3 :: Maybe a1) = Apply (Apply (TFHelper_6989586621680072834Sym0 :: TyFun (Maybe (a1 ~> b)) (Maybe a1 ~> Maybe b) -> Type) a2) a3
type (a1 :: k1) <$ (a2 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a1 :: k1) <$ (a2 :: Maybe b) = Apply (Apply (TFHelper_6989586621680072713Sym0 :: TyFun k1 (Maybe b ~> Maybe k1) -> Type) a1) a2
type FoldMap (a2 :: a1 ~> k2) (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type FoldMap (a2 :: a1 ~> k2) (a3 :: Maybe a1) = Apply (Apply (FoldMap_6989586621680823084Sym0 :: TyFun (a1 ~> k2) (Maybe a1 ~> k2) -> Type) a2) a3
type Foldl (a2 :: k2 ~> (a1 ~> k2)) (a3 :: k2) (a4 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl (a2 :: k2 ~> (a1 ~> k2)) (a3 :: k2) (a4 :: Maybe a1) = Apply (Apply (Apply (Foldl_6989586621680823116Sym0 :: TyFun (k2 ~> (a1 ~> k2)) (k2 ~> (Maybe a1 ~> k2)) -> Type) a2) a3) a4
type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl' (arg1 :: b ~> (a ~> b)) (arg2 :: b) (arg3 :: Maybe a) = Apply (Apply (Apply (Foldl'_6989586621680822913Sym0 :: TyFun (b ~> (a ~> b)) (b ~> (Maybe a ~> b)) -> Type) arg1) arg2) arg3
type Foldr (a2 :: a1 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr (a2 :: a1 ~> (k2 ~> k2)) (a3 :: k2) (a4 :: Maybe a1) = Apply (Apply (Apply (Foldr_6989586621680823100Sym0 :: TyFun (a1 ~> (k2 ~> k2)) (k2 ~> (Maybe a1 ~> k2)) -> Type) a2) a3) a4
type MapM (arg1 :: a ~> m b) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Traversable type MapM (arg1 :: a ~> m b) (arg2 :: Maybe a) = Apply (Apply (MapM_6989586621681082084Sym0 :: TyFun (a ~> m b) (Maybe a ~> m (Maybe b)) -> Type) arg1) arg2
type Traverse (a2 :: a1 ~> f b) (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Traversable type Traverse (a2 :: a1 ~> f b) (a3 :: Maybe a1) = Apply (Apply (Traverse_6989586621681088303Sym0 :: TyFun (a1 ~> f b) (Maybe a1 ~> f (Maybe b)) -> Type) a2) a3
type Foldr' (arg1 :: a ~> (b ~> b)) (arg2 :: b) (arg3 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr' (arg1 :: a ~> (b ~> b)) (arg2 :: b) (arg3 :: Maybe a) = Apply (Apply (Apply (Foldr'_6989586621680822875Sym0 :: TyFun (a ~> (b ~> b)) (b ~> (Maybe a ~> b)) -> Type) arg1) arg2) arg3
type LiftA2 (a2 :: a1 ~> (b ~> c)) (a3 :: Maybe a1) (a4 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type LiftA2 (a2 :: a1 ~> (b ~> c)) (a3 :: Maybe a1) (a4 :: Maybe b) = Apply (Apply (Apply (LiftA2_6989586621680072847Sym0 :: TyFun (a1 ~> (b ~> c)) (Maybe a1 ~> (Maybe b ~> Maybe c)) -> Type) a2) a3) a4
type Apply (Pure_6989586621680072824Sym0 :: TyFun a (Maybe a) -> Type) (a6989586621680072830 :: a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Pure_6989586621680072824Sym0 :: TyFun a (Maybe a) -> Type) (a6989586621680072830 :: a) = Pure_6989586621680072824Sym1 a6989586621680072830
type Apply (Let6989586621680073091LSym0 :: TyFun k1 (Maybe k1) -> Type) (wild_69895866216800721896989586621680073090 :: k1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Let6989586621680073091LSym0 :: TyFun k1 (Maybe k1) -> Type) (wild_69895866216800721896989586621680073090 :: k1) = Let6989586621680073091LSym1 wild_69895866216800721896989586621680073090
type Apply (JustSym0 :: TyFun a (Maybe a) -> Type) (a6989586621679750144 :: a)
Instance details Defined in Data.Singletons.Prelude.Instances type Apply (JustSym0 :: TyFun a (Maybe a) -> Type) (a6989586621679750144 :: a) = JustSym1 a6989586621679750144
type Apply (Let6989586621680814103NSym1 x6989586621680814101 :: TyFun k1 (Maybe k1) -> Type) (y6989586621680814102 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814103NSym1 x6989586621680814101 :: TyFun k1 (Maybe k1) -> Type) (y6989586621680814102 :: k1) = Let6989586621680814103NSym2 x6989586621680814101 y6989586621680814102
type Apply (Let6989586621680814103MSym1 x6989586621680814101 :: TyFun k (Maybe k1) -> Type) (y6989586621680814102 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814103MSym1 x6989586621680814101 :: TyFun k (Maybe k1) -> Type) (y6989586621680814102 :: k) = Let6989586621680814103MSym2 x6989586621680814101 y6989586621680814102
type Apply (Let6989586621680814127NSym1 x6989586621680814125 :: TyFun k1 (Maybe k1) -> Type) (y6989586621680814126 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814127NSym1 x6989586621680814125 :: TyFun k1 (Maybe k1) -> Type) (y6989586621680814126 :: k1) = Let6989586621680814127NSym2 x6989586621680814125 y6989586621680814126
type Apply (Let6989586621680814127MSym1 x6989586621680814125 :: TyFun k (Maybe k1) -> Type) (y6989586621680814126 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814127MSym1 x6989586621680814125 :: TyFun k (Maybe k1) -> Type) (y6989586621680814126 :: k) = Let6989586621680814127MSym2 x6989586621680814125 y6989586621680814126
type Apply (Let6989586621680823043MkJustSym1 a_69895866216808230376989586621680823042 :: TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type) (a6989586621680823046 :: a6989586621680822215)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680823043MkJustSym1 a_69895866216808230376989586621680823042 :: TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type) (a6989586621680823046 :: a6989586621680822215) = Let6989586621680823043MkJustSym2 a_69895866216808230376989586621680823042 a6989586621680823046
type Apply (Let6989586621680823058MkJustSym1 a_69895866216808230526989586621680823057 :: TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type) (a6989586621680823061 :: a6989586621680822216)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680823058MkJustSym1 a_69895866216808230526989586621680823057 :: TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type) (a6989586621680823061 :: a6989586621680822216) = Let6989586621680823058MkJustSym2 a_69895866216808230526989586621680823057 a6989586621680823061
type Apply (Lambda_6989586621680701053Sym2 a6989586621680701051 k6989586621680701052 :: TyFun k1 (Maybe a) -> Type) (x6989586621680701055 :: k1)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701053Sym2 a6989586621680701051 k6989586621680701052 :: TyFun k1 (Maybe a) -> Type) (x6989586621680701055 :: k1) = Lambda_6989586621680701053Sym3 a6989586621680701051 k6989586621680701052 x6989586621680701055
type Apply (Lambda_6989586621680701132Sym2 a6989586621680701130 k6989586621680701131 :: TyFun k1 (Maybe a) -> Type) (x6989586621680701134 :: k1)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701132Sym2 a6989586621680701130 k6989586621680701131 :: TyFun k1 (Maybe a) -> Type) (x6989586621680701134 :: k1) = Lambda_6989586621680701132Sym3 a6989586621680701130 k6989586621680701131 x6989586621680701134
type Apply (Let6989586621680822965MfSym3 f6989586621680822963 xs6989586621680822964 a6989586621680822966 :: TyFun k3 (Maybe k3) -> Type) (a6989586621680822967 :: k3)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822965MfSym3 f6989586621680822963 xs6989586621680822964 a6989586621680822966 :: TyFun k3 (Maybe k3) -> Type) (a6989586621680822967 :: k3) = Let6989586621680822965MfSym4 f6989586621680822963 xs6989586621680822964 a6989586621680822966 a6989586621680822967
type Apply (ShowsPrec_6989586621680653944Sym0 :: TyFun Nat (Maybe a ~> (Symbol ~> Symbol)) -> Type) (a6989586621680653954 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680653944Sym0 :: TyFun Nat (Maybe a ~> (Symbol ~> Symbol)) -> Type) (a6989586621680653954 :: Nat) = ShowsPrec_6989586621680653944Sym1 a6989586621680653954 :: TyFun (Maybe a) (Symbol ~> Symbol) -> Type
type Apply (ElemIndexSym0 :: TyFun a ([a] ~> Maybe Nat) -> Type) (a6989586621680379670 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (ElemIndexSym0 :: TyFun a ([a] ~> Maybe Nat) -> Type) (a6989586621680379670 :: a) = ElemIndexSym1 a6989586621680379670
type Apply (FromMaybeSym0 :: TyFun a (Maybe a ~> a) -> Type) (a6989586621679959450 :: a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (FromMaybeSym0 :: TyFun a (Maybe a ~> a) -> Type) (a6989586621679959450 :: a) = FromMaybeSym1 a6989586621679959450
type Apply (TFHelper_6989586621680072713Sym0 :: TyFun a (Maybe b ~> Maybe a) -> Type) (a6989586621680072718 :: a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072713Sym0 :: TyFun a (Maybe b ~> Maybe a) -> Type) (a6989586621680072718 :: a) = TFHelper_6989586621680072713Sym1 a6989586621680072718 :: TyFun (Maybe b) (Maybe a) -> Type
type Apply (Maybe_Sym0 :: TyFun b ((a ~> b) ~> (Maybe a ~> b)) -> Type) (a6989586621679957884 :: b)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (Maybe_Sym0 :: TyFun b ((a ~> b) ~> (Maybe a ~> b)) -> Type) (a6989586621679957884 :: b) = Maybe_Sym1 a6989586621679957884 :: TyFun (a ~> b) (Maybe a ~> b) -> Type
type Apply (Let6989586621680814103NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type) (x6989586621680814101 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814103NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type) (x6989586621680814101 :: k) = Let6989586621680814103NSym1 x6989586621680814101 :: TyFun k1 (Maybe k1) -> Type
type Apply (Let6989586621680814103MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type) (x6989586621680814101 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814103MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type) (x6989586621680814101 :: k1) = Let6989586621680814103MSym1 x6989586621680814101 :: TyFun k (Maybe k1) -> Type
type Apply (Let6989586621680814127NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type) (x6989586621680814125 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814127NSym0 :: TyFun k (TyFun k1 (Maybe k1) -> Type) -> Type) (x6989586621680814125 :: k) = Let6989586621680814127NSym1 x6989586621680814125 :: TyFun k1 (Maybe k1) -> Type
type Apply (Let6989586621680814127MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type) (x6989586621680814125 :: k1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680814127MSym0 :: TyFun k1 (TyFun k (Maybe k1) -> Type) -> Type) (x6989586621680814125 :: k1) = Let6989586621680814127MSym1 x6989586621680814125 :: TyFun k (Maybe k1) -> Type
type Apply (Let6989586621680823043MkJustSym0 :: TyFun k (TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type) -> Type) (a_69895866216808230376989586621680823042 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680823043MkJustSym0 :: TyFun k (TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type) -> Type) (a_69895866216808230376989586621680823042 :: k) = Let6989586621680823043MkJustSym1 a_69895866216808230376989586621680823042 :: TyFun a6989586621680822215 (Maybe a6989586621680822215) -> Type
type Apply (Let6989586621680823058MkJustSym0 :: TyFun k (TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type) -> Type) (a_69895866216808230526989586621680823057 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680823058MkJustSym0 :: TyFun k (TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type) -> Type) (a_69895866216808230526989586621680823057 :: k) = Let6989586621680823058MkJustSym1 a_69895866216808230526989586621680823057 :: TyFun a6989586621680822216 (Maybe a6989586621680822216) -> Type
type Apply (LookupSym0 :: TyFun a ([(a, b)] ~> Maybe b) -> Type) (a6989586621680379377 :: a)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (LookupSym0 :: TyFun a ([(a, b)] ~> Maybe b) -> Type) (a6989586621680379377 :: a) = LookupSym1 a6989586621680379377 :: TyFun [(a, b)] (Maybe b) -> Type
type Apply (Foldr_6989586621680823100Sym1 a6989586621680823106 :: TyFun b (Maybe a ~> b) -> Type) (a6989586621680823107 :: b)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823100Sym1 a6989586621680823106 :: TyFun b (Maybe a ~> b) -> Type) (a6989586621680823107 :: b) = Foldr_6989586621680823100Sym2 a6989586621680823106 a6989586621680823107
type Apply (Foldl_6989586621680823116Sym1 a6989586621680823122 :: TyFun b (Maybe a ~> b) -> Type) (a6989586621680823123 :: b)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldl_6989586621680823116Sym1 a6989586621680823122 :: TyFun b (Maybe a ~> b) -> Type) (a6989586621680823123 :: b) = Foldl_6989586621680823116Sym2 a6989586621680823122 a6989586621680823123
type Apply (Lambda_6989586621680701053Sym0 :: TyFun k (TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type) (a6989586621680701051 :: k)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701053Sym0 :: TyFun k (TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type) (a6989586621680701051 :: k) = Lambda_6989586621680701053Sym1 a6989586621680701051 :: TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type
type Apply (Lambda_6989586621680701132Sym0 :: TyFun k (TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type) (a6989586621680701130 :: k)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701132Sym0 :: TyFun k (TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type) -> Type) (a6989586621680701130 :: k) = Lambda_6989586621680701132Sym1 a6989586621680701130 :: TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type
type Apply (Let6989586621680822944MfSym1 f6989586621680822942 :: TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type) (xs6989586621680822943 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822944MfSym1 f6989586621680822942 :: TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type) (xs6989586621680822943 :: k) = Let6989586621680822944MfSym2 f6989586621680822942 xs6989586621680822943
type Apply (Let6989586621680822965MfSym1 f6989586621680822963 :: TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type) (xs6989586621680822964 :: k)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822965MfSym1 f6989586621680822963 :: TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type) (xs6989586621680822964 :: k) = Let6989586621680822965MfSym2 f6989586621680822963 xs6989586621680822964
type Apply (Let6989586621680822944MfSym2 f6989586621680822942 xs6989586621680822943 :: TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) (a6989586621680822945 :: k2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822944MfSym2 f6989586621680822942 xs6989586621680822943 :: TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) (a6989586621680822945 :: k2) = Let6989586621680822944MfSym3 f6989586621680822942 xs6989586621680822943 a6989586621680822945
type Rep (Maybe a)
Instance details Defined in GHC.Generics type Rep (Maybe a) = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Sing
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SMaybe :: Maybe a -> Type
type Demote (Maybe a)
Instance details Defined in Data.Singletons.Prelude.Instances type Demote (Maybe a) = Maybe (Demote a)
type Index (Maybe a)
Instance details Defined in Control.Lens.At type Index (Maybe a) = ()
type Element (Maybe a)
Instance details Defined in Data.MonoTraversable type Element (Maybe a) = a
type IxValue (Maybe a)
Instance details Defined in Control.Lens.At type IxValue (Maybe a) = a
type Mempty
Instance details Defined in Data.Singletons.Prelude.Monoid type Mempty = Mempty_6989586621680691432Sym0 :: Maybe a
type DemoteRep (Maybe a)
Instance details Defined in GHC.Generics type DemoteRep (Maybe a) = Maybe (DemoteRep a)
data Sing (b :: Maybe a)
Instance details Defined in GHC.Generics data Sing (b :: Maybe a) where SNothing :: forall a. Sing ('Nothing :: Maybe a) SJust :: forall a (a1 :: a). Sing a1 -> Sing ('Just a1)
type Rep1 Maybe
Instance details Defined in GHC.Generics type Rep1 Maybe = D1 ('MetaData "Maybe" "GHC.Maybe" "base" 'False) (C1 ('MetaCons "Nothing" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Just" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Sconcat (arg :: NonEmpty (Maybe a))
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sconcat (arg :: NonEmpty (Maybe a)) = Apply (Sconcat_6989586621680240682Sym0 :: TyFun (NonEmpty (Maybe a)) (Maybe a) -> Type) arg
type Mconcat (arg :: [Maybe a])
Instance details Defined in Data.Singletons.Prelude.Monoid type Mconcat (arg :: [Maybe a]) = Apply (Mconcat_6989586621680691385Sym0 :: TyFun [Maybe a] (Maybe a) -> Type) arg
type Show_ (arg :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Show type Show_ (arg :: Maybe a) = Apply (Show__6989586621680636786Sym0 :: TyFun (Maybe a) Symbol -> Type) arg
type (x :: Maybe a) /= (y :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Eq type (x :: Maybe a) /= (y :: Maybe a) = Not (x == y)
type (a2 :: Maybe a1) == (b :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Eq type (a2 :: Maybe a1) == (b :: Maybe a1) = Equals_6989586621679820269 a2 b
type (a2 :: Maybe a1) <> (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type (a2 :: Maybe a1) <> (a3 :: Maybe a1) = Apply (Apply (TFHelper_6989586621680240831Sym0 :: TyFun (Maybe a1) (Maybe a1 ~> Maybe a1) -> Type) a2) a3
type Mzero
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Mzero = Mzero_6989586621680012075Sym0 :: Maybe a
type Mappend (arg1 :: Maybe a) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Mappend (arg1 :: Maybe a) (arg2 :: Maybe a) = Apply (Apply (Mappend_6989586621680691371Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) arg1) arg2
type Empty
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Empty = Empty_6989586621680073077Sym0 :: Maybe a
type Max (arg1 :: Maybe a) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Max (arg1 :: Maybe a) (arg2 :: Maybe a) = Apply (Apply (Max_6989586621679837511Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) arg1) arg2
type Min (arg1 :: Maybe a) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Min (arg1 :: Maybe a) (arg2 :: Maybe a) = Apply (Apply (Min_6989586621679837527Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) arg1) arg2
type Compare (a2 :: Maybe a1) (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Ord type Compare (a2 :: Maybe a1) (a3 :: Maybe a1) = Apply (Apply (Compare_6989586621679848508Sym0 :: TyFun (Maybe a1) (Maybe a1 ~> Ordering) -> Type) a2) a3
type (arg1 :: Maybe a) <= (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Maybe a) <= (arg2 :: Maybe a) = Apply (Apply (TFHelper_6989586621679837463Sym0 :: TyFun (Maybe a) (Maybe a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Maybe a) < (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Maybe a) < (arg2 :: Maybe a) = Apply (Apply (TFHelper_6989586621679837447Sym0 :: TyFun (Maybe a) (Maybe a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Maybe a) >= (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Maybe a) >= (arg2 :: Maybe a) = Apply (Apply (TFHelper_6989586621679837495Sym0 :: TyFun (Maybe a) (Maybe a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Maybe a) > (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Maybe a) > (arg2 :: Maybe a) = Apply (Apply (TFHelper_6989586621679837479Sym0 :: TyFun (Maybe a) (Maybe a ~> Bool) -> Type) arg1) arg2
type ShowList (arg1 :: [Maybe a]) arg2
Instance details Defined in Data.Singletons.Prelude.Show type ShowList (arg1 :: [Maybe a]) arg2 = Apply (Apply (ShowList_6989586621680636794Sym0 :: TyFun [Maybe a] (Symbol ~> Symbol) -> Type) arg1) arg2
type Fail a2
Instance details Defined in Data.Singletons.Prelude.Monad.Fail type Fail a2 = Apply (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a1) -> Type) a2
type ShowsPrec a2 (a3 :: Maybe a1) a4
Instance details Defined in Data.Singletons.Prelude.Show type ShowsPrec a2 (a3 :: Maybe a1) a4 = Apply (Apply (Apply (ShowsPrec_6989586621680653944Sym0 :: TyFun Nat (Maybe a1 ~> (Symbol ~> Symbol)) -> Type) a2) a3) a4
type Mplus (arg1 :: Maybe a) (arg2 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Mplus (arg1 :: Maybe a) (arg2 :: Maybe a) = Apply (Apply (Mplus_6989586621680012080Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) arg1) arg2
type (a2 :: Maybe a1) <\|> (a3 :: Maybe a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Maybe a1) <\|> (a3 :: Maybe a1) = Apply (Apply (TFHelper_6989586621680073082Sym0 :: TyFun (Maybe a1) (Maybe a1 ~> Maybe a1) -> Type) a2) a3
type Apply (FromJustSym0 :: TyFun (Maybe a) a -> Type) (a6989586621679959460 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (FromJustSym0 :: TyFun (Maybe a) a -> Type) (a6989586621679959460 :: Maybe a) = FromJustSym1 a6989586621679959460
type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959464 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959464 :: Maybe a) = IsNothingSym1 a6989586621679959464
type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959467 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> Type) (a6989586621679959467 :: Maybe a) = IsJustSym1 a6989586621679959467
type Apply (FromMaybeSym1 a6989586621679959450 :: TyFun (Maybe a) a -> Type) (a6989586621679959451 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (FromMaybeSym1 a6989586621679959450 :: TyFun (Maybe a) a -> Type) (a6989586621679959451 :: Maybe a) = FromMaybeSym2 a6989586621679959450 a6989586621679959451
type Apply (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type) (a6989586621679848514 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type) (a6989586621679848514 :: Maybe a) = Compare_6989586621679848508Sym2 a6989586621679848513 a6989586621679848514
type Apply (FoldMap_6989586621680823084Sym1 a6989586621680823093 :: TyFun (Maybe a) m -> Type) (a6989586621680823094 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FoldMap_6989586621680823084Sym1 a6989586621680823093 :: TyFun (Maybe a) m -> Type) (a6989586621680823094 :: Maybe a) = FoldMap_6989586621680823084Sym2 a6989586621680823093 a6989586621680823094
type Apply (Maybe_Sym2 a6989586621679957884 a6989586621679957885 :: TyFun (Maybe a) b -> Type) (a6989586621679957886 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (Maybe_Sym2 a6989586621679957884 a6989586621679957885 :: TyFun (Maybe a) b -> Type) (a6989586621679957886 :: Maybe a) = Maybe_Sym3 a6989586621679957884 a6989586621679957885 a6989586621679957886
type Apply (Foldr_6989586621680823100Sym2 a6989586621680823106 a6989586621680823107 :: TyFun (Maybe a) b -> Type) (a6989586621680823108 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823100Sym2 a6989586621680823106 a6989586621680823107 :: TyFun (Maybe a) b -> Type) (a6989586621680823108 :: Maybe a) = Foldr_6989586621680823100Sym3 a6989586621680823106 a6989586621680823107 a6989586621680823108
type Apply (Foldl_6989586621680823116Sym2 a6989586621680823122 a6989586621680823123 :: TyFun (Maybe a) b -> Type) (a6989586621680823124 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldl_6989586621680823116Sym2 a6989586621680823122 a6989586621680823123 :: TyFun (Maybe a) b -> Type) (a6989586621680823124 :: Maybe a) = Foldl_6989586621680823116Sym3 a6989586621680823122 a6989586621680823123 a6989586621680823124
type Apply (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type) (a6989586621680156265 :: [Char])
Instance details Defined in Data.Singletons.Prelude.Monad.Fail type Apply (Fail_6989586621680156261Sym0 :: TyFun [Char] (Maybe a) -> Type) (a6989586621680156265 :: [Char]) = Fail_6989586621680156261Sym1 a6989586621680156265 :: Maybe a
type Apply (CatMaybesSym0 :: TyFun [Maybe a] [a] -> Type) (a6989586621679959435 :: [Maybe a])
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (CatMaybesSym0 :: TyFun [Maybe a] [a] -> Type) (a6989586621679959435 :: [Maybe a]) = CatMaybesSym1 a6989586621679959435
type Apply (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> Type) (a6989586621679959441 :: [a])
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> Type) (a6989586621679959441 :: [a]) = ListToMaybeSym1 a6989586621679959441
type Apply (MaybeToListSym0 :: TyFun (Maybe a) [a] -> Type) (a6989586621679959445 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (MaybeToListSym0 :: TyFun (Maybe a) [a] -> Type) (a6989586621679959445 :: Maybe a) = MaybeToListSym1 a6989586621679959445
type Apply (MaxInternalSym0 :: TyFun (Maybe a) (MaxInternal a) -> Type) (a6989586621680812523 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (MaxInternalSym0 :: TyFun (Maybe a) (MaxInternal a) -> Type) (a6989586621680812523 :: Maybe a) = MaxInternalSym1 a6989586621680812523
type Apply (MinInternalSym0 :: TyFun (Maybe a) (MinInternal a) -> Type) (a6989586621680812526 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (MinInternalSym0 :: TyFun (Maybe a) (MinInternal a) -> Type) (a6989586621680812526 :: Maybe a) = MinInternalSym1 a6989586621680812526
type Apply (OptionSym0 :: TyFun (Maybe a) (Option a) -> Type) (a6989586621680250034 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (OptionSym0 :: TyFun (Maybe a) (Option a) -> Type) (a6989586621680250034 :: Maybe a) = OptionSym1 a6989586621680250034
type Apply (FirstSym0 :: TyFun (Maybe a) (First a) -> Type) (a6989586621680694827 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (FirstSym0 :: TyFun (Maybe a) (First a) -> Type) (a6989586621680694827 :: Maybe a) = FirstSym1 a6989586621680694827
type Apply (LastSym0 :: TyFun (Maybe a) (Last a) -> Type) (a6989586621680694854 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (LastSym0 :: TyFun (Maybe a) (Last a) -> Type) (a6989586621680694854 :: Maybe a) = LastSym1 a6989586621680694854
type Apply (GetOptionSym0 :: TyFun (Option a) (Maybe a) -> Type) (a6989586621680250037 :: Option a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (GetOptionSym0 :: TyFun (Option a) (Maybe a) -> Type) (a6989586621680250037 :: Option a) = GetOptionSym1 a6989586621680250037
type Apply (GetFirstSym0 :: TyFun (First a) (Maybe a) -> Type) (a6989586621680694830 :: First a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (GetFirstSym0 :: TyFun (First a) (Maybe a) -> Type) (a6989586621680694830 :: First a) = GetFirstSym1 a6989586621680694830
type Apply (GetLastSym0 :: TyFun (Last a) (Maybe a) -> Type) (a6989586621680694857 :: Last a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (GetLastSym0 :: TyFun (Last a) (Maybe a) -> Type) (a6989586621680694857 :: Last a) = GetLastSym1 a6989586621680694857
type Apply (GetMaxInternalSym0 :: TyFun (MaxInternal a) (Maybe a) -> Type) (a6989586621680812533 :: MaxInternal a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (GetMaxInternalSym0 :: TyFun (MaxInternal a) (Maybe a) -> Type) (a6989586621680812533 :: MaxInternal a) = GetMaxInternalSym1 a6989586621680812533
type Apply (GetMinInternalSym0 :: TyFun (MinInternal a) (Maybe a) -> Type) (a6989586621680812529 :: MinInternal a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (GetMinInternalSym0 :: TyFun (MinInternal a) (Maybe a) -> Type) (a6989586621680812529 :: MinInternal a) = GetMinInternalSym1 a6989586621680812529
type Apply (ElemIndexSym1 a6989586621680379670 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621680379671 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (ElemIndexSym1 a6989586621680379670 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621680379671 :: [a]) = ElemIndexSym2 a6989586621680379670 a6989586621680379671
type Apply (FindIndexSym1 a6989586621680379652 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621680379653 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindIndexSym1 a6989586621680379652 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621680379653 :: [a]) = FindIndexSym2 a6989586621680379652 a6989586621680379653
type Apply (FindSym1 a6989586621680379679 :: TyFun [a] (Maybe a) -> Type) (a6989586621680379680 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindSym1 a6989586621680379679 :: TyFun [a] (Maybe a) -> Type) (a6989586621680379680 :: [a]) = FindSym2 a6989586621680379679 a6989586621680379680
type Apply (StripPrefixSym1 a6989586621680499001 :: TyFun [a] (Maybe [a]) -> Type) (a6989586621680499002 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (StripPrefixSym1 a6989586621680499001 :: TyFun [a] (Maybe [a]) -> Type) (a6989586621680499002 :: [a]) = StripPrefixSym2 a6989586621680499001 a6989586621680499002
type Apply (TFHelper_6989586621680073082Sym1 a6989586621680073087 :: TyFun (Maybe a) (Maybe a) -> Type) (a6989586621680073088 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073082Sym1 a6989586621680073087 :: TyFun (Maybe a) (Maybe a) -> Type) (a6989586621680073088 :: Maybe a) = TFHelper_6989586621680073082Sym2 a6989586621680073087 a6989586621680073088
type Apply (TFHelper_6989586621680240831Sym1 a6989586621680240836 :: TyFun (Maybe a) (Maybe a) -> Type) (a6989586621680240837 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240831Sym1 a6989586621680240836 :: TyFun (Maybe a) (Maybe a) -> Type) (a6989586621680240837 :: Maybe a) = TFHelper_6989586621680240831Sym2 a6989586621680240836 a6989586621680240837
type Apply (OptionalSym0 :: TyFun (f a) (f (Maybe a)) -> Type) (a6989586621681492747 :: f a)
Instance details Defined in Data.Singletons.Prelude.Applicative type Apply (OptionalSym0 :: TyFun (f a) (f (Maybe a)) -> Type) (a6989586621681492747 :: f a) = OptionalSym1 a6989586621681492747
type Apply (LookupSym1 a6989586621680379377 :: TyFun [(a, b)] (Maybe b) -> Type) (a6989586621680379378 :: [(a, b)])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (LookupSym1 a6989586621680379377 :: TyFun [(a, b)] (Maybe b) -> Type) (a6989586621680379378 :: [(a, b)]) = LookupSym2 a6989586621680379377 a6989586621680379378
type Apply (Fmap_6989586621680072701Sym1 a6989586621680072706 :: TyFun (Maybe a) (Maybe b) -> Type) (a6989586621680072707 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Fmap_6989586621680072701Sym1 a6989586621680072706 :: TyFun (Maybe a) (Maybe b) -> Type) (a6989586621680072707 :: Maybe a) = Fmap_6989586621680072701Sym2 a6989586621680072706 a6989586621680072707
type Apply (TFHelper_6989586621680072713Sym1 a6989586621680072718 :: TyFun (Maybe b) (Maybe a) -> Type) (a6989586621680072719 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072713Sym1 a6989586621680072718 :: TyFun (Maybe b) (Maybe a) -> Type) (a6989586621680072719 :: Maybe b) = TFHelper_6989586621680072713Sym2 a6989586621680072718 a6989586621680072719
type Apply (TFHelper_6989586621680072834Sym1 a6989586621680072839 :: TyFun (Maybe a) (Maybe b) -> Type) (a6989586621680072840 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072834Sym1 a6989586621680072839 :: TyFun (Maybe a) (Maybe b) -> Type) (a6989586621680072840 :: Maybe a) = TFHelper_6989586621680072834Sym2 a6989586621680072839 a6989586621680072840
type Apply (TFHelper_6989586621680072861Sym1 a6989586621680072866 :: TyFun (Maybe b) (Maybe b) -> Type) (a6989586621680072867 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072861Sym1 a6989586621680072866 :: TyFun (Maybe b) (Maybe b) -> Type) (a6989586621680072867 :: Maybe b) = TFHelper_6989586621680072861Sym2 a6989586621680072866 a6989586621680072867
type Apply (TFHelper_6989586621680073006Sym1 a6989586621680073015 :: TyFun (Maybe b) (Maybe b) -> Type) (a6989586621680073016 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073006Sym1 a6989586621680073015 :: TyFun (Maybe b) (Maybe b) -> Type) (a6989586621680073016 :: Maybe b) = TFHelper_6989586621680073006Sym2 a6989586621680073015 a6989586621680073016
type Apply (FindSym1 a6989586621680822550 :: TyFun (t a) (Maybe a) -> Type) (a6989586621680822551 :: t a)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FindSym1 a6989586621680822550 :: TyFun (t a) (Maybe a) -> Type) (a6989586621680822551 :: t a) = FindSym2 a6989586621680822550 a6989586621680822551
type Apply (Traverse_6989586621681088303Sym1 a6989586621681088308 :: TyFun (Maybe a) (f (Maybe b)) -> Type) (a6989586621681088309 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Traversable type Apply (Traverse_6989586621681088303Sym1 a6989586621681088308 :: TyFun (Maybe a) (f (Maybe b)) -> Type) (a6989586621681088309 :: Maybe a) = Traverse_6989586621681088303Sym2 a6989586621681088308 a6989586621681088309
type Apply (LiftA2_6989586621680072847Sym2 a6989586621680072853 a6989586621680072854 :: TyFun (Maybe b) (Maybe c) -> Type) (a6989586621680072855 :: Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (LiftA2_6989586621680072847Sym2 a6989586621680072853 a6989586621680072854 :: TyFun (Maybe b) (Maybe c) -> Type) (a6989586621680072855 :: Maybe b) = LiftA2_6989586621680072847Sym3 a6989586621680072853 a6989586621680072854 a6989586621680072855
type Apply (Let6989586621680822944MfSym3 f6989586621680822942 xs6989586621680822943 a6989586621680822945 :: TyFun (Maybe k3) (Maybe k2) -> Type) (a6989586621680822946 :: Maybe k3)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822944MfSym3 f6989586621680822942 xs6989586621680822943 a6989586621680822945 :: TyFun (Maybe k3) (Maybe k2) -> Type) (a6989586621680822946 :: Maybe k3) = Let6989586621680822944MfSym4 f6989586621680822942 xs6989586621680822943 a6989586621680822945 a6989586621680822946
type Apply (StripPrefixSym0 :: TyFun [a] ([a] ~> Maybe [a]) -> Type) (a6989586621680499001 :: [a])
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (StripPrefixSym0 :: TyFun [a] ([a] ~> Maybe [a]) -> Type) (a6989586621680499001 :: [a]) = StripPrefixSym1 a6989586621680499001
type Apply (TFHelper_6989586621680073082Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) (a6989586621680073087 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073082Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) (a6989586621680073087 :: Maybe a) = TFHelper_6989586621680073082Sym1 a6989586621680073087
type Apply (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type) (a6989586621679848513 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type) (a6989586621679848513 :: Maybe a) = Compare_6989586621679848508Sym1 a6989586621679848513
type Apply (TFHelper_6989586621680240831Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) (a6989586621680240836 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240831Sym0 :: TyFun (Maybe a) (Maybe a ~> Maybe a) -> Type) (a6989586621680240836 :: Maybe a) = TFHelper_6989586621680240831Sym1 a6989586621680240836
type Apply (ShowsPrec_6989586621680653944Sym1 a6989586621680653954 :: TyFun (Maybe a) (Symbol ~> Symbol) -> Type) (a6989586621680653955 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680653944Sym1 a6989586621680653954 :: TyFun (Maybe a) (Symbol ~> Symbol) -> Type) (a6989586621680653955 :: Maybe a) = ShowsPrec_6989586621680653944Sym2 a6989586621680653954 a6989586621680653955
type Apply (TFHelper_6989586621680072861Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type) (a6989586621680072866 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072861Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type) (a6989586621680072866 :: Maybe a) = TFHelper_6989586621680072861Sym1 a6989586621680072866 :: TyFun (Maybe b) (Maybe b) -> Type
type Apply (TFHelper_6989586621680072995Sym0 :: TyFun (Maybe a) ((a ~> Maybe b) ~> Maybe b) -> Type) (a6989586621680073000 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072995Sym0 :: TyFun (Maybe a) ((a ~> Maybe b) ~> Maybe b) -> Type) (a6989586621680073000 :: Maybe a) = TFHelper_6989586621680072995Sym1 a6989586621680073000 :: TyFun (a ~> Maybe b) (Maybe b) -> Type
type Apply (TFHelper_6989586621680073006Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type) (a6989586621680073015 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073006Sym0 :: TyFun (Maybe a) (Maybe b ~> Maybe b) -> Type) (a6989586621680073015 :: Maybe a) = TFHelper_6989586621680073006Sym1 a6989586621680073015 :: TyFun (Maybe b) (Maybe b) -> Type
type Apply (TFHelper_6989586621680072834Sym0 :: TyFun (Maybe (a ~> b)) (Maybe a ~> Maybe b) -> Type) (a6989586621680072839 :: Maybe (a ~> b))
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072834Sym0 :: TyFun (Maybe (a ~> b)) (Maybe a ~> Maybe b) -> Type) (a6989586621680072839 :: Maybe (a ~> b)) = TFHelper_6989586621680072834Sym1 a6989586621680072839
type Apply (LiftA2_6989586621680072847Sym1 a6989586621680072853 :: TyFun (Maybe a) (Maybe b ~> Maybe c) -> Type) (a6989586621680072854 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (LiftA2_6989586621680072847Sym1 a6989586621680072853 :: TyFun (Maybe a) (Maybe b ~> Maybe c) -> Type) (a6989586621680072854 :: Maybe a) = LiftA2_6989586621680072847Sym2 a6989586621680072853 a6989586621680072854
type Apply (Let6989586621680822965MfSym2 f6989586621680822963 xs6989586621680822964 :: TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) (a6989586621680822966 :: Maybe k2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822965MfSym2 f6989586621680822963 xs6989586621680822964 :: TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) (a6989586621680822966 :: Maybe k2) = Let6989586621680822965MfSym3 f6989586621680822963 xs6989586621680822964 a6989586621680822966
type Apply (TFHelper_6989586621680072995Sym1 a6989586621680073000 :: TyFun (a ~> Maybe b) (Maybe b) -> Type) (a6989586621680073001 :: a ~> Maybe b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072995Sym1 a6989586621680073000 :: TyFun (a ~> Maybe b) (Maybe b) -> Type) (a6989586621680073001 :: a ~> Maybe b) = TFHelper_6989586621680072995Sym2 a6989586621680073000 a6989586621680073001
type Apply (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type) (a6989586621680379652 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type) (a6989586621680379652 :: a ~> Bool) = FindIndexSym1 a6989586621680379652
type Apply (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type) (a6989586621680379679 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (FindSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe a) -> Type) (a6989586621680379679 :: a ~> Bool) = FindSym1 a6989586621680379679
type Apply (Fmap_6989586621680072701Sym0 :: TyFun (a ~> b) (Maybe a ~> Maybe b) -> Type) (a6989586621680072706 :: a ~> b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Fmap_6989586621680072701Sym0 :: TyFun (a ~> b) (Maybe a ~> Maybe b) -> Type) (a6989586621680072706 :: a ~> b) = Fmap_6989586621680072701Sym1 a6989586621680072706
type Apply (MapMaybeSym0 :: TyFun (a ~> Maybe b) ([a] ~> [b]) -> Type) (a6989586621679959420 :: a ~> Maybe b)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (MapMaybeSym0 :: TyFun (a ~> Maybe b) ([a] ~> [b]) -> Type) (a6989586621679959420 :: a ~> Maybe b) = MapMaybeSym1 a6989586621679959420
type Apply (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type) (a6989586621680822550 :: a ~> Bool)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FindSym0 :: TyFun (a ~> Bool) (t a ~> Maybe a) -> Type) (a6989586621680822550 :: a ~> Bool) = FindSym1 a6989586621680822550 :: TyFun (t a) (Maybe a) -> Type
type Apply (FoldMap_6989586621680823084Sym0 :: TyFun (a ~> m) (Maybe a ~> m) -> Type) (a6989586621680823093 :: a ~> m)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FoldMap_6989586621680823084Sym0 :: TyFun (a ~> m) (Maybe a ~> m) -> Type) (a6989586621680823093 :: a ~> m) = FoldMap_6989586621680823084Sym1 a6989586621680823093
type Apply (Foldr_6989586621680823100Sym0 :: TyFun (a ~> (b ~> b)) (b ~> (Maybe a ~> b)) -> Type) (a6989586621680823106 :: a ~> (b ~> b))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823100Sym0 :: TyFun (a ~> (b ~> b)) (b ~> (Maybe a ~> b)) -> Type) (a6989586621680823106 :: a ~> (b ~> b)) = Foldr_6989586621680823100Sym1 a6989586621680823106
type Apply (Foldl_6989586621680823116Sym0 :: TyFun (b ~> (a ~> b)) (b ~> (Maybe a ~> b)) -> Type) (a6989586621680823122 :: b ~> (a ~> b))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldl_6989586621680823116Sym0 :: TyFun (b ~> (a ~> b)) (b ~> (Maybe a ~> b)) -> Type) (a6989586621680823122 :: b ~> (a ~> b)) = Foldl_6989586621680823116Sym1 a6989586621680823122
type Apply (UnfoldrSym0 :: TyFun (b ~> Maybe (a, b)) (b ~> [a]) -> Type) (a6989586621680380069 :: b ~> Maybe (a, b))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (UnfoldrSym0 :: TyFun (b ~> Maybe (a, b)) (b ~> [a]) -> Type) (a6989586621680380069 :: b ~> Maybe (a, b)) = UnfoldrSym1 a6989586621680380069
type Apply (Traverse_6989586621681088303Sym0 :: TyFun (a ~> f b) (Maybe a ~> f (Maybe b)) -> Type) (a6989586621681088308 :: a ~> f b)
Instance details Defined in Data.Singletons.Prelude.Traversable type Apply (Traverse_6989586621681088303Sym0 :: TyFun (a ~> f b) (Maybe a ~> f (Maybe b)) -> Type) (a6989586621681088308 :: a ~> f b) = Traverse_6989586621681088303Sym1 a6989586621681088308
type Apply (LiftA2_6989586621680072847Sym0 :: TyFun (a ~> (b ~> c)) (Maybe a ~> (Maybe b ~> Maybe c)) -> Type) (a6989586621680072853 :: a ~> (b ~> c))
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (LiftA2_6989586621680072847Sym0 :: TyFun (a ~> (b ~> c)) (Maybe a ~> (Maybe b ~> Maybe c)) -> Type) (a6989586621680072853 :: a ~> (b ~> c)) = LiftA2_6989586621680072847Sym1 a6989586621680072853
type Apply (Maybe_Sym1 a6989586621679957884 :: TyFun (a ~> b) (Maybe a ~> b) -> Type) (a6989586621679957885 :: a ~> b)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (Maybe_Sym1 a6989586621679957884 :: TyFun (a ~> b) (Maybe a ~> b) -> Type) (a6989586621679957885 :: a ~> b) = Maybe_Sym2 a6989586621679957884 a6989586621679957885
type Apply (Let6989586621679959425RsSym0 :: TyFun (a ~> Maybe k1) (TyFun k (TyFun [a] [k1] -> Type) -> Type) -> Type) (f6989586621679959422 :: a ~> Maybe k1)
Instance details Defined in Data.Singletons.Prelude.Maybe type Apply (Let6989586621679959425RsSym0 :: TyFun (a ~> Maybe k1) (TyFun k (TyFun [a] [k1] -> Type) -> Type) -> Type) (f6989586621679959422 :: a ~> Maybe k1) = Let6989586621679959425RsSym1 f6989586621679959422 :: TyFun k (TyFun [a] [k1] -> Type) -> Type
type Apply (Let6989586621680822944MfSym0 :: TyFun (k2 ~> (k3 ~> k2)) (TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type) -> Type) (f6989586621680822942 :: k2 ~> (k3 ~> k2))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822944MfSym0 :: TyFun (k2 ~> (k3 ~> k2)) (TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type) -> Type) (f6989586621680822942 :: k2 ~> (k3 ~> k2)) = Let6989586621680822944MfSym1 f6989586621680822942 :: TyFun k (TyFun k2 (TyFun (Maybe k3) (Maybe k2) -> Type) -> Type) -> Type
type Apply (Let6989586621680822965MfSym0 :: TyFun (k2 ~> (k3 ~> k3)) (TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type) -> Type) (f6989586621680822963 :: k2 ~> (k3 ~> k3))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822965MfSym0 :: TyFun (k2 ~> (k3 ~> k3)) (TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type) -> Type) (f6989586621680822963 :: k2 ~> (k3 ~> k3)) = Let6989586621680822965MfSym1 f6989586621680822963 :: TyFun k (TyFun (Maybe k2) (TyFun k3 (Maybe k3) -> Type) -> Type) -> Type
type Apply (Lambda_6989586621680701053Sym1 a6989586621680701051 :: TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type) (k6989586621680701052 :: k1 ~> First a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701053Sym1 a6989586621680701051 :: TyFun (k1 ~> First a) (TyFun k1 (Maybe a) -> Type) -> Type) (k6989586621680701052 :: k1 ~> First a) = Lambda_6989586621680701053Sym2 a6989586621680701051 k6989586621680701052
type Apply (Lambda_6989586621680701132Sym1 a6989586621680701130 :: TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type) (k6989586621680701131 :: k1 ~> Last a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Lambda_6989586621680701132Sym1 a6989586621680701130 :: TyFun (k1 ~> Last a) (TyFun k1 (Maybe a) -> Type) -> Type) (k6989586621680701131 :: k1 ~> Last a) = Lambda_6989586621680701132Sym2 a6989586621680701130 k6989586621680701131

data Ordering #

Constructors

LT
EQ
GT

Instances

Instances details

Bounded Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering # maxBound :: Ordering #
Enum Ordering	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Ordering -> Ordering # pred :: Ordering -> Ordering # toEnum :: Int -> Ordering # fromEnum :: Ordering -> Int # enumFrom :: Ordering -> [Ordering] # enumFromThen :: Ordering -> Ordering -> [Ordering] # enumFromTo :: Ordering -> Ordering -> [Ordering] # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] #
Eq Ordering
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool # (/=) :: Ordering -> Ordering -> Bool #
Ord Ordering
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering # (<) :: Ordering -> Ordering -> Bool # (<=) :: Ordering -> Ordering -> Bool # (>) :: Ordering -> Ordering -> Bool # (>=) :: Ordering -> Ordering -> Bool # max :: Ordering -> Ordering -> Ordering # min :: Ordering -> Ordering -> Ordering #
Read Ordering	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering # readList :: ReadS [Ordering] # readPrec :: ReadPrec Ordering # readListPrec :: ReadPrec [Ordering] #
Show Ordering	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS # show :: Ordering -> String # showList :: [Ordering] -> ShowS #
Ix Ordering	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Ordering, Ordering) -> [Ordering] # index :: (Ordering, Ordering) -> Ordering -> Int # unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int # inRange :: (Ordering, Ordering) -> Ordering -> Bool # rangeSize :: (Ordering, Ordering) -> Int # unsafeRangeSize :: (Ordering, Ordering) -> Int #
Generic Ordering	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep Ordering :: Type -> Type # Methods from :: Ordering -> Rep Ordering x # to :: Rep Ordering x -> Ordering #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Hashable Ordering
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ordering -> Int # hash :: Ordering -> Int #
NFData Ordering
Instance details Defined in Control.DeepSeq Methods rnf :: Ordering -> () #
AsEmpty Ordering
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Ordering ()
SBounded Ordering
Instance details Defined in Data.Singletons.Prelude.Enum Methods sMinBound :: Sing MinBoundSym0 sMaxBound :: Sing MaxBoundSym0
SEnum Ordering
Instance details Defined in Data.Singletons.Prelude.Enum Methods sSucc :: forall (t :: Ordering). Sing t -> Sing (Apply SuccSym0 t) sPred :: forall (t :: Ordering). Sing t -> Sing (Apply PredSym0 t) sToEnum :: forall (t :: Nat). Sing t -> Sing (Apply ToEnumSym0 t) sFromEnum :: forall (t :: Ordering). Sing t -> Sing (Apply FromEnumSym0 t) sEnumFromTo :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply EnumFromToSym0 t1) t2) sEnumFromThenTo :: forall (t1 :: Ordering) (t2 :: Ordering) (t3 :: Ordering). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply EnumFromThenToSym0 t1) t2) t3)
SEq Ordering
Instance details Defined in Data.Singletons.Prelude.Eq Methods (%==) :: forall (a :: Ordering) (b :: Ordering). Sing a -> Sing b -> Sing (a == b) (%/=) :: forall (a :: Ordering) (b :: Ordering). Sing a -> Sing b -> Sing (a /= b)
SMonoid Ordering
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sMempty :: Sing MemptySym0 sMappend :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply MappendSym0 t1) t2) sMconcat :: forall (t :: [Ordering]). Sing t -> Sing (Apply MconcatSym0 t)
SSemigroup Ordering
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%<>) :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sSconcat :: forall (t :: NonEmpty Ordering). Sing t -> Sing (Apply SconcatSym0 t)
SOrd Ordering
Instance details Defined in Data.Singletons.Prelude.Ord Methods sCompare :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply CompareSym0 t1) t2) (%<) :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2) (%<=) :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<=@#@$) t1) t2) (%>) :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%>=) :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>=@#@$) t1) t2) sMax :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply MaxSym0 t1) t2) sMin :: forall (t1 :: Ordering) (t2 :: Ordering). Sing t1 -> Sing t2 -> Sing (Apply (Apply MinSym0 t1) t2)
PSemigroup Ordering
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Associated Types type arg <> arg1 :: a type Sconcat arg :: a
PEnum Ordering
Instance details Defined in Data.Singletons.Prelude.Enum Associated Types type Succ arg :: a type Pred arg :: a type ToEnum arg :: a type FromEnum arg :: Nat type EnumFromTo arg arg1 :: [a] type EnumFromThenTo arg arg1 arg2 :: [a]
PEq Ordering
Instance details Defined in Data.Singletons.Prelude.Eq Associated Types type x == y :: Bool type x /= y :: Bool
PMonoid Ordering
Instance details Defined in Data.Singletons.Prelude.Monoid Associated Types type Mempty :: a type Mappend arg arg1 :: a type Mconcat arg :: a
POrd Ordering
Instance details Defined in Data.Singletons.Prelude.Ord Associated Types type Compare arg arg1 :: Ordering type arg < arg1 :: Bool type arg <= arg1 :: Bool type arg > arg1 :: Bool type arg >= arg1 :: Bool type Max arg arg1 :: a type Min arg arg1 :: a
PShow Ordering
Instance details Defined in Data.Singletons.Prelude.Show Associated Types type ShowsPrec arg arg1 arg2 :: Symbol type Show_ arg :: Symbol type ShowList arg arg1 :: Symbol
SShow Ordering
Instance details Defined in Data.Singletons.Prelude.Show Methods sShowsPrec :: forall (t1 :: Nat) (t2 :: Ordering) (t3 :: Symbol). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply ShowsPrecSym0 t1) t2) t3) sShow_ :: forall (t :: Ordering). Sing t -> Sing (Apply Show_Sym0 t) sShowList :: forall (t1 :: [Ordering]) (t2 :: Symbol). Sing t1 -> Sing t2 -> Sing (Apply (Apply ShowListSym0 t1) t2)
PBounded Ordering
Instance details Defined in Data.Singletons.Prelude.Enum Associated Types type MinBound :: a type MaxBound :: a
TestCoercion SOrdering
Instance details Defined in Data.Singletons.Prelude.Instances Methods testCoercion :: forall (a :: k) (b :: k). SOrdering a -> SOrdering b -> Maybe (Coercion a b) #
TestEquality SOrdering
Instance details Defined in Data.Singletons.Prelude.Instances Methods testEquality :: forall (a :: k) (b :: k). SOrdering a -> SOrdering b -> Maybe (a :~: b) #
SingI ThenCmpSym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ThenCmpSym0 #
SuppressUnusedWarnings Compare_6989586621679849009Sym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings FromEnum_6989586621680204277Sym0
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ThenCmpSym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings TFHelper_6989586621680240821Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621679849018Sym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ToEnum_6989586621680204261Sym0
Instance details Defined in Data.Singletons.Prelude.Enum Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings ShowsPrec_6989586621680654084Sym0
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621679849027Sym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621679848629Sym0
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621680260883Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings Compare_6989586621680260900Sym0
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SingI d => SingI (ThenCmpSym1 d :: TyFun Ordering Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (ThenCmpSym1 d) #
SOrd a => SingI (CompareSym0 :: TyFun a (a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing CompareSym0 #
SingI (ListsortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods sing :: Sing ListsortBySym0 #
SingI (SortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing SortBySym0 #
SingI (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing MinimumBySym0 #
SingI (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing MaximumBySym0 #
SingI (InsertBySym0 :: TyFun (a ~> (a ~> Ordering)) (a ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods sing :: Sing InsertBySym0 #
SuppressUnusedWarnings (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848539Sym0 :: TyFun [a] ([a] ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240821Sym1 a6989586621680240826 :: TyFun Ordering Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ThenCmpSym1 a6989586621679848140 :: TyFun Ordering Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679849018Sym1 a6989586621679849023 :: TyFun Ordering Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ShowsPrec_6989586621680654084Sym1 a6989586621680654096 :: TyFun Ordering (Symbol ~> Symbol) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679849027Sym1 a6989586621679849032 :: TyFun () Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837504Scrutinee_6989586621679837360Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837488Scrutinee_6989586621679837358Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837472Scrutinee_6989586621679837356Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837456Scrutinee_6989586621679837354Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679837426Sym0 :: TyFun a (a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (CompareSym0 :: TyFun a (a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848629Sym1 a6989586621679848634 :: TyFun Void Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260960Sym0 :: TyFun (Min a) (Min a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260980Sym0 :: TyFun (Max a) (Max a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261000Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261020Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261040Sym0 :: TyFun (WrappedMonoid m) (WrappedMonoid m ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260846Sym0 :: TyFun (Option a) (Option a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848996Sym0 :: TyFun (Identity a) (Identity a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680696778Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680696798Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260866Sym0 :: TyFun (Dual a) (Dual a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260883Sym1 a6989586621680260888 :: TyFun All Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260900Sym1 a6989586621680260905 :: TyFun Any Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260920Sym0 :: TyFun (Sum a) (Sum a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260940Sym0 :: TyFun (Product a) (Product a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848612Sym0 :: TyFun (NonEmpty a) (NonEmpty a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ListsortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (SortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (InsertBySym0 :: TyFun (a ~> (a ~> Ordering)) (a ~> ([a] ~> [a])) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
(SOrd a, SingI d) => SingI (CompareSym1 d :: TyFun a Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (CompareSym1 d) #
SFoldable t => SingI (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing MinimumBySym0 #
SFoldable t => SingI (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sing :: Sing MaximumBySym0 #
SOrd a => SingI (ComparingSym0 :: TyFun (b ~> a) (b ~> (b ~> Ordering)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing ComparingSym0 #
SuppressUnusedWarnings (Compare_6989586621679848539Sym1 a6989586621679848544 :: TyFun [a] Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848652Sym0 :: TyFun (a, b) ((a, b) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837504Scrutinee_6989586621679837360Sym1 x6989586621679837502 :: TyFun k1 Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837488Scrutinee_6989586621679837358Sym1 x6989586621679837486 :: TyFun k1 Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837472Scrutinee_6989586621679837356Sym1 x6989586621679837470 :: TyFun k1 Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621679837456Scrutinee_6989586621679837354Sym1 x6989586621679837454 :: TyFun k1 Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679837426Sym1 a6989586621679837431 :: TyFun a Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (CompareSym1 a6989586621679837392 :: TyFun a Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260960Sym1 a6989586621680260965 :: TyFun (Min a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260980Sym1 a6989586621680260985 :: TyFun (Max a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621681203650Sym0 :: TyFun (Arg a b) (Arg a b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261000Sym1 a6989586621680261005 :: TyFun (First a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261020Sym1 a6989586621680261025 :: TyFun (Last a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680261040Sym1 a6989586621680261045 :: TyFun (WrappedMonoid m) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260846Sym1 a6989586621680260851 :: TyFun (Option a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848996Sym1 a6989586621679849001 :: TyFun (Identity a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680696778Sym1 a6989586621680696783 :: TyFun (First a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680696798Sym1 a6989586621680696803 :: TyFun (Last a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260866Sym1 a6989586621680260871 :: TyFun (Dual a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260920Sym1 a6989586621680260925 :: TyFun (Sum a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680260940Sym1 a6989586621680260945 :: TyFun (Product a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680787223Sym0 :: TyFun (Proxy s) (Proxy s ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848612Sym1 a6989586621679848617 :: TyFun (NonEmpty a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822601Max'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680822581Min'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ComparingSym0 :: TyFun (b ~> a) (b ~> (b ~> Ordering)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
(SOrd a, SingI d) => SingI (ComparingSym1 d :: TyFun b (b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (ComparingSym1 d) #
SuppressUnusedWarnings (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848652Sym1 a6989586621679848657 :: TyFun (a, b) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848690Sym0 :: TyFun (a, b, c) ((a, b, c) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ComparingSym1 a6989586621679837383 :: TyFun b (b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621681203650Sym1 a6989586621681203655 :: TyFun (Arg a b) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621681044522Sym0 :: TyFun (Const a b) (Const a b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Const Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621680787223Sym1 a6989586621680787228 :: TyFun (Proxy s) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Proxy Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379728MaxBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680379707MinBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type)
Instance details Defined in Data.Singletons.Prelude.List.Internal Methods suppressUnusedWarnings :: ()
(SOrd a, SingI d1, SingI d2) => SingI (ComparingSym2 d1 d2 :: TyFun b Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing (ComparingSym2 d1 d2) #
SuppressUnusedWarnings (Compare_6989586621679848690Sym1 a6989586621679848695 :: TyFun (a, b, c) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848739Sym0 :: TyFun (a, b, c, d) ((a, b, c, d) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ComparingSym2 a6989586621679837383 a6989586621679837384 :: TyFun b Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621681044522Sym1 a6989586621681044527 :: TyFun (Const a b) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Const Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848739Sym1 a6989586621679848744 :: TyFun (a, b, c, d) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848799Sym0 :: TyFun (a, b, c, d, e) ((a, b, c, d, e) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848799Sym1 a6989586621679848804 :: TyFun (a, b, c, d, e) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848870Sym0 :: TyFun (a, b, c, d, e, f) ((a, b, c, d, e, f) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848870Sym1 a6989586621679848875 :: TyFun (a, b, c, d, e, f) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848952Sym0 :: TyFun (a, b, c, d, e, f, g) ((a, b, c, d, e, f, g) ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848952Sym1 a6989586621679848957 :: TyFun (a, b, c, d, e, f, g) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
type Rep Ordering
Instance details Defined in GHC.Generics type Rep Ordering = D1 ('MetaData "Ordering" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "LT" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "EQ" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "GT" 'PrefixI 'False) (U1 :: Type -> Type)))
type Sing
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SOrdering
type Demote Ordering
Instance details Defined in Data.Singletons.Prelude.Instances type Demote Ordering = Ordering
type MaxBound
Instance details Defined in Data.Singletons.Prelude.Enum type MaxBound = MaxBound_6989586621680176883Sym0
type MinBound
Instance details Defined in Data.Singletons.Prelude.Enum type MinBound = MinBound_6989586621680176880Sym0
type Mempty
Instance details Defined in Data.Singletons.Prelude.Monoid type Mempty = Mempty_6989586621680691429Sym0
type FromEnum (a :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type FromEnum (a :: Ordering) = Apply FromEnum_6989586621680204277Sym0 a
type Pred (arg :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type Pred (arg :: Ordering) = Apply (Pred_6989586621680181017Sym0 :: TyFun Ordering Ordering -> Type) arg
type Succ (arg :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type Succ (arg :: Ordering) = Apply (Succ_6989586621680181004Sym0 :: TyFun Ordering Ordering -> Type) arg
type ToEnum a
Instance details Defined in Data.Singletons.Prelude.Enum type ToEnum a = Apply ToEnum_6989586621680204261Sym0 a
type Sconcat (arg :: NonEmpty Ordering)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sconcat (arg :: NonEmpty Ordering) = Apply (Sconcat_6989586621680240682Sym0 :: TyFun (NonEmpty Ordering) Ordering -> Type) arg
type Mconcat (arg :: [Ordering])
Instance details Defined in Data.Singletons.Prelude.Monoid type Mconcat (arg :: [Ordering]) = Apply (Mconcat_6989586621680691385Sym0 :: TyFun [Ordering] Ordering -> Type) arg
type Show_ (arg :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Show type Show_ (arg :: Ordering) = Apply (Show__6989586621680636786Sym0 :: TyFun Ordering Symbol -> Type) arg
type EnumFromTo (arg1 :: Ordering) (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type EnumFromTo (arg1 :: Ordering) (arg2 :: Ordering) = Apply (Apply (EnumFromTo_6989586621680181027Sym0 :: TyFun Ordering (Ordering ~> [Ordering]) -> Type) arg1) arg2
type (x :: Ordering) /= (y :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Eq type (x :: Ordering) /= (y :: Ordering) = Not (x == y)
type (a :: Ordering) == (b :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Eq type (a :: Ordering) == (b :: Ordering) = Equals_6989586621679820693 a b
type (a1 :: Ordering) <> (a2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type (a1 :: Ordering) <> (a2 :: Ordering) = Apply (Apply TFHelper_6989586621680240821Sym0 a1) a2
type Mappend (arg1 :: Ordering) (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Monoid type Mappend (arg1 :: Ordering) (arg2 :: Ordering) = Apply (Apply (Mappend_6989586621680691371Sym0 :: TyFun Ordering (Ordering ~> Ordering) -> Type) arg1) arg2
type Max (arg1 :: Ordering) (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Max (arg1 :: Ordering) (arg2 :: Ordering) = Apply (Apply (Max_6989586621679837511Sym0 :: TyFun Ordering (Ordering ~> Ordering) -> Type) arg1) arg2
type Min (arg1 :: Ordering) (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Min (arg1 :: Ordering) (arg2 :: Ordering) = Apply (Apply (Min_6989586621679837527Sym0 :: TyFun Ordering (Ordering ~> Ordering) -> Type) arg1) arg2
type Compare (a1 :: Ordering) (a2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Compare (a1 :: Ordering) (a2 :: Ordering) = Apply (Apply Compare_6989586621679849018Sym0 a1) a2
type (arg1 :: Ordering) <= (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Ordering) <= (arg2 :: Ordering) = Apply (Apply (TFHelper_6989586621679837463Sym0 :: TyFun Ordering (Ordering ~> Bool) -> Type) arg1) arg2
type (arg1 :: Ordering) < (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Ordering) < (arg2 :: Ordering) = Apply (Apply (TFHelper_6989586621679837447Sym0 :: TyFun Ordering (Ordering ~> Bool) -> Type) arg1) arg2
type (arg1 :: Ordering) >= (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Ordering) >= (arg2 :: Ordering) = Apply (Apply (TFHelper_6989586621679837495Sym0 :: TyFun Ordering (Ordering ~> Bool) -> Type) arg1) arg2
type (arg1 :: Ordering) > (arg2 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Ordering) > (arg2 :: Ordering) = Apply (Apply (TFHelper_6989586621679837479Sym0 :: TyFun Ordering (Ordering ~> Bool) -> Type) arg1) arg2
type ShowList (arg1 :: [Ordering]) arg2
Instance details Defined in Data.Singletons.Prelude.Show type ShowList (arg1 :: [Ordering]) arg2 = Apply (Apply (ShowList_6989586621680636794Sym0 :: TyFun [Ordering] (Symbol ~> Symbol) -> Type) arg1) arg2
type Apply FromEnum_6989586621680204277Sym0 (a6989586621680204281 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply FromEnum_6989586621680204277Sym0 (a6989586621680204281 :: Ordering) = FromEnum_6989586621680204277Sym1 a6989586621680204281
type Apply ToEnum_6989586621680204261Sym0 (a6989586621680204265 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Enum type Apply ToEnum_6989586621680204261Sym0 (a6989586621680204265 :: Nat) = ToEnum_6989586621680204261Sym1 a6989586621680204265
type EnumFromThenTo (arg1 :: Ordering) (arg2 :: Ordering) (arg3 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Enum type EnumFromThenTo (arg1 :: Ordering) (arg2 :: Ordering) (arg3 :: Ordering) = Apply (Apply (Apply (EnumFromThenTo_6989586621680181039Sym0 :: TyFun Ordering (Ordering ~> (Ordering ~> [Ordering])) -> Type) arg1) arg2) arg3
type ShowsPrec a1 (a2 :: Ordering) a3
Instance details Defined in Data.Singletons.Prelude.Show type ShowsPrec a1 (a2 :: Ordering) a3 = Apply (Apply (Apply ShowsPrec_6989586621680654084Sym0 a1) a2) a3
type Apply (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type) (a6989586621679849015 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679849009Sym1 a6989586621679849014 :: TyFun Bool Ordering -> Type) (a6989586621679849015 :: Bool) = Compare_6989586621679849009Sym2 a6989586621679849014 a6989586621679849015
type Apply (TFHelper_6989586621680240821Sym1 a6989586621680240826 :: TyFun Ordering Ordering -> Type) (a6989586621680240827 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240821Sym1 a6989586621680240826 :: TyFun Ordering Ordering -> Type) (a6989586621680240827 :: Ordering) = TFHelper_6989586621680240821Sym2 a6989586621680240826 a6989586621680240827
type Apply (ThenCmpSym1 a6989586621679848140 :: TyFun Ordering Ordering -> Type) (a6989586621679848141 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (ThenCmpSym1 a6989586621679848140 :: TyFun Ordering Ordering -> Type) (a6989586621679848141 :: Ordering) = ThenCmpSym2 a6989586621679848140 a6989586621679848141
type Apply (Compare_6989586621679849018Sym1 a6989586621679849023 :: TyFun Ordering Ordering -> Type) (a6989586621679849024 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679849018Sym1 a6989586621679849023 :: TyFun Ordering Ordering -> Type) (a6989586621679849024 :: Ordering) = Compare_6989586621679849018Sym2 a6989586621679849023 a6989586621679849024
type Apply (Compare_6989586621679849027Sym1 a6989586621679849032 :: TyFun () Ordering -> Type) (a6989586621679849033 :: ())
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679849027Sym1 a6989586621679849032 :: TyFun () Ordering -> Type) (a6989586621679849033 :: ()) = Compare_6989586621679849027Sym2 a6989586621679849032 a6989586621679849033
type Apply (Compare_6989586621679848629Sym1 a6989586621679848634 :: TyFun Void Ordering -> Type) (a6989586621679848635 :: Void)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848629Sym1 a6989586621679848634 :: TyFun Void Ordering -> Type) (a6989586621679848635 :: Void) = Compare_6989586621679848629Sym2 a6989586621679848634 a6989586621679848635
type Apply (Compare_6989586621680260883Sym1 a6989586621680260888 :: TyFun All Ordering -> Type) (a6989586621680260889 :: All)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260883Sym1 a6989586621680260888 :: TyFun All Ordering -> Type) (a6989586621680260889 :: All) = Compare_6989586621680260883Sym2 a6989586621680260888 a6989586621680260889
type Apply (Compare_6989586621680260900Sym1 a6989586621680260905 :: TyFun Any Ordering -> Type) (a6989586621680260906 :: Any)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260900Sym1 a6989586621680260905 :: TyFun Any Ordering -> Type) (a6989586621680260906 :: Any) = Compare_6989586621680260900Sym2 a6989586621680260905 a6989586621680260906
type Apply (Compare_6989586621679837426Sym1 a6989586621679837431 :: TyFun a Ordering -> Type) (a6989586621679837432 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679837426Sym1 a6989586621679837431 :: TyFun a Ordering -> Type) (a6989586621679837432 :: a) = Compare_6989586621679837426Sym2 a6989586621679837431 a6989586621679837432
type Apply (CompareSym1 a6989586621679837392 :: TyFun a Ordering -> Type) (a6989586621679837393 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (CompareSym1 a6989586621679837392 :: TyFun a Ordering -> Type) (a6989586621679837393 :: a) = CompareSym2 a6989586621679837392 a6989586621679837393
type Apply (Let6989586621679837504Scrutinee_6989586621679837360Sym1 x6989586621679837502 :: TyFun k1 Ordering -> Type) (y6989586621679837503 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837504Scrutinee_6989586621679837360Sym1 x6989586621679837502 :: TyFun k1 Ordering -> Type) (y6989586621679837503 :: k1) = Let6989586621679837504Scrutinee_6989586621679837360Sym2 x6989586621679837502 y6989586621679837503
type Apply (Let6989586621679837488Scrutinee_6989586621679837358Sym1 x6989586621679837486 :: TyFun k1 Ordering -> Type) (y6989586621679837487 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837488Scrutinee_6989586621679837358Sym1 x6989586621679837486 :: TyFun k1 Ordering -> Type) (y6989586621679837487 :: k1) = Let6989586621679837488Scrutinee_6989586621679837358Sym2 x6989586621679837486 y6989586621679837487
type Apply (Let6989586621679837472Scrutinee_6989586621679837356Sym1 x6989586621679837470 :: TyFun k1 Ordering -> Type) (y6989586621679837471 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837472Scrutinee_6989586621679837356Sym1 x6989586621679837470 :: TyFun k1 Ordering -> Type) (y6989586621679837471 :: k1) = Let6989586621679837472Scrutinee_6989586621679837356Sym2 x6989586621679837470 y6989586621679837471
type Apply (Let6989586621679837456Scrutinee_6989586621679837354Sym1 x6989586621679837454 :: TyFun k1 Ordering -> Type) (y6989586621679837455 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837456Scrutinee_6989586621679837354Sym1 x6989586621679837454 :: TyFun k1 Ordering -> Type) (y6989586621679837455 :: k1) = Let6989586621679837456Scrutinee_6989586621679837354Sym2 x6989586621679837454 y6989586621679837455
type Apply (ComparingSym2 a6989586621679837383 a6989586621679837384 :: TyFun b Ordering -> Type) (a6989586621679837385 :: b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (ComparingSym2 a6989586621679837383 a6989586621679837384 :: TyFun b Ordering -> Type) (a6989586621679837385 :: b) = ComparingSym3 a6989586621679837383 a6989586621679837384 a6989586621679837385
type Apply Compare_6989586621679849009Sym0 (a6989586621679849014 :: Bool)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply Compare_6989586621679849009Sym0 (a6989586621679849014 :: Bool) = Compare_6989586621679849009Sym1 a6989586621679849014
type Apply ThenCmpSym0 (a6989586621679848140 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply ThenCmpSym0 (a6989586621679848140 :: Ordering) = ThenCmpSym1 a6989586621679848140
type Apply TFHelper_6989586621680240821Sym0 (a6989586621680240826 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply TFHelper_6989586621680240821Sym0 (a6989586621680240826 :: Ordering) = TFHelper_6989586621680240821Sym1 a6989586621680240826
type Apply Compare_6989586621679849018Sym0 (a6989586621679849023 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply Compare_6989586621679849018Sym0 (a6989586621679849023 :: Ordering) = Compare_6989586621679849018Sym1 a6989586621679849023
type Apply ShowsPrec_6989586621680654084Sym0 (a6989586621680654096 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Show type Apply ShowsPrec_6989586621680654084Sym0 (a6989586621680654096 :: Nat) = ShowsPrec_6989586621680654084Sym1 a6989586621680654096
type Apply Compare_6989586621679849027Sym0 (a6989586621679849032 :: ())
Instance details Defined in Data.Singletons.Prelude.Ord type Apply Compare_6989586621679849027Sym0 (a6989586621679849032 :: ()) = Compare_6989586621679849027Sym1 a6989586621679849032
type Apply Compare_6989586621679848629Sym0 (a6989586621679848634 :: Void)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply Compare_6989586621679848629Sym0 (a6989586621679848634 :: Void) = Compare_6989586621679848629Sym1 a6989586621679848634
type Apply Compare_6989586621680260883Sym0 (a6989586621680260888 :: All)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply Compare_6989586621680260883Sym0 (a6989586621680260888 :: All) = Compare_6989586621680260883Sym1 a6989586621680260888
type Apply Compare_6989586621680260900Sym0 (a6989586621680260905 :: Any)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply Compare_6989586621680260900Sym0 (a6989586621680260905 :: Any) = Compare_6989586621680260900Sym1 a6989586621680260905
type Apply (ShowsPrec_6989586621680654084Sym1 a6989586621680654096 :: TyFun Ordering (Symbol ~> Symbol) -> Type) (a6989586621680654097 :: Ordering)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680654084Sym1 a6989586621680654096 :: TyFun Ordering (Symbol ~> Symbol) -> Type) (a6989586621680654097 :: Ordering) = ShowsPrec_6989586621680654084Sym2 a6989586621680654096 a6989586621680654097
type Apply (Compare_6989586621679837426Sym0 :: TyFun a (a ~> Ordering) -> Type) (a6989586621679837431 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679837426Sym0 :: TyFun a (a ~> Ordering) -> Type) (a6989586621679837431 :: a) = Compare_6989586621679837426Sym1 a6989586621679837431
type Apply (CompareSym0 :: TyFun a (a ~> Ordering) -> Type) (a6989586621679837392 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (CompareSym0 :: TyFun a (a ~> Ordering) -> Type) (a6989586621679837392 :: a) = CompareSym1 a6989586621679837392
type Apply (Let6989586621679837504Scrutinee_6989586621679837360Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837502 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837504Scrutinee_6989586621679837360Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837502 :: k1) = Let6989586621679837504Scrutinee_6989586621679837360Sym1 x6989586621679837502
type Apply (Let6989586621679837488Scrutinee_6989586621679837358Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837486 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837488Scrutinee_6989586621679837358Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837486 :: k1) = Let6989586621679837488Scrutinee_6989586621679837358Sym1 x6989586621679837486
type Apply (Let6989586621679837472Scrutinee_6989586621679837356Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837470 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837472Scrutinee_6989586621679837356Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837470 :: k1) = Let6989586621679837472Scrutinee_6989586621679837356Sym1 x6989586621679837470
type Apply (Let6989586621679837456Scrutinee_6989586621679837354Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837454 :: k1)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Let6989586621679837456Scrutinee_6989586621679837354Sym0 :: TyFun k1 (TyFun k1 Ordering -> Type) -> Type) (x6989586621679837454 :: k1) = Let6989586621679837456Scrutinee_6989586621679837354Sym1 x6989586621679837454
type Apply (ComparingSym1 a6989586621679837383 :: TyFun b (b ~> Ordering) -> Type) (a6989586621679837384 :: b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (ComparingSym1 a6989586621679837383 :: TyFun b (b ~> Ordering) -> Type) (a6989586621679837384 :: b) = ComparingSym2 a6989586621679837383 a6989586621679837384
type Apply (Compare_6989586621679848539Sym1 a6989586621679848544 :: TyFun [a] Ordering -> Type) (a6989586621679848545 :: [a])
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848539Sym1 a6989586621679848544 :: TyFun [a] Ordering -> Type) (a6989586621679848545 :: [a]) = Compare_6989586621679848539Sym2 a6989586621679848544 a6989586621679848545
type Apply (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type) (a6989586621679848514 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848508Sym1 a6989586621679848513 :: TyFun (Maybe a) Ordering -> Type) (a6989586621679848514 :: Maybe a) = Compare_6989586621679848508Sym2 a6989586621679848513 a6989586621679848514
type Apply (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type) (a6989586621679847280 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type) (a6989586621679847280 :: Down a) = Compare_6989586621679847274Sym2 a6989586621679847279 a6989586621679847280
type Apply (Compare_6989586621680260960Sym1 a6989586621680260965 :: TyFun (Min a) Ordering -> Type) (a6989586621680260966 :: Min a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260960Sym1 a6989586621680260965 :: TyFun (Min a) Ordering -> Type) (a6989586621680260966 :: Min a) = Compare_6989586621680260960Sym2 a6989586621680260965 a6989586621680260966
type Apply (Compare_6989586621680260980Sym1 a6989586621680260985 :: TyFun (Max a) Ordering -> Type) (a6989586621680260986 :: Max a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260980Sym1 a6989586621680260985 :: TyFun (Max a) Ordering -> Type) (a6989586621680260986 :: Max a) = Compare_6989586621680260980Sym2 a6989586621680260985 a6989586621680260986
type Apply (Compare_6989586621680261000Sym1 a6989586621680261005 :: TyFun (First a) Ordering -> Type) (a6989586621680261006 :: First a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261000Sym1 a6989586621680261005 :: TyFun (First a) Ordering -> Type) (a6989586621680261006 :: First a) = Compare_6989586621680261000Sym2 a6989586621680261005 a6989586621680261006
type Apply (Compare_6989586621680261020Sym1 a6989586621680261025 :: TyFun (Last a) Ordering -> Type) (a6989586621680261026 :: Last a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261020Sym1 a6989586621680261025 :: TyFun (Last a) Ordering -> Type) (a6989586621680261026 :: Last a) = Compare_6989586621680261020Sym2 a6989586621680261025 a6989586621680261026
type Apply (Compare_6989586621680261040Sym1 a6989586621680261045 :: TyFun (WrappedMonoid m) Ordering -> Type) (a6989586621680261046 :: WrappedMonoid m)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261040Sym1 a6989586621680261045 :: TyFun (WrappedMonoid m) Ordering -> Type) (a6989586621680261046 :: WrappedMonoid m) = Compare_6989586621680261040Sym2 a6989586621680261045 a6989586621680261046
type Apply (Compare_6989586621680260846Sym1 a6989586621680260851 :: TyFun (Option a) Ordering -> Type) (a6989586621680260852 :: Option a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260846Sym1 a6989586621680260851 :: TyFun (Option a) Ordering -> Type) (a6989586621680260852 :: Option a) = Compare_6989586621680260846Sym2 a6989586621680260851 a6989586621680260852
type Apply (Compare_6989586621679848996Sym1 a6989586621679849001 :: TyFun (Identity a) Ordering -> Type) (a6989586621679849002 :: Identity a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848996Sym1 a6989586621679849001 :: TyFun (Identity a) Ordering -> Type) (a6989586621679849002 :: Identity a) = Compare_6989586621679848996Sym2 a6989586621679849001 a6989586621679849002
type Apply (Compare_6989586621680696778Sym1 a6989586621680696783 :: TyFun (First a) Ordering -> Type) (a6989586621680696784 :: First a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Compare_6989586621680696778Sym1 a6989586621680696783 :: TyFun (First a) Ordering -> Type) (a6989586621680696784 :: First a) = Compare_6989586621680696778Sym2 a6989586621680696783 a6989586621680696784
type Apply (Compare_6989586621680696798Sym1 a6989586621680696803 :: TyFun (Last a) Ordering -> Type) (a6989586621680696804 :: Last a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Compare_6989586621680696798Sym1 a6989586621680696803 :: TyFun (Last a) Ordering -> Type) (a6989586621680696804 :: Last a) = Compare_6989586621680696798Sym2 a6989586621680696803 a6989586621680696804
type Apply (Compare_6989586621680260866Sym1 a6989586621680260871 :: TyFun (Dual a) Ordering -> Type) (a6989586621680260872 :: Dual a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260866Sym1 a6989586621680260871 :: TyFun (Dual a) Ordering -> Type) (a6989586621680260872 :: Dual a) = Compare_6989586621680260866Sym2 a6989586621680260871 a6989586621680260872
type Apply (Compare_6989586621680260920Sym1 a6989586621680260925 :: TyFun (Sum a) Ordering -> Type) (a6989586621680260926 :: Sum a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260920Sym1 a6989586621680260925 :: TyFun (Sum a) Ordering -> Type) (a6989586621680260926 :: Sum a) = Compare_6989586621680260920Sym2 a6989586621680260925 a6989586621680260926
type Apply (Compare_6989586621680260940Sym1 a6989586621680260945 :: TyFun (Product a) Ordering -> Type) (a6989586621680260946 :: Product a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260940Sym1 a6989586621680260945 :: TyFun (Product a) Ordering -> Type) (a6989586621680260946 :: Product a) = Compare_6989586621680260940Sym2 a6989586621680260945 a6989586621680260946
type Apply (Compare_6989586621679848612Sym1 a6989586621679848617 :: TyFun (NonEmpty a) Ordering -> Type) (a6989586621679848618 :: NonEmpty a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848612Sym1 a6989586621679848617 :: TyFun (NonEmpty a) Ordering -> Type) (a6989586621679848618 :: NonEmpty a) = Compare_6989586621679848612Sym2 a6989586621679848617 a6989586621679848618
type Apply (Compare_6989586621679848539Sym0 :: TyFun [a] ([a] ~> Ordering) -> Type) (a6989586621679848544 :: [a])
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848539Sym0 :: TyFun [a] ([a] ~> Ordering) -> Type) (a6989586621679848544 :: [a]) = Compare_6989586621679848539Sym1 a6989586621679848544
type Apply (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type) (a6989586621679848513 :: Maybe a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848508Sym0 :: TyFun (Maybe a) (Maybe a ~> Ordering) -> Type) (a6989586621679848513 :: Maybe a) = Compare_6989586621679848508Sym1 a6989586621679848513
type Apply (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type) (a6989586621679847279 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type) (a6989586621679847279 :: Down a) = Compare_6989586621679847274Sym1 a6989586621679847279
type Apply (Compare_6989586621680260960Sym0 :: TyFun (Min a) (Min a ~> Ordering) -> Type) (a6989586621680260965 :: Min a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260960Sym0 :: TyFun (Min a) (Min a ~> Ordering) -> Type) (a6989586621680260965 :: Min a) = Compare_6989586621680260960Sym1 a6989586621680260965
type Apply (Compare_6989586621680260980Sym0 :: TyFun (Max a) (Max a ~> Ordering) -> Type) (a6989586621680260985 :: Max a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260980Sym0 :: TyFun (Max a) (Max a ~> Ordering) -> Type) (a6989586621680260985 :: Max a) = Compare_6989586621680260980Sym1 a6989586621680260985
type Apply (Compare_6989586621680261000Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type) (a6989586621680261005 :: First a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261000Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type) (a6989586621680261005 :: First a) = Compare_6989586621680261000Sym1 a6989586621680261005
type Apply (Compare_6989586621680261020Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type) (a6989586621680261025 :: Last a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261020Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type) (a6989586621680261025 :: Last a) = Compare_6989586621680261020Sym1 a6989586621680261025
type Apply (Compare_6989586621680261040Sym0 :: TyFun (WrappedMonoid m) (WrappedMonoid m ~> Ordering) -> Type) (a6989586621680261045 :: WrappedMonoid m)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680261040Sym0 :: TyFun (WrappedMonoid m) (WrappedMonoid m ~> Ordering) -> Type) (a6989586621680261045 :: WrappedMonoid m) = Compare_6989586621680261040Sym1 a6989586621680261045
type Apply (Compare_6989586621680260846Sym0 :: TyFun (Option a) (Option a ~> Ordering) -> Type) (a6989586621680260851 :: Option a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260846Sym0 :: TyFun (Option a) (Option a ~> Ordering) -> Type) (a6989586621680260851 :: Option a) = Compare_6989586621680260846Sym1 a6989586621680260851
type Apply (Compare_6989586621679848996Sym0 :: TyFun (Identity a) (Identity a ~> Ordering) -> Type) (a6989586621679849001 :: Identity a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848996Sym0 :: TyFun (Identity a) (Identity a ~> Ordering) -> Type) (a6989586621679849001 :: Identity a) = Compare_6989586621679848996Sym1 a6989586621679849001
type Apply (Compare_6989586621680696778Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type) (a6989586621680696783 :: First a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Compare_6989586621680696778Sym0 :: TyFun (First a) (First a ~> Ordering) -> Type) (a6989586621680696783 :: First a) = Compare_6989586621680696778Sym1 a6989586621680696783
type Apply (Compare_6989586621680696798Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type) (a6989586621680696803 :: Last a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Apply (Compare_6989586621680696798Sym0 :: TyFun (Last a) (Last a ~> Ordering) -> Type) (a6989586621680696803 :: Last a) = Compare_6989586621680696798Sym1 a6989586621680696803
type Apply (Compare_6989586621680260866Sym0 :: TyFun (Dual a) (Dual a ~> Ordering) -> Type) (a6989586621680260871 :: Dual a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260866Sym0 :: TyFun (Dual a) (Dual a ~> Ordering) -> Type) (a6989586621680260871 :: Dual a) = Compare_6989586621680260866Sym1 a6989586621680260871
type Apply (Compare_6989586621680260920Sym0 :: TyFun (Sum a) (Sum a ~> Ordering) -> Type) (a6989586621680260925 :: Sum a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260920Sym0 :: TyFun (Sum a) (Sum a ~> Ordering) -> Type) (a6989586621680260925 :: Sum a) = Compare_6989586621680260920Sym1 a6989586621680260925
type Apply (Compare_6989586621680260940Sym0 :: TyFun (Product a) (Product a ~> Ordering) -> Type) (a6989586621680260945 :: Product a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Compare_6989586621680260940Sym0 :: TyFun (Product a) (Product a ~> Ordering) -> Type) (a6989586621680260945 :: Product a) = Compare_6989586621680260940Sym1 a6989586621680260945
type Apply (Compare_6989586621679848612Sym0 :: TyFun (NonEmpty a) (NonEmpty a ~> Ordering) -> Type) (a6989586621679848617 :: NonEmpty a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848612Sym0 :: TyFun (NonEmpty a) (NonEmpty a ~> Ordering) -> Type) (a6989586621679848617 :: NonEmpty a) = Compare_6989586621679848612Sym1 a6989586621679848617
type Apply (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type) (a6989586621679848590 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type) (a6989586621679848590 :: Either a b) = Compare_6989586621679848584Sym2 a6989586621679848589 a6989586621679848590
type Apply (Compare_6989586621679848652Sym1 a6989586621679848657 :: TyFun (a, b) Ordering -> Type) (a6989586621679848658 :: (a, b))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848652Sym1 a6989586621679848657 :: TyFun (a, b) Ordering -> Type) (a6989586621679848658 :: (a, b)) = Compare_6989586621679848652Sym2 a6989586621679848657 a6989586621679848658
type Apply (Compare_6989586621681203650Sym1 a6989586621681203655 :: TyFun (Arg a b) Ordering -> Type) (a6989586621681203656 :: Arg a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup type Apply (Compare_6989586621681203650Sym1 a6989586621681203655 :: TyFun (Arg a b) Ordering -> Type) (a6989586621681203656 :: Arg a b) = Compare_6989586621681203650Sym2 a6989586621681203655 a6989586621681203656
type Apply (Compare_6989586621680787223Sym1 a6989586621680787228 :: TyFun (Proxy s) Ordering -> Type) (a6989586621680787229 :: Proxy s)
Instance details Defined in Data.Singletons.Prelude.Proxy type Apply (Compare_6989586621680787223Sym1 a6989586621680787228 :: TyFun (Proxy s) Ordering -> Type) (a6989586621680787229 :: Proxy s) = Compare_6989586621680787223Sym2 a6989586621680787228 a6989586621680787229
type Apply (ListsortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type) (a6989586621680749526 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal.Disambiguation type Apply (ListsortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type) (a6989586621680749526 :: a ~> (a ~> Ordering)) = ListsortBySym1 a6989586621680749526
type Apply (InsertBySym0 :: TyFun (a ~> (a ~> Ordering)) (a ~> ([a] ~> [a])) -> Type) (a6989586621680379743 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (InsertBySym0 :: TyFun (a ~> (a ~> Ordering)) (a ~> ([a] ~> [a])) -> Type) (a6989586621680379743 :: a ~> (a ~> Ordering)) = InsertBySym1 a6989586621680379743
type Apply (SortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type) (a6989586621680379763 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (SortBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> [a]) -> Type) (a6989586621680379763 :: a ~> (a ~> Ordering)) = SortBySym1 a6989586621680379763
type Apply (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type) (a6989586621680379721 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type) (a6989586621680379721 :: a ~> (a ~> Ordering)) = MaximumBySym1 a6989586621680379721
type Apply (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type) (a6989586621680379700 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) ([a] ~> a) -> Type) (a6989586621680379700 :: a ~> (a ~> Ordering)) = MinimumBySym1 a6989586621680379700
type Apply (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type) (a6989586621679848589 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type) (a6989586621679848589 :: Either a b) = Compare_6989586621679848584Sym1 a6989586621679848589
type Apply (Compare_6989586621679848652Sym0 :: TyFun (a, b) ((a, b) ~> Ordering) -> Type) (a6989586621679848657 :: (a, b))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848652Sym0 :: TyFun (a, b) ((a, b) ~> Ordering) -> Type) (a6989586621679848657 :: (a, b)) = Compare_6989586621679848652Sym1 a6989586621679848657
type Apply (Compare_6989586621681203650Sym0 :: TyFun (Arg a b) (Arg a b ~> Ordering) -> Type) (a6989586621681203655 :: Arg a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup type Apply (Compare_6989586621681203650Sym0 :: TyFun (Arg a b) (Arg a b ~> Ordering) -> Type) (a6989586621681203655 :: Arg a b) = Compare_6989586621681203650Sym1 a6989586621681203655
type Apply (Compare_6989586621680787223Sym0 :: TyFun (Proxy s) (Proxy s ~> Ordering) -> Type) (a6989586621680787228 :: Proxy s)
Instance details Defined in Data.Singletons.Prelude.Proxy type Apply (Compare_6989586621680787223Sym0 :: TyFun (Proxy s) (Proxy s ~> Ordering) -> Type) (a6989586621680787228 :: Proxy s) = Compare_6989586621680787223Sym1 a6989586621680787228
type Apply (Let6989586621680822581Min'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (cmp6989586621680822579 :: k1 ~> (k1 ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822581Min'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (cmp6989586621680822579 :: k1 ~> (k1 ~> Ordering)) = Let6989586621680822581Min'Sym1 cmp6989586621680822579 :: TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type
type Apply (Let6989586621680822601Max'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (cmp6989586621680822599 :: k1 ~> (k1 ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Let6989586621680822601Max'Sym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) (cmp6989586621680822599 :: k1 ~> (k1 ~> Ordering)) = Let6989586621680822601Max'Sym1 cmp6989586621680822599 :: TyFun k2 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type
type Apply (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type) (a6989586621680822597 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (MaximumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type) (a6989586621680822597 :: a ~> (a ~> Ordering)) = MaximumBySym1 a6989586621680822597 :: TyFun (t a) a -> Type
type Apply (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type) (a6989586621680822577 :: a ~> (a ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (MinimumBySym0 :: TyFun (a ~> (a ~> Ordering)) (t a ~> a) -> Type) (a6989586621680822577 :: a ~> (a ~> Ordering)) = MinimumBySym1 a6989586621680822577 :: TyFun (t a) a -> Type
type Apply (ComparingSym0 :: TyFun (b ~> a) (b ~> (b ~> Ordering)) -> Type) (a6989586621679837383 :: b ~> a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (ComparingSym0 :: TyFun (b ~> a) (b ~> (b ~> Ordering)) -> Type) (a6989586621679837383 :: b ~> a) = ComparingSym1 a6989586621679837383
type Apply (Let6989586621680379707MinBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type) (cmp6989586621680379702 :: k1 ~> (k1 ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379707MinBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type) (cmp6989586621680379702 :: k1 ~> (k1 ~> Ordering)) = Let6989586621680379707MinBySym1 cmp6989586621680379702 :: TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type
type Apply (Let6989586621680379728MaxBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type) (cmp6989586621680379723 :: k1 ~> (k1 ~> Ordering))
Instance details Defined in Data.Singletons.Prelude.List.Internal type Apply (Let6989586621680379728MaxBySym0 :: TyFun (k1 ~> (k1 ~> Ordering)) (TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type) -> Type) (cmp6989586621680379723 :: k1 ~> (k1 ~> Ordering)) = Let6989586621680379728MaxBySym1 cmp6989586621680379723 :: TyFun k2 (TyFun k3 (TyFun k1 (TyFun k1 k1 -> Type) -> Type) -> Type) -> Type
type Apply (Compare_6989586621679848690Sym1 a6989586621679848695 :: TyFun (a, b, c) Ordering -> Type) (a6989586621679848696 :: (a, b, c))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848690Sym1 a6989586621679848695 :: TyFun (a, b, c) Ordering -> Type) (a6989586621679848696 :: (a, b, c)) = Compare_6989586621679848690Sym2 a6989586621679848695 a6989586621679848696
type Apply (Compare_6989586621681044522Sym1 a6989586621681044527 :: TyFun (Const a b) Ordering -> Type) (a6989586621681044528 :: Const a b)
Instance details Defined in Data.Singletons.Prelude.Const type Apply (Compare_6989586621681044522Sym1 a6989586621681044527 :: TyFun (Const a b) Ordering -> Type) (a6989586621681044528 :: Const a b) = Compare_6989586621681044522Sym2 a6989586621681044527 a6989586621681044528
type Apply (Compare_6989586621679848690Sym0 :: TyFun (a, b, c) ((a, b, c) ~> Ordering) -> Type) (a6989586621679848695 :: (a, b, c))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848690Sym0 :: TyFun (a, b, c) ((a, b, c) ~> Ordering) -> Type) (a6989586621679848695 :: (a, b, c)) = Compare_6989586621679848690Sym1 a6989586621679848695
type Apply (Compare_6989586621681044522Sym0 :: TyFun (Const a b) (Const a b ~> Ordering) -> Type) (a6989586621681044527 :: Const a b)
Instance details Defined in Data.Singletons.Prelude.Const type Apply (Compare_6989586621681044522Sym0 :: TyFun (Const a b) (Const a b ~> Ordering) -> Type) (a6989586621681044527 :: Const a b) = Compare_6989586621681044522Sym1 a6989586621681044527
type Apply (Compare_6989586621679848739Sym1 a6989586621679848744 :: TyFun (a, b, c, d) Ordering -> Type) (a6989586621679848745 :: (a, b, c, d))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848739Sym1 a6989586621679848744 :: TyFun (a, b, c, d) Ordering -> Type) (a6989586621679848745 :: (a, b, c, d)) = Compare_6989586621679848739Sym2 a6989586621679848744 a6989586621679848745
type Apply (Compare_6989586621679848739Sym0 :: TyFun (a, b, c, d) ((a, b, c, d) ~> Ordering) -> Type) (a6989586621679848744 :: (a, b, c, d))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848739Sym0 :: TyFun (a, b, c, d) ((a, b, c, d) ~> Ordering) -> Type) (a6989586621679848744 :: (a, b, c, d)) = Compare_6989586621679848739Sym1 a6989586621679848744
type Apply (Compare_6989586621679848799Sym1 a6989586621679848804 :: TyFun (a, b, c, d, e) Ordering -> Type) (a6989586621679848805 :: (a, b, c, d, e))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848799Sym1 a6989586621679848804 :: TyFun (a, b, c, d, e) Ordering -> Type) (a6989586621679848805 :: (a, b, c, d, e)) = Compare_6989586621679848799Sym2 a6989586621679848804 a6989586621679848805
type Apply (Compare_6989586621679848799Sym0 :: TyFun (a, b, c, d, e) ((a, b, c, d, e) ~> Ordering) -> Type) (a6989586621679848804 :: (a, b, c, d, e))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848799Sym0 :: TyFun (a, b, c, d, e) ((a, b, c, d, e) ~> Ordering) -> Type) (a6989586621679848804 :: (a, b, c, d, e)) = Compare_6989586621679848799Sym1 a6989586621679848804
type Apply (Compare_6989586621679848870Sym1 a6989586621679848875 :: TyFun (a, b, c, d, e, f) Ordering -> Type) (a6989586621679848876 :: (a, b, c, d, e, f))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848870Sym1 a6989586621679848875 :: TyFun (a, b, c, d, e, f) Ordering -> Type) (a6989586621679848876 :: (a, b, c, d, e, f)) = Compare_6989586621679848870Sym2 a6989586621679848875 a6989586621679848876
type Apply (Compare_6989586621679848870Sym0 :: TyFun (a, b, c, d, e, f) ((a, b, c, d, e, f) ~> Ordering) -> Type) (a6989586621679848875 :: (a, b, c, d, e, f))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848870Sym0 :: TyFun (a, b, c, d, e, f) ((a, b, c, d, e, f) ~> Ordering) -> Type) (a6989586621679848875 :: (a, b, c, d, e, f)) = Compare_6989586621679848870Sym1 a6989586621679848875
type Apply (Compare_6989586621679848952Sym1 a6989586621679848957 :: TyFun (a, b, c, d, e, f, g) Ordering -> Type) (a6989586621679848958 :: (a, b, c, d, e, f, g))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848952Sym1 a6989586621679848957 :: TyFun (a, b, c, d, e, f, g) Ordering -> Type) (a6989586621679848958 :: (a, b, c, d, e, f, g)) = Compare_6989586621679848952Sym2 a6989586621679848957 a6989586621679848958
type Apply (Compare_6989586621679848952Sym0 :: TyFun (a, b, c, d, e, f, g) ((a, b, c, d, e, f, g) ~> Ordering) -> Type) (a6989586621679848957 :: (a, b, c, d, e, f, g))
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848952Sym0 :: TyFun (a, b, c, d, e, f, g) ((a, b, c, d, e, f, g) ~> Ordering) -> Type) (a6989586621679848957 :: (a, b, c, d, e, f, g)) = Compare_6989586621679848952Sym1 a6989586621679848957

data IO a #

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Instances details

Monad IO	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b # (>>) :: IO a -> IO b -> IO b # return :: a -> IO a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
MonadFail IO	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fail Methods fail :: String -> IO a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
MonadPlus IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a # mplus :: IO a -> IO a -> IO a #
MonadIO IO	Since: base-4.9.0.0
Instance details Defined in Control.Monad.IO.Class Methods liftIO :: IO a -> IO a #
Alternative IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a # (<\|>) :: IO a -> IO a -> IO a # some :: IO a -> IO [a] # many :: IO a -> IO [a] #
Quasi IO
Instance details Defined in Language.Haskell.TH.Syntax Methods qNewName :: String -> IO Name # qReport :: Bool -> String -> IO () # qRecover :: IO a -> IO a -> IO a # qLookupName :: Bool -> String -> IO (Maybe Name) # qReify :: Name -> IO Info # qReifyFixity :: Name -> IO (Maybe Fixity) # qReifyType :: Name -> IO Type # qReifyInstances :: Name -> [Type] -> IO [Dec] # qReifyRoles :: Name -> IO [Role] # qReifyAnnotations :: Data a => AnnLookup -> IO [a] # qReifyModule :: Module -> IO ModuleInfo # qReifyConStrictness :: Name -> IO [DecidedStrictness] # qLocation :: IO Loc # qRunIO :: IO a -> IO a # qAddDependentFile :: FilePath -> IO () # qAddTempFile :: String -> IO FilePath # qAddTopDecls :: [Dec] -> IO () # qAddForeignFilePath :: ForeignSrcLang -> String -> IO () # qAddModFinalizer :: Q () -> IO () # qAddCorePlugin :: String -> IO () # qGetQ :: Typeable a => IO (Maybe a) # qPutQ :: Typeable a => a -> IO () # qIsExtEnabled :: Extension -> IO Bool # qExtsEnabled :: IO [Extension] #
PrimMonad IO
Instance details Defined in Control.Monad.Primitive Associated Types type PrimState IO Methods primitive :: (State# (PrimState IO) -> (# State# (PrimState IO), a #)) -> IO a
CFunctor IO
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom IO a, Dom IO b) => (a -> b) -> IO a -> IO b (<$:) :: (Dom IO a, Dom IO b) => a -> IO b -> IO a
CPointed IO
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom IO a => a -> IO a
Apply IO
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: IO (a -> b) -> IO a -> IO b (.>) :: IO a -> IO b -> IO b (<.) :: IO a -> IO b -> IO a liftF2 :: (a -> b -> c) -> IO a -> IO b -> IO c
Bind IO
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: IO a -> (a -> IO b) -> IO b join :: IO (IO a) -> IO a
Constrained IO
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom IO a
PrimBase IO
Instance details Defined in Control.Monad.Primitive Methods internal :: IO a -> State# (PrimState IO) -> (# State# (PrimState IO), a #)
MArray IOArray e IO
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => IOArray i e -> IO (i, i) # getNumElements :: Ix i => IOArray i e -> IO Int newArray :: Ix i => (i, i) -> e -> IO (IOArray i e) # newArray_ :: Ix i => (i, i) -> IO (IOArray i e) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOArray i e) unsafeRead :: Ix i => IOArray i e -> Int -> IO e unsafeWrite :: Ix i => IOArray i e -> Int -> e -> IO ()
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
MonoFunctor (IO a)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (IO a) -> Element (IO a)) -> IO a -> IO a
MonoPointed (IO a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (IO a) -> IO a
type PrimState IO
Instance details Defined in Control.Monad.Primitive type PrimState IO = RealWorld
type Dom IO a
Instance details Defined in Control.Subcategory.Functor type Dom IO a = ()
type Element (IO a)
Instance details Defined in Data.MonoTraversable type Element (IO a) = a

data Word #

A Word is an unsigned integral type, with the same size as Int.

Instances

Instances details

Bounded Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word # maxBound :: Word #
Enum Word	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word # pred :: Word -> Word # toEnum :: Int -> Word # fromEnum :: Word -> Int # enumFrom :: Word -> [Word] # enumFromThen :: Word -> Word -> [Word] # enumFromTo :: Word -> Word -> [Word] # enumFromThenTo :: Word -> Word -> Word -> [Word] #
Eq Word
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool # (/=) :: Word -> Word -> Bool #
Integral Word	Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word # rem :: Word -> Word -> Word # div :: Word -> Word -> Word # mod :: Word -> Word -> Word # quotRem :: Word -> Word -> (Word, Word) # divMod :: Word -> Word -> (Word, Word) # toInteger :: Word -> Integer #
Num Word	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word # (-) :: Word -> Word -> Word # (*) :: Word -> Word -> Word # negate :: Word -> Word # abs :: Word -> Word # signum :: Word -> Word # fromInteger :: Integer -> Word #
Ord Word
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering # (<) :: Word -> Word -> Bool # (<=) :: Word -> Word -> Bool # (>) :: Word -> Word -> Bool # (>=) :: Word -> Word -> Bool # max :: Word -> Word -> Word # min :: Word -> Word -> Word #
Read Word	Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word # readList :: ReadS [Word] # readPrec :: ReadPrec Word # readListPrec :: ReadPrec [Word] #
Real Word	Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational #
Show Word	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS # show :: Word -> String # showList :: [Word] -> ShowS #
Ix Word	Since: base-4.6.0.0
Instance details Defined in GHC.Ix Methods range :: (Word, Word) -> [Word] # index :: (Word, Word) -> Word -> Int # unsafeIndex :: (Word, Word) -> Word -> Int # inRange :: (Word, Word) -> Word -> Bool # rangeSize :: (Word, Word) -> Int # unsafeRangeSize :: (Word, Word) -> Int #
Ring Word
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word
Rig Word
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word #
Characteristic Word
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word -> Natural #
LocallyFiniteOrder Word
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word -> Word -> [Word] rangeSize :: Word -> Word -> Natural moebiusInversion :: Ring r => Word -> Word -> r
DecidableZero Word
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word -> Bool #
DecidableUnits Word
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word -> Maybe Word # isUnit :: Word -> Bool # (^?) :: Integral n => Word -> n -> Maybe Word #
DecidableAssociates Word
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word -> Word -> Bool #
Unital Word
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word # pow :: Word -> Natural -> Word # productWith :: Foldable f => (a -> Word) -> f a -> Word #
TriviallyInvolutive Word
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Word
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word -> Word #
Commutative Word
Instance details Defined in Numeric.Algebra.Commutative
Semiring Word
Instance details Defined in Numeric.Algebra.Class
Multiplicative Word
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word -> Word -> Word # pow1p :: Word -> Natural -> Word # productWith1 :: Foldable1 f => (a -> Word) -> f a -> Word #
Monoidal Word
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word # sinnum :: Natural -> Word -> Word # sumWith :: Foldable f => (a -> Word) -> f a -> Word #
Group Word
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word -> Word -> Word # negate :: Word -> Word # subtract :: Word -> Word -> Word # times :: Integral n => n -> Word -> Word #
Additive Word
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word -> Word -> Word # sinnum1p :: Natural -> Word -> Word # sumWith1 :: Foldable1 f => (a -> Word) -> f a -> Word #
Abelian Word
Instance details Defined in Numeric.Additive.Class
Unbox Word
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Word
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word -> Int # hash :: Word -> Int #
Storable Word	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word -> Int # alignment :: Word -> Int # peekElemOff :: Ptr Word -> Int -> IO Word # pokeElemOff :: Ptr Word -> Int -> Word -> IO () # peekByteOff :: Ptr b -> Int -> IO Word # pokeByteOff :: Ptr b -> Int -> Word -> IO () # peek :: Ptr Word -> IO Word # poke :: Ptr Word -> Word -> IO () #
Bits Word	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Word -> Word -> Word # (.\|.) :: Word -> Word -> Word # xor :: Word -> Word -> Word # complement :: Word -> Word # shift :: Word -> Int -> Word # rotate :: Word -> Int -> Word # zeroBits :: Word # bit :: Int -> Word # setBit :: Word -> Int -> Word # clearBit :: Word -> Int -> Word # complementBit :: Word -> Int -> Word # testBit :: Word -> Int -> Bool # bitSizeMaybe :: Word -> Maybe Int # bitSize :: Word -> Int # isSigned :: Word -> Bool # shiftL :: Word -> Int -> Word # unsafeShiftL :: Word -> Int -> Word # shiftR :: Word -> Int -> Word # unsafeShiftR :: Word -> Int -> Word # rotateL :: Word -> Int -> Word # rotateR :: Word -> Int -> Word # popCount :: Word -> Int #
FiniteBits Word	Since: base-4.6.0.0
Instance details Defined in Data.Bits Methods finiteBitSize :: Word -> Int # countLeadingZeros :: Word -> Int # countTrailingZeros :: Word -> Int #
NFData Word
Instance details Defined in Control.DeepSeq Methods rnf :: Word -> () #
Prim Word
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Word -> Int# alignment# :: Word -> Int# indexByteArray# :: ByteArray# -> Int# -> Word readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Word #) writeByteArray# :: MutableByteArray# s -> Int# -> Word -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Word -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Word readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Word #) writeOffAddr# :: Addr# -> Int# -> Word -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Word -> State# s -> State# s
Uniform Word
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word
UniformRange Word
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Word, Word) -> g -> m Word
Lift Word
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Word -> Q Exp # liftTyped :: Word -> Q (TExp Word) #
Rig r => Quadrance r Word
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word -> r #
RightModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Integer -> Word #
RightModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Natural -> Word #
LeftModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word -> Word #
LeftModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word -> Word #
IArray UArray Word
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word -> (i, i) # numElements :: Ix i => UArray i Word -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word)] -> UArray i Word unsafeAt :: Ix i => UArray i Word -> Int -> Word unsafeReplace :: Ix i => UArray i Word -> [(Int, Word)] -> UArray i Word unsafeAccum :: Ix i => (Word -> e' -> Word) -> UArray i Word -> [(Int, e')] -> UArray i Word unsafeAccumArray :: Ix i => (Word -> e' -> Word) -> Word -> (i, i) -> [(Int, e')] -> UArray i Word
MVector MVector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word -> Int basicUnsafeSlice :: Int -> Int -> MVector s Word -> MVector s Word basicOverlaps :: MVector s Word -> MVector s Word -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word) basicInitialize :: PrimMonad m => MVector (PrimState m) Word -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Word -> m (MVector (PrimState m) Word) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word -> Int -> m Word basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word -> Int -> Word -> m () basicClear :: PrimMonad m => MVector (PrimState m) Word -> m () basicSet :: PrimMonad m => MVector (PrimState m) Word -> Word -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word -> Int -> m (MVector (PrimState m) Word)
Vector Vector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word -> m (Vector Word) basicUnsafeThaw :: PrimMonad m => Vector Word -> m (Mutable Vector (PrimState m) Word) basicLength :: Vector Word -> Int basicUnsafeSlice :: Int -> Int -> Vector Word -> Vector Word basicUnsafeIndexM :: Monad m => Vector Word -> Int -> m Word basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word -> Vector Word -> m () elemseq :: Vector Word -> Word -> b -> b
Generic1 (URec Word :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Word) :: k -> Type # Methods from1 :: forall (a :: k0). URec Word a -> Rep1 (URec Word) a # to1 :: forall (a :: k0). Rep1 (URec Word) a -> URec Word a #
Foldable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # toList :: UWord a -> [a] # null :: UWord a -> Bool # length :: UWord a -> Int # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # sum :: Num a => UWord a -> a # product :: Num a => UWord a -> a #
Traversable (UWord :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) # sequenceA :: Applicative f => UWord (f a) -> f (UWord a) # mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) # sequence :: Monad m => UWord (m a) -> m (UWord a) #
MArray (STUArray s) Word (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word -> ST s Int newArray :: Ix i => (i, i) -> Word -> ST s (STUArray s i Word) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word) unsafeRead :: Ix i => STUArray s i Word -> Int -> ST s Word unsafeWrite :: Ix i => STUArray s i Word -> Int -> Word -> ST s ()
Functor (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
CFoldable (URec Word :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (URec Word) a, Monoid w) => (a -> w) -> URec Word a -> w cfoldMap' :: (Dom (URec Word) a, Monoid m) => (a -> m) -> URec Word a -> m cfold :: (Dom (URec Word) w, Monoid w) => URec Word w -> w cfoldr :: Dom (URec Word) a => (a -> b -> b) -> b -> URec Word a -> b cfoldlM :: (Monad m, Dom (URec Word) b) => (a -> b -> m a) -> a -> URec Word b -> m a cfoldlM' :: (Monad m, Dom (URec Word) b) => (a -> b -> m a) -> a -> URec Word b -> m a cfoldrM :: (Monad m, Dom (URec Word) a) => (a -> b -> m b) -> b -> URec Word a -> m b cfoldrM' :: (Monad m, Dom (URec Word) a) => (a -> b -> m b) -> b -> URec Word a -> m b cfoldl :: Dom (URec Word) a => (b -> a -> b) -> b -> URec Word a -> b cfoldr' :: Dom (URec Word) a => (a -> b -> b) -> b -> URec Word a -> b cfoldl' :: Dom (URec Word) a => (b -> a -> b) -> b -> URec Word a -> b cbasicToList :: Dom (URec Word) a => URec Word a -> [a] cfoldr1 :: Dom (URec Word) a => (a -> a -> a) -> URec Word a -> a cfoldl1 :: Dom (URec Word) a => (a -> a -> a) -> URec Word a -> a cindex :: Dom (URec Word) a => URec Word a -> Int -> a cnull :: Dom (URec Word) a => URec Word a -> Bool clength :: Dom (URec Word) a => URec Word a -> Int cany :: Dom (URec Word) a => (a -> Bool) -> URec Word a -> Bool call :: Dom (URec Word) a => (a -> Bool) -> URec Word a -> Bool celem :: (Eq a, Dom (URec Word) a) => a -> URec Word a -> Bool cnotElem :: (Eq a, Dom (URec Word) a) => a -> URec Word a -> Bool cminimum :: (Ord a, Dom (URec Word) a) => URec Word a -> a cmaximum :: (Ord a, Dom (URec Word) a) => URec Word a -> a csum :: (Num a, Dom (URec Word) a) => URec Word a -> a cproduct :: (Num a, Dom (URec Word) a) => URec Word a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (URec Word) a, Dom g b) => (a -> g b) -> URec Word a -> g () ctraverse_ :: (Applicative g, Dom (URec Word) a) => (a -> g b) -> URec Word a -> g () clast :: Dom (URec Word) a => URec Word a -> a chead :: Dom (URec Word) a => URec Word a -> a cfind :: Dom (URec Word) a => (a -> Bool) -> URec Word a -> Maybe a cfindIndex :: Dom (URec Word) a => (a -> Bool) -> URec Word a -> Maybe Int cfindIndices :: Dom (URec Word) a => (a -> Bool) -> URec Word a -> [Int] celemIndex :: (Dom (URec Word) a, Eq a) => a -> URec Word a -> Maybe Int celemIndices :: (Dom (URec Word) a, Eq a) => a -> URec Word a -> [Int]
CFunctor (URec Word :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (URec Word) a, Dom (URec Word) b) => (a -> b) -> URec Word a -> URec Word b (<$:) :: (Dom (URec Word) a, Dom (URec Word) b) => a -> URec Word b -> URec Word a
CTraversable (URec Word :: Type -> Type)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (URec Word) a, Dom (URec Word) b, Applicative g) => (a -> g b) -> URec Word a -> g (URec Word b)
Constrained (URec Word :: Type -> Type)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (URec Word) a
Eq (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: URec Word p -> URec Word p -> Bool # (/=) :: URec Word p -> URec Word p -> Bool #
Ord (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering # (<) :: URec Word p -> URec Word p -> Bool # (<=) :: URec Word p -> URec Word p -> Bool # (>) :: URec Word p -> URec Word p -> Bool # (>=) :: URec Word p -> URec Word p -> Bool # max :: URec Word p -> URec Word p -> URec Word p # min :: URec Word p -> URec Word p -> URec Word p #
Show (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Word p -> ShowS # show :: URec Word p -> String # showList :: [URec Word p] -> ShowS #
Generic (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (URec Word p) :: Type -> Type # Methods from :: URec Word p -> Rep (URec Word p) x # to :: Rep (URec Word p) x -> URec Word p #
newtype Vector Word
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word = V_Word (Vector Word)
data URec Word (p :: k)	Used for marking occurrences of `Word#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Word (p :: k) = UWord { uWord# :: Word# }
newtype MVector s Word
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word = MV_Word (MVector s Word)
type Rep1 (URec Word :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))
type Dom (URec Word :: Type -> Type) a
Instance details Defined in Control.Subcategory.Functor type Dom (URec Word :: Type -> Type) a = ()
type Rep (URec Word p)
Instance details Defined in GHC.Generics type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

data Word8 #

8-bit unsigned integer type

Instances

Instances details

Bounded Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word8 # maxBound :: Word8 #
Enum Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word8 -> Word8 # pred :: Word8 -> Word8 # toEnum :: Int -> Word8 # fromEnum :: Word8 -> Int # enumFrom :: Word8 -> [Word8] # enumFromThen :: Word8 -> Word8 -> [Word8] # enumFromTo :: Word8 -> Word8 -> [Word8] # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] #
Eq Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word8 -> Word8 -> Bool # (/=) :: Word8 -> Word8 -> Bool #
Integral Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word8 -> Word8 -> Word8 # rem :: Word8 -> Word8 -> Word8 # div :: Word8 -> Word8 -> Word8 # mod :: Word8 -> Word8 -> Word8 # quotRem :: Word8 -> Word8 -> (Word8, Word8) # divMod :: Word8 -> Word8 -> (Word8, Word8) # toInteger :: Word8 -> Integer #
Num Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word8 -> Word8 -> Word8 # (-) :: Word8 -> Word8 -> Word8 # (*) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # abs :: Word8 -> Word8 # signum :: Word8 -> Word8 # fromInteger :: Integer -> Word8 #
Ord Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word8 -> Word8 -> Ordering # (<) :: Word8 -> Word8 -> Bool # (<=) :: Word8 -> Word8 -> Bool # (>) :: Word8 -> Word8 -> Bool # (>=) :: Word8 -> Word8 -> Bool # max :: Word8 -> Word8 -> Word8 # min :: Word8 -> Word8 -> Word8 #
Read Word8	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word8 # readList :: ReadS [Word8] # readPrec :: ReadPrec Word8 # readListPrec :: ReadPrec [Word8] #
Real Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word8 -> Rational #
Show Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word8 -> ShowS # show :: Word8 -> String # showList :: [Word8] -> ShowS #
Ix Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods range :: (Word8, Word8) -> [Word8] # index :: (Word8, Word8) -> Word8 -> Int # unsafeIndex :: (Word8, Word8) -> Word8 -> Int # inRange :: (Word8, Word8) -> Word8 -> Bool # rangeSize :: (Word8, Word8) -> Int # unsafeRangeSize :: (Word8, Word8) -> Int #
Ring Word8
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word8
Rig Word8
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word8 #
Characteristic Word8
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word8 -> Natural #
LocallyFiniteOrder Word8
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word8 -> Word8 -> [Word8] rangeSize :: Word8 -> Word8 -> Natural moebiusInversion :: Ring r => Word8 -> Word8 -> r
DecidableZero Word8
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word8 -> Bool #
DecidableUnits Word8
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word8 -> Maybe Word8 # isUnit :: Word8 -> Bool # (^?) :: Integral n => Word8 -> n -> Maybe Word8 #
DecidableAssociates Word8
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word8 -> Word8 -> Bool #
Unital Word8
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word8 # pow :: Word8 -> Natural -> Word8 # productWith :: Foldable f => (a -> Word8) -> f a -> Word8 #
TriviallyInvolutive Word8
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word8
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Word8
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word8 -> Word8 #
Commutative Word8
Instance details Defined in Numeric.Algebra.Commutative
Semiring Word8
Instance details Defined in Numeric.Algebra.Class
Multiplicative Word8
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word8 -> Word8 -> Word8 # pow1p :: Word8 -> Natural -> Word8 # productWith1 :: Foldable1 f => (a -> Word8) -> f a -> Word8 #
Monoidal Word8
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word8 # sinnum :: Natural -> Word8 -> Word8 # sumWith :: Foldable f => (a -> Word8) -> f a -> Word8 #
Group Word8
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # subtract :: Word8 -> Word8 -> Word8 # times :: Integral n => n -> Word8 -> Word8 #
Additive Word8
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word8 -> Word8 -> Word8 # sinnum1p :: Natural -> Word8 -> Word8 # sumWith1 :: Foldable1 f => (a -> Word8) -> f a -> Word8 #
Abelian Word8
Instance details Defined in Numeric.Additive.Class
Unbox Word8
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Word8
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word8 -> Int # hash :: Word8 -> Int #
Storable Word8	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word8 -> Int # alignment :: Word8 -> Int # peekElemOff :: Ptr Word8 -> Int -> IO Word8 # pokeElemOff :: Ptr Word8 -> Int -> Word8 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word8 # pokeByteOff :: Ptr b -> Int -> Word8 -> IO () # peek :: Ptr Word8 -> IO Word8 # poke :: Ptr Word8 -> Word8 -> IO () #
Bits Word8	Since: base-2.1
Instance details Defined in GHC.Word Methods (.&.) :: Word8 -> Word8 -> Word8 # (.\|.) :: Word8 -> Word8 -> Word8 # xor :: Word8 -> Word8 -> Word8 # complement :: Word8 -> Word8 # shift :: Word8 -> Int -> Word8 # rotate :: Word8 -> Int -> Word8 # zeroBits :: Word8 # bit :: Int -> Word8 # setBit :: Word8 -> Int -> Word8 # clearBit :: Word8 -> Int -> Word8 # complementBit :: Word8 -> Int -> Word8 # testBit :: Word8 -> Int -> Bool # bitSizeMaybe :: Word8 -> Maybe Int # bitSize :: Word8 -> Int # isSigned :: Word8 -> Bool # shiftL :: Word8 -> Int -> Word8 # unsafeShiftL :: Word8 -> Int -> Word8 # shiftR :: Word8 -> Int -> Word8 # unsafeShiftR :: Word8 -> Int -> Word8 # rotateL :: Word8 -> Int -> Word8 # rotateR :: Word8 -> Int -> Word8 # popCount :: Word8 -> Int #
FiniteBits Word8	Since: base-4.6.0.0
Instance details Defined in GHC.Word Methods finiteBitSize :: Word8 -> Int # countLeadingZeros :: Word8 -> Int # countTrailingZeros :: Word8 -> Int #
NFData Word8
Instance details Defined in Control.DeepSeq Methods rnf :: Word8 -> () #
PrettyCoeff Word8
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Word8 -> ShowSCoeff #
Prim Word8
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Word8 -> Int# alignment# :: Word8 -> Int# indexByteArray# :: ByteArray# -> Int# -> Word8 readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Word8 #) writeByteArray# :: MutableByteArray# s -> Int# -> Word8 -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Word8 -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Word8 readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Word8 #) writeOffAddr# :: Addr# -> Int# -> Word8 -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Word8 -> State# s -> State# s
Uniform Word8
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word8
UniformRange Word8
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Word8, Word8) -> g -> m Word8
Lift Word8
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Word8 -> Q Exp # liftTyped :: Word8 -> Q (TExp Word8) #
Rig r => Quadrance r Word8
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word8 -> r #
RightModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Integer -> Word8 #
RightModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Natural -> Word8 #
LeftModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word8 -> Word8 #
LeftModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word8 -> Word8 #
IArray UArray Word8
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word8 -> (i, i) # numElements :: Ix i => UArray i Word8 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word8)] -> UArray i Word8 unsafeAt :: Ix i => UArray i Word8 -> Int -> Word8 unsafeReplace :: Ix i => UArray i Word8 -> [(Int, Word8)] -> UArray i Word8 unsafeAccum :: Ix i => (Word8 -> e' -> Word8) -> UArray i Word8 -> [(Int, e')] -> UArray i Word8 unsafeAccumArray :: Ix i => (Word8 -> e' -> Word8) -> Word8 -> (i, i) -> [(Int, e')] -> UArray i Word8
MVector MVector Word8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word8 -> Int basicUnsafeSlice :: Int -> Int -> MVector s Word8 -> MVector s Word8 basicOverlaps :: MVector s Word8 -> MVector s Word8 -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word8) basicInitialize :: PrimMonad m => MVector (PrimState m) Word8 -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Word8 -> m (MVector (PrimState m) Word8) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> m Word8 basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> Word8 -> m () basicClear :: PrimMonad m => MVector (PrimState m) Word8 -> m () basicSet :: PrimMonad m => MVector (PrimState m) Word8 -> Word8 -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word8 -> MVector (PrimState m) Word8 -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word8 -> MVector (PrimState m) Word8 -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> m (MVector (PrimState m) Word8)
Vector Vector Word8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> m (Vector Word8) basicUnsafeThaw :: PrimMonad m => Vector Word8 -> m (Mutable Vector (PrimState m) Word8) basicLength :: Vector Word8 -> Int basicUnsafeSlice :: Int -> Int -> Vector Word8 -> Vector Word8 basicUnsafeIndexM :: Monad m => Vector Word8 -> Int -> m Word8 basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> Vector Word8 -> m () elemseq :: Vector Word8 -> Word8 -> b -> b
Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString)
Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString)
Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8)
Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8)
MArray (STUArray s) Word8 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word8 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word8 -> ST s Int newArray :: Ix i => (i, i) -> Word8 -> ST s (STUArray s i Word8) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word8) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word8) unsafeRead :: Ix i => STUArray s i Word8 -> Int -> ST s Word8 unsafeWrite :: Ix i => STUArray s i Word8 -> Int -> Word8 -> ST s ()
newtype Vector Word8
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word8 = V_Word8 (Vector Word8)
newtype MVector s Word8
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word8 = MV_Word8 (MVector s Word8)

data Word32 #

32-bit unsigned integer type

Instances

Instances details

Bounded Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word32 # maxBound :: Word32 #
Enum Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word32 -> Word32 # pred :: Word32 -> Word32 # toEnum :: Int -> Word32 # fromEnum :: Word32 -> Int # enumFrom :: Word32 -> [Word32] # enumFromThen :: Word32 -> Word32 -> [Word32] # enumFromTo :: Word32 -> Word32 -> [Word32] # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] #
Eq Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word32 -> Word32 -> Bool # (/=) :: Word32 -> Word32 -> Bool #
Integral Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word32 -> Word32 -> Word32 # rem :: Word32 -> Word32 -> Word32 # div :: Word32 -> Word32 -> Word32 # mod :: Word32 -> Word32 -> Word32 # quotRem :: Word32 -> Word32 -> (Word32, Word32) # divMod :: Word32 -> Word32 -> (Word32, Word32) # toInteger :: Word32 -> Integer #
Num Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word32 -> Word32 -> Word32 # (-) :: Word32 -> Word32 -> Word32 # (*) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # abs :: Word32 -> Word32 # signum :: Word32 -> Word32 # fromInteger :: Integer -> Word32 #
Ord Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word32 -> Word32 -> Ordering # (<) :: Word32 -> Word32 -> Bool # (<=) :: Word32 -> Word32 -> Bool # (>) :: Word32 -> Word32 -> Bool # (>=) :: Word32 -> Word32 -> Bool # max :: Word32 -> Word32 -> Word32 # min :: Word32 -> Word32 -> Word32 #
Read Word32	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word32 # readList :: ReadS [Word32] # readPrec :: ReadPrec Word32 # readListPrec :: ReadPrec [Word32] #
Real Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word32 -> Rational #
Show Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word32 -> ShowS # show :: Word32 -> String # showList :: [Word32] -> ShowS #
Ix Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods range :: (Word32, Word32) -> [Word32] # index :: (Word32, Word32) -> Word32 -> Int # unsafeIndex :: (Word32, Word32) -> Word32 -> Int # inRange :: (Word32, Word32) -> Word32 -> Bool # rangeSize :: (Word32, Word32) -> Int # unsafeRangeSize :: (Word32, Word32) -> Int #
Ring Word32
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word32
Rig Word32
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word32 #
Characteristic Word32
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word32 -> Natural #
LocallyFiniteOrder Word32
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word32 -> Word32 -> [Word32] rangeSize :: Word32 -> Word32 -> Natural moebiusInversion :: Ring r => Word32 -> Word32 -> r
DecidableZero Word32
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word32 -> Bool #
DecidableUnits Word32
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word32 -> Maybe Word32 # isUnit :: Word32 -> Bool # (^?) :: Integral n => Word32 -> n -> Maybe Word32 #
DecidableAssociates Word32
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word32 -> Word32 -> Bool #
Unital Word32
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word32 # pow :: Word32 -> Natural -> Word32 # productWith :: Foldable f => (a -> Word32) -> f a -> Word32 #
TriviallyInvolutive Word32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Word32
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word32 -> Word32 #
Commutative Word32
Instance details Defined in Numeric.Algebra.Commutative
Semiring Word32
Instance details Defined in Numeric.Algebra.Class
Multiplicative Word32
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word32 -> Word32 -> Word32 # pow1p :: Word32 -> Natural -> Word32 # productWith1 :: Foldable1 f => (a -> Word32) -> f a -> Word32 #
Monoidal Word32
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word32 # sinnum :: Natural -> Word32 -> Word32 # sumWith :: Foldable f => (a -> Word32) -> f a -> Word32 #
Group Word32
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # subtract :: Word32 -> Word32 -> Word32 # times :: Integral n => n -> Word32 -> Word32 #
Additive Word32
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word32 -> Word32 -> Word32 # sinnum1p :: Natural -> Word32 -> Word32 # sumWith1 :: Foldable1 f => (a -> Word32) -> f a -> Word32 #
Abelian Word32
Instance details Defined in Numeric.Additive.Class
Unbox Word32
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Word32
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word32 -> Int # hash :: Word32 -> Int #
Storable Word32	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word32 -> Int # alignment :: Word32 -> Int # peekElemOff :: Ptr Word32 -> Int -> IO Word32 # pokeElemOff :: Ptr Word32 -> Int -> Word32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word32 # pokeByteOff :: Ptr b -> Int -> Word32 -> IO () # peek :: Ptr Word32 -> IO Word32 # poke :: Ptr Word32 -> Word32 -> IO () #
Bits Word32	Since: base-2.1
Instance details Defined in GHC.Word Methods (.&.) :: Word32 -> Word32 -> Word32 # (.\|.) :: Word32 -> Word32 -> Word32 # xor :: Word32 -> Word32 -> Word32 # complement :: Word32 -> Word32 # shift :: Word32 -> Int -> Word32 # rotate :: Word32 -> Int -> Word32 # zeroBits :: Word32 # bit :: Int -> Word32 # setBit :: Word32 -> Int -> Word32 # clearBit :: Word32 -> Int -> Word32 # complementBit :: Word32 -> Int -> Word32 # testBit :: Word32 -> Int -> Bool # bitSizeMaybe :: Word32 -> Maybe Int # bitSize :: Word32 -> Int # isSigned :: Word32 -> Bool # shiftL :: Word32 -> Int -> Word32 # unsafeShiftL :: Word32 -> Int -> Word32 # shiftR :: Word32 -> Int -> Word32 # unsafeShiftR :: Word32 -> Int -> Word32 # rotateL :: Word32 -> Int -> Word32 # rotateR :: Word32 -> Int -> Word32 # popCount :: Word32 -> Int #
FiniteBits Word32	Since: base-4.6.0.0
Instance details Defined in GHC.Word Methods finiteBitSize :: Word32 -> Int # countLeadingZeros :: Word32 -> Int # countTrailingZeros :: Word32 -> Int #
NFData Word32
Instance details Defined in Control.DeepSeq Methods rnf :: Word32 -> () #
PrettyCoeff Word32
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Word32 -> ShowSCoeff #
Prim Word32
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Word32 -> Int# alignment# :: Word32 -> Int# indexByteArray# :: ByteArray# -> Int# -> Word32 readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Word32 #) writeByteArray# :: MutableByteArray# s -> Int# -> Word32 -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Word32 -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Word32 readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Word32 #) writeOffAddr# :: Addr# -> Int# -> Word32 -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Word32 -> State# s -> State# s
Uniform Word32
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word32
UniformRange Word32
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Word32, Word32) -> g -> m Word32
Lift Word32
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Word32 -> Q Exp # liftTyped :: Word32 -> Q (TExp Word32) #
Rig r => Quadrance r Word32
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word32 -> r #
RightModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Integer -> Word32 #
RightModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Natural -> Word32 #
LeftModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word32 -> Word32 #
LeftModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word32 -> Word32 #
IArray UArray Word32
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word32 -> (i, i) # numElements :: Ix i => UArray i Word32 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word32)] -> UArray i Word32 unsafeAt :: Ix i => UArray i Word32 -> Int -> Word32 unsafeReplace :: Ix i => UArray i Word32 -> [(Int, Word32)] -> UArray i Word32 unsafeAccum :: Ix i => (Word32 -> e' -> Word32) -> UArray i Word32 -> [(Int, e')] -> UArray i Word32 unsafeAccumArray :: Ix i => (Word32 -> e' -> Word32) -> Word32 -> (i, i) -> [(Int, e')] -> UArray i Word32
MVector MVector Word32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word32 -> Int basicUnsafeSlice :: Int -> Int -> MVector s Word32 -> MVector s Word32 basicOverlaps :: MVector s Word32 -> MVector s Word32 -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word32) basicInitialize :: PrimMonad m => MVector (PrimState m) Word32 -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Word32 -> m (MVector (PrimState m) Word32) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> m Word32 basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> Word32 -> m () basicClear :: PrimMonad m => MVector (PrimState m) Word32 -> m () basicSet :: PrimMonad m => MVector (PrimState m) Word32 -> Word32 -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word32 -> MVector (PrimState m) Word32 -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word32 -> MVector (PrimState m) Word32 -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> m (MVector (PrimState m) Word32)
Vector Vector Word32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> m (Vector Word32) basicUnsafeThaw :: PrimMonad m => Vector Word32 -> m (Mutable Vector (PrimState m) Word32) basicLength :: Vector Word32 -> Int basicUnsafeSlice :: Int -> Int -> Vector Word32 -> Vector Word32 basicUnsafeIndexM :: Monad m => Vector Word32 -> Int -> m Word32 basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> Vector Word32 -> m () elemseq :: Vector Word32 -> Word32 -> b -> b
MArray (STUArray s) Word32 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word32 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word32 -> ST s Int newArray :: Ix i => (i, i) -> Word32 -> ST s (STUArray s i Word32) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word32) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word32) unsafeRead :: Ix i => STUArray s i Word32 -> Int -> ST s Word32 unsafeWrite :: Ix i => STUArray s i Word32 -> Int -> Word32 -> ST s ()
newtype Vector Word32
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word32 = V_Word32 (Vector Word32)
newtype MVector s Word32
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word32 = MV_Word32 (MVector s Word32)

data Word64 #

64-bit unsigned integer type

Instances

Instances details

Bounded Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods minBound :: Word64 # maxBound :: Word64 #
Enum Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods succ :: Word64 -> Word64 # pred :: Word64 -> Word64 # toEnum :: Int -> Word64 # fromEnum :: Word64 -> Int # enumFrom :: Word64 -> [Word64] # enumFromThen :: Word64 -> Word64 -> [Word64] # enumFromTo :: Word64 -> Word64 -> [Word64] # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] #
Eq Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (==) :: Word64 -> Word64 -> Bool # (/=) :: Word64 -> Word64 -> Bool #
Integral Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods quot :: Word64 -> Word64 -> Word64 # rem :: Word64 -> Word64 -> Word64 # div :: Word64 -> Word64 -> Word64 # mod :: Word64 -> Word64 -> Word64 # quotRem :: Word64 -> Word64 -> (Word64, Word64) # divMod :: Word64 -> Word64 -> (Word64, Word64) # toInteger :: Word64 -> Integer #
Num Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (+) :: Word64 -> Word64 -> Word64 # (-) :: Word64 -> Word64 -> Word64 # (*) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # abs :: Word64 -> Word64 # signum :: Word64 -> Word64 # fromInteger :: Integer -> Word64 #
Ord Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods compare :: Word64 -> Word64 -> Ordering # (<) :: Word64 -> Word64 -> Bool # (<=) :: Word64 -> Word64 -> Bool # (>) :: Word64 -> Word64 -> Bool # (>=) :: Word64 -> Word64 -> Bool # max :: Word64 -> Word64 -> Word64 # min :: Word64 -> Word64 -> Word64 #
Read Word64	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word64 # readList :: ReadS [Word64] # readPrec :: ReadPrec Word64 # readListPrec :: ReadPrec [Word64] #
Real Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods toRational :: Word64 -> Rational #
Show Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods showsPrec :: Int -> Word64 -> ShowS # show :: Word64 -> String # showList :: [Word64] -> ShowS #
Ix Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods range :: (Word64, Word64) -> [Word64] # index :: (Word64, Word64) -> Word64 -> Int # unsafeIndex :: (Word64, Word64) -> Word64 -> Int # inRange :: (Word64, Word64) -> Word64 -> Bool # rangeSize :: (Word64, Word64) -> Int # unsafeRangeSize :: (Word64, Word64) -> Int #
Ring Word64
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word64
Rig Word64
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word64 #
Characteristic Word64
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word64 -> Natural #
LocallyFiniteOrder Word64
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word64 -> Word64 -> [Word64] rangeSize :: Word64 -> Word64 -> Natural moebiusInversion :: Ring r => Word64 -> Word64 -> r
DecidableZero Word64
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word64 -> Bool #
DecidableUnits Word64
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word64 -> Maybe Word64 # isUnit :: Word64 -> Bool # (^?) :: Integral n => Word64 -> n -> Maybe Word64 #
DecidableAssociates Word64
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word64 -> Word64 -> Bool #
Unital Word64
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word64 # pow :: Word64 -> Natural -> Word64 # productWith :: Foldable f => (a -> Word64) -> f a -> Word64 #
TriviallyInvolutive Word64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveMultiplication Word64
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word64 -> Word64 #
Commutative Word64
Instance details Defined in Numeric.Algebra.Commutative
Semiring Word64
Instance details Defined in Numeric.Algebra.Class
Multiplicative Word64
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word64 -> Word64 -> Word64 # pow1p :: Word64 -> Natural -> Word64 # productWith1 :: Foldable1 f => (a -> Word64) -> f a -> Word64 #
Monoidal Word64
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word64 # sinnum :: Natural -> Word64 -> Word64 # sumWith :: Foldable f => (a -> Word64) -> f a -> Word64 #
Group Word64
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # subtract :: Word64 -> Word64 -> Word64 # times :: Integral n => n -> Word64 -> Word64 #
Additive Word64
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word64 -> Word64 -> Word64 # sinnum1p :: Natural -> Word64 -> Word64 # sumWith1 :: Foldable1 f => (a -> Word64) -> f a -> Word64 #
Abelian Word64
Instance details Defined in Numeric.Additive.Class
Unbox Word64
Instance details Defined in Data.Vector.Unboxed.Base
Hashable Word64
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word64 -> Int # hash :: Word64 -> Int #
Storable Word64	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word64 -> Int # alignment :: Word64 -> Int # peekElemOff :: Ptr Word64 -> Int -> IO Word64 # pokeElemOff :: Ptr Word64 -> Int -> Word64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word64 # pokeByteOff :: Ptr b -> Int -> Word64 -> IO () # peek :: Ptr Word64 -> IO Word64 # poke :: Ptr Word64 -> Word64 -> IO () #
Bits Word64	Since: base-2.1
Instance details Defined in GHC.Word Methods (.&.) :: Word64 -> Word64 -> Word64 # (.\|.) :: Word64 -> Word64 -> Word64 # xor :: Word64 -> Word64 -> Word64 # complement :: Word64 -> Word64 # shift :: Word64 -> Int -> Word64 # rotate :: Word64 -> Int -> Word64 # zeroBits :: Word64 # bit :: Int -> Word64 # setBit :: Word64 -> Int -> Word64 # clearBit :: Word64 -> Int -> Word64 # complementBit :: Word64 -> Int -> Word64 # testBit :: Word64 -> Int -> Bool # bitSizeMaybe :: Word64 -> Maybe Int # bitSize :: Word64 -> Int # isSigned :: Word64 -> Bool # shiftL :: Word64 -> Int -> Word64 # unsafeShiftL :: Word64 -> Int -> Word64 # shiftR :: Word64 -> Int -> Word64 # unsafeShiftR :: Word64 -> Int -> Word64 # rotateL :: Word64 -> Int -> Word64 # rotateR :: Word64 -> Int -> Word64 # popCount :: Word64 -> Int #
FiniteBits Word64	Since: base-4.6.0.0
Instance details Defined in GHC.Word Methods finiteBitSize :: Word64 -> Int # countLeadingZeros :: Word64 -> Int # countTrailingZeros :: Word64 -> Int #
NFData Word64
Instance details Defined in Control.DeepSeq Methods rnf :: Word64 -> () #
PrettyCoeff Word64
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Word64 -> ShowSCoeff #
Prim Word64
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Word64 -> Int# alignment# :: Word64 -> Int# indexByteArray# :: ByteArray# -> Int# -> Word64 readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Word64 #) writeByteArray# :: MutableByteArray# s -> Int# -> Word64 -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Word64 -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Word64 readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Word64 #) writeOffAddr# :: Addr# -> Int# -> Word64 -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Word64 -> State# s -> State# s
Uniform Word64
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word64
UniformRange Word64
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Word64, Word64) -> g -> m Word64
Lift Word64
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Word64 -> Q Exp # liftTyped :: Word64 -> Q (TExp Word64) #
Rig r => Quadrance r Word64
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word64 -> r #
RightModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Integer -> Word64 #
RightModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Natural -> Word64 #
LeftModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word64 -> Word64 #
LeftModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word64 -> Word64 #
IArray UArray Word64
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word64 -> (i, i) # numElements :: Ix i => UArray i Word64 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word64)] -> UArray i Word64 unsafeAt :: Ix i => UArray i Word64 -> Int -> Word64 unsafeReplace :: Ix i => UArray i Word64 -> [(Int, Word64)] -> UArray i Word64 unsafeAccum :: Ix i => (Word64 -> e' -> Word64) -> UArray i Word64 -> [(Int, e')] -> UArray i Word64 unsafeAccumArray :: Ix i => (Word64 -> e' -> Word64) -> Word64 -> (i, i) -> [(Int, e')] -> UArray i Word64
MVector MVector Word64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word64 -> Int basicUnsafeSlice :: Int -> Int -> MVector s Word64 -> MVector s Word64 basicOverlaps :: MVector s Word64 -> MVector s Word64 -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word64) basicInitialize :: PrimMonad m => MVector (PrimState m) Word64 -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Word64 -> m (MVector (PrimState m) Word64) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> m Word64 basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> Word64 -> m () basicClear :: PrimMonad m => MVector (PrimState m) Word64 -> m () basicSet :: PrimMonad m => MVector (PrimState m) Word64 -> Word64 -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word64 -> MVector (PrimState m) Word64 -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word64 -> MVector (PrimState m) Word64 -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> m (MVector (PrimState m) Word64)
Vector Vector Word64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> m (Vector Word64) basicUnsafeThaw :: PrimMonad m => Vector Word64 -> m (Mutable Vector (PrimState m) Word64) basicLength :: Vector Word64 -> Int basicUnsafeSlice :: Int -> Int -> Vector Word64 -> Vector Word64 basicUnsafeIndexM :: Monad m => Vector Word64 -> Int -> m Word64 basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> Vector Word64 -> m () elemseq :: Vector Word64 -> Word64 -> b -> b
MArray (STUArray s) Word64 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word64 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word64 -> ST s Int newArray :: Ix i => (i, i) -> Word64 -> ST s (STUArray s i Word64) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word64) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word64) unsafeRead :: Ix i => STUArray s i Word64 -> Int -> ST s Word64 unsafeWrite :: Ix i => STUArray s i Word64 -> Int -> Word64 -> ST s ()
newtype Vector Word64
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word64 = V_Word64 (Vector Word64)
newtype MVector s Word64
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word64 = MV_Word64 (MVector s Word64)

data Either a b #

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples

Expand

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}

>>> parseMultiple
Left "parse error"

Constructors

Left a
Right b

Instances

Instances details

Bifunctor Either	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Eq2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool #
Ord2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering #
Read2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] #
Show2 Either	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS #
NFData2 Either	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> Either a b -> () #
Swapped Either
Instance details Defined in Control.Lens.Iso Methods swapped :: Iso (Either a b) (Either c d) (Either b a) (Either d c)
Hashable2 Either
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Either a b -> Int
Bifoldable1 Either
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Either m m -> m bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Either a b -> m
Bitraversable1 Either
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Either a c -> f (Either b d) bisequence1 :: Apply f => Either (f a) (f b) -> f (Either a b)
(Lift a, Lift b) => Lift (Either a b :: Type)
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Either a b -> Q Exp # liftTyped :: Either a b -> Q (TExp (Either a b)) #
Monad (Either e)	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b # (>>) :: Either e a -> Either e b -> Either e b # return :: a -> Either e a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Foldable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # null :: Either a a0 -> Bool # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # sum :: Num a0 => Either a a0 -> a0 # product :: Num a0 => Either a a0 -> a0 #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Eq a => Eq1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a0 -> b -> Bool) -> Either a a0 -> Either a b -> Bool #
Ord a => Ord1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a0 -> b -> Ordering) -> Either a a0 -> Either a b -> Ordering #
Read a => Read1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] #
Show a => Show1 (Either a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Either a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Either a a0] -> ShowS #
NFData a => NFData1 (Either a)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a0 -> ()) -> Either a a0 -> () #
PFoldable (Either a)
Instance details Defined in Data.Singletons.Prelude.Foldable Associated Types type Fold arg :: m type FoldMap arg arg1 :: m type Foldr arg arg1 arg2 :: b type Foldr' arg arg1 arg2 :: b type Foldl arg arg1 arg2 :: b type Foldl' arg arg1 arg2 :: b type Foldr1 arg arg1 :: a type Foldl1 arg arg1 :: a type ToList arg :: [a] type Null arg :: Bool type Length arg :: Nat type Elem arg arg1 :: Bool type Maximum arg :: a type Minimum arg :: a type Sum arg :: a type Product arg :: a
SFoldable (Either a)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods sFold :: forall m (t1 :: Either a m). SMonoid m => Sing t1 -> Sing (Apply FoldSym0 t1) sFoldMap :: forall a0 m (t1 :: a0 ~> m) (t2 :: Either a a0). SMonoid m => Sing t1 -> Sing t2 -> Sing (Apply (Apply FoldMapSym0 t1) t2) sFoldr :: forall a0 b (t1 :: a0 ~> (b ~> b)) (t2 :: b) (t3 :: Either a a0). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldrSym0 t1) t2) t3) sFoldr' :: forall a0 b (t1 :: a0 ~> (b ~> b)) (t2 :: b) (t3 :: Either a a0). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldr'Sym0 t1) t2) t3) sFoldl :: forall b a0 (t1 :: b ~> (a0 ~> b)) (t2 :: b) (t3 :: Either a a0). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldlSym0 t1) t2) t3) sFoldl' :: forall b a0 (t1 :: b ~> (a0 ~> b)) (t2 :: b) (t3 :: Either a a0). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldl'Sym0 t1) t2) t3) sFoldr1 :: forall a0 (t1 :: a0 ~> (a0 ~> a0)) (t2 :: Either a a0). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldr1Sym0 t1) t2) sFoldl1 :: forall a0 (t1 :: a0 ~> (a0 ~> a0)) (t2 :: Either a a0). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldl1Sym0 t1) t2) sToList :: forall a0 (t1 :: Either a a0). Sing t1 -> Sing (Apply ToListSym0 t1) sNull :: forall a0 (t1 :: Either a a0). Sing t1 -> Sing (Apply NullSym0 t1) sLength :: forall a0 (t1 :: Either a a0). Sing t1 -> Sing (Apply LengthSym0 t1) sElem :: forall a0 (t1 :: a0) (t2 :: Either a a0). SEq a0 => Sing t1 -> Sing t2 -> Sing (Apply (Apply ElemSym0 t1) t2) sMaximum :: forall a0 (t1 :: Either a a0). SOrd a0 => Sing t1 -> Sing (Apply MaximumSym0 t1) sMinimum :: forall a0 (t1 :: Either a a0). SOrd a0 => Sing t1 -> Sing (Apply MinimumSym0 t1) sSum :: forall a0 (t1 :: Either a a0). SNum a0 => Sing t1 -> Sing (Apply SumSym0 t1) sProduct :: forall a0 (t1 :: Either a a0). SNum a0 => Sing t1 -> Sing (Apply ProductSym0 t1)
CFoldable (Either e)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (Either e) a, Monoid w) => (a -> w) -> Either e a -> w cfoldMap' :: (Dom (Either e) a, Monoid m) => (a -> m) -> Either e a -> m cfold :: (Dom (Either e) w, Monoid w) => Either e w -> w cfoldr :: Dom (Either e) a => (a -> b -> b) -> b -> Either e a -> b cfoldlM :: (Monad m, Dom (Either e) b) => (a -> b -> m a) -> a -> Either e b -> m a cfoldlM' :: (Monad m, Dom (Either e) b) => (a -> b -> m a) -> a -> Either e b -> m a cfoldrM :: (Monad m, Dom (Either e) a) => (a -> b -> m b) -> b -> Either e a -> m b cfoldrM' :: (Monad m, Dom (Either e) a) => (a -> b -> m b) -> b -> Either e a -> m b cfoldl :: Dom (Either e) a => (b -> a -> b) -> b -> Either e a -> b cfoldr' :: Dom (Either e) a => (a -> b -> b) -> b -> Either e a -> b cfoldl' :: Dom (Either e) a => (b -> a -> b) -> b -> Either e a -> b cbasicToList :: Dom (Either e) a => Either e a -> [a] cfoldr1 :: Dom (Either e) a => (a -> a -> a) -> Either e a -> a cfoldl1 :: Dom (Either e) a => (a -> a -> a) -> Either e a -> a cindex :: Dom (Either e) a => Either e a -> Int -> a cnull :: Dom (Either e) a => Either e a -> Bool clength :: Dom (Either e) a => Either e a -> Int cany :: Dom (Either e) a => (a -> Bool) -> Either e a -> Bool call :: Dom (Either e) a => (a -> Bool) -> Either e a -> Bool celem :: (Eq a, Dom (Either e) a) => a -> Either e a -> Bool cnotElem :: (Eq a, Dom (Either e) a) => a -> Either e a -> Bool cminimum :: (Ord a, Dom (Either e) a) => Either e a -> a cmaximum :: (Ord a, Dom (Either e) a) => Either e a -> a csum :: (Num a, Dom (Either e) a) => Either e a -> a cproduct :: (Num a, Dom (Either e) a) => Either e a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (Either e) a, Dom g b) => (a -> g b) -> Either e a -> g () ctraverse_ :: (Applicative g, Dom (Either e) a) => (a -> g b) -> Either e a -> g () clast :: Dom (Either e) a => Either e a -> a chead :: Dom (Either e) a => Either e a -> a cfind :: Dom (Either e) a => (a -> Bool) -> Either e a -> Maybe a cfindIndex :: Dom (Either e) a => (a -> Bool) -> Either e a -> Maybe Int cfindIndices :: Dom (Either e) a => (a -> Bool) -> Either e a -> [Int] celemIndex :: (Dom (Either e) a, Eq a) => a -> Either e a -> Maybe Int celemIndices :: (Dom (Either e) a, Eq a) => a -> Either e a -> [Int]
CFunctor (Either a)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (Either a) a0, Dom (Either a) b) => (a0 -> b) -> Either a a0 -> Either a b (<$:) :: (Dom (Either a) a0, Dom (Either a) b) => a0 -> Either a b -> Either a a0
CPointed (Either a)
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom (Either a) a0 => a0 -> Either a a0
CTraversable (Either e)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (Either e) a, Dom (Either e) b, Applicative g) => (a -> g b) -> Either e a -> g (Either e b)
PFunctor (Either a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Fmap arg arg1 :: f b type arg <$ arg1 :: f a
PMonad (Either e)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type arg >>= arg1 :: m b type arg >> arg1 :: m b type Return arg :: m a
SFunctor (Either a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sFmap :: forall a0 b (t1 :: a0 ~> b) (t2 :: Either a a0). Sing t1 -> Sing t2 -> Sing (Apply (Apply FmapSym0 t1) t2) (%<$) :: forall a0 b (t1 :: a0) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<$@#@$) t1) t2)
SMonad (Either e)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods (%>>=) :: forall a b (t1 :: Either e a) (t2 :: a ~> Either e b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>=@#@$) t1) t2) (%>>) :: forall a b (t1 :: Either e a) (t2 :: Either e b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>@#@$) t1) t2) sReturn :: forall a (t :: a). Sing t -> Sing (Apply ReturnSym0 t)
PTraversable (Either a)
Instance details Defined in Data.Singletons.Prelude.Traversable Associated Types type Traverse arg arg1 :: f (t b) type SequenceA arg :: f (t a) type MapM arg arg1 :: m (t b) type Sequence arg :: m (t a)
STraversable (Either a)
Instance details Defined in Data.Singletons.Prelude.Traversable Methods sTraverse :: forall a0 (f :: Type -> Type) b (t1 :: a0 ~> f b) (t2 :: Either a a0). SApplicative f => Sing t1 -> Sing t2 -> Sing (Apply (Apply TraverseSym0 t1) t2) sSequenceA :: forall (f :: Type -> Type) a0 (t1 :: Either a (f a0)). SApplicative f => Sing t1 -> Sing (Apply SequenceASym0 t1) sMapM :: forall a0 (m :: Type -> Type) b (t1 :: a0 ~> m b) (t2 :: Either a a0). SMonad m => Sing t1 -> Sing t2 -> Sing (Apply (Apply MapMSym0 t1) t2) sSequence :: forall (m :: Type -> Type) a0 (t1 :: Either a (m a0)). SMonad m => Sing t1 -> Sing (Apply SequenceSym0 t1)
SApplicative (Either e)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods sPure :: forall a (t :: a). Sing t -> Sing (Apply PureSym0 t) (%<>) :: forall a b (t1 :: Either e (a ~> b)) (t2 :: Either e a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sLiftA2 :: forall a b c (t1 :: a ~> (b ~> c)) (t2 :: Either e a) (t3 :: Either e b). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply LiftA2Sym0 t1) t2) t3) (%>) :: forall a b (t1 :: Either e a) (t2 :: Either e b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%<) :: forall a b (t1 :: Either e a) (t2 :: Either e b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2)
PApplicative (Either e)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Associated Types type Pure arg :: f a type arg <> arg1 :: f b type LiftA2 arg arg1 arg2 :: f c type arg > arg1 :: f b type arg <* arg1 :: f a
Apply (Either a)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Either a (a0 -> b) -> Either a a0 -> Either a b (.>) :: Either a a0 -> Either a b -> Either a b (<.) :: Either a a0 -> Either a b -> Either a a0 liftF2 :: (a0 -> b -> c) -> Either a a0 -> Either a b -> Either a c
Bind (Either a)
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Either a a0 -> (a0 -> Either a b) -> Either a b join :: Either a (Either a a0) -> Either a a0
Constrained (Either a)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (Either a) a
Hashable a => Hashable1 (Either a)
Instance details Defined in Data.Hashable.Class Methods liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Either a a0 -> Int
Generic1 (Either a :: Type -> Type)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 (Either a) :: k -> Type # Methods from1 :: forall (a0 :: k). Either a a0 -> Rep1 (Either a) a0 # to1 :: forall (a0 :: k). Rep1 (Either a) a0 -> Either a a0 #
(Eq a, Eq b) => Eq (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool # (/=) :: Either a b -> Either a b -> Bool #
(Ord a, Ord b) => Ord (Either a b)	Since: base-2.1
Instance details Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering # (<) :: Either a b -> Either a b -> Bool # (<=) :: Either a b -> Either a b -> Bool # (>) :: Either a b -> Either a b -> Bool # (>=) :: Either a b -> Either a b -> Bool # max :: Either a b -> Either a b -> Either a b # min :: Either a b -> Either a b -> Either a b #
(Read a, Read b) => Read (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) # readList :: ReadS [Either a b] # readPrec :: ReadPrec (Either a b) # readListPrec :: ReadPrec [Either a b] #
(Show a, Show b) => Show (Either a b)	Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS # show :: Either a b -> String # showList :: [Either a b] -> ShowS #
Generic (Either a b)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (Either a b) :: Type -> Type # Methods from :: Either a b -> Rep (Either a b) x # to :: Rep (Either a b) x -> Either a b #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
(Hashable a, Hashable b) => Hashable (Either a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Either a b -> Int # hash :: Either a b -> Int #
(NFData a, NFData b) => NFData (Either a b)
Instance details Defined in Control.DeepSeq Methods rnf :: Either a b -> () #
MonoFoldable (Either a b)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Either a b) -> m) -> Either a b -> m ofoldr :: (Element (Either a b) -> b0 -> b0) -> b0 -> Either a b -> b0 ofoldl' :: (a0 -> Element (Either a b) -> a0) -> a0 -> Either a b -> a0 otoList :: Either a b -> [Element (Either a b)] oall :: (Element (Either a b) -> Bool) -> Either a b -> Bool oany :: (Element (Either a b) -> Bool) -> Either a b -> Bool onull :: Either a b -> Bool olength :: Either a b -> Int olength64 :: Either a b -> Int64 ocompareLength :: Integral i => Either a b -> i -> Ordering otraverse_ :: Applicative f => (Element (Either a b) -> f b0) -> Either a b -> f () ofor_ :: Applicative f => Either a b -> (Element (Either a b) -> f b0) -> f () omapM_ :: Applicative m => (Element (Either a b) -> m ()) -> Either a b -> m () oforM_ :: Applicative m => Either a b -> (Element (Either a b) -> m ()) -> m () ofoldlM :: Monad m => (a0 -> Element (Either a b) -> m a0) -> a0 -> Either a b -> m a0 ofoldMap1Ex :: Semigroup m => (Element (Either a b) -> m) -> Either a b -> m ofoldr1Ex :: (Element (Either a b) -> Element (Either a b) -> Element (Either a b)) -> Either a b -> Element (Either a b) ofoldl1Ex' :: (Element (Either a b) -> Element (Either a b) -> Element (Either a b)) -> Either a b -> Element (Either a b) headEx :: Either a b -> Element (Either a b) lastEx :: Either a b -> Element (Either a b) unsafeHead :: Either a b -> Element (Either a b) unsafeLast :: Either a b -> Element (Either a b) maximumByEx :: (Element (Either a b) -> Element (Either a b) -> Ordering) -> Either a b -> Element (Either a b) minimumByEx :: (Element (Either a b) -> Element (Either a b) -> Ordering) -> Either a b -> Element (Either a b) oelem :: Element (Either a b) -> Either a b -> Bool onotElem :: Element (Either a b) -> Either a b -> Bool
MonoFunctor (Either a b)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (Either a b) -> Element (Either a b)) -> Either a b -> Either a b
MonoPointed (Either a b)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (Either a b) -> Either a b
MonoTraversable (Either a b)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (Either a b) -> f (Element (Either a b))) -> Either a b -> f (Either a b) omapM :: Applicative m => (Element (Either a b) -> m (Element (Either a b))) -> Either a b -> m (Either a b)
(SEq a, SEq b) => SEq (Either a b)
Instance details Defined in Data.Singletons.Prelude.Eq Methods (%==) :: forall (a0 :: Either a b) (b0 :: Either a b). Sing a0 -> Sing b0 -> Sing (a0 == b0) (%/=) :: forall (a0 :: Either a b) (b0 :: Either a b). Sing a0 -> Sing b0 -> Sing (a0 /= b0)
SSemigroup (Either a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%<>) :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sSconcat :: forall (t :: NonEmpty (Either a b)). Sing t -> Sing (Apply SconcatSym0 t)
(SOrd a, SOrd b) => SOrd (Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sCompare :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply CompareSym0 t1) t2) (%<) :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2) (%<=) :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<=@#@$) t1) t2) (%>) :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%>=) :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>=@#@$) t1) t2) sMax :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply MaxSym0 t1) t2) sMin :: forall (t1 :: Either a b) (t2 :: Either a b). Sing t1 -> Sing t2 -> Sing (Apply (Apply MinSym0 t1) t2)
PSemigroup (Either a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Associated Types type arg <> arg1 :: a type Sconcat arg :: a
PEq (Either a b)
Instance details Defined in Data.Singletons.Prelude.Eq Associated Types type x == y :: Bool type x /= y :: Bool
POrd (Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord Associated Types type Compare arg arg1 :: Ordering type arg < arg1 :: Bool type arg <= arg1 :: Bool type arg > arg1 :: Bool type arg >= arg1 :: Bool type Max arg arg1 :: a type Min arg arg1 :: a
PShow (Either a b)
Instance details Defined in Data.Singletons.Prelude.Show Associated Types type ShowsPrec arg arg1 arg2 :: Symbol type Show_ arg :: Symbol type ShowList arg arg1 :: Symbol
(SShow a, SShow b) => SShow (Either a b)
Instance details Defined in Data.Singletons.Prelude.Show Methods sShowsPrec :: forall (t1 :: Nat) (t2 :: Either a b) (t3 :: Symbol). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply ShowsPrecSym0 t1) t2) t3) sShow_ :: forall (t :: Either a b). Sing t -> Sing (Apply Show_Sym0 t) sShowList :: forall (t1 :: [Either a b]) (t2 :: Symbol). Sing t1 -> Sing t2 -> Sing (Apply (Apply ShowListSym0 t1) t2)
(Empty a, Empty b) => Empty (Either a b)
Instance details Defined in Proof.Propositional.Empty Methods eliminate :: Either a b -> x
(SDecide a, SDecide b) => TestCoercion (SEither :: Either a b -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods testCoercion :: forall (a0 :: k) (b0 :: k). SEither a0 -> SEither b0 -> Maybe (Coercion a0 b0) #
(SDecide a, SDecide b) => TestEquality (SEither :: Either a b -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods testEquality :: forall (a0 :: k) (b0 :: k). SEither a0 -> SEither b0 -> Maybe (a0 :~: b0) #
SingI (RightsSym0 :: TyFun [Either a b] [b] -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing RightsSym0 #
SingI (PartitionEithersSym0 :: TyFun [Either a b] ([a], [b]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing PartitionEithersSym0 #
SingI (LeftsSym0 :: TyFun [Either a b] [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing LeftsSym0 #
SingI (IsRightSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsRightSym0 #
SingI (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsLeftSym0 #
SingI (RightSym0 :: TyFun b (Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods sing :: Sing RightSym0 #
SingI (LeftSym0 :: TyFun a (Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods sing :: Sing LeftSym0 #
SuppressUnusedWarnings (RightsSym0 :: TyFun [Either a b] [b] -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (PartitionEithersSym0 :: TyFun [Either a b] ([a], [b]) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LeftsSym0 :: TyFun [Either a b] [a] -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Length_6989586621680823420Sym0 :: TyFun (Either a1 a2) Nat -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240844Sym0 :: TyFun (Either a b) (Either a b ~> Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (ShowsPrec_6989586621680653998Sym0 :: TyFun Nat (Either a b ~> (Symbol ~> Symbol)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Pure_6989586621680072973Sym0 :: TyFun a (Either e a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (RightSym0 :: TyFun b (Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (LeftSym0 :: TyFun a (Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Instances Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Let6989586621680240853ASym0 :: TyFun k1 (Either a k1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
(a ~ a', b ~ b') => Each (Either a a') (Either b b') a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Either a a') (Either b b') a b
SingI (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing Either_Sym0 #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Sum f g a -> m ifolded :: IndexedFold (Either i j) (Sum f g a) a ifoldr :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b ifoldl :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b ifoldr' :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b ifoldl' :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Product f g a -> m ifolded :: IndexedFold (Either i j) (Product f g a) a ifoldr :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b ifoldl :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b ifoldr' :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b ifoldl' :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :+: g) a -> m ifolded :: IndexedFold (Either i j) ((f :+: g) a) a ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :: g) a -> m ifolded :: IndexedFold (Either i j) ((f :: g) a) a ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Sum f g a -> Sum f g b imapped :: IndexedSetter (Either i j) (Sum f g a) (Sum f g b) a b
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Product f g a -> Product f g b imapped :: IndexedSetter (Either i j) (Product f g a) (Product f g b) a b
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :+: g) a -> (f :+: g) b imapped :: IndexedSetter (Either i j) ((f :+: g) a) ((f :+: g) b) a b
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :: g) a -> (f :: g) b imapped :: IndexedSetter (Either i j) ((f :: g) a) ((f :: g) b) a b
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Sum f g a -> f0 (Sum f g b) itraversed :: IndexedTraversal (Either i j) (Sum f g a) (Sum f g b) a b
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Product f g a -> f0 (Product f g b) itraversed :: IndexedTraversal (Either i j) (Product f g a) (Product f g b) a b
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) itraversed :: IndexedTraversal (Either i j) ((f :+: g) a) ((f :+: g) b) a b
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) itraversed :: IndexedTraversal (Either i j) ((f :: g) a) ((f :: g) b) a b
SuppressUnusedWarnings (ShowsPrec_6989586621680653998Sym1 a6989586621680654008 :: TyFun (Either a b) (Symbol ~> Symbol) -> Type)
Instance details Defined in Data.Singletons.Prelude.Show Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073067Sym0 :: TyFun (Either e a) ((a ~> Either e b) ~> Either e b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072983Sym0 :: TyFun (Either e (a ~> b)) (Either e a ~> Either e b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240844Sym1 a6989586621680240849 :: TyFun (Either a b) (Either a b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072804Sym0 :: TyFun a1 (Either a2 b ~> Either a2 a1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680072787Sym0 :: TyFun (a1 ~> b) (Either a2 a1 ~> Either a2 b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823406Sym0 :: TyFun (a1 ~> (b ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FoldMap_6989586621680823394Sym0 :: TyFun (a1 ~> m) (Either a2 a1 ~> m) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
SingI d => SingI (Either_Sym1 d :: TyFun (b ~> c) (Either a b ~> c) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing (Either_Sym1 d) #
SuppressUnusedWarnings (TFHelper_6989586621680072983Sym1 a6989586621680072988 :: TyFun (Either e a) (Either e b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680072804Sym1 a6989586621680072809 :: TyFun (Either a2 b) (Either a2 a1) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680072787Sym1 a6989586621680072792 :: TyFun (Either a2 a1) (Either a2 b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (FoldMap_6989586621680823394Sym1 a6989586621680823399 :: TyFun (Either a2 a1) m -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823406Sym1 a6989586621680823412 :: TyFun b (Either a2 a1 ~> b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Traverse_6989586621681088340Sym0 :: TyFun (a1 ~> f b) (Either a2 a1 ~> f (Either a2 b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Traversable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680073067Sym1 a6989586621680073072 :: TyFun (a ~> Either e b) (Either e b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Either_Sym1 a6989586621680802381 :: TyFun (b ~> c) (Either a b ~> c) -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
(SingI d1, SingI d2) => SingI (Either_Sym2 d1 d2 :: TyFun (Either a b) c -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing (Either_Sym2 d1 d2) #
SuppressUnusedWarnings (Traverse_6989586621681088340Sym1 a6989586621681088345 :: TyFun (Either a2 a1) (f (Either a2 b)) -> Type)
Instance details Defined in Data.Singletons.Prelude.Traversable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Foldr_6989586621680823406Sym2 a6989586621680823412 a6989586621680823413 :: TyFun (Either a2 a1) b -> Type)
Instance details Defined in Data.Singletons.Prelude.Foldable Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Either_Sym2 a6989586621680802381 a6989586621680802382 :: TyFun (Either a b) c -> Type)
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: ()
type MapM (arg1 :: a1 ~> m b) (arg2 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Traversable type MapM (arg1 :: a1 ~> m b) (arg2 :: Either a2 a1) = Apply (Apply (MapM_6989586621681082084Sym0 :: TyFun (a1 ~> m b) (Either a2 a1 ~> m (Either a2 b)) -> Type) arg1) arg2
type Traverse (a3 :: a1 ~> f b) (a4 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Traversable type Traverse (a3 :: a1 ~> f b) (a4 :: Either a2 a1) = Apply (Apply (Traverse_6989586621681088340Sym0 :: TyFun (a1 ~> f b) (Either a2 a1 ~> f (Either a2 b)) -> Type) a3) a4
type LiftA2 (arg1 :: a ~> (b ~> c)) (arg2 :: Either e a) (arg3 :: Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type LiftA2 (arg1 :: a ~> (b ~> c)) (arg2 :: Either e a) (arg3 :: Either e b) = Apply (Apply (Apply (LiftA2_6989586621680011983Sym0 :: TyFun (a ~> (b ~> c)) (Either e a ~> (Either e b ~> Either e c)) -> Type) arg1) arg2) arg3
type Fmap (a3 :: a1 ~> b) (a4 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Fmap (a3 :: a1 ~> b) (a4 :: Either a2 a1) = Apply (Apply (Fmap_6989586621680072787Sym0 :: TyFun (a1 ~> b) (Either a2 a1 ~> Either a2 b) -> Type) a3) a4
type FoldMap (a3 :: a1 ~> k2) (a4 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type FoldMap (a3 :: a1 ~> k2) (a4 :: Either a2 a1) = Apply (Apply (FoldMap_6989586621680823394Sym0 :: TyFun (a1 ~> k2) (Either a2 a1 ~> k2) -> Type) a3) a4
type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1) = Apply (Apply (Apply (Foldl_6989586621680822898Sym0 :: TyFun (b ~> (a1 ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type) arg1) arg2) arg3
type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl' (arg1 :: b ~> (a1 ~> b)) (arg2 :: b) (arg3 :: Either a2 a1) = Apply (Apply (Apply (Foldl'_6989586621680822913Sym0 :: TyFun (b ~> (a1 ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type) arg1) arg2) arg3
type Foldr (a3 :: a1 ~> (k2 ~> k2)) (a4 :: k2) (a5 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr (a3 :: a1 ~> (k2 ~> k2)) (a4 :: k2) (a5 :: Either a2 a1) = Apply (Apply (Apply (Foldr_6989586621680823406Sym0 :: TyFun (a1 ~> (k2 ~> k2)) (k2 ~> (Either a2 a1 ~> k2)) -> Type) a3) a4) a5
type Foldr' (arg1 :: a1 ~> (b ~> b)) (arg2 :: b) (arg3 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr' (arg1 :: a1 ~> (b ~> b)) (arg2 :: b) (arg3 :: Either a2 a1) = Apply (Apply (Apply (Foldr'_6989586621680822875Sym0 :: TyFun (a1 ~> (b ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type) arg1) arg2) arg3
type Return (arg :: a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Return (arg :: a) = Apply (Return_6989586621680012055Sym0 :: TyFun a (Either e a) -> Type) arg
type Pure (a :: k1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Pure (a :: k1) = Apply (Pure_6989586621680072973Sym0 :: TyFun k1 (Either e k1) -> Type) a
type Elem (arg1 :: a1) (arg2 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Elem (arg1 :: a1) (arg2 :: Either a2 a1) = Apply (Apply (Elem_6989586621680823021Sym0 :: TyFun a1 (Either a2 a1 ~> Bool) -> Type) arg1) arg2
type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldl1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1) = Apply (Apply (Foldl1_6989586621680822956Sym0 :: TyFun (a1 ~> (a1 ~> a1)) (Either a2 a1 ~> a1) -> Type) arg1) arg2
type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Foldr1 (arg1 :: a1 ~> (a1 ~> a1)) (arg2 :: Either a2 a1) = Apply (Apply (Foldr1_6989586621680822935Sym0 :: TyFun (a1 ~> (a1 ~> a1)) (Either a2 a1 ~> a1) -> Type) arg1) arg2
type (a2 :: k1) <$ (a3 :: Either a1 b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: k1) <$ (a3 :: Either a1 b) = Apply (Apply (TFHelper_6989586621680072804Sym0 :: TyFun k1 (Either a1 b ~> Either a1 k1) -> Type) a2) a3
type Apply (ShowsPrec_6989586621680653998Sym0 :: TyFun Nat (Either a b ~> (Symbol ~> Symbol)) -> Type) (a6989586621680654008 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680653998Sym0 :: TyFun Nat (Either a b ~> (Symbol ~> Symbol)) -> Type) (a6989586621680654008 :: Nat) = ShowsPrec_6989586621680653998Sym1 a6989586621680654008 :: TyFun (Either a b) (Symbol ~> Symbol) -> Type
type Apply (Pure_6989586621680072973Sym0 :: TyFun a (Either e a) -> Type) (a6989586621680072979 :: a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Pure_6989586621680072973Sym0 :: TyFun a (Either e a) -> Type) (a6989586621680072979 :: a) = Pure_6989586621680072973Sym1 a6989586621680072979 :: Either e a
type Apply (LeftSym0 :: TyFun a (Either a b) -> Type) (a6989586621679750213 :: a)
Instance details Defined in Data.Singletons.Prelude.Instances type Apply (LeftSym0 :: TyFun a (Either a b) -> Type) (a6989586621679750213 :: a) = LeftSym1 a6989586621679750213 :: Either a b
type Apply (RightSym0 :: TyFun b (Either a b) -> Type) (a6989586621679750215 :: b)
Instance details Defined in Data.Singletons.Prelude.Instances type Apply (RightSym0 :: TyFun b (Either a b) -> Type) (a6989586621679750215 :: b) = RightSym1 a6989586621679750215 :: Either a b
type Apply (Let6989586621680240853ASym0 :: TyFun k1 (Either a k1) -> Type) (wild_69895866216802405176989586621680240852 :: k1)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (Let6989586621680240853ASym0 :: TyFun k1 (Either a k1) -> Type) (wild_69895866216802405176989586621680240852 :: k1) = Let6989586621680240853ASym1 wild_69895866216802405176989586621680240852 :: Either a k1
type Apply (TFHelper_6989586621680072804Sym0 :: TyFun a1 (Either a2 b ~> Either a2 a1) -> Type) (a6989586621680072809 :: a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072804Sym0 :: TyFun a1 (Either a2 b ~> Either a2 a1) -> Type) (a6989586621680072809 :: a1) = TFHelper_6989586621680072804Sym1 a6989586621680072809 :: TyFun (Either a2 b) (Either a2 a1) -> Type
type Apply (Foldr_6989586621680823406Sym1 a6989586621680823412 :: TyFun b (Either a2 a1 ~> b) -> Type) (a6989586621680823413 :: b)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823406Sym1 a6989586621680823412 :: TyFun b (Either a2 a1 ~> b) -> Type) (a6989586621680823413 :: b) = Foldr_6989586621680823406Sym2 a6989586621680823412 a6989586621680823413 :: TyFun (Either a2 a1) b -> Type
type Dom (Either a1) a2
Instance details Defined in Control.Subcategory.Functor type Dom (Either a1) a2 = ()
type Length (a3 :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Length (a3 :: Either a1 a2) = Apply (Length_6989586621680823420Sym0 :: TyFun (Either a1 a2) Nat -> Type) a3
type Maximum (arg :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Maximum (arg :: Either a1 a2) = Apply (Maximum_6989586621680823035Sym0 :: TyFun (Either a1 a2) a2 -> Type) arg
type Minimum (arg :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Minimum (arg :: Either a1 a2) = Apply (Minimum_6989586621680823050Sym0 :: TyFun (Either a1 a2) a2 -> Type) arg
type Null (a3 :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Null (a3 :: Either a1 a2) = Apply (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type) a3
type Product (arg :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Product (arg :: Either a1 a2) = Apply (Product_6989586621680823074Sym0 :: TyFun (Either a1 a2) a2 -> Type) arg
type Sum (arg :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Sum (arg :: Either a1 a2) = Apply (Sum_6989586621680823065Sym0 :: TyFun (Either a1 a2) a2 -> Type) arg
type Fold (arg :: Either a m)
Instance details Defined in Data.Singletons.Prelude.Foldable type Fold (arg :: Either a m) = Apply (Fold_6989586621680822836Sym0 :: TyFun (Either a m) m -> Type) arg
type ToList (arg :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type ToList (arg :: Either a1 a2) = Apply (ToList_6989586621680822976Sym0 :: TyFun (Either a1 a2) [a2] -> Type) arg
type Sequence (arg :: Either a1 (m a2))
Instance details Defined in Data.Singletons.Prelude.Traversable type Sequence (arg :: Either a1 (m a2)) = Apply (Sequence_6989586621681082098Sym0 :: TyFun (Either a1 (m a2)) (m (Either a1 a2)) -> Type) arg
type SequenceA (arg :: Either a1 (f a2))
Instance details Defined in Data.Singletons.Prelude.Traversable type SequenceA (arg :: Either a1 (f a2)) = Apply (SequenceA_6989586621681082074Sym0 :: TyFun (Either a1 (f a2)) (f (Either a1 a2)) -> Type) arg
type (arg1 :: Either e a) >> (arg2 :: Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (arg1 :: Either e a) >> (arg2 :: Either e b) = Apply (Apply (TFHelper_6989586621680012038Sym0 :: TyFun (Either e a) (Either e b ~> Either e b) -> Type) arg1) arg2
type (a2 :: Either e a1) >>= (a3 :: a1 ~> Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Either e a1) >>= (a3 :: a1 ~> Either e b) = Apply (Apply (TFHelper_6989586621680073067Sym0 :: TyFun (Either e a1) ((a1 ~> Either e b) ~> Either e b) -> Type) a2) a3
type (arg1 :: Either e a) *> (arg2 :: Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (arg1 :: Either e a) *> (arg2 :: Either e b) = Apply (Apply (TFHelper_6989586621680011999Sym0 :: TyFun (Either e a) (Either e b ~> Either e b) -> Type) arg1) arg2
type (arg1 :: Either e a) <* (arg2 :: Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (arg1 :: Either e a) <* (arg2 :: Either e b) = Apply (Apply (TFHelper_6989586621680012010Sym0 :: TyFun (Either e a) (Either e b ~> Either e a) -> Type) arg1) arg2
type (a2 :: Either e (a1 ~> b)) <*> (a3 :: Either e a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type (a2 :: Either e (a1 ~> b)) <*> (a3 :: Either e a1) = Apply (Apply (TFHelper_6989586621680072983Sym0 :: TyFun (Either e (a1 ~> b)) (Either e a1 ~> Either e b) -> Type) a2) a3
type Rep1 (Either a :: Type -> Type)
Instance details Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621680804065 :: [Either a b])
Instance details Defined in Data.Singletons.Prelude.Either type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621680804065 :: [Either a b]) = RightsSym1 a6989586621680804065
type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621680804071 :: [Either a b])
Instance details Defined in Data.Singletons.Prelude.Either type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621680804071 :: [Either a b]) = LeftsSym1 a6989586621680804071
type Apply (PartitionEithersSym0 :: TyFun [Either a b] ([a], [b]) -> Type) (a6989586621680804048 :: [Either a b])
Instance details Defined in Data.Singletons.Prelude.Either type Apply (PartitionEithersSym0 :: TyFun [Either a b] ([a], [b]) -> Type) (a6989586621680804048 :: [Either a b]) = PartitionEithersSym1 a6989586621680804048
type Rep (Either a b)
Instance details Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))
type Sing
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SEither :: Either a b -> Type
type Demote (Either a b)
Instance details Defined in Data.Singletons.Prelude.Instances type Demote (Either a b) = Either (Demote a) (Demote b)
type Element (Either a b)
Instance details Defined in Data.MonoTraversable type Element (Either a b) = b
type Sconcat (arg :: NonEmpty (Either a b))
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sconcat (arg :: NonEmpty (Either a b)) = Apply (Sconcat_6989586621680240682Sym0 :: TyFun (NonEmpty (Either a b)) (Either a b) -> Type) arg
type Show_ (arg :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Show type Show_ (arg :: Either a b) = Apply (Show__6989586621680636786Sym0 :: TyFun (Either a b) Symbol -> Type) arg
type (x :: Either a b) /= (y :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Eq type (x :: Either a b) /= (y :: Either a b) = Not (x == y)
type (a2 :: Either a1 b1) == (b2 :: Either a1 b1)
Instance details Defined in Data.Singletons.Prelude.Eq type (a2 :: Either a1 b1) == (b2 :: Either a1 b1) = Equals_6989586621679820321 a2 b2
type (a2 :: Either a1 b) <> (a3 :: Either a1 b)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type (a2 :: Either a1 b) <> (a3 :: Either a1 b) = Apply (Apply (TFHelper_6989586621680240844Sym0 :: TyFun (Either a1 b) (Either a1 b ~> Either a1 b) -> Type) a2) a3
type Max (arg1 :: Either a b) (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Max (arg1 :: Either a b) (arg2 :: Either a b) = Apply (Apply (Max_6989586621679837511Sym0 :: TyFun (Either a b) (Either a b ~> Either a b) -> Type) arg1) arg2
type Min (arg1 :: Either a b) (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Min (arg1 :: Either a b) (arg2 :: Either a b) = Apply (Apply (Min_6989586621679837527Sym0 :: TyFun (Either a b) (Either a b ~> Either a b) -> Type) arg1) arg2
type Compare (a2 :: Either a1 b) (a3 :: Either a1 b)
Instance details Defined in Data.Singletons.Prelude.Ord type Compare (a2 :: Either a1 b) (a3 :: Either a1 b) = Apply (Apply (Compare_6989586621679848584Sym0 :: TyFun (Either a1 b) (Either a1 b ~> Ordering) -> Type) a2) a3
type (arg1 :: Either a b) <= (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Either a b) <= (arg2 :: Either a b) = Apply (Apply (TFHelper_6989586621679837463Sym0 :: TyFun (Either a b) (Either a b ~> Bool) -> Type) arg1) arg2
type (arg1 :: Either a b) < (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Either a b) < (arg2 :: Either a b) = Apply (Apply (TFHelper_6989586621679837447Sym0 :: TyFun (Either a b) (Either a b ~> Bool) -> Type) arg1) arg2
type (arg1 :: Either a b) >= (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Either a b) >= (arg2 :: Either a b) = Apply (Apply (TFHelper_6989586621679837495Sym0 :: TyFun (Either a b) (Either a b ~> Bool) -> Type) arg1) arg2
type (arg1 :: Either a b) > (arg2 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Either a b) > (arg2 :: Either a b) = Apply (Apply (TFHelper_6989586621679837479Sym0 :: TyFun (Either a b) (Either a b ~> Bool) -> Type) arg1) arg2
type ShowList (arg1 :: [Either a b]) arg2
Instance details Defined in Data.Singletons.Prelude.Show type ShowList (arg1 :: [Either a b]) arg2 = Apply (Apply (ShowList_6989586621680636794Sym0 :: TyFun [Either a b] (Symbol ~> Symbol) -> Type) arg1) arg2
type ShowsPrec a2 (a3 :: Either a1 b) a4
Instance details Defined in Data.Singletons.Prelude.Show type ShowsPrec a2 (a3 :: Either a1 b) a4 = Apply (Apply (Apply (ShowsPrec_6989586621680653998Sym0 :: TyFun Nat (Either a1 b ~> (Symbol ~> Symbol)) -> Type) a2) a3) a4
type Apply (Length_6989586621680823420Sym0 :: TyFun (Either a1 a2) Nat -> Type) (a6989586621680823424 :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Length_6989586621680823420Sym0 :: TyFun (Either a1 a2) Nat -> Type) (a6989586621680823424 :: Either a1 a2) = Length_6989586621680823420Sym1 a6989586621680823424
type Apply (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type) (a6989586621680823432 :: Either a1 a2)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Null_6989586621680823426Sym0 :: TyFun (Either a1 a2) Bool -> Type) (a6989586621680823432 :: Either a1 a2) = Null_6989586621680823426Sym1 a6989586621680823432
type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804040 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804040 :: Either a b) = IsRightSym1 a6989586621680804040
type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804043 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680804043 :: Either a b) = IsLeftSym1 a6989586621680804043
type Apply (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type) (a6989586621679848590 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848584Sym1 a6989586621679848589 :: TyFun (Either a b) Ordering -> Type) (a6989586621679848590 :: Either a b) = Compare_6989586621679848584Sym2 a6989586621679848589 a6989586621679848590
type Apply (FoldMap_6989586621680823394Sym1 a6989586621680823399 :: TyFun (Either a2 a1) m -> Type) (a6989586621680823400 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FoldMap_6989586621680823394Sym1 a6989586621680823399 :: TyFun (Either a2 a1) m -> Type) (a6989586621680823400 :: Either a2 a1) = FoldMap_6989586621680823394Sym2 a6989586621680823399 a6989586621680823400
type Apply (Foldr_6989586621680823406Sym2 a6989586621680823412 a6989586621680823413 :: TyFun (Either a2 a1) b -> Type) (a6989586621680823414 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823406Sym2 a6989586621680823412 a6989586621680823413 :: TyFun (Either a2 a1) b -> Type) (a6989586621680823414 :: Either a2 a1) = Foldr_6989586621680823406Sym3 a6989586621680823412 a6989586621680823413 a6989586621680823414
type Apply (Either_Sym2 a6989586621680802381 a6989586621680802382 :: TyFun (Either a b) c -> Type) (a6989586621680802383 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym2 a6989586621680802381 a6989586621680802382 :: TyFun (Either a b) c -> Type) (a6989586621680802383 :: Either a b) = Either_Sym3 a6989586621680802381 a6989586621680802382 a6989586621680802383
type Apply (Traverse_6989586621681088340Sym1 a6989586621681088345 :: TyFun (Either a2 a1) (f (Either a2 b)) -> Type) (a6989586621681088346 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Traversable type Apply (Traverse_6989586621681088340Sym1 a6989586621681088345 :: TyFun (Either a2 a1) (f (Either a2 b)) -> Type) (a6989586621681088346 :: Either a2 a1) = Traverse_6989586621681088340Sym2 a6989586621681088345 a6989586621681088346
type Apply (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type) (a6989586621679848589 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679848584Sym0 :: TyFun (Either a b) (Either a b ~> Ordering) -> Type) (a6989586621679848589 :: Either a b) = Compare_6989586621679848584Sym1 a6989586621679848589
type Apply (TFHelper_6989586621680240844Sym0 :: TyFun (Either a b) (Either a b ~> Either a b) -> Type) (a6989586621680240849 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240844Sym0 :: TyFun (Either a b) (Either a b ~> Either a b) -> Type) (a6989586621680240849 :: Either a b) = TFHelper_6989586621680240844Sym1 a6989586621680240849
type Apply (ShowsPrec_6989586621680653998Sym1 a6989586621680654008 :: TyFun (Either a b) (Symbol ~> Symbol) -> Type) (a6989586621680654009 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Show type Apply (ShowsPrec_6989586621680653998Sym1 a6989586621680654008 :: TyFun (Either a b) (Symbol ~> Symbol) -> Type) (a6989586621680654009 :: Either a b) = ShowsPrec_6989586621680653998Sym2 a6989586621680654008 a6989586621680654009
type Apply (TFHelper_6989586621680072983Sym0 :: TyFun (Either e (a ~> b)) (Either e a ~> Either e b) -> Type) (a6989586621680072988 :: Either e (a ~> b))
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072983Sym0 :: TyFun (Either e (a ~> b)) (Either e a ~> Either e b) -> Type) (a6989586621680072988 :: Either e (a ~> b)) = TFHelper_6989586621680072983Sym1 a6989586621680072988
type Apply (TFHelper_6989586621680073067Sym0 :: TyFun (Either e a) ((a ~> Either e b) ~> Either e b) -> Type) (a6989586621680073072 :: Either e a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073067Sym0 :: TyFun (Either e a) ((a ~> Either e b) ~> Either e b) -> Type) (a6989586621680073072 :: Either e a) = TFHelper_6989586621680073067Sym1 a6989586621680073072 :: TyFun (a ~> Either e b) (Either e b) -> Type
type Apply (TFHelper_6989586621680240844Sym1 a6989586621680240849 :: TyFun (Either a b) (Either a b) -> Type) (a6989586621680240850 :: Either a b)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240844Sym1 a6989586621680240849 :: TyFun (Either a b) (Either a b) -> Type) (a6989586621680240850 :: Either a b) = TFHelper_6989586621680240844Sym2 a6989586621680240849 a6989586621680240850
type Apply (Fmap_6989586621680072787Sym0 :: TyFun (a1 ~> b) (Either a2 a1 ~> Either a2 b) -> Type) (a6989586621680072792 :: a1 ~> b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Fmap_6989586621680072787Sym0 :: TyFun (a1 ~> b) (Either a2 a1 ~> Either a2 b) -> Type) (a6989586621680072792 :: a1 ~> b) = Fmap_6989586621680072787Sym1 a6989586621680072792 :: TyFun (Either a2 a1) (Either a2 b) -> Type
type Apply (FoldMap_6989586621680823394Sym0 :: TyFun (a1 ~> m) (Either a2 a1 ~> m) -> Type) (a6989586621680823399 :: a1 ~> m)
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (FoldMap_6989586621680823394Sym0 :: TyFun (a1 ~> m) (Either a2 a1 ~> m) -> Type) (a6989586621680823399 :: a1 ~> m) = FoldMap_6989586621680823394Sym1 a6989586621680823399 :: TyFun (Either a2 a1) m -> Type
type Apply (Foldr_6989586621680823406Sym0 :: TyFun (a1 ~> (b ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type) (a6989586621680823412 :: a1 ~> (b ~> b))
Instance details Defined in Data.Singletons.Prelude.Foldable type Apply (Foldr_6989586621680823406Sym0 :: TyFun (a1 ~> (b ~> b)) (b ~> (Either a2 a1 ~> b)) -> Type) (a6989586621680823412 :: a1 ~> (b ~> b)) = Foldr_6989586621680823406Sym1 a6989586621680823412 :: TyFun b (Either a2 a1 ~> b) -> Type
type Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) (a6989586621680802381 :: a ~> c)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) (a6989586621680802381 :: a ~> c) = Either_Sym1 a6989586621680802381 :: TyFun (b ~> c) (Either a b ~> c) -> Type
type Apply (Fmap_6989586621680072787Sym1 a6989586621680072792 :: TyFun (Either a2 a1) (Either a2 b) -> Type) (a6989586621680072793 :: Either a2 a1)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (Fmap_6989586621680072787Sym1 a6989586621680072792 :: TyFun (Either a2 a1) (Either a2 b) -> Type) (a6989586621680072793 :: Either a2 a1) = Fmap_6989586621680072787Sym2 a6989586621680072792 a6989586621680072793
type Apply (TFHelper_6989586621680072804Sym1 a6989586621680072809 :: TyFun (Either a2 b) (Either a2 a1) -> Type) (a6989586621680072810 :: Either a2 b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072804Sym1 a6989586621680072809 :: TyFun (Either a2 b) (Either a2 a1) -> Type) (a6989586621680072810 :: Either a2 b) = TFHelper_6989586621680072804Sym2 a6989586621680072809 a6989586621680072810
type Apply (TFHelper_6989586621680072983Sym1 a6989586621680072988 :: TyFun (Either e a) (Either e b) -> Type) (a6989586621680072989 :: Either e a)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680072983Sym1 a6989586621680072988 :: TyFun (Either e a) (Either e b) -> Type) (a6989586621680072989 :: Either e a) = TFHelper_6989586621680072983Sym2 a6989586621680072988 a6989586621680072989
type Apply (Traverse_6989586621681088340Sym0 :: TyFun (a1 ~> f b) (Either a2 a1 ~> f (Either a2 b)) -> Type) (a6989586621681088345 :: a1 ~> f b)
Instance details Defined in Data.Singletons.Prelude.Traversable type Apply (Traverse_6989586621681088340Sym0 :: TyFun (a1 ~> f b) (Either a2 a1 ~> f (Either a2 b)) -> Type) (a6989586621681088345 :: a1 ~> f b) = Traverse_6989586621681088340Sym1 a6989586621681088345 :: TyFun (Either a2 a1) (f (Either a2 b)) -> Type
type Apply (TFHelper_6989586621680073067Sym1 a6989586621680073072 :: TyFun (a ~> Either e b) (Either e b) -> Type) (a6989586621680073073 :: a ~> Either e b)
Instance details Defined in Data.Singletons.Prelude.Monad.Internal type Apply (TFHelper_6989586621680073067Sym1 a6989586621680073072 :: TyFun (a ~> Either e b) (Either e b) -> Type) (a6989586621680073073 :: a ~> Either e b) = TFHelper_6989586621680073067Sym2 a6989586621680073072 a6989586621680073073
type Apply (Either_Sym1 a6989586621680802381 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621680802382 :: b ~> c)
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym1 a6989586621680802381 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621680802382 :: b ~> c) = Either_Sym2 a6989586621680802381 a6989586621680802382

ifThenElse :: Bool -> a -> a -> a #

(^^) :: Division r => r -> Integer -> r infixr 8 #

The original power function (^) of algebra

(^) :: Unital r => r -> Natural -> r infixr 8 #

Specialised version of pow which takes Naturals as a power.

normaliseUnit :: UnitNormalForm r => r -> r #

fromRational :: DivisionRing r => Rational -> r #

fromInteger' :: Ring r => Integer -> r #

algebra package's original fromInteger.

fromInteger :: Num r => Integer -> r #

To work with Num literals.

type Rational = Fraction Integer #

We use Fraction instead of Ratio for consistency.

newtype WrapNum a #

Wrapping Prelude's numerical types to treat with Algebra hierachy.

For Field or Euclidean instances, see WrapIntegral and WrapField.

N.B. This type provides a mean to convert from Nums to Rings, but there is no guarantee that WrapNum a is actually ring. For example, due to precision limitation, WrapPreldue Double even fails to be semigroup! For another simpler example, even though Natural comes with Num instance, but it doesn't support negate, so it cannot be Group.

Constructors

WrapNum
Fields unwrapNum :: a

Instances

Instances details

Num a => RightModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Integer -> WrapNum a #
Num a => RightModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Natural -> WrapNum a #
Num a => LeftModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapNum a -> WrapNum a #
Num a => LeftModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapNum a -> WrapNum a #
Eq a => Eq (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapNum a -> WrapNum a -> Bool # (/=) :: WrapNum a -> WrapNum a -> Bool #
Num a => Num (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapNum a -> WrapNum a -> WrapNum a # (-) :: WrapNum a -> WrapNum a -> WrapNum a # (*) :: WrapNum a -> WrapNum a -> WrapNum a # negate :: WrapNum a -> WrapNum a # abs :: WrapNum a -> WrapNum a # signum :: WrapNum a -> WrapNum a # fromInteger :: Integer -> WrapNum a #
Ord a => Ord (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapNum a -> WrapNum a -> Ordering # (<) :: WrapNum a -> WrapNum a -> Bool # (<=) :: WrapNum a -> WrapNum a -> Bool # (>) :: WrapNum a -> WrapNum a -> Bool # (>=) :: WrapNum a -> WrapNum a -> Bool # max :: WrapNum a -> WrapNum a -> WrapNum a # min :: WrapNum a -> WrapNum a -> WrapNum a #
Read a => Read (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapNum a) # readList :: ReadS [WrapNum a] # readPrec :: ReadPrec (WrapNum a) # readListPrec :: ReadPrec [WrapNum a] #
Show a => Show (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapNum a -> ShowS # show :: WrapNum a -> String # showList :: [WrapNum a] -> ShowS #
Num a => Ring (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapNum a
Num a => Rig (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapNum a #
(Num a, Eq a) => DecidableZero (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapNum a -> Bool #
Num a => Unital (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapNum a # pow :: WrapNum a -> Natural -> WrapNum a # productWith :: Foldable f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Commutative (WrapNum a)
Instance details Defined in AlgebraicPrelude
Num a => Semiring (WrapNum a)
Instance details Defined in AlgebraicPrelude
Num a => Multiplicative (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapNum a -> WrapNum a -> WrapNum a # pow1p :: WrapNum a -> Natural -> WrapNum a # productWith1 :: Foldable1 f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Monoidal (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapNum a # sinnum :: Natural -> WrapNum a -> WrapNum a # sumWith :: Foldable f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Group (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapNum a -> WrapNum a -> WrapNum a # negate :: WrapNum a -> WrapNum a # subtract :: WrapNum a -> WrapNum a -> WrapNum a # times :: Integral n => n -> WrapNum a -> WrapNum a #
Num a => Additive (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapNum a -> WrapNum a -> WrapNum a # sinnum1p :: Natural -> WrapNum a -> WrapNum a # sumWith1 :: Foldable1 f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Abelian (WrapNum a)
Instance details Defined in AlgebraicPrelude
Storable a => Storable (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapNum a -> Int # alignment :: WrapNum a -> Int # peekElemOff :: Ptr (WrapNum a) -> Int -> IO (WrapNum a) # pokeElemOff :: Ptr (WrapNum a) -> Int -> WrapNum a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapNum a) # pokeByteOff :: Ptr b -> Int -> WrapNum a -> IO () # peek :: Ptr (WrapNum a) -> IO (WrapNum a) # poke :: Ptr (WrapNum a) -> WrapNum a -> IO () #
Normed a => Normed (WrapNum a)
Instance details Defined in Algebra.Normed Associated Types type Norm (WrapNum a) # Methods norm :: WrapNum a -> Norm (WrapNum a) # liftNorm :: Norm (WrapNum a) -> WrapNum a #
Wrapped (WrapNum a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (WrapNum a) Methods _Wrapped' :: Iso' (WrapNum a) (Unwrapped (WrapNum a))
WrapNum a1 ~ t => Rewrapped (WrapNum a2) t
Instance details Defined in AlgebraicPrelude
type Norm (WrapNum a)
Instance details Defined in Algebra.Normed type Norm (WrapNum a) = Norm a
type Unwrapped (WrapNum a)
Instance details Defined in AlgebraicPrelude type Unwrapped (WrapNum a) = a

newtype WrapFractional a #

Similar to WrapNum, but produces Field instances from Fractionals.

Instances

Instances details

Num a => RightModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Integer -> WrapFractional a #
Num a => RightModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Natural -> WrapFractional a #
Num a => LeftModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapFractional a -> WrapFractional a #
Num a => LeftModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapFractional a -> WrapFractional a #
Enum a => Enum (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods succ :: WrapFractional a -> WrapFractional a # pred :: WrapFractional a -> WrapFractional a # toEnum :: Int -> WrapFractional a # fromEnum :: WrapFractional a -> Int # enumFrom :: WrapFractional a -> [WrapFractional a] # enumFromThen :: WrapFractional a -> WrapFractional a -> [WrapFractional a] # enumFromTo :: WrapFractional a -> WrapFractional a -> [WrapFractional a] # enumFromThenTo :: WrapFractional a -> WrapFractional a -> WrapFractional a -> [WrapFractional a] #
Eq a => Eq (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapFractional a -> WrapFractional a -> Bool # (/=) :: WrapFractional a -> WrapFractional a -> Bool #
Fractional a => Fractional (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (/) :: WrapFractional a -> WrapFractional a -> WrapFractional a # recip :: WrapFractional a -> WrapFractional a # fromRational :: Rational -> WrapFractional a #
Num a => Num (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (-) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (*) :: WrapFractional a -> WrapFractional a -> WrapFractional a # negate :: WrapFractional a -> WrapFractional a # abs :: WrapFractional a -> WrapFractional a # signum :: WrapFractional a -> WrapFractional a # fromInteger :: Integer -> WrapFractional a #
Ord a => Ord (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapFractional a -> WrapFractional a -> Ordering # (<) :: WrapFractional a -> WrapFractional a -> Bool # (<=) :: WrapFractional a -> WrapFractional a -> Bool # (>) :: WrapFractional a -> WrapFractional a -> Bool # (>=) :: WrapFractional a -> WrapFractional a -> Bool # max :: WrapFractional a -> WrapFractional a -> WrapFractional a # min :: WrapFractional a -> WrapFractional a -> WrapFractional a #
Read a => Read (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapFractional a) # readList :: ReadS [WrapFractional a] # readPrec :: ReadPrec (WrapFractional a) # readListPrec :: ReadPrec [WrapFractional a] #
Real a => Real (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods toRational :: WrapFractional a -> Rational #
Show a => Show (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapFractional a -> ShowS # show :: WrapFractional a -> String # showList :: [WrapFractional a] -> ShowS #
(Eq a, Fractional a) => UFD (WrapFractional a)
Instance details Defined in AlgebraicPrelude
(Eq a, Fractional a) => PID (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a, WrapFractional a) #
(Eq a, Fractional a) => GCDDomain (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapFractional a -> WrapFractional a -> WrapFractional a # reduceFraction :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a) # lcm :: WrapFractional a -> WrapFractional a -> WrapFractional a #
(Eq a, Fractional a) => IntegralDomain (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapFractional a -> WrapFractional a -> Bool # maybeQuot :: WrapFractional a -> WrapFractional a -> Maybe (WrapFractional a) #
(Eq a, Fractional a) => Euclidean (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapFractional a -> Maybe Natural # divide :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a) # quot :: WrapFractional a -> WrapFractional a -> WrapFractional a # rem :: WrapFractional a -> WrapFractional a -> WrapFractional a #
(Eq a, Fractional a) => ZeroProductSemiring (WrapFractional a)
Instance details Defined in AlgebraicPrelude
(Eq a, Fractional a) => UnitNormalForm (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapFractional a -> (WrapFractional a, WrapFractional a) #
Num a => Ring (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapFractional a
Num a => Rig (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapFractional a #
(Num a, Eq a) => DecidableZero (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapFractional a -> Bool #
(Eq a, Fractional a) => DecidableUnits (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapFractional a -> Maybe (WrapFractional a) # isUnit :: WrapFractional a -> Bool # (^?) :: Integral n => WrapFractional a -> n -> Maybe (WrapFractional a) #
(Eq a, Fractional a) => DecidableAssociates (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapFractional a -> WrapFractional a -> Bool #
Num a => Unital (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapFractional a # pow :: WrapFractional a -> Natural -> WrapFractional a # productWith :: Foldable f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Fractional a => Division (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods recip :: WrapFractional a -> WrapFractional a # (/) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (\\) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (^) :: Integral n => WrapFractional a -> n -> WrapFractional a
Num a => Commutative (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Num a => Semiring (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Num a => Multiplicative (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapFractional a -> WrapFractional a -> WrapFractional a # pow1p :: WrapFractional a -> Natural -> WrapFractional a # productWith1 :: Foldable1 f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Monoidal (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapFractional a # sinnum :: Natural -> WrapFractional a -> WrapFractional a # sumWith :: Foldable f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Group (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapFractional a -> WrapFractional a -> WrapFractional a # negate :: WrapFractional a -> WrapFractional a # subtract :: WrapFractional a -> WrapFractional a -> WrapFractional a # times :: Integral n => n -> WrapFractional a -> WrapFractional a #
Num a => Additive (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapFractional a -> WrapFractional a -> WrapFractional a # sinnum1p :: Natural -> WrapFractional a -> WrapFractional a # sumWith1 :: Foldable1 f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Abelian (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Storable a => Storable (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapFractional a -> Int # alignment :: WrapFractional a -> Int # peekElemOff :: Ptr (WrapFractional a) -> Int -> IO (WrapFractional a) # pokeElemOff :: Ptr (WrapFractional a) -> Int -> WrapFractional a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapFractional a) # pokeByteOff :: Ptr b -> Int -> WrapFractional a -> IO () # peek :: Ptr (WrapFractional a) -> IO (WrapFractional a) # poke :: Ptr (WrapFractional a) -> WrapFractional a -> IO () #
Normed a => Normed (WrapFractional a)
Instance details Defined in Algebra.Normed Associated Types type Norm (WrapFractional a) # Methods norm :: WrapFractional a -> Norm (WrapFractional a) # liftNorm :: Norm (WrapFractional a) -> WrapFractional a #
Wrapped (WrapFractional a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (WrapFractional a) Methods _Wrapped' :: Iso' (WrapFractional a) (Unwrapped (WrapFractional a))
WrapFractional a1 ~ t => Rewrapped (WrapFractional a2) t
Instance details Defined in AlgebraicPrelude
type Norm (WrapFractional a)
Instance details Defined in Algebra.Normed type Norm (WrapFractional a) = Norm a
type Unwrapped (WrapFractional a)
Instance details Defined in AlgebraicPrelude type Unwrapped (WrapFractional a) = a

newtype WrapIntegral a #

Similar to WrapNum, but produces Euclidean instances from Integrals.

See also: WrapFractional and WrapNum.

Constructors

WrapIntegral
Fields unwrapIntegral :: a

Instances

Instances details

Num a => RightModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Integer -> WrapIntegral a #
Num a => RightModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Natural -> WrapIntegral a #
Num a => LeftModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapIntegral a -> WrapIntegral a #
Num a => LeftModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapIntegral a -> WrapIntegral a #
Enum a => Enum (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods succ :: WrapIntegral a -> WrapIntegral a # pred :: WrapIntegral a -> WrapIntegral a # toEnum :: Int -> WrapIntegral a # fromEnum :: WrapIntegral a -> Int # enumFrom :: WrapIntegral a -> [WrapIntegral a] # enumFromThen :: WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] # enumFromTo :: WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] # enumFromThenTo :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a -> [WrapIntegral a] #
Eq a => Eq (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapIntegral a -> WrapIntegral a -> Bool # (/=) :: WrapIntegral a -> WrapIntegral a -> Bool #
Integral a => Integral (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods quot :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # rem :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # div :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # mod :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # quotRem :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # divMod :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # toInteger :: WrapIntegral a -> Integer #
Num a => Num (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # (-) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # (*) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # negate :: WrapIntegral a -> WrapIntegral a # abs :: WrapIntegral a -> WrapIntegral a # signum :: WrapIntegral a -> WrapIntegral a # fromInteger :: Integer -> WrapIntegral a #
Ord a => Ord (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapIntegral a -> WrapIntegral a -> Ordering # (<) :: WrapIntegral a -> WrapIntegral a -> Bool # (<=) :: WrapIntegral a -> WrapIntegral a -> Bool # (>) :: WrapIntegral a -> WrapIntegral a -> Bool # (>=) :: WrapIntegral a -> WrapIntegral a -> Bool # max :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # min :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
Read a => Read (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapIntegral a) # readList :: ReadS [WrapIntegral a] # readPrec :: ReadPrec (WrapIntegral a) # readListPrec :: ReadPrec [WrapIntegral a] #
Real a => Real (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods toRational :: WrapIntegral a -> Rational #
Show a => Show (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapIntegral a -> ShowS # show :: WrapIntegral a -> String # showList :: [WrapIntegral a] -> ShowS #
(Eq a, Integral a) => UFD (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
(Eq a, Integral a) => PID (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a, WrapIntegral a) #
(Eq a, Integral a) => GCDDomain (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # reduceFraction :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # lcm :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
(Eq a, Integral a) => IntegralDomain (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapIntegral a -> WrapIntegral a -> Bool # maybeQuot :: WrapIntegral a -> WrapIntegral a -> Maybe (WrapIntegral a) #
(Eq a, Integral a) => Euclidean (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapIntegral a -> Maybe Natural # divide :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # quot :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # rem :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
(Eq a, Integral a) => ZeroProductSemiring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
(Eq a, Integral a) => UnitNormalForm (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapIntegral a -> (WrapIntegral a, WrapIntegral a) #
Num a => Ring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapIntegral a
Num a => Rig (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapIntegral a #
(Num a, Eq a) => DecidableZero (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapIntegral a -> Bool #
(Eq a, Integral a) => DecidableUnits (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapIntegral a -> Maybe (WrapIntegral a) # isUnit :: WrapIntegral a -> Bool # (^?) :: Integral n => WrapIntegral a -> n -> Maybe (WrapIntegral a) #
(Eq a, Integral a) => DecidableAssociates (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapIntegral a -> WrapIntegral a -> Bool #
Num a => Unital (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapIntegral a # pow :: WrapIntegral a -> Natural -> WrapIntegral a # productWith :: Foldable f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Num a => Commutative (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
Num a => Semiring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
Num a => Multiplicative (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # pow1p :: WrapIntegral a -> Natural -> WrapIntegral a # productWith1 :: Foldable1 f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Num a => Monoidal (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapIntegral a # sinnum :: Natural -> WrapIntegral a -> WrapIntegral a # sumWith :: Foldable f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Num a => Group (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # negate :: WrapIntegral a -> WrapIntegral a # subtract :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # times :: Integral n => n -> WrapIntegral a -> WrapIntegral a #
Num a => Additive (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # sinnum1p :: Natural -> WrapIntegral a -> WrapIntegral a # sumWith1 :: Foldable1 f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Num a => Abelian (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
Storable a => Storable (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapIntegral a -> Int # alignment :: WrapIntegral a -> Int # peekElemOff :: Ptr (WrapIntegral a) -> Int -> IO (WrapIntegral a) # pokeElemOff :: Ptr (WrapIntegral a) -> Int -> WrapIntegral a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapIntegral a) # pokeByteOff :: Ptr b -> Int -> WrapIntegral a -> IO () # peek :: Ptr (WrapIntegral a) -> IO (WrapIntegral a) # poke :: Ptr (WrapIntegral a) -> WrapIntegral a -> IO () #
Normed a => Normed (WrapIntegral a)
Instance details Defined in Algebra.Normed Associated Types type Norm (WrapIntegral a) # Methods norm :: WrapIntegral a -> Norm (WrapIntegral a) # liftNorm :: Norm (WrapIntegral a) -> WrapIntegral a #
Wrapped (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (WrapIntegral a) Methods _Wrapped' :: Iso' (WrapIntegral a) (Unwrapped (WrapIntegral a))
WrapIntegral a1 ~ t => Rewrapped (WrapIntegral a2) t
Instance details Defined in AlgebraicPrelude
type Norm (WrapIntegral a)
Instance details Defined in Algebra.Normed type Norm (WrapIntegral a) = Norm a
type Unwrapped (WrapIntegral a)
Instance details Defined in AlgebraicPrelude type Unwrapped (WrapIntegral a) = a

newtype WrapAlgebra a #

Turning types from Algebra into Prelude's Num instances.

N.B. Since Real's toRational constraint is too tight, we won't provide the inverse of WrapIntegral and provide Fractional instance only.

Constructors

WrapAlgebra
Fields unwrapAlgebra :: a

Instances

Instances details

RightModule Integer a => RightModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Integer -> WrapAlgebra a #
RightModule Natural a => RightModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Natural -> WrapAlgebra a #
LeftModule Integer a => LeftModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapAlgebra a -> WrapAlgebra a #
LeftModule Natural a => LeftModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapAlgebra a -> WrapAlgebra a #
Eq a => Eq (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (==) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (/=) :: WrapAlgebra a -> WrapAlgebra a -> Bool #
(DivisionRing a, UnitNormalForm a) => Fractional (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (/) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # recip :: WrapAlgebra a -> WrapAlgebra a # fromRational :: Rational -> WrapAlgebra a #
(Ring a, UnitNormalForm a) => Num (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (-) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (*) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # negate :: WrapAlgebra a -> WrapAlgebra a # abs :: WrapAlgebra a -> WrapAlgebra a # signum :: WrapAlgebra a -> WrapAlgebra a # fromInteger :: Integer -> WrapAlgebra a #
Ord a => Ord (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods compare :: WrapAlgebra a -> WrapAlgebra a -> Ordering # (<) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (<=) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (>) :: WrapAlgebra a -> WrapAlgebra a -> Bool # (>=) :: WrapAlgebra a -> WrapAlgebra a -> Bool # max :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # min :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
Read a => Read (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (WrapAlgebra a) # readList :: ReadS [WrapAlgebra a] # readPrec :: ReadPrec (WrapAlgebra a) # readListPrec :: ReadPrec [WrapAlgebra a] #
Show a => Show (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> WrapAlgebra a -> ShowS # show :: WrapAlgebra a -> String # showList :: [WrapAlgebra a] -> ShowS #
GCDDomain a => UFD (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
PID a => PID (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a, WrapAlgebra a) #
GCDDomain a => GCDDomain (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # reduceFraction :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) # lcm :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
IntegralDomain a => IntegralDomain (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapAlgebra a -> WrapAlgebra a -> Bool # maybeQuot :: WrapAlgebra a -> WrapAlgebra a -> Maybe (WrapAlgebra a) #
Euclidean a => Euclidean (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapAlgebra a -> Maybe Natural # divide :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) # quot :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # rem :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
(Monoidal a, Multiplicative a) => ZeroProductSemiring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
UnitNormalForm a => UnitNormalForm (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) #
Ring a => Ring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapAlgebra a
Rig a => Rig (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapAlgebra a #
DecidableZero a => DecidableZero (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapAlgebra a -> Bool #
DecidableUnits a => DecidableUnits (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapAlgebra a -> Maybe (WrapAlgebra a) # isUnit :: WrapAlgebra a -> Bool # (^?) :: Integral n => WrapAlgebra a -> n -> Maybe (WrapAlgebra a) #
DecidableAssociates a => DecidableAssociates (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapAlgebra a -> WrapAlgebra a -> Bool #
Unital a => Unital (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapAlgebra a # pow :: WrapAlgebra a -> Natural -> WrapAlgebra a # productWith :: Foldable f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Division a => Division (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods recip :: WrapAlgebra a -> WrapAlgebra a # (/) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (\\) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (^) :: Integral n => WrapAlgebra a -> n -> WrapAlgebra a
Multiplicative a => Commutative (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
(Additive a, Multiplicative a) => Semiring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
Multiplicative a => Multiplicative (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # pow1p :: WrapAlgebra a -> Natural -> WrapAlgebra a # productWith1 :: Foldable1 f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Monoidal a => Monoidal (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapAlgebra a # sinnum :: Natural -> WrapAlgebra a -> WrapAlgebra a # sumWith :: Foldable f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Group a => Group (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # negate :: WrapAlgebra a -> WrapAlgebra a # subtract :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # times :: Integral n => n -> WrapAlgebra a -> WrapAlgebra a #
Additive a => Additive (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # sinnum1p :: Natural -> WrapAlgebra a -> WrapAlgebra a # sumWith1 :: Foldable1 f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Additive a => Abelian (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
Storable a => Storable (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapAlgebra a -> Int # alignment :: WrapAlgebra a -> Int # peekElemOff :: Ptr (WrapAlgebra a) -> Int -> IO (WrapAlgebra a) # pokeElemOff :: Ptr (WrapAlgebra a) -> Int -> WrapAlgebra a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapAlgebra a) # pokeByteOff :: Ptr b -> Int -> WrapAlgebra a -> IO () # peek :: Ptr (WrapAlgebra a) -> IO (WrapAlgebra a) # poke :: Ptr (WrapAlgebra a) -> WrapAlgebra a -> IO () #
Normed a => Normed (WrapAlgebra a)
Instance details Defined in Algebra.Normed Associated Types type Norm (WrapAlgebra a) # Methods norm :: WrapAlgebra a -> Norm (WrapAlgebra a) # liftNorm :: Norm (WrapAlgebra a) -> WrapAlgebra a #
Wrapped (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (WrapAlgebra a) Methods _Wrapped' :: Iso' (WrapAlgebra a) (Unwrapped (WrapAlgebra a))
WrapAlgebra a1 ~ t => Rewrapped (WrapAlgebra a2) t
Instance details Defined in AlgebraicPrelude
type Norm (WrapAlgebra a)
Instance details Defined in Algebra.Normed type Norm (WrapAlgebra a) = Norm a
type Unwrapped (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude type Unwrapped (WrapAlgebra a) = a

newtype Add a #

Monoid instances for Additives. N.B. Unlike WrapNum, Num instance is just inhereted from the unwrapped data.

Constructors

Add
Fields runAdd :: a

Instances

Instances details

RightModule Integer a => RightModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Integer -> Add a #
RightModule Natural a => RightModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Natural -> Add a #
LeftModule Integer a => LeftModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> Add a -> Add a #
LeftModule Natural a => LeftModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> Add a -> Add a #
Eq a => Eq (Add a)
Instance details Defined in AlgebraicPrelude Methods (==) :: Add a -> Add a -> Bool # (/=) :: Add a -> Add a -> Bool #
Num a => Num (Add a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Add a -> Add a -> Add a # (-) :: Add a -> Add a -> Add a # (*) :: Add a -> Add a -> Add a # negate :: Add a -> Add a # abs :: Add a -> Add a # signum :: Add a -> Add a # fromInteger :: Integer -> Add a #
Ord a => Ord (Add a)
Instance details Defined in AlgebraicPrelude Methods compare :: Add a -> Add a -> Ordering # (<) :: Add a -> Add a -> Bool # (<=) :: Add a -> Add a -> Bool # (>) :: Add a -> Add a -> Bool # (>=) :: Add a -> Add a -> Bool # max :: Add a -> Add a -> Add a # min :: Add a -> Add a -> Add a #
Read a => Read (Add a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (Add a) # readList :: ReadS [Add a] # readPrec :: ReadPrec (Add a) # readListPrec :: ReadPrec [Add a] #
Show a => Show (Add a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> Add a -> ShowS # show :: Add a -> String # showList :: [Add a] -> ShowS #
Additive a => Semigroup (Add a)
Instance details Defined in AlgebraicPrelude Methods (<>) :: Add a -> Add a -> Add a # sconcat :: NonEmpty (Add a) -> Add a # stimes :: Integral b => b -> Add a -> Add a #
Monoidal a => Monoid (Add a)
Instance details Defined in AlgebraicPrelude Methods mempty :: Add a # mappend :: Add a -> Add a -> Add a # mconcat :: [Add a] -> Add a #
Monoidal a => Monoidal (Add a)
Instance details Defined in AlgebraicPrelude Methods zero :: Add a # sinnum :: Natural -> Add a -> Add a # sumWith :: Foldable f => (a0 -> Add a) -> f a0 -> Add a #
Additive a => Additive (Add a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Add a -> Add a -> Add a # sinnum1p :: Natural -> Add a -> Add a # sumWith1 :: Foldable1 f => (a0 -> Add a) -> f a0 -> Add a #
Additive a => Abelian (Add a)
Instance details Defined in AlgebraicPrelude
Storable a => Storable (Add a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: Add a -> Int # alignment :: Add a -> Int # peekElemOff :: Ptr (Add a) -> Int -> IO (Add a) # pokeElemOff :: Ptr (Add a) -> Int -> Add a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Add a) # pokeByteOff :: Ptr b -> Int -> Add a -> IO () # peek :: Ptr (Add a) -> IO (Add a) # poke :: Ptr (Add a) -> Add a -> IO () #
Normed a => Normed (Add a)
Instance details Defined in Algebra.Normed Associated Types type Norm (Add a) # Methods norm :: Add a -> Norm (Add a) # liftNorm :: Norm (Add a) -> Add a #
Wrapped (Add a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (Add a) Methods _Wrapped' :: Iso' (Add a) (Unwrapped (Add a))
Add a1 ~ t => Rewrapped (Add a2) t
Instance details Defined in AlgebraicPrelude
type Norm (Add a)
Instance details Defined in Algebra.Normed type Norm (Add a) = Norm a
type Unwrapped (Add a)
Instance details Defined in AlgebraicPrelude type Unwrapped (Add a) = a

newtype Mult a #

Monoid instances for Additives. N.B. Unlike WrapNum, Num instance is just inhereted from the unwrapped data.

Constructors

Mult
Fields runMult :: a

Instances

Instances details

Eq a => Eq (Mult a)
Instance details Defined in AlgebraicPrelude Methods (==) :: Mult a -> Mult a -> Bool # (/=) :: Mult a -> Mult a -> Bool #
Num a => Num (Mult a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Mult a -> Mult a -> Mult a # (-) :: Mult a -> Mult a -> Mult a # (*) :: Mult a -> Mult a -> Mult a # negate :: Mult a -> Mult a # abs :: Mult a -> Mult a # signum :: Mult a -> Mult a # fromInteger :: Integer -> Mult a #
Ord a => Ord (Mult a)
Instance details Defined in AlgebraicPrelude Methods compare :: Mult a -> Mult a -> Ordering # (<) :: Mult a -> Mult a -> Bool # (<=) :: Mult a -> Mult a -> Bool # (>) :: Mult a -> Mult a -> Bool # (>=) :: Mult a -> Mult a -> Bool # max :: Mult a -> Mult a -> Mult a # min :: Mult a -> Mult a -> Mult a #
Read a => Read (Mult a)
Instance details Defined in AlgebraicPrelude Methods readsPrec :: Int -> ReadS (Mult a) # readList :: ReadS [Mult a] # readPrec :: ReadPrec (Mult a) # readListPrec :: ReadPrec [Mult a] #
Show a => Show (Mult a)
Instance details Defined in AlgebraicPrelude Methods showsPrec :: Int -> Mult a -> ShowS # show :: Mult a -> String # showList :: [Mult a] -> ShowS #
Multiplicative a => Semigroup (Mult a)
Instance details Defined in AlgebraicPrelude Methods (<>) :: Mult a -> Mult a -> Mult a # sconcat :: NonEmpty (Mult a) -> Mult a # stimes :: Integral b => b -> Mult a -> Mult a #
Unital a => Monoid (Mult a)
Instance details Defined in AlgebraicPrelude Methods mempty :: Mult a # mappend :: Mult a -> Mult a -> Mult a # mconcat :: [Mult a] -> Mult a #
Unital a => Unital (Mult a)
Instance details Defined in AlgebraicPrelude Methods one :: Mult a # pow :: Mult a -> Natural -> Mult a # productWith :: Foldable f => (a0 -> Mult a) -> f a0 -> Mult a #
Multiplicative a => Commutative (Mult a)
Instance details Defined in AlgebraicPrelude
Multiplicative a => Multiplicative (Mult a)
Instance details Defined in AlgebraicPrelude Methods (*) :: Mult a -> Mult a -> Mult a # pow1p :: Mult a -> Natural -> Mult a # productWith1 :: Foldable1 f => (a0 -> Mult a) -> f a0 -> Mult a #
Storable a => Storable (Mult a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: Mult a -> Int # alignment :: Mult a -> Int # peekElemOff :: Ptr (Mult a) -> Int -> IO (Mult a) # pokeElemOff :: Ptr (Mult a) -> Int -> Mult a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Mult a) # pokeByteOff :: Ptr b -> Int -> Mult a -> IO () # peek :: Ptr (Mult a) -> IO (Mult a) # poke :: Ptr (Mult a) -> Mult a -> IO () #
Normed a => Normed (Mult a)
Instance details Defined in Algebra.Normed Associated Types type Norm (Mult a) # Methods norm :: Mult a -> Norm (Mult a) # liftNorm :: Norm (Mult a) -> Mult a #
Wrapped (Mult a)
Instance details Defined in AlgebraicPrelude Associated Types type Unwrapped (Mult a) Methods _Wrapped' :: Iso' (Mult a) (Unwrapped (Mult a))
Mult a1 ~ t => Rewrapped (Mult a2) t
Instance details Defined in AlgebraicPrelude
type Norm (Mult a)
Instance details Defined in Algebra.Normed type Norm (Mult a) = Norm a
type Unwrapped (Mult a)
Instance details Defined in AlgebraicPrelude type Unwrapped (Mult a) = a

type Ratio = Fraction #

data Fraction d #

Instances

Instances details

GCDDomain d => RightModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Integer -> Fraction d #
GCDDomain d => RightModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Natural -> Fraction d #
GCDDomain d => LeftModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Integer -> Fraction d -> Fraction d #
GCDDomain d => LeftModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Natural -> Fraction d -> Fraction d #
(Eq d, GCDDomain d) => Eq (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (==) :: Fraction d -> Fraction d -> Bool # (/=) :: Fraction d -> Fraction d -> Bool #
(Ord d, GCDDomain d) => Ord (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods compare :: Fraction d -> Fraction d -> Ordering # (<) :: Fraction d -> Fraction d -> Bool # (<=) :: Fraction d -> Fraction d -> Bool # (>) :: Fraction d -> Fraction d -> Bool # (>=) :: Fraction d -> Fraction d -> Bool # max :: Fraction d -> Fraction d -> Fraction d # min :: Fraction d -> Fraction d -> Fraction d #
(Eq d, Show d, Unital d) => Show (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods showsPrec :: Int -> Fraction d -> ShowS # show :: Fraction d -> String # showList :: [Fraction d] -> ShowS #
GCDDomain d => UFD (Fraction d)
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => PID (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods egcd :: Fraction d -> Fraction d -> (Fraction d, Fraction d, Fraction d) #
GCDDomain d => GCDDomain (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods gcd :: Fraction d -> Fraction d -> Fraction d # reduceFraction :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # lcm :: Fraction d -> Fraction d -> Fraction d #
GCDDomain d => IntegralDomain (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods divides :: Fraction d -> Fraction d -> Bool # maybeQuot :: Fraction d -> Fraction d -> Maybe (Fraction d) #
GCDDomain d => Euclidean (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods degree :: Fraction d -> Maybe Natural # divide :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # quot :: Fraction d -> Fraction d -> Fraction d # rem :: Fraction d -> Fraction d -> Fraction d #
GCDDomain d => ZeroProductSemiring (Fraction d)
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => UnitNormalForm (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods splitUnit :: Fraction d -> (Fraction d, Fraction d) #
GCDDomain d => Ring (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods fromInteger :: Integer -> Fraction d
GCDDomain d => Rig (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods fromNatural :: Natural -> Fraction d #
(Characteristic d, GCDDomain d) => Characteristic (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods char :: proxy (Fraction d) -> Natural #
GCDDomain d => DecidableZero (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods isZero :: Fraction d -> Bool #
GCDDomain d => DecidableUnits (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods recipUnit :: Fraction d -> Maybe (Fraction d) # isUnit :: Fraction d -> Bool # (^?) :: Integral n => Fraction d -> n -> Maybe (Fraction d) #
GCDDomain d => DecidableAssociates (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods isAssociate :: Fraction d -> Fraction d -> Bool #
GCDDomain d => Unital (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods one :: Fraction d # pow :: Fraction d -> Natural -> Fraction d # productWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Division (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods recip :: Fraction d -> Fraction d # (/) :: Fraction d -> Fraction d -> Fraction d # (\\) :: Fraction d -> Fraction d -> Fraction d # (^) :: Integral n => Fraction d -> n -> Fraction d
GCDDomain d => Commutative (Fraction d)
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => Semiring (Fraction d)
Instance details Defined in Numeric.Field.Fraction
GCDDomain d => Multiplicative (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*) :: Fraction d -> Fraction d -> Fraction d # pow1p :: Fraction d -> Natural -> Fraction d # productWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Monoidal (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods zero :: Fraction d # sinnum :: Natural -> Fraction d -> Fraction d # sumWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Group (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (-) :: Fraction d -> Fraction d -> Fraction d # negate :: Fraction d -> Fraction d # subtract :: Fraction d -> Fraction d -> Fraction d # times :: Integral n => n -> Fraction d -> Fraction d #
GCDDomain d => Additive (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (+) :: Fraction d -> Fraction d -> Fraction d # sinnum1p :: Natural -> Fraction d -> Fraction d # sumWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
GCDDomain d => Abelian (Fraction d)
Instance details Defined in Numeric.Field.Fraction
PrettyCoeff (Fraction Integer)
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Fraction Integer -> ShowSCoeff #
(PrettyCoeff r, Eq r, Euclidean r) => PrettyCoeff (Fraction r)
Instance details Defined in Algebra.Ring.Polynomial.Class Methods showsCoeff :: Int -> Fraction r -> ShowSCoeff #
(Ord (Norm d), Euclidean d, Euclidean (Norm d), Normed d) => Normed (Fraction d)
Instance details Defined in Algebra.Normed Associated Types type Norm (Fraction d) # Methods norm :: Fraction d -> Norm (Fraction d) # liftNorm :: Norm (Fraction d) -> Fraction d #
type Norm (Fraction d)
Instance details Defined in Algebra.Normed type Norm (Fraction d) = Fraction (Norm d)

numerator :: Fraction t -> t #

denominator :: Fraction t -> t #

class GCDDomain d => UFD d #

Instances

Instances details

UFD Integer
Instance details Defined in Numeric.Domain.Internal
(Eq a, Fractional a) => UFD (WrapFractional a)
Instance details Defined in AlgebraicPrelude
(Eq a, Integral a) => UFD (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
GCDDomain a => UFD (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
GCDDomain d => UFD (Fraction d)
Instance details Defined in Numeric.Field.Fraction
(Eq r, Field r) => UFD (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate
(UFD poly, Wraps vars poly) => UFD (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => UFD (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(KnownNat n, Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => UFD (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial

class UFD d => PID d where #

Minimal complete definition

Nothing

Methods

egcd :: d -> d -> (d, d, d) #

Instances

Instances details

PID Integer
Instance details Defined in Numeric.Domain.Internal Methods egcd :: Integer -> Integer -> (Integer, Integer, Integer) #
(Eq a, Fractional a) => PID (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a, WrapFractional a) #
(Eq a, Integral a) => PID (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a, WrapIntegral a) #
PID a => PID (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods egcd :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a, WrapAlgebra a) #
GCDDomain d => PID (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods egcd :: Fraction d -> Fraction d -> (Fraction d, Fraction d, Fraction d) #
(Eq r, Field r) => PID (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods egcd :: Unipol r -> Unipol r -> (Unipol r, Unipol r, Unipol r) #
(PID poly, Wraps vars poly) => PID (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods egcd :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars, LabPolynomial poly vars) #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => PID (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods egcd :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) #

class (IntegralDomain d, UnitNormalForm d, DecidableZero d) => GCDDomain d where #

Minimal complete definition

Nothing

Methods

gcd :: d -> d -> d #

reduceFraction :: d -> d -> (d, d) #

lcm :: d -> d -> d #

Instances

Instances details

GCDDomain Integer
Instance details Defined in Numeric.Domain.Internal Methods gcd :: Integer -> Integer -> Integer # reduceFraction :: Integer -> Integer -> (Integer, Integer) # lcm :: Integer -> Integer -> Integer #
(Eq a, Fractional a) => GCDDomain (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapFractional a -> WrapFractional a -> WrapFractional a # reduceFraction :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a) # lcm :: WrapFractional a -> WrapFractional a -> WrapFractional a #
(Eq a, Integral a) => GCDDomain (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # reduceFraction :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # lcm :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
GCDDomain a => GCDDomain (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods gcd :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # reduceFraction :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) # lcm :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
GCDDomain d => GCDDomain (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods gcd :: Fraction d -> Fraction d -> Fraction d # reduceFraction :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # lcm :: Fraction d -> Fraction d -> Fraction d #
(Eq r, Field r) => GCDDomain (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods gcd :: Unipol r -> Unipol r -> Unipol r # reduceFraction :: Unipol r -> Unipol r -> (Unipol r, Unipol r) # lcm :: Unipol r -> Unipol r -> Unipol r #
(GCDDomain poly, Wraps vars poly) => GCDDomain (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods gcd :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # reduceFraction :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) # lcm :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => GCDDomain (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods gcd :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 # reduceFraction :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) # lcm :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 #
(KnownNat n, Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => GCDDomain (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial Methods gcd :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # reduceFraction :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> (OrderedPolynomial r ord n, OrderedPolynomial r ord n) # lcm :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #

gcd' :: GCDDomain r => NonEmpty r -> r #

class (Domain d, Commutative d) => IntegralDomain d where #

Minimal complete definition

Nothing

Methods

divides :: d -> d -> Bool #

maybeQuot :: d -> d -> Maybe d #

Instances

Instances details

IntegralDomain Integer
Instance details Defined in Numeric.Domain.Internal Methods divides :: Integer -> Integer -> Bool # maybeQuot :: Integer -> Integer -> Maybe Integer #
(Eq a, Fractional a) => IntegralDomain (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapFractional a -> WrapFractional a -> Bool # maybeQuot :: WrapFractional a -> WrapFractional a -> Maybe (WrapFractional a) #
(Eq a, Integral a) => IntegralDomain (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapIntegral a -> WrapIntegral a -> Bool # maybeQuot :: WrapIntegral a -> WrapIntegral a -> Maybe (WrapIntegral a) #
IntegralDomain a => IntegralDomain (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods divides :: WrapAlgebra a -> WrapAlgebra a -> Bool # maybeQuot :: WrapAlgebra a -> WrapAlgebra a -> Maybe (WrapAlgebra a) #
GCDDomain d => IntegralDomain (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods divides :: Fraction d -> Fraction d -> Bool # maybeQuot :: Fraction d -> Fraction d -> Maybe (Fraction d) #
(Eq r, Field r) => IntegralDomain (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods divides :: Unipol r -> Unipol r -> Bool # maybeQuot :: Unipol r -> Unipol r -> Maybe (Unipol r) #
(IntegralDomain poly, Wraps vars poly) => IntegralDomain (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods divides :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # maybeQuot :: LabPolynomial poly vars -> LabPolynomial poly vars -> Maybe (LabPolynomial poly vars) #
(Eq r, DecidableUnits r, DecidableZero r, KnownNat n, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => IntegralDomain (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods divides :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # maybeQuot :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Maybe (OrderedPolynomial r ord n) #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => IntegralDomain (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods divides :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> Bool # maybeQuot :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> Maybe (OrderedPolynomial r ord 1) #

class PID d => Euclidean d where #

Minimal complete definition

Nothing

Methods

degree :: d -> Maybe Natural #

divide :: d -> d -> (d, d) #

quot :: d -> d -> d #

rem :: d -> d -> d #

Instances

Instances details

Euclidean Integer
Instance details Defined in Numeric.Domain.Internal Methods degree :: Integer -> Maybe Natural # divide :: Integer -> Integer -> (Integer, Integer) # quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer #
(Eq a, Fractional a) => Euclidean (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapFractional a -> Maybe Natural # divide :: WrapFractional a -> WrapFractional a -> (WrapFractional a, WrapFractional a) # quot :: WrapFractional a -> WrapFractional a -> WrapFractional a # rem :: WrapFractional a -> WrapFractional a -> WrapFractional a #
(Eq a, Integral a) => Euclidean (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapIntegral a -> Maybe Natural # divide :: WrapIntegral a -> WrapIntegral a -> (WrapIntegral a, WrapIntegral a) # quot :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # rem :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a #
Euclidean a => Euclidean (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods degree :: WrapAlgebra a -> Maybe Natural # divide :: WrapAlgebra a -> WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) # quot :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # rem :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a #
GCDDomain d => Euclidean (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods degree :: Fraction d -> Maybe Natural # divide :: Fraction d -> Fraction d -> (Fraction d, Fraction d) # quot :: Fraction d -> Fraction d -> Fraction d # rem :: Fraction d -> Fraction d -> Fraction d #
(Eq r, Field r) => Euclidean (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods degree :: Unipol r -> Maybe Natural # divide :: Unipol r -> Unipol r -> (Unipol r, Unipol r) # quot :: Unipol r -> Unipol r -> Unipol r # rem :: Unipol r -> Unipol r -> Unipol r #
(Euclidean poly, Wraps vars poly) => Euclidean (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods degree :: LabPolynomial poly vars -> Maybe Natural # divide :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) # quot :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # rem :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => Euclidean (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods degree :: OrderedPolynomial r ord 1 -> Maybe Natural # divide :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) # quot :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 # rem :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 #

euclid :: Euclidean d => d -> d -> [(d, d, d)] #

prs :: Euclidean r => r -> r -> [(r, r, r)] #

chineseRemainder :: Euclidean r => [(r, r)] -> r #

class (ZeroProductSemiring d, Ring d) => Domain d #

Instances

Instances details

(ZeroProductSemiring d, Ring d) => Domain d
Instance details Defined in Numeric.Domain.Internal

recipUnitWhole :: Integral r => r -> Maybe r #

recipUnitIntegral :: Integral r => r -> Maybe r #

isAssociateWhole :: Eq n => n -> n -> Bool #

isAssociateIntegral :: (Eq n, Num n) => n -> n -> Bool #

class (Monoidal r, Semiring r) => ZeroProductSemiring r #

Instances

Instances details

ZeroProductSemiring Bool
Instance details Defined in Numeric.Semiring.ZeroProduct
ZeroProductSemiring Integer
Instance details Defined in Numeric.Semiring.ZeroProduct
ZeroProductSemiring Natural
Instance details Defined in Numeric.Semiring.ZeroProduct
(Eq a, Fractional a) => ZeroProductSemiring (WrapFractional a)
Instance details Defined in AlgebraicPrelude
(Eq a, Integral a) => ZeroProductSemiring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
(Monoidal a, Multiplicative a) => ZeroProductSemiring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
GCDDomain d => ZeroProductSemiring (Fraction d)
Instance details Defined in Numeric.Field.Fraction
(Eq r, Field r) => ZeroProductSemiring (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate
(ZeroProductSemiring poly, Wraps vars poly) => ZeroProductSemiring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Eq r, DecidableUnits r, DecidableZero r, KnownNat n, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => ZeroProductSemiring (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal

class (DecidableUnits r, DecidableAssociates r) => UnitNormalForm r where #

Minimal complete definition

Nothing

Methods

splitUnit :: r -> (r, r) #

Instances

Instances details

UnitNormalForm Integer
Instance details Defined in Numeric.Algebra.Unital.UnitNormalForm Methods splitUnit :: Integer -> (Integer, Integer) #
(Eq a, Fractional a) => UnitNormalForm (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapFractional a -> (WrapFractional a, WrapFractional a) #
(Eq a, Integral a) => UnitNormalForm (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapIntegral a -> (WrapIntegral a, WrapIntegral a) #
UnitNormalForm a => UnitNormalForm (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods splitUnit :: WrapAlgebra a -> (WrapAlgebra a, WrapAlgebra a) #
GCDDomain d => UnitNormalForm (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods splitUnit :: Fraction d -> (Fraction d, Fraction d) #
UnitNormalForm r => UnitNormalForm (Scalar r)
Instance details Defined in Algebra.Scalar Methods splitUnit :: Scalar r -> (Scalar r, Scalar r) #
(Eq r, Field r) => UnitNormalForm (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods splitUnit :: Unipol r -> (Unipol r, Unipol r) #
(UnitNormalForm poly, Wraps vars poly) => UnitNormalForm (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods splitUnit :: LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) #
(Eq r, Euclidean r, KnownNat n, IsMonomialOrder n ord) => UnitNormalForm (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods splitUnit :: OrderedPolynomial r ord n -> (OrderedPolynomial r ord n, OrderedPolynomial r ord n) #

leadingUnit :: UnitNormalForm r => r -> r #

class (Group r, Semiring r) => Rng r #

Instances

Instances details

(Group r, Semiring r) => Rng r
Instance details Defined in Numeric.Rng.Class

class Ring r => LocalRing r #

class (Division r, Ring r) => DivisionRing r #

Instances

Instances details

(Division r, Ring r) => DivisionRing r
Instance details Defined in Numeric.Ring.Division

class (Rig r, Rng r) => Ring r #

Instances

Instances details

Ring Int
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int
Ring Int8
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int8
Ring Int16
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int16
Ring Int32
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int32
Ring Int64
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Int64
Ring Integer
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Integer
Ring Word
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word
Ring Word8
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word8
Ring Word16
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word16
Ring Word32
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word32
Ring Word64
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> Word64
Ring ()
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> ()
Num a => Ring (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapNum a
Num a => Ring (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapFractional a
Num a => Ring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapIntegral a
Ring a => Ring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods fromInteger :: Integer -> WrapAlgebra a
GCDDomain d => Ring (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods fromInteger :: Integer -> Fraction d
Ring r => Ring (Scalar r)
Instance details Defined in Algebra.Scalar Methods fromInteger :: Integer -> Scalar r
(Commutative r, Ring r) => Ring (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods fromInteger :: Integer -> Complex r
(CoeffRing r, DecidableZero r) => Ring (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods fromInteger :: Integer -> Unipol r
(Ring a, Ring b) => Ring (a, b)
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> (a, b)
(Ring r, CounitalCoalgebra r m) => Ring (Covector r m)
Instance details Defined in Numeric.Covector Methods fromInteger :: Integer -> Covector r m
(Wraps vars poly, Ring poly) => Ring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromInteger :: Integer -> LabPolynomial poly vars
(Ring a, Ring b, Ring c) => Ring (a, b, c)
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> (a, b, c)
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Ring (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromInteger :: Integer -> PadPolyL n ord poly
(Field (Coefficient poly), IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Ring (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods fromInteger :: Integer -> Quotient poly ideal
(Ring a, Ring b, Ring c, Ring d) => Ring (a, b, c, d)
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> (a, b, c, d)
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Ring (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromInteger :: Integer -> OrderedPolynomial r order n
(Ring a, Ring b, Ring c, Ring d, Ring e) => Ring (a, b, c, d, e)
Instance details Defined in Numeric.Ring.Class Methods fromInteger :: Integer -> (a, b, c, d, e)

class (AdditiveOrder r, Rig r) => OrderedRig r #

Instances

Instances details

OrderedRig Bool
Instance details Defined in Numeric.Rig.Ordered
OrderedRig Integer
Instance details Defined in Numeric.Rig.Ordered
OrderedRig Natural
Instance details Defined in Numeric.Rig.Ordered
OrderedRig ()
Instance details Defined in Numeric.Rig.Ordered
(OrderedRig a, OrderedRig b) => OrderedRig (a, b)
Instance details Defined in Numeric.Rig.Ordered
(OrderedRig a, OrderedRig b, OrderedRig c) => OrderedRig (a, b, c)
Instance details Defined in Numeric.Rig.Ordered
(OrderedRig a, OrderedRig b, OrderedRig c, OrderedRig d) => OrderedRig (a, b, c, d)
Instance details Defined in Numeric.Rig.Ordered
(OrderedRig a, OrderedRig b, OrderedRig c, OrderedRig d, OrderedRig e) => OrderedRig (a, b, c, d, e)
Instance details Defined in Numeric.Rig.Ordered

class (Semiring r, Unital r, Monoidal r) => Rig r where #

Minimal complete definition

Nothing

Methods

fromNatural :: Natural -> r #

Instances

Instances details

Rig Bool
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Bool #
Rig Int
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int #
Rig Int8
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int8 #
Rig Int16
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int16 #
Rig Int32
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int32 #
Rig Int64
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Int64 #
Rig Integer
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Integer #
Rig Natural
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Natural #
Rig Word
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word #
Rig Word8
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word8 #
Rig Word16
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word16 #
Rig Word32
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word32 #
Rig Word64
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> Word64 #
Rig ()
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> () #
Num a => Rig (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapNum a #
Num a => Rig (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapFractional a #
Num a => Rig (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapIntegral a #
Rig a => Rig (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods fromNatural :: Natural -> WrapAlgebra a #
GCDDomain d => Rig (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods fromNatural :: Natural -> Fraction d #
Rig r => Rig (Scalar r)
Instance details Defined in Algebra.Scalar Methods fromNatural :: Natural -> Scalar r #
(Commutative r, Ring r) => Rig (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods fromNatural :: Natural -> Complex r #
(CoeffRing r, DecidableZero r) => Rig (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods fromNatural :: Natural -> Unipol r #
(Rig a, Rig b) => Rig (a, b)
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> (a, b) #
(Rig r, CounitalCoalgebra r m) => Rig (Covector r m)
Instance details Defined in Numeric.Covector Methods fromNatural :: Natural -> Covector r m #
(Wraps vars poly, Rig poly) => Rig (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromNatural :: Natural -> LabPolynomial poly vars #
(Rig a, Rig b, Rig c) => Rig (a, b, c)
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> (a, b, c) #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Rig (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromNatural :: Natural -> PadPolyL n ord poly #
(Field (Coefficient poly), IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Rig (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods fromNatural :: Natural -> Quotient poly ideal #
(Rig a, Rig b, Rig c, Rig d) => Rig (a, b, c, d)
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Rig (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromNatural :: Natural -> OrderedPolynomial r order n #
(Rig a, Rig b, Rig c, Rig d, Rig e) => Rig (a, b, c, d, e)
Instance details Defined in Numeric.Rig.Class Methods fromNatural :: Natural -> (a, b, c, d, e) #

class Rig r => Characteristic r where #

Methods

char :: proxy r -> Natural #

Instances

Instances details

Characteristic Bool
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Bool -> Natural #
Characteristic Int
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int -> Natural #
Characteristic Int8
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int8 -> Natural #
Characteristic Int16
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int16 -> Natural #
Characteristic Int32
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int32 -> Natural #
Characteristic Int64
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Int64 -> Natural #
Characteristic Integer
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Integer -> Natural #
Characteristic Natural
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Natural -> Natural #
Characteristic Word
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word -> Natural #
Characteristic Word8
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word8 -> Natural #
Characteristic Word16
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word16 -> Natural #
Characteristic Word32
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word32 -> Natural #
Characteristic Word64
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy Word64 -> Natural #
Characteristic ()
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy () -> Natural #
(Characteristic d, GCDDomain d) => Characteristic (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods char :: proxy (Fraction d) -> Natural #
(Characteristic a, Characteristic b) => Characteristic (a, b)
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy (a, b) -> Natural #
(Characteristic a, Characteristic b, Characteristic c) => Characteristic (a, b, c)
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy (a, b, c) -> Natural #
(Characteristic a, Characteristic b, Characteristic c, Characteristic d) => Characteristic (a, b, c, d)
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy (a, b, c, d) -> Natural #
(IsMonomialOrder n ord, Characteristic r, KnownNat n, CoeffRing r) => Characteristic (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods char :: proxy (OrderedPolynomial r ord n) -> Natural #
(Characteristic a, Characteristic b, Characteristic c, Characteristic d, Characteristic e) => Characteristic (a, b, c, d, e)
Instance details Defined in Numeric.Rig.Characteristic Methods char :: proxy (a, b, c, d, e) -> Natural #

class Additive r => Quadrance r m where #

Methods

quadrance :: m -> r #

Instances

Instances details

Quadrance () a
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: a -> () #
Rig r => Quadrance r Word8
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word8 -> r #
Rig r => Quadrance r Word64
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word64 -> r #
Rig r => Quadrance r Word32
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word32 -> r #
Rig r => Quadrance r Word16
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word16 -> r #
Rig r => Quadrance r Word
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Word -> r #
Rig r => Quadrance r Natural
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Natural -> r #
Rig r => Quadrance r Integer
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Integer -> r #
Rig r => Quadrance r Int8
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int8 -> r #
Rig r => Quadrance r Int64
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int64 -> r #
Rig r => Quadrance r Int32
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int32 -> r #
Rig r => Quadrance r Int16
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int16 -> r #
Rig r => Quadrance r Int
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Int -> r #
Rig r => Quadrance r Bool
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: Bool -> r #
(Additive r, Monoidal r) => Quadrance r ()
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: () -> r #
(Commutative r, Rng r, InvolutiveSemiring r) => Quadrance r (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods quadrance :: Complex r -> r #
(Quadrance r a, Quadrance r b) => Quadrance r (a, b)
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: (a, b) -> r #
(Quadrance r a, Quadrance r b, Quadrance r c) => Quadrance r (a, b, c)
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: (a, b, c) -> r #
(Quadrance r a, Quadrance r b, Quadrance r c, Quadrance r d) => Quadrance r (a, b, c, d)
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: (a, b, c, d) -> r #
(Quadrance r a, Quadrance r b, Quadrance r c, Quadrance r d, Quadrance r e) => Quadrance r (a, b, c, d, e)
Instance details Defined in Numeric.Quadrance.Class Methods quadrance :: (a, b, c, d, e) -> r #

class Order a => LocallyFiniteOrder a #

Minimal complete definition

range, rangeSize

Instances

Instances details

LocallyFiniteOrder Bool
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Bool -> Bool -> [Bool] rangeSize :: Bool -> Bool -> Natural moebiusInversion :: Ring r => Bool -> Bool -> r
LocallyFiniteOrder Int
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int -> Int -> [Int] rangeSize :: Int -> Int -> Natural moebiusInversion :: Ring r => Int -> Int -> r
LocallyFiniteOrder Int8
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int8 -> Int8 -> [Int8] rangeSize :: Int8 -> Int8 -> Natural moebiusInversion :: Ring r => Int8 -> Int8 -> r
LocallyFiniteOrder Int16
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int16 -> Int16 -> [Int16] rangeSize :: Int16 -> Int16 -> Natural moebiusInversion :: Ring r => Int16 -> Int16 -> r
LocallyFiniteOrder Int32
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int32 -> Int32 -> [Int32] rangeSize :: Int32 -> Int32 -> Natural moebiusInversion :: Ring r => Int32 -> Int32 -> r
LocallyFiniteOrder Int64
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Int64 -> Int64 -> [Int64] rangeSize :: Int64 -> Int64 -> Natural moebiusInversion :: Ring r => Int64 -> Int64 -> r
LocallyFiniteOrder Integer
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Integer -> Integer -> [Integer] rangeSize :: Integer -> Integer -> Natural moebiusInversion :: Ring r => Integer -> Integer -> r
LocallyFiniteOrder Natural
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Natural -> Natural -> [Natural] rangeSize :: Natural -> Natural -> Natural moebiusInversion :: Ring r => Natural -> Natural -> r
LocallyFiniteOrder Word
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word -> Word -> [Word] rangeSize :: Word -> Word -> Natural moebiusInversion :: Ring r => Word -> Word -> r
LocallyFiniteOrder Word8
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word8 -> Word8 -> [Word8] rangeSize :: Word8 -> Word8 -> Natural moebiusInversion :: Ring r => Word8 -> Word8 -> r
LocallyFiniteOrder Word16
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word16 -> Word16 -> [Word16] rangeSize :: Word16 -> Word16 -> Natural moebiusInversion :: Ring r => Word16 -> Word16 -> r
LocallyFiniteOrder Word32
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word32 -> Word32 -> [Word32] rangeSize :: Word32 -> Word32 -> Natural moebiusInversion :: Ring r => Word32 -> Word32 -> r
LocallyFiniteOrder Word64
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Word64 -> Word64 -> [Word64] rangeSize :: Word64 -> Word64 -> Natural moebiusInversion :: Ring r => Word64 -> Word64 -> r
LocallyFiniteOrder ()
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: () -> () -> [()] rangeSize :: () -> () -> Natural moebiusInversion :: Ring r => () -> () -> r
Ord a => LocallyFiniteOrder (Set a)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Set a -> Set a -> [Set a] rangeSize :: Set a -> Set a -> Natural moebiusInversion :: Ring r => Set a -> Set a -> r
(LocallyFiniteOrder a, LocallyFiniteOrder b) => LocallyFiniteOrder (a, b)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: (a, b) -> (a, b) -> [(a, b)] rangeSize :: (a, b) -> (a, b) -> Natural moebiusInversion :: Ring r => (a, b) -> (a, b) -> r
(LocallyFiniteOrder a, LocallyFiniteOrder b, LocallyFiniteOrder c) => LocallyFiniteOrder (a, b, c)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: (a, b, c) -> (a, b, c) -> [(a, b, c)] rangeSize :: (a, b, c) -> (a, b, c) -> Natural moebiusInversion :: Ring r => (a, b, c) -> (a, b, c) -> r
(LocallyFiniteOrder a, LocallyFiniteOrder b, LocallyFiniteOrder c, LocallyFiniteOrder d) => LocallyFiniteOrder (a, b, c, d)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: (a, b, c, d) -> (a, b, c, d) -> [(a, b, c, d)] rangeSize :: (a, b, c, d) -> (a, b, c, d) -> Natural moebiusInversion :: Ring r => (a, b, c, d) -> (a, b, c, d) -> r
(LocallyFiniteOrder a, LocallyFiniteOrder b, LocallyFiniteOrder c, LocallyFiniteOrder d, LocallyFiniteOrder e) => LocallyFiniteOrder (a, b, c, d, e)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: (a, b, c, d, e) -> (a, b, c, d, e) -> [(a, b, c, d, e)] rangeSize :: (a, b, c, d, e) -> (a, b, c, d, e) -> Natural moebiusInversion :: Ring r => (a, b, c, d, e) -> (a, b, c, d, e) -> r

class (Additive r, Order r) => AdditiveOrder r #

Instances

Instances details

AdditiveOrder Bool
Instance details Defined in Numeric.Order.Additive
AdditiveOrder Integer
Instance details Defined in Numeric.Order.Additive
AdditiveOrder Natural
Instance details Defined in Numeric.Order.Additive
AdditiveOrder ()
Instance details Defined in Numeric.Order.Additive
(AdditiveOrder a, AdditiveOrder b) => AdditiveOrder (a, b)
Instance details Defined in Numeric.Order.Additive
(AdditiveOrder a, AdditiveOrder b, AdditiveOrder c) => AdditiveOrder (a, b, c)
Instance details Defined in Numeric.Order.Additive
(AdditiveOrder a, AdditiveOrder b, AdditiveOrder c, AdditiveOrder d) => AdditiveOrder (a, b, c, d)
Instance details Defined in Numeric.Order.Additive
(AdditiveOrder a, AdditiveOrder b, AdditiveOrder c, AdditiveOrder d, AdditiveOrder e) => AdditiveOrder (a, b, c, d, e)
Instance details Defined in Numeric.Order.Additive

class (Euclidean d, Division d) => Field d #

Instances

Instances details

(Euclidean d, Division d) => Field d
Instance details Defined in Numeric.Field.Class

class (Semiring r, Idempotent r) => Dioid r #

Instances

Instances details

(Semiring r, Idempotent r) => Dioid r
Instance details Defined in Numeric.Dioid.Class

class Monoidal r => DecidableZero r where #

Methods

isZero :: r -> Bool #

Instances

Instances details

DecidableZero Bool
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Bool -> Bool #
DecidableZero Int
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int -> Bool #
DecidableZero Int8
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int8 -> Bool #
DecidableZero Int16
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int16 -> Bool #
DecidableZero Int32
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int32 -> Bool #
DecidableZero Int64
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Int64 -> Bool #
DecidableZero Integer
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Integer -> Bool #
DecidableZero Natural
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Natural -> Bool #
DecidableZero Word
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word -> Bool #
DecidableZero Word8
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word8 -> Bool #
DecidableZero Word16
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word16 -> Bool #
DecidableZero Word32
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word32 -> Bool #
DecidableZero Word64
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: Word64 -> Bool #
DecidableZero ()
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: () -> Bool #
(Num a, Eq a) => DecidableZero (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapNum a -> Bool #
(Num a, Eq a) => DecidableZero (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapFractional a -> Bool #
(Num a, Eq a) => DecidableZero (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapIntegral a -> Bool #
DecidableZero a => DecidableZero (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods isZero :: WrapAlgebra a -> Bool #
GCDDomain d => DecidableZero (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods isZero :: Fraction d -> Bool #
DecidableZero r => DecidableZero (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods isZero :: Unipol r -> Bool #
(DecidableZero a, DecidableZero b) => DecidableZero (a, b)
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: (a, b) -> Bool #
(Wraps vars poly, DecidableZero poly) => DecidableZero (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods isZero :: LabPolynomial poly vars -> Bool #
(DecidableZero a, DecidableZero b, DecidableZero c) => DecidableZero (a, b, c)
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: (a, b, c) -> Bool #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => DecidableZero (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isZero :: PadPolyL n ord poly -> Bool #
(DecidableZero a, DecidableZero b, DecidableZero c, DecidableZero d) => DecidableZero (a, b, c, d)
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: (a, b, c, d) -> Bool #
(CoeffRing r, KnownNat n, IsMonomialOrder n ord) => DecidableZero (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isZero :: OrderedPolynomial r ord n -> Bool #
(DecidableZero a, DecidableZero b, DecidableZero c, DecidableZero d, DecidableZero e) => DecidableZero (a, b, c, d, e)
Instance details Defined in Numeric.Decidable.Zero Methods isZero :: (a, b, c, d, e) -> Bool #

class Unital r => DecidableUnits r where #

Minimal complete definition

recipUnit

Methods

recipUnit :: r -> Maybe r #

isUnit :: r -> Bool #

(^?) :: Integral n => r -> n -> Maybe r #

Instances

Instances details

DecidableUnits Bool
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Bool -> Maybe Bool # isUnit :: Bool -> Bool # (^?) :: Integral n => Bool -> n -> Maybe Bool #
DecidableUnits Int
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int -> Maybe Int # isUnit :: Int -> Bool # (^?) :: Integral n => Int -> n -> Maybe Int #
DecidableUnits Int8
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int8 -> Maybe Int8 # isUnit :: Int8 -> Bool # (^?) :: Integral n => Int8 -> n -> Maybe Int8 #
DecidableUnits Int16
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int16 -> Maybe Int16 # isUnit :: Int16 -> Bool # (^?) :: Integral n => Int16 -> n -> Maybe Int16 #
DecidableUnits Int32
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int32 -> Maybe Int32 # isUnit :: Int32 -> Bool # (^?) :: Integral n => Int32 -> n -> Maybe Int32 #
DecidableUnits Int64
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Int64 -> Maybe Int64 # isUnit :: Int64 -> Bool # (^?) :: Integral n => Int64 -> n -> Maybe Int64 #
DecidableUnits Integer
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Integer -> Maybe Integer # isUnit :: Integer -> Bool # (^?) :: Integral n => Integer -> n -> Maybe Integer #
DecidableUnits Natural
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Natural -> Maybe Natural # isUnit :: Natural -> Bool # (^?) :: Integral n => Natural -> n -> Maybe Natural #
DecidableUnits Word
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word -> Maybe Word # isUnit :: Word -> Bool # (^?) :: Integral n => Word -> n -> Maybe Word #
DecidableUnits Word8
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word8 -> Maybe Word8 # isUnit :: Word8 -> Bool # (^?) :: Integral n => Word8 -> n -> Maybe Word8 #
DecidableUnits Word16
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word16 -> Maybe Word16 # isUnit :: Word16 -> Bool # (^?) :: Integral n => Word16 -> n -> Maybe Word16 #
DecidableUnits Word32
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word32 -> Maybe Word32 # isUnit :: Word32 -> Bool # (^?) :: Integral n => Word32 -> n -> Maybe Word32 #
DecidableUnits Word64
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: Word64 -> Maybe Word64 # isUnit :: Word64 -> Bool # (^?) :: Integral n => Word64 -> n -> Maybe Word64 #
DecidableUnits ()
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: () -> Maybe () # isUnit :: () -> Bool # (^?) :: Integral n => () -> n -> Maybe () #
(Eq a, Fractional a) => DecidableUnits (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapFractional a -> Maybe (WrapFractional a) # isUnit :: WrapFractional a -> Bool # (^?) :: Integral n => WrapFractional a -> n -> Maybe (WrapFractional a) #
(Eq a, Integral a) => DecidableUnits (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapIntegral a -> Maybe (WrapIntegral a) # isUnit :: WrapIntegral a -> Bool # (^?) :: Integral n => WrapIntegral a -> n -> Maybe (WrapIntegral a) #
DecidableUnits a => DecidableUnits (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods recipUnit :: WrapAlgebra a -> Maybe (WrapAlgebra a) # isUnit :: WrapAlgebra a -> Bool # (^?) :: Integral n => WrapAlgebra a -> n -> Maybe (WrapAlgebra a) #
GCDDomain d => DecidableUnits (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods recipUnit :: Fraction d -> Maybe (Fraction d) # isUnit :: Fraction d -> Bool # (^?) :: Integral n => Fraction d -> n -> Maybe (Fraction d) #
DecidableUnits r => DecidableUnits (Scalar r)
Instance details Defined in Algebra.Scalar Methods recipUnit :: Scalar r -> Maybe (Scalar r) # isUnit :: Scalar r -> Bool # (^?) :: Integral n => Scalar r -> n -> Maybe (Scalar r) #
(Eq r, Field r) => DecidableUnits (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods recipUnit :: Unipol r -> Maybe (Unipol r) # isUnit :: Unipol r -> Bool # (^?) :: Integral n => Unipol r -> n -> Maybe (Unipol r) #
(DecidableUnits a, DecidableUnits b) => DecidableUnits (a, b)
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: (a, b) -> Maybe (a, b) # isUnit :: (a, b) -> Bool # (^?) :: Integral n => (a, b) -> n -> Maybe (a, b) #
(DecidableUnits poly, Wraps vars poly) => DecidableUnits (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods recipUnit :: LabPolynomial poly vars -> Maybe (LabPolynomial poly vars) # isUnit :: LabPolynomial poly vars -> Bool # (^?) :: Integral n => LabPolynomial poly vars -> n -> Maybe (LabPolynomial poly vars) #
(DecidableUnits a, DecidableUnits b, DecidableUnits c) => DecidableUnits (a, b, c)
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: (a, b, c) -> Maybe (a, b, c) # isUnit :: (a, b, c) -> Bool # (^?) :: Integral n => (a, b, c) -> n -> Maybe (a, b, c) #
(DecidableUnits a, DecidableUnits b, DecidableUnits c, DecidableUnits d) => DecidableUnits (a, b, c, d)
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: (a, b, c, d) -> Maybe (a, b, c, d) # isUnit :: (a, b, c, d) -> Bool # (^?) :: Integral n => (a, b, c, d) -> n -> Maybe (a, b, c, d) #
(CoeffRing r, IsMonomialOrder n ord, DecidableUnits r, KnownNat n) => DecidableUnits (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods recipUnit :: OrderedPolynomial r ord n -> Maybe (OrderedPolynomial r ord n) # isUnit :: OrderedPolynomial r ord n -> Bool # (^?) :: Integral n0 => OrderedPolynomial r ord n -> n0 -> Maybe (OrderedPolynomial r ord n) #
(DecidableUnits a, DecidableUnits b, DecidableUnits c, DecidableUnits d, DecidableUnits e) => DecidableUnits (a, b, c, d, e)
Instance details Defined in Numeric.Decidable.Units Methods recipUnit :: (a, b, c, d, e) -> Maybe (a, b, c, d, e) # isUnit :: (a, b, c, d, e) -> Bool # (^?) :: Integral n => (a, b, c, d, e) -> n -> Maybe (a, b, c, d, e) #

class Unital r => DecidableAssociates r where #

Methods

isAssociate :: r -> r -> Bool #

Instances

Instances details

DecidableAssociates Bool
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Bool -> Bool -> Bool #
DecidableAssociates Int
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int -> Int -> Bool #
DecidableAssociates Int8
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int8 -> Int8 -> Bool #
DecidableAssociates Int16
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int16 -> Int16 -> Bool #
DecidableAssociates Int32
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int32 -> Int32 -> Bool #
DecidableAssociates Int64
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Int64 -> Int64 -> Bool #
DecidableAssociates Integer
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Integer -> Integer -> Bool #
DecidableAssociates Natural
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Natural -> Natural -> Bool #
DecidableAssociates Word
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word -> Word -> Bool #
DecidableAssociates Word8
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word8 -> Word8 -> Bool #
DecidableAssociates Word16
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word16 -> Word16 -> Bool #
DecidableAssociates Word32
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word32 -> Word32 -> Bool #
DecidableAssociates Word64
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: Word64 -> Word64 -> Bool #
DecidableAssociates ()
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: () -> () -> Bool #
(Eq a, Fractional a) => DecidableAssociates (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapFractional a -> WrapFractional a -> Bool #
(Eq a, Integral a) => DecidableAssociates (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapIntegral a -> WrapIntegral a -> Bool #
DecidableAssociates a => DecidableAssociates (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods isAssociate :: WrapAlgebra a -> WrapAlgebra a -> Bool #
GCDDomain d => DecidableAssociates (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods isAssociate :: Fraction d -> Fraction d -> Bool #
DecidableAssociates r => DecidableAssociates (Scalar r)
Instance details Defined in Algebra.Scalar Methods isAssociate :: Scalar r -> Scalar r -> Bool #
(Eq r, Field r) => DecidableAssociates (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods isAssociate :: Unipol r -> Unipol r -> Bool #
(DecidableAssociates a, DecidableAssociates b) => DecidableAssociates (a, b)
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: (a, b) -> (a, b) -> Bool #
(DecidableAssociates poly, Wraps vars poly) => DecidableAssociates (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods isAssociate :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool #
(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c) => DecidableAssociates (a, b, c)
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: (a, b, c) -> (a, b, c) -> Bool #
(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c, DecidableAssociates d) => DecidableAssociates (a, b, c, d)
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: (a, b, c, d) -> (a, b, c, d) -> Bool #
(Eq r, KnownNat n, Euclidean r, IsMonomialOrder n ord) => DecidableAssociates (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isAssociate :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool #
(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c, DecidableAssociates d, DecidableAssociates e) => DecidableAssociates (a, b, c, d, e)
Instance details Defined in Numeric.Decidable.Associates Methods isAssociate :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

newtype Covector r a #

Constructors

Covector
Fields ($*) :: (a -> r) -> r

Instances

Instances details

RightModule r s => RightModule r (Covector s m)
Instance details Defined in Numeric.Covector Methods (*.) :: Covector s m -> r -> Covector s m #
LeftModule r s => LeftModule r (Covector s m)
Instance details Defined in Numeric.Covector Methods (.*) :: r -> Covector s m -> Covector s m #
Monad (Covector r)
Instance details Defined in Numeric.Covector Methods (>>=) :: Covector r a -> (a -> Covector r b) -> Covector r b # (>>) :: Covector r a -> Covector r b -> Covector r b # return :: a -> Covector r a #
Functor (Covector r)
Instance details Defined in Numeric.Covector Methods fmap :: (a -> b) -> Covector r a -> Covector r b # (<$) :: a -> Covector r b -> Covector r a #
Applicative (Covector r)
Instance details Defined in Numeric.Covector Methods pure :: a -> Covector r a # (<>) :: Covector r (a -> b) -> Covector r a -> Covector r b # liftA2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c # (>) :: Covector r a -> Covector r b -> Covector r b # (<*) :: Covector r a -> Covector r b -> Covector r a #
Monoidal r => MonadPlus (Covector r)
Instance details Defined in Numeric.Covector Methods mzero :: Covector r a # mplus :: Covector r a -> Covector r a -> Covector r a #
Monoidal r => Alternative (Covector r)
Instance details Defined in Numeric.Covector Methods empty :: Covector r a # (<\|>) :: Covector r a -> Covector r a -> Covector r a # some :: Covector r a -> Covector r [a] # many :: Covector r a -> Covector r [a] #
Additive r => Alt (Covector r)
Instance details Defined in Numeric.Covector Methods (<!>) :: Covector r a -> Covector r a -> Covector r a some :: Applicative (Covector r) => Covector r a -> Covector r [a] many :: Applicative (Covector r) => Covector r a -> Covector r [a]
Apply (Covector r)
Instance details Defined in Numeric.Covector Methods (<.>) :: Covector r (a -> b) -> Covector r a -> Covector r b (.>) :: Covector r a -> Covector r b -> Covector r b (<.) :: Covector r a -> Covector r b -> Covector r a liftF2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c
Bind (Covector r)
Instance details Defined in Numeric.Covector Methods (>>-) :: Covector r a -> (a -> Covector r b) -> Covector r b join :: Covector r (Covector r a) -> Covector r a
Monoidal r => Plus (Covector r)
Instance details Defined in Numeric.Covector Methods zero :: Covector r a
(Ring r, CounitalCoalgebra r m) => Ring (Covector r m)
Instance details Defined in Numeric.Covector Methods fromInteger :: Integer -> Covector r m
(Rig r, CounitalCoalgebra r m) => Rig (Covector r m)
Instance details Defined in Numeric.Covector Methods fromNatural :: Natural -> Covector r m #
CounitalCoalgebra r m => Unital (Covector r m)
Instance details Defined in Numeric.Covector Methods one :: Covector r m # pow :: Covector r m -> Natural -> Covector r m # productWith :: Foldable f => (a -> Covector r m) -> f a -> Covector r m #
(Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a)
Instance details Defined in Numeric.Covector
(Commutative m, Coalgebra r m) => Commutative (Covector r m)
Instance details Defined in Numeric.Covector
Coalgebra r m => Semiring (Covector r m)
Instance details Defined in Numeric.Covector
Coalgebra r m => Multiplicative (Covector r m)
Instance details Defined in Numeric.Covector Methods (*) :: Covector r m -> Covector r m -> Covector r m # pow1p :: Covector r m -> Natural -> Covector r m # productWith1 :: Foldable1 f => (a -> Covector r m) -> f a -> Covector r m #
Monoidal s => Monoidal (Covector s a)
Instance details Defined in Numeric.Covector Methods zero :: Covector s a # sinnum :: Natural -> Covector s a -> Covector s a # sumWith :: Foldable f => (a0 -> Covector s a) -> f a0 -> Covector s a #
Group s => Group (Covector s a)
Instance details Defined in Numeric.Covector Methods (-) :: Covector s a -> Covector s a -> Covector s a # negate :: Covector s a -> Covector s a # subtract :: Covector s a -> Covector s a -> Covector s a # times :: Integral n => n -> Covector s a -> Covector s a #
Idempotent r => Idempotent (Covector r a)
Instance details Defined in Numeric.Covector
Additive r => Additive (Covector r a)
Instance details Defined in Numeric.Covector Methods (+) :: Covector r a -> Covector r a -> Covector r a # sinnum1p :: Natural -> Covector r a -> Covector r a # sumWith1 :: Foldable1 f => (a0 -> Covector r a) -> f a0 -> Covector r a #
Abelian s => Abelian (Covector s a)
Instance details Defined in Numeric.Covector
Coalgebra r m => RightModule (Covector r m) (Covector r m)
Instance details Defined in Numeric.Covector Methods (*.) :: Covector r m -> Covector r m -> Covector r m #
Coalgebra r m => LeftModule (Covector r m) (Covector r m)
Instance details Defined in Numeric.Covector Methods (.*) :: Covector r m -> Covector r m -> Covector r m #

class Algebra r a => UnitalAlgebra r a where #

Methods

unit :: r -> a -> r #

Instances

Instances details

Rng k => UnitalAlgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods unit :: k -> ComplexBasis -> k #
Semiring r => UnitalAlgebra r ()
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> () -> r #
(Monoidal r, Semiring r) => UnitalAlgebra r [a]
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> [a] -> r #
(Monoidal r, Semiring r) => UnitalAlgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> Seq a -> r #
(UnitalAlgebra r a, UnitalAlgebra r b) => UnitalAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> (a, b) -> r #
(UnitalAlgebra r a, UnitalAlgebra r b, UnitalAlgebra r c) => UnitalAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> (a, b, c) -> r #
(UnitalAlgebra r a, UnitalAlgebra r b, UnitalAlgebra r c, UnitalAlgebra r d) => UnitalAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> (a, b, c, d) -> r #
(UnitalAlgebra r a, UnitalAlgebra r b, UnitalAlgebra r c, UnitalAlgebra r d, UnitalAlgebra r e) => UnitalAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> (a, b, c, d, e) -> r #

class Multiplicative r => Unital r where #

Minimal complete definition

one

Methods

one :: r #

pow :: r -> Natural -> r #

productWith :: Foldable f => (a -> r) -> f a -> r #

Instances

Instances details

Unital Bool
Instance details Defined in Numeric.Algebra.Unital Methods one :: Bool # pow :: Bool -> Natural -> Bool # productWith :: Foldable f => (a -> Bool) -> f a -> Bool #
Unital Int
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int # pow :: Int -> Natural -> Int # productWith :: Foldable f => (a -> Int) -> f a -> Int #
Unital Int8
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int8 # pow :: Int8 -> Natural -> Int8 # productWith :: Foldable f => (a -> Int8) -> f a -> Int8 #
Unital Int16
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int16 # pow :: Int16 -> Natural -> Int16 # productWith :: Foldable f => (a -> Int16) -> f a -> Int16 #
Unital Int32
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int32 # pow :: Int32 -> Natural -> Int32 # productWith :: Foldable f => (a -> Int32) -> f a -> Int32 #
Unital Int64
Instance details Defined in Numeric.Algebra.Unital Methods one :: Int64 # pow :: Int64 -> Natural -> Int64 # productWith :: Foldable f => (a -> Int64) -> f a -> Int64 #
Unital Integer
Instance details Defined in Numeric.Algebra.Unital Methods one :: Integer # pow :: Integer -> Natural -> Integer # productWith :: Foldable f => (a -> Integer) -> f a -> Integer #
Unital Natural
Instance details Defined in Numeric.Algebra.Unital Methods one :: Natural # pow :: Natural -> Natural -> Natural # productWith :: Foldable f => (a -> Natural) -> f a -> Natural #
Unital Word
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word # pow :: Word -> Natural -> Word # productWith :: Foldable f => (a -> Word) -> f a -> Word #
Unital Word8
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word8 # pow :: Word8 -> Natural -> Word8 # productWith :: Foldable f => (a -> Word8) -> f a -> Word8 #
Unital Word16
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word16 # pow :: Word16 -> Natural -> Word16 # productWith :: Foldable f => (a -> Word16) -> f a -> Word16 #
Unital Word32
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word32 # pow :: Word32 -> Natural -> Word32 # productWith :: Foldable f => (a -> Word32) -> f a -> Word32 #
Unital Word64
Instance details Defined in Numeric.Algebra.Unital Methods one :: Word64 # pow :: Word64 -> Natural -> Word64 # productWith :: Foldable f => (a -> Word64) -> f a -> Word64 #
Unital ()
Instance details Defined in Numeric.Algebra.Unital Methods one :: () # pow :: () -> Natural -> () # productWith :: Foldable f => (a -> ()) -> f a -> () #
Num a => Unital (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapNum a # pow :: WrapNum a -> Natural -> WrapNum a # productWith :: Foldable f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Unital (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapFractional a # pow :: WrapFractional a -> Natural -> WrapFractional a # productWith :: Foldable f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Unital (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapIntegral a # pow :: WrapIntegral a -> Natural -> WrapIntegral a # productWith :: Foldable f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Unital a => Unital (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods one :: WrapAlgebra a # pow :: WrapAlgebra a -> Natural -> WrapAlgebra a # productWith :: Foldable f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Unital a => Unital (Mult a)
Instance details Defined in AlgebraicPrelude Methods one :: Mult a # pow :: Mult a -> Natural -> Mult a # productWith :: Foldable f => (a0 -> Mult a) -> f a0 -> Mult a #
GCDDomain d => Unital (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods one :: Fraction d # pow :: Fraction d -> Natural -> Fraction d # productWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
Unital r => Unital (Scalar r)
Instance details Defined in Algebra.Scalar Methods one :: Scalar r # pow :: Scalar r -> Natural -> Scalar r # productWith :: Foldable f => (a -> Scalar r) -> f a -> Scalar r #
(Commutative r, Ring r) => Unital (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods one :: Complex r # pow :: Complex r -> Natural -> Complex r # productWith :: Foldable f => (a -> Complex r) -> f a -> Complex r #
(CoeffRing r, Unital r) => Unital (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods one :: Unipol r # pow :: Unipol r -> Natural -> Unipol r # productWith :: Foldable f => (a -> Unipol r) -> f a -> Unipol r #
(Unital r, UnitalAlgebra r a) => Unital (a -> r)
Instance details Defined in Numeric.Algebra.Unital Methods one :: a -> r # pow :: (a -> r) -> Natural -> a -> r # productWith :: Foldable f => (a0 -> a -> r) -> f a0 -> a -> r #
(Unital a, Unital b) => Unital (a, b)
Instance details Defined in Numeric.Algebra.Unital Methods one :: (a, b) # pow :: (a, b) -> Natural -> (a, b) # productWith :: Foldable f => (a0 -> (a, b)) -> f a0 -> (a, b) #
CounitalCoalgebra r m => Unital (Covector r m)
Instance details Defined in Numeric.Covector Methods one :: Covector r m # pow :: Covector r m -> Natural -> Covector r m # productWith :: Foldable f => (a -> Covector r m) -> f a -> Covector r m #
(Wraps vars poly, Unital poly) => Unital (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods one :: LabPolynomial poly vars # pow :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars # productWith :: Foldable f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Unital a, Unital b, Unital c) => Unital (a, b, c)
Instance details Defined in Numeric.Algebra.Unital Methods one :: (a, b, c) # pow :: (a, b, c) -> Natural -> (a, b, c) # productWith :: Foldable f => (a0 -> (a, b, c)) -> f a0 -> (a, b, c) #
KnownNat n => Unital (OrderedMonomial ord n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods one :: OrderedMonomial ord n # pow :: OrderedMonomial ord n -> Natural -> OrderedMonomial ord n # productWith :: Foldable f => (a -> OrderedMonomial ord n) -> f a -> OrderedMonomial ord n #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Unital (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods one :: PadPolyL n ord poly # pow :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly # productWith :: Foldable f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(Field (Coefficient poly), IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Unital (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods one :: Quotient poly ideal # pow :: Quotient poly ideal -> Natural -> Quotient poly ideal # productWith :: Foldable f => (a -> Quotient poly ideal) -> f a -> Quotient poly ideal #
(Unital a, Unital b, Unital c, Unital d) => Unital (a, b, c, d)
Instance details Defined in Numeric.Algebra.Unital Methods one :: (a, b, c, d) # pow :: (a, b, c, d) -> Natural -> (a, b, c, d) # productWith :: Foldable f => (a0 -> (a, b, c, d)) -> f a0 -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Unital (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods one :: OrderedPolynomial r order n # pow :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n # productWith :: Foldable f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(Unital a, Unital b, Unital c, Unital d, Unital e) => Unital (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Unital Methods one :: (a, b, c, d, e) # pow :: (a, b, c, d, e) -> Natural -> (a, b, c, d, e) # productWith :: Foldable f => (a0 -> (a, b, c, d, e)) -> f a0 -> (a, b, c, d, e) #

class Coalgebra r c => CounitalCoalgebra r c where #

Methods

counit :: (c -> r) -> r #

Instances

Instances details

Rng k => CounitalCoalgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods counit :: (ComplexBasis -> k) -> k #
Semiring r => CounitalCoalgebra r ()
Instance details Defined in Numeric.Algebra.Unital Methods counit :: (() -> r) -> r #
Semiring r => CounitalCoalgebra r [a]
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ([a] -> r) -> r #
Semiring r => CounitalCoalgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: (Seq a -> r) -> r #
(Unital r, UnitalAlgebra r m) => CounitalCoalgebra r (m -> r)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ((m -> r) -> r) -> r #
(CounitalCoalgebra r a, CounitalCoalgebra r b) => CounitalCoalgebra r (a, b)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ((a, b) -> r) -> r #
(CounitalCoalgebra r a, CounitalCoalgebra r b, CounitalCoalgebra r c) => CounitalCoalgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ((a, b, c) -> r) -> r #
(CounitalCoalgebra r a, CounitalCoalgebra r b, CounitalCoalgebra r c, CounitalCoalgebra r d) => CounitalCoalgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ((a, b, c, d) -> r) -> r #
(CounitalCoalgebra r a, CounitalCoalgebra r b, CounitalCoalgebra r c, CounitalCoalgebra r d, CounitalCoalgebra r e) => CounitalCoalgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: ((a, b, c, d, e) -> r) -> r #

class (UnitalAlgebra r a, CounitalCoalgebra r a) => Bialgebra r a #

Instances

Instances details

Rng k => Bialgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex
Semiring r => Bialgebra r ()
Instance details Defined in Numeric.Algebra.Unital
(Monoidal r, Semiring r) => Bialgebra r [a]
Instance details Defined in Numeric.Algebra.Unital
(Monoidal r, Semiring r) => Bialgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital
(Bialgebra r a, Bialgebra r b) => Bialgebra r (a, b)
Instance details Defined in Numeric.Algebra.Unital
(Bialgebra r a, Bialgebra r b, Bialgebra r c) => Bialgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Unital
(Bialgebra r a, Bialgebra r b, Bialgebra r c, Bialgebra r d) => Bialgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Unital
(Bialgebra r a, Bialgebra r b, Bialgebra r c, Bialgebra r d, Bialgebra r e) => Bialgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Unital

class (CocommutativeCoalgebra r a, TriviallyInvolutive r, InvolutiveCoalgebra r a) => TriviallyInvolutiveCoalgebra r a #

Instances

Instances details

(TriviallyInvolutive r, InvolutiveSemiring r) => TriviallyInvolutiveCoalgebra r ()
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveCoalgebra r a, TriviallyInvolutiveCoalgebra r b) => TriviallyInvolutiveCoalgebra r (a, b)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveCoalgebra r a, TriviallyInvolutiveCoalgebra r b, TriviallyInvolutiveCoalgebra r c) => TriviallyInvolutiveCoalgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveCoalgebra r a, TriviallyInvolutiveCoalgebra r b, TriviallyInvolutiveCoalgebra r c, TriviallyInvolutiveCoalgebra r d) => TriviallyInvolutiveCoalgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveCoalgebra r a, TriviallyInvolutiveCoalgebra r b, TriviallyInvolutiveCoalgebra r c, TriviallyInvolutiveCoalgebra r d, TriviallyInvolutiveCoalgebra r e) => TriviallyInvolutiveCoalgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive

class (InvolutiveBialgebra r h, TriviallyInvolutiveAlgebra r h, TriviallyInvolutiveCoalgebra r h) => TriviallyInvolutiveBialgebra r h #

Instances

Instances details

(InvolutiveBialgebra r h, TriviallyInvolutiveAlgebra r h, TriviallyInvolutiveCoalgebra r h) => TriviallyInvolutiveBialgebra r h
Instance details Defined in Numeric.Algebra.Involutive

class (CommutativeAlgebra r a, TriviallyInvolutive r, InvolutiveAlgebra r a) => TriviallyInvolutiveAlgebra r a #

Instances

Instances details

(TriviallyInvolutive r, InvolutiveSemiring r) => TriviallyInvolutiveAlgebra r ()
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveAlgebra r a, TriviallyInvolutiveAlgebra r b) => TriviallyInvolutiveAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveAlgebra r a, TriviallyInvolutiveAlgebra r b, TriviallyInvolutiveAlgebra r c) => TriviallyInvolutiveAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveAlgebra r a, TriviallyInvolutiveAlgebra r b, TriviallyInvolutiveAlgebra r c, TriviallyInvolutiveAlgebra r d) => TriviallyInvolutiveAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutiveAlgebra r a, TriviallyInvolutiveAlgebra r b, TriviallyInvolutiveAlgebra r c, TriviallyInvolutiveAlgebra r d, TriviallyInvolutiveAlgebra r e) => TriviallyInvolutiveAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive

class (Commutative r, InvolutiveMultiplication r) => TriviallyInvolutive r #

Instances

Instances details

TriviallyInvolutive Bool
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Int
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Int8
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Int16
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Int32
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Int64
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Integer
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Natural
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Word
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Word8
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Word16
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Word32
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive Word64
Instance details Defined in Numeric.Algebra.Involutive
TriviallyInvolutive ()
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutive r, TriviallyInvolutiveAlgebra r a) => TriviallyInvolutive (a -> r)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutive a, TriviallyInvolutive b) => TriviallyInvolutive (a, b)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutive a, TriviallyInvolutive b, TriviallyInvolutive c) => TriviallyInvolutive (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutive a, TriviallyInvolutive b, TriviallyInvolutive c, TriviallyInvolutive d) => TriviallyInvolutive (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive
(TriviallyInvolutive a, TriviallyInvolutive b, TriviallyInvolutive c, TriviallyInvolutive d, TriviallyInvolutive e) => TriviallyInvolutive (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive

class (Semiring r, InvolutiveMultiplication r) => InvolutiveSemiring r #

Instances

Instances details

InvolutiveSemiring Bool
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int8
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int16
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Int64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Integer
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Natural
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word8
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word16
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word32
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring Word64
Instance details Defined in Numeric.Algebra.Involutive
InvolutiveSemiring ()
Instance details Defined in Numeric.Algebra.Involutive
(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveSemiring (Complex r)
Instance details Defined in Numeric.Algebra.Complex
(InvolutiveSemiring a, InvolutiveSemiring b) => InvolutiveSemiring (a, b)
Instance details Defined in Numeric.Algebra.Involutive
(InvolutiveSemiring a, InvolutiveSemiring b, InvolutiveSemiring c) => InvolutiveSemiring (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive
(InvolutiveSemiring a, InvolutiveSemiring b, InvolutiveSemiring c, InvolutiveSemiring d) => InvolutiveSemiring (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive
(InvolutiveSemiring a, InvolutiveSemiring b, InvolutiveSemiring c, InvolutiveSemiring d, InvolutiveSemiring e) => InvolutiveSemiring (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive

class Multiplicative r => InvolutiveMultiplication r where #

Methods

adjoint :: r -> r #

Instances

Instances details

InvolutiveMultiplication Bool
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Bool -> Bool #
InvolutiveMultiplication Int
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int -> Int #
InvolutiveMultiplication Int8
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int8 -> Int8 #
InvolutiveMultiplication Int16
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int16 -> Int16 #
InvolutiveMultiplication Int32
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int32 -> Int32 #
InvolutiveMultiplication Int64
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Int64 -> Int64 #
InvolutiveMultiplication Integer
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Integer -> Integer #
InvolutiveMultiplication Natural
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Natural -> Natural #
InvolutiveMultiplication Word
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word -> Word #
InvolutiveMultiplication Word8
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word8 -> Word8 #
InvolutiveMultiplication Word16
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word16 -> Word16 #
InvolutiveMultiplication Word32
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word32 -> Word32 #
InvolutiveMultiplication Word64
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: Word64 -> Word64 #
InvolutiveMultiplication ()
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: () -> () #
(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods adjoint :: Complex r -> Complex r #
InvolutiveAlgebra r h => InvolutiveMultiplication (h -> r)
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: (h -> r) -> h -> r #
(InvolutiveMultiplication a, InvolutiveMultiplication b) => InvolutiveMultiplication (a, b)
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: (a, b) -> (a, b) #
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c) => InvolutiveMultiplication (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: (a, b, c) -> (a, b, c) #
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c, InvolutiveMultiplication d) => InvolutiveMultiplication (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: (a, b, c, d) -> (a, b, c, d) #
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c, InvolutiveMultiplication d, InvolutiveMultiplication e) => InvolutiveMultiplication (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive Methods adjoint :: (a, b, c, d, e) -> (a, b, c, d, e) #

class (InvolutiveSemiring r, Coalgebra r c) => InvolutiveCoalgebra r c where #

Methods

coinv :: (c -> r) -> c -> r #

Instances

Instances details

InvolutiveSemiring r => InvolutiveCoalgebra r ()
Instance details Defined in Numeric.Algebra.Involutive Methods coinv :: (() -> r) -> () -> r #
(InvolutiveSemiring k, Rng k) => InvolutiveCoalgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods coinv :: (ComplexBasis -> k) -> ComplexBasis -> k #
(InvolutiveCoalgebra r a, InvolutiveCoalgebra r b) => InvolutiveCoalgebra r (a, b)
Instance details Defined in Numeric.Algebra.Involutive Methods coinv :: ((a, b) -> r) -> (a, b) -> r #
(InvolutiveCoalgebra r a, InvolutiveCoalgebra r b, InvolutiveCoalgebra r c) => InvolutiveCoalgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive Methods coinv :: ((a, b, c) -> r) -> (a, b, c) -> r #
(InvolutiveCoalgebra r a, InvolutiveCoalgebra r b, InvolutiveCoalgebra r c, InvolutiveCoalgebra r d) => InvolutiveCoalgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive Methods coinv :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r #
(InvolutiveCoalgebra r a, InvolutiveCoalgebra r b, InvolutiveCoalgebra r c, InvolutiveCoalgebra r d, InvolutiveCoalgebra r e) => InvolutiveCoalgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive Methods coinv :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r #

class (Bialgebra r h, InvolutiveAlgebra r h, InvolutiveCoalgebra r h) => InvolutiveBialgebra r h #

Instances

Instances details

(Bialgebra r h, InvolutiveAlgebra r h, InvolutiveCoalgebra r h) => InvolutiveBialgebra r h
Instance details Defined in Numeric.Algebra.Involutive

class (InvolutiveSemiring r, Algebra r a) => InvolutiveAlgebra r a where #

Methods

inv :: (a -> r) -> a -> r #

Instances

Instances details

InvolutiveSemiring r => InvolutiveAlgebra r ()
Instance details Defined in Numeric.Algebra.Involutive Methods inv :: (() -> r) -> () -> r #
(InvolutiveSemiring k, Rng k) => InvolutiveAlgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods inv :: (ComplexBasis -> k) -> ComplexBasis -> k #
(InvolutiveAlgebra r a, InvolutiveAlgebra r b) => InvolutiveAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Involutive Methods inv :: ((a, b) -> r) -> (a, b) -> r #
(InvolutiveAlgebra r a, InvolutiveAlgebra r b, InvolutiveAlgebra r c) => InvolutiveAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Involutive Methods inv :: ((a, b, c) -> r) -> (a, b, c) -> r #
(InvolutiveAlgebra r a, InvolutiveAlgebra r b, InvolutiveAlgebra r c, InvolutiveAlgebra r d) => InvolutiveAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Involutive Methods inv :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r #
(InvolutiveAlgebra r a, InvolutiveAlgebra r b, InvolutiveAlgebra r c, InvolutiveAlgebra r d, InvolutiveAlgebra r e) => InvolutiveAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Involutive Methods inv :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r #

class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h #

Instances

Instances details

(Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h
Instance details Defined in Numeric.Algebra.Idempotent

class Algebra r a => IdempotentAlgebra r a #

Instances

Instances details

(Semiring r, Band r) => IdempotentAlgebra r IntSet
Instance details Defined in Numeric.Algebra.Idempotent
(Semiring r, Band r) => IdempotentAlgebra r ()
Instance details Defined in Numeric.Algebra.Idempotent
(Semiring r, Band r, Ord a) => IdempotentAlgebra r (Set a)
Instance details Defined in Numeric.Algebra.Idempotent
(IdempotentAlgebra r a, IdempotentAlgebra r b) => IdempotentAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Idempotent
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c) => IdempotentAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Idempotent
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d) => IdempotentAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Idempotent
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d, IdempotentAlgebra r e) => IdempotentAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Idempotent

class Multiplicative r => Band r #

Instances

Instances details

Band Bool
Instance details Defined in Numeric.Algebra.Idempotent
Band ()
Instance details Defined in Numeric.Algebra.Idempotent
(Band a, Band b) => Band (a, b)
Instance details Defined in Numeric.Algebra.Idempotent
(Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a)
Instance details Defined in Numeric.Covector
(Band a, Band b, Band c) => Band (a, b, c)
Instance details Defined in Numeric.Algebra.Idempotent
(Band a, Band b, Band c, Band d) => Band (a, b, c, d)
Instance details Defined in Numeric.Algebra.Idempotent
(Band a, Band b, Band c, Band d, Band e) => Band (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Idempotent

class Bialgebra r h => HopfAlgebra r h where #

Methods

antipode :: (h -> r) -> h -> r #

Instances

Instances details

(InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods antipode :: (ComplexBasis -> k) -> ComplexBasis -> k #
(HopfAlgebra r a, HopfAlgebra r b) => HopfAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Hopf Methods antipode :: ((a, b) -> r) -> (a, b) -> r #
(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c) => HopfAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Hopf Methods antipode :: ((a, b, c) -> r) -> (a, b, c) -> r #
(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d) => HopfAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Hopf Methods antipode :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r #
(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d, HopfAlgebra r e) => HopfAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Hopf Methods antipode :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r #

class Multiplicative m => Factorable m where #

Methods

factorWith :: (m -> m -> r) -> m -> NonEmpty r #

Instances

Instances details

Factorable Bool
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: (Bool -> Bool -> r) -> Bool -> NonEmpty r #
Factorable ()
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: (() -> () -> r) -> () -> NonEmpty r #
(Factorable a, Factorable b) => Factorable (a, b)
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: ((a, b) -> (a, b) -> r) -> (a, b) -> NonEmpty r #
(Factorable a, Factorable b, Factorable c) => Factorable (a, b, c)
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: ((a, b, c) -> (a, b, c) -> r) -> (a, b, c) -> NonEmpty r #
(Factorable a, Factorable b, Factorable c, Factorable d) => Factorable (a, b, c, d)
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: ((a, b, c, d) -> (a, b, c, d) -> r) -> (a, b, c, d) -> NonEmpty r #
(Factorable a, Factorable b, Factorable c, Factorable d, Factorable e) => Factorable (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Factorable Methods factorWith :: ((a, b, c, d, e) -> (a, b, c, d, e) -> r) -> (a, b, c, d, e) -> NonEmpty r #

class UnitalAlgebra r a => DivisionAlgebra r a where #

Methods

recipriocal :: (a -> r) -> a -> r #

class Unital r => Division r where #

Minimal complete definition

Nothing

Methods

recip :: r -> r #

(/) :: r -> r -> r #

(\\) :: r -> r -> r #

Instances

Instances details

Division ()
Instance details Defined in Numeric.Algebra.Division Methods recip :: () -> () # (/) :: () -> () -> () # (\\) :: () -> () -> () # (^) :: Integral n => () -> n -> ()
Fractional a => Division (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods recip :: WrapFractional a -> WrapFractional a # (/) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (\\) :: WrapFractional a -> WrapFractional a -> WrapFractional a # (^) :: Integral n => WrapFractional a -> n -> WrapFractional a
Division a => Division (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods recip :: WrapAlgebra a -> WrapAlgebra a # (/) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (\\) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # (^) :: Integral n => WrapAlgebra a -> n -> WrapAlgebra a
GCDDomain d => Division (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods recip :: Fraction d -> Fraction d # (/) :: Fraction d -> Fraction d -> Fraction d # (\\) :: Fraction d -> Fraction d -> Fraction d # (^) :: Integral n => Fraction d -> n -> Fraction d
Division r => Division (Scalar r)
Instance details Defined in Algebra.Scalar Methods recip :: Scalar r -> Scalar r # (/) :: Scalar r -> Scalar r -> Scalar r # (\\) :: Scalar r -> Scalar r -> Scalar r # (^) :: Integral n => Scalar r -> n -> Scalar r
(Commutative r, InvolutiveSemiring r, DivisionRing r) => Division (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods recip :: Complex r -> Complex r # (/) :: Complex r -> Complex r -> Complex r # (\\) :: Complex r -> Complex r -> Complex r # (^) :: Integral n => Complex r -> n -> Complex r
(Unital r, DivisionAlgebra r a) => Division (a -> r)
Instance details Defined in Numeric.Algebra.Division Methods recip :: (a -> r) -> a -> r # (/) :: (a -> r) -> (a -> r) -> a -> r # (\\) :: (a -> r) -> (a -> r) -> a -> r # (^) :: Integral n => (a -> r) -> n -> a -> r
(Division a, Division b) => Division (a, b)
Instance details Defined in Numeric.Algebra.Division Methods recip :: (a, b) -> (a, b) # (/) :: (a, b) -> (a, b) -> (a, b) # (\\) :: (a, b) -> (a, b) -> (a, b) # (^) :: Integral n => (a, b) -> n -> (a, b)
(Division a, Division b, Division c) => Division (a, b, c)
Instance details Defined in Numeric.Algebra.Division Methods recip :: (a, b, c) -> (a, b, c) # (/) :: (a, b, c) -> (a, b, c) -> (a, b, c) # (\\) :: (a, b, c) -> (a, b, c) -> (a, b, c) # (^) :: Integral n => (a, b, c) -> n -> (a, b, c)
KnownNat n => Division (OrderedMonomial ord n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods recip :: OrderedMonomial ord n -> OrderedMonomial ord n # (/) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # (\\) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # (^) :: Integral n0 => OrderedMonomial ord n -> n0 -> OrderedMonomial ord n
(Division a, Division b, Division c, Division d) => Division (a, b, c, d)
Instance details Defined in Numeric.Algebra.Division Methods recip :: (a, b, c, d) -> (a, b, c, d) # (/) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # (\\) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # (^) :: Integral n => (a, b, c, d) -> n -> (a, b, c, d)
(Division a, Division b, Division c, Division d, Division e) => Division (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Division Methods recip :: (a, b, c, d, e) -> (a, b, c, d, e) # (/) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # (\\) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # (^) :: Integral n => (a, b, c, d, e) -> n -> (a, b, c, d, e)

class (Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h #

Instances

Instances details

(Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h
Instance details Defined in Numeric.Algebra.Commutative

class Algebra r a => CommutativeAlgebra r a #

Instances

Instances details

(Commutative r, Semiring r) => CommutativeAlgebra r IntSet
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r) => CommutativeAlgebra r ()
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a) => CommutativeAlgebra r (Set a)
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b) => CommutativeAlgebra r (a, b)
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c) => CommutativeAlgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d) => CommutativeAlgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d, CommutativeAlgebra r e) => CommutativeAlgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Commutative

class Multiplicative r => Commutative r #

Instances

Instances details

Commutative Bool
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int8
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int16
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int32
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int64
Instance details Defined in Numeric.Algebra.Commutative
Commutative Integer
Instance details Defined in Numeric.Algebra.Commutative
Commutative Natural
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word8
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word16
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word32
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word64
Instance details Defined in Numeric.Algebra.Commutative
Commutative ()
Instance details Defined in Numeric.Algebra.Commutative
Num a => Commutative (WrapNum a)
Instance details Defined in AlgebraicPrelude
Num a => Commutative (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Num a => Commutative (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
Multiplicative a => Commutative (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
Multiplicative a => Commutative (Mult a)
Instance details Defined in AlgebraicPrelude
GCDDomain d => Commutative (Fraction d)
Instance details Defined in Numeric.Field.Fraction
Commutative r => Commutative (Scalar r)
Instance details Defined in Algebra.Scalar
(TriviallyInvolutive r, Rng r) => Commutative (Complex r)
Instance details Defined in Numeric.Algebra.Complex
(CoeffRing r, Commutative r) => Commutative (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate
CommutativeAlgebra r a => Commutative (a -> r)
Instance details Defined in Numeric.Algebra.Commutative
(Commutative a, Commutative b) => Commutative (a, b)
Instance details Defined in Numeric.Algebra.Commutative
(Commutative m, Coalgebra r m) => Commutative (Covector r m)
Instance details Defined in Numeric.Covector
(Wraps vars poly, Commutative poly) => Commutative (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Commutative a, Commutative b, Commutative c) => Commutative (a, b, c)
Instance details Defined in Numeric.Algebra.Commutative
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Commutative (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Commutative a, Commutative b, Commutative c, Commutative d) => Commutative (a, b, c, d)
Instance details Defined in Numeric.Algebra.Commutative
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Commutative (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Commutative a, Commutative b, Commutative c, Commutative d, Commutative e) => Commutative (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Commutative

class Coalgebra r c => CocommutativeCoalgebra r c #

Instances

Instances details

(Commutative r, Semiring r) => CocommutativeCoalgebra r IntSet
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r) => CocommutativeCoalgebra r ()
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a) => CocommutativeCoalgebra r (Set a)
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Abelian b) => CocommutativeCoalgebra r (IntMap b)
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a, Abelian b) => CocommutativeCoalgebra r (Map a b)
Instance details Defined in Numeric.Algebra.Commutative
CommutativeAlgebra r m => CocommutativeCoalgebra r (m -> r)
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b) => CocommutativeCoalgebra r (a, b)
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c) => CocommutativeCoalgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d) => CocommutativeCoalgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d, CocommutativeCoalgebra r e) => CocommutativeCoalgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Commutative

class (Additive r, Abelian r, Multiplicative r) => Semiring r #

Instances

Instances details

Semiring Bool
Instance details Defined in Numeric.Algebra.Class
Semiring Int
Instance details Defined in Numeric.Algebra.Class
Semiring Int8
Instance details Defined in Numeric.Algebra.Class
Semiring Int16
Instance details Defined in Numeric.Algebra.Class
Semiring Int32
Instance details Defined in Numeric.Algebra.Class
Semiring Int64
Instance details Defined in Numeric.Algebra.Class
Semiring Integer
Instance details Defined in Numeric.Algebra.Class
Semiring Natural
Instance details Defined in Numeric.Algebra.Class
Semiring Word
Instance details Defined in Numeric.Algebra.Class
Semiring Word8
Instance details Defined in Numeric.Algebra.Class
Semiring Word16
Instance details Defined in Numeric.Algebra.Class
Semiring Word32
Instance details Defined in Numeric.Algebra.Class
Semiring Word64
Instance details Defined in Numeric.Algebra.Class
Semiring ()
Instance details Defined in Numeric.Algebra.Class
Num a => Semiring (WrapNum a)
Instance details Defined in AlgebraicPrelude
Num a => Semiring (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Num a => Semiring (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
(Additive a, Multiplicative a) => Semiring (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
GCDDomain d => Semiring (Fraction d)
Instance details Defined in Numeric.Field.Fraction
Semiring r => Semiring (Scalar r)
Instance details Defined in Algebra.Scalar
(Commutative r, Rng r) => Semiring (Complex r)
Instance details Defined in Numeric.Algebra.Complex
(CoeffRing r, DecidableZero r) => Semiring (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate
Algebra r a => Semiring (a -> r)
Instance details Defined in Numeric.Algebra.Class
(Semiring a, Semiring b) => Semiring (a, b)
Instance details Defined in Numeric.Algebra.Class
Coalgebra r m => Semiring (Covector r m)
Instance details Defined in Numeric.Covector
(Wraps vars poly, Semiring poly) => Semiring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Semiring a, Semiring b, Semiring c) => Semiring (a, b, c)
Instance details Defined in Numeric.Algebra.Class
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Semiring (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Field (Coefficient poly), IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Semiring (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient
(Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Semiring (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class

class (Semiring r, Additive m) => RightModule r m where #

Methods

(*.) :: m -> r -> m #

Instances

Instances details

RightModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Integer -> Int #
RightModule Integer Int8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int8 -> Integer -> Int8 #
RightModule Integer Int16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int16 -> Integer -> Int16 #
RightModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Integer -> Int32 #
RightModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Integer -> Int64 #
RightModule Integer Integer
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Integer -> Integer -> Integer #
RightModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Integer -> Word #
RightModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Integer -> Word8 #
RightModule Integer Word16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word16 -> Integer -> Word16 #
RightModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Integer -> Word32 #
RightModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Integer -> Word64 #
RightModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Bool -> Natural -> Bool #
RightModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int -> Natural -> Int #
RightModule Natural Int8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int8 -> Natural -> Int8 #
RightModule Natural Int16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int16 -> Natural -> Int16 #
RightModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int32 -> Natural -> Int32 #
RightModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Int64 -> Natural -> Int64 #
RightModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Integer -> Natural -> Integer #
RightModule Natural Natural
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Natural -> Natural -> Natural #
RightModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word -> Natural -> Word #
RightModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word8 -> Natural -> Word8 #
RightModule Natural Word16
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word16 -> Natural -> Word16 #
RightModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word32 -> Natural -> Word32 #
RightModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: Word64 -> Natural -> Word64 #
Additive m => RightModule () m
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: m -> () -> m #
Semiring r => RightModule r ()
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: () -> r -> () #
Num a => RightModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Integer -> WrapNum a #
Num a => RightModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Integer -> WrapFractional a #
Num a => RightModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Integer -> WrapIntegral a #
RightModule Integer a => RightModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Integer -> WrapAlgebra a #
RightModule Integer a => RightModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Integer -> Add a #
GCDDomain d => RightModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Integer -> Fraction d #
RightModule Integer r => RightModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Integer -> Scalar r #
(DecidableZero r, RightModule Integer r) => RightModule Integer (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Integer -> Unipol r #
Num a => RightModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapNum a -> Natural -> WrapNum a #
Num a => RightModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapFractional a -> Natural -> WrapFractional a #
Num a => RightModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapIntegral a -> Natural -> WrapIntegral a #
RightModule Natural a => RightModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: WrapAlgebra a -> Natural -> WrapAlgebra a #
RightModule Natural a => RightModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (*.) :: Add a -> Natural -> Add a #
GCDDomain d => RightModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*.) :: Fraction d -> Natural -> Fraction d #
RightModule Natural r => RightModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Natural -> Scalar r #
(DecidableZero r, RightModule Natural r) => RightModule Natural (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Natural -> Unipol r #
RightModule r s => RightModule r (Complex s)
Instance details Defined in Numeric.Algebra.Complex Methods (*.) :: Complex s -> r -> Complex s #
Semiring r => RightModule r (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> r -> Scalar r #
(Wraps vars poly, RightModule Integer poly) => RightModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Integer -> LabPolynomial poly vars #
(Wraps vars poly, RightModule Natural poly) => RightModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars #
RightModule r m => RightModule r (e -> m)
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: (e -> m) -> r -> e -> m #
(RightModule r a, RightModule r b) => RightModule r (a, b)
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: (a, b) -> r -> (a, b) #
RightModule r s => RightModule r (Covector s m)
Instance details Defined in Numeric.Covector Methods (*.) :: Covector s m -> r -> Covector s m #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Integer -> PadPolyL n ord poly #
Group poly => RightModule Integer (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Integer -> Quotient poly ideal #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly #
Monoidal poly => RightModule Natural (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Natural -> Quotient poly ideal #
(RightModule r a, RightModule r b, RightModule r c) => RightModule r (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: (a, b, c) -> r -> (a, b, c) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Integer -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n #
(RightModule r a, RightModule r b, RightModule r c, RightModule r d) => RightModule r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: (a, b, c, d) -> r -> (a, b, c, d) #
(RightModule r a, RightModule r b, RightModule r c, RightModule r d, RightModule r e) => RightModule r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods (*.) :: (a, b, c, d, e) -> r -> (a, b, c, d, e) #
Semiring r => RightModule (Scalar r) (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*.) :: Scalar r -> Scalar r -> Scalar r #
(DecidableZero r, Semiring r) => RightModule (Scalar r) (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*.) :: Unipol r -> Scalar r -> Unipol r #
(Commutative r, Rng r) => RightModule (Complex r) (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods (*.) :: Complex r -> Complex r -> Complex r #
(Wraps vars poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Scalar r -> LabPolynomial poly vars #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Scalar r -> PadPolyL n ord poly #
(r ~ Coefficient poly, IsOrderedPolynomial poly) => RightModule (Scalar r) (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*.) :: Quotient poly ideal -> Scalar r -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Scalar r -> OrderedPolynomial r order n #
Coalgebra r m => RightModule (Covector r m) (Covector r m)
Instance details Defined in Numeric.Covector Methods (*.) :: Covector r m -> Covector r m -> Covector r m #

class Multiplicative r where #

Minimal complete definition

(*)

Methods

(*) :: r -> r -> r #

pow1p :: r -> Natural -> r #

productWith1 :: Foldable1 f => (a -> r) -> f a -> r #

Instances

Instances details

Multiplicative Bool
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Bool -> Bool -> Bool # pow1p :: Bool -> Natural -> Bool # productWith1 :: Foldable1 f => (a -> Bool) -> f a -> Bool #
Multiplicative Int
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int -> Int -> Int # pow1p :: Int -> Natural -> Int # productWith1 :: Foldable1 f => (a -> Int) -> f a -> Int #
Multiplicative Int8
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int8 -> Int8 -> Int8 # pow1p :: Int8 -> Natural -> Int8 # productWith1 :: Foldable1 f => (a -> Int8) -> f a -> Int8 #
Multiplicative Int16
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int16 -> Int16 -> Int16 # pow1p :: Int16 -> Natural -> Int16 # productWith1 :: Foldable1 f => (a -> Int16) -> f a -> Int16 #
Multiplicative Int32
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int32 -> Int32 -> Int32 # pow1p :: Int32 -> Natural -> Int32 # productWith1 :: Foldable1 f => (a -> Int32) -> f a -> Int32 #
Multiplicative Int64
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Int64 -> Int64 -> Int64 # pow1p :: Int64 -> Natural -> Int64 # productWith1 :: Foldable1 f => (a -> Int64) -> f a -> Int64 #
Multiplicative Integer
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Integer -> Integer -> Integer # pow1p :: Integer -> Natural -> Integer # productWith1 :: Foldable1 f => (a -> Integer) -> f a -> Integer #
Multiplicative Natural
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Natural -> Natural -> Natural # pow1p :: Natural -> Natural -> Natural # productWith1 :: Foldable1 f => (a -> Natural) -> f a -> Natural #
Multiplicative Word
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word -> Word -> Word # pow1p :: Word -> Natural -> Word # productWith1 :: Foldable1 f => (a -> Word) -> f a -> Word #
Multiplicative Word8
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word8 -> Word8 -> Word8 # pow1p :: Word8 -> Natural -> Word8 # productWith1 :: Foldable1 f => (a -> Word8) -> f a -> Word8 #
Multiplicative Word16
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word16 -> Word16 -> Word16 # pow1p :: Word16 -> Natural -> Word16 # productWith1 :: Foldable1 f => (a -> Word16) -> f a -> Word16 #
Multiplicative Word32
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word32 -> Word32 -> Word32 # pow1p :: Word32 -> Natural -> Word32 # productWith1 :: Foldable1 f => (a -> Word32) -> f a -> Word32 #
Multiplicative Word64
Instance details Defined in Numeric.Algebra.Class Methods (*) :: Word64 -> Word64 -> Word64 # pow1p :: Word64 -> Natural -> Word64 # productWith1 :: Foldable1 f => (a -> Word64) -> f a -> Word64 #
Multiplicative ()
Instance details Defined in Numeric.Algebra.Class Methods (*) :: () -> () -> () # pow1p :: () -> Natural -> () # productWith1 :: Foldable1 f => (a -> ()) -> f a -> () #
Num a => Multiplicative (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapNum a -> WrapNum a -> WrapNum a # pow1p :: WrapNum a -> Natural -> WrapNum a # productWith1 :: Foldable1 f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Multiplicative (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapFractional a -> WrapFractional a -> WrapFractional a # pow1p :: WrapFractional a -> Natural -> WrapFractional a # productWith1 :: Foldable1 f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Multiplicative (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # pow1p :: WrapIntegral a -> Natural -> WrapIntegral a # productWith1 :: Foldable1 f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Multiplicative a => Multiplicative (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (*) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # pow1p :: WrapAlgebra a -> Natural -> WrapAlgebra a # productWith1 :: Foldable1 f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Multiplicative a => Multiplicative (Mult a)
Instance details Defined in AlgebraicPrelude Methods (*) :: Mult a -> Mult a -> Mult a # pow1p :: Mult a -> Natural -> Mult a # productWith1 :: Foldable1 f => (a0 -> Mult a) -> f a0 -> Mult a #
GCDDomain d => Multiplicative (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (*) :: Fraction d -> Fraction d -> Fraction d # pow1p :: Fraction d -> Natural -> Fraction d # productWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
Multiplicative r => Multiplicative (Scalar r)
Instance details Defined in Algebra.Scalar Methods (*) :: Scalar r -> Scalar r -> Scalar r # pow1p :: Scalar r -> Natural -> Scalar r # productWith1 :: Foldable1 f => (a -> Scalar r) -> f a -> Scalar r #
(Commutative r, Rng r) => Multiplicative (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods (*) :: Complex r -> Complex r -> Complex r # pow1p :: Complex r -> Natural -> Complex r # productWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r #
(CoeffRing r, Multiplicative r) => Multiplicative (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (*) :: Unipol r -> Unipol r -> Unipol r # pow1p :: Unipol r -> Natural -> Unipol r # productWith1 :: Foldable1 f => (a -> Unipol r) -> f a -> Unipol r #
Algebra r a => Multiplicative (a -> r)
Instance details Defined in Numeric.Algebra.Class Methods (*) :: (a -> r) -> (a -> r) -> a -> r # pow1p :: (a -> r) -> Natural -> a -> r # productWith1 :: Foldable1 f => (a0 -> a -> r) -> f a0 -> a -> r #
(Multiplicative a, Multiplicative b) => Multiplicative (a, b)
Instance details Defined in Numeric.Algebra.Class Methods (*) :: (a, b) -> (a, b) -> (a, b) # pow1p :: (a, b) -> Natural -> (a, b) # productWith1 :: Foldable1 f => (a0 -> (a, b)) -> f a0 -> (a, b) #
Coalgebra r m => Multiplicative (Covector r m)
Instance details Defined in Numeric.Covector Methods (*) :: Covector r m -> Covector r m -> Covector r m # pow1p :: Covector r m -> Natural -> Covector r m # productWith1 :: Foldable1 f => (a -> Covector r m) -> f a -> Covector r m #
(Wraps vars poly, Multiplicative poly) => Multiplicative (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # pow1p :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars # productWith1 :: Foldable1 f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Multiplicative a, Multiplicative b, Multiplicative c) => Multiplicative (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods (*) :: (a, b, c) -> (a, b, c) -> (a, b, c) # pow1p :: (a, b, c) -> Natural -> (a, b, c) # productWith1 :: Foldable1 f => (a0 -> (a, b, c)) -> f a0 -> (a, b, c) #
KnownNat n => Multiplicative (OrderedMonomial ord n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (*) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # pow1p :: OrderedMonomial ord n -> Natural -> OrderedMonomial ord n # productWith1 :: Foldable1 f => (a -> OrderedMonomial ord n) -> f a -> OrderedMonomial ord n #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Multiplicative (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # pow1p :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly # productWith1 :: Foldable1 f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(Field (Coefficient poly), IsOrderedPolynomial poly, Reifies ideal (QIdeal poly)) => Multiplicative (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (*) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # pow1p :: Quotient poly ideal -> Natural -> Quotient poly ideal # productWith1 :: Foldable1 f => (a -> Quotient poly ideal) -> f a -> Quotient poly ideal #
(Multiplicative a, Multiplicative b, Multiplicative c, Multiplicative d) => Multiplicative (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods (*) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # pow1p :: (a, b, c, d) -> Natural -> (a, b, c, d) # productWith1 :: Foldable1 f => (a0 -> (a, b, c, d)) -> f a0 -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Multiplicative (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # pow1p :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n # productWith1 :: Foldable1 f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(Multiplicative a, Multiplicative b, Multiplicative c, Multiplicative d, Multiplicative e) => Multiplicative (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods (*) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # pow1p :: (a, b, c, d, e) -> Natural -> (a, b, c, d, e) # productWith1 :: Foldable1 f => (a0 -> (a, b, c, d, e)) -> f a0 -> (a, b, c, d, e) #

class (LeftModule Natural m, RightModule Natural m) => Monoidal m where #

Minimal complete definition

zero

Methods

zero :: m #

sinnum :: Natural -> m -> m #

sumWith :: Foldable f => (a -> m) -> f a -> m #

Instances

Instances details

Monoidal Bool
Instance details Defined in Numeric.Algebra.Class Methods zero :: Bool # sinnum :: Natural -> Bool -> Bool # sumWith :: Foldable f => (a -> Bool) -> f a -> Bool #
Monoidal Int
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int # sinnum :: Natural -> Int -> Int # sumWith :: Foldable f => (a -> Int) -> f a -> Int #
Monoidal Int8
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int8 # sinnum :: Natural -> Int8 -> Int8 # sumWith :: Foldable f => (a -> Int8) -> f a -> Int8 #
Monoidal Int16
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int16 # sinnum :: Natural -> Int16 -> Int16 # sumWith :: Foldable f => (a -> Int16) -> f a -> Int16 #
Monoidal Int32
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int32 # sinnum :: Natural -> Int32 -> Int32 # sumWith :: Foldable f => (a -> Int32) -> f a -> Int32 #
Monoidal Int64
Instance details Defined in Numeric.Algebra.Class Methods zero :: Int64 # sinnum :: Natural -> Int64 -> Int64 # sumWith :: Foldable f => (a -> Int64) -> f a -> Int64 #
Monoidal Integer
Instance details Defined in Numeric.Algebra.Class Methods zero :: Integer # sinnum :: Natural -> Integer -> Integer # sumWith :: Foldable f => (a -> Integer) -> f a -> Integer #
Monoidal Natural
Instance details Defined in Numeric.Algebra.Class Methods zero :: Natural # sinnum :: Natural -> Natural -> Natural # sumWith :: Foldable f => (a -> Natural) -> f a -> Natural #
Monoidal Word
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word # sinnum :: Natural -> Word -> Word # sumWith :: Foldable f => (a -> Word) -> f a -> Word #
Monoidal Word8
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word8 # sinnum :: Natural -> Word8 -> Word8 # sumWith :: Foldable f => (a -> Word8) -> f a -> Word8 #
Monoidal Word16
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word16 # sinnum :: Natural -> Word16 -> Word16 # sumWith :: Foldable f => (a -> Word16) -> f a -> Word16 #
Monoidal Word32
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word32 # sinnum :: Natural -> Word32 -> Word32 # sumWith :: Foldable f => (a -> Word32) -> f a -> Word32 #
Monoidal Word64
Instance details Defined in Numeric.Algebra.Class Methods zero :: Word64 # sinnum :: Natural -> Word64 -> Word64 # sumWith :: Foldable f => (a -> Word64) -> f a -> Word64 #
Monoidal ()
Instance details Defined in Numeric.Algebra.Class Methods zero :: () # sinnum :: Natural -> () -> () # sumWith :: Foldable f => (a -> ()) -> f a -> () #
Num a => Monoidal (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapNum a # sinnum :: Natural -> WrapNum a -> WrapNum a # sumWith :: Foldable f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Monoidal (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapFractional a # sinnum :: Natural -> WrapFractional a -> WrapFractional a # sumWith :: Foldable f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Monoidal (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapIntegral a # sinnum :: Natural -> WrapIntegral a -> WrapIntegral a # sumWith :: Foldable f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Monoidal a => Monoidal (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods zero :: WrapAlgebra a # sinnum :: Natural -> WrapAlgebra a -> WrapAlgebra a # sumWith :: Foldable f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Monoidal a => Monoidal (Add a)
Instance details Defined in AlgebraicPrelude Methods zero :: Add a # sinnum :: Natural -> Add a -> Add a # sumWith :: Foldable f => (a0 -> Add a) -> f a0 -> Add a #
GCDDomain d => Monoidal (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods zero :: Fraction d # sinnum :: Natural -> Fraction d -> Fraction d # sumWith :: Foldable f => (a -> Fraction d) -> f a -> Fraction d #
Monoidal r => Monoidal (Scalar r)
Instance details Defined in Algebra.Scalar Methods zero :: Scalar r # sinnum :: Natural -> Scalar r -> Scalar r # sumWith :: Foldable f => (a -> Scalar r) -> f a -> Scalar r #
Monoidal r => Monoidal (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods zero :: Complex r # sinnum :: Natural -> Complex r -> Complex r # sumWith :: Foldable f => (a -> Complex r) -> f a -> Complex r #
DecidableZero r => Monoidal (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods zero :: Unipol r # sinnum :: Natural -> Unipol r -> Unipol r # sumWith :: Foldable f => (a -> Unipol r) -> f a -> Unipol r #
Monoidal r => Monoidal (e -> r)
Instance details Defined in Numeric.Algebra.Class Methods zero :: e -> r # sinnum :: Natural -> (e -> r) -> e -> r # sumWith :: Foldable f => (a -> e -> r) -> f a -> e -> r #
(Monoidal a, Monoidal b) => Monoidal (a, b)
Instance details Defined in Numeric.Algebra.Class Methods zero :: (a, b) # sinnum :: Natural -> (a, b) -> (a, b) # sumWith :: Foldable f => (a0 -> (a, b)) -> f a0 -> (a, b) #
Monoidal s => Monoidal (Covector s a)
Instance details Defined in Numeric.Covector Methods zero :: Covector s a # sinnum :: Natural -> Covector s a -> Covector s a # sumWith :: Foldable f => (a0 -> Covector s a) -> f a0 -> Covector s a #
(Wraps vars poly, Monoidal poly) => Monoidal (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods zero :: LabPolynomial poly vars # sinnum :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars # sumWith :: Foldable f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Monoidal a, Monoidal b, Monoidal c) => Monoidal (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods zero :: (a, b, c) # sinnum :: Natural -> (a, b, c) -> (a, b, c) # sumWith :: Foldable f => (a0 -> (a, b, c)) -> f a0 -> (a, b, c) #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Monoidal (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods zero :: PadPolyL n ord poly # sinnum :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly # sumWith :: Foldable f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
Monoidal poly => Monoidal (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods zero :: Quotient poly ideal # sinnum :: Natural -> Quotient poly ideal -> Quotient poly ideal # sumWith :: Foldable f => (a -> Quotient poly ideal) -> f a -> Quotient poly ideal #
(Monoidal a, Monoidal b, Monoidal c, Monoidal d) => Monoidal (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods zero :: (a, b, c, d) # sinnum :: Natural -> (a, b, c, d) -> (a, b, c, d) # sumWith :: Foldable f => (a0 -> (a, b, c, d)) -> f a0 -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Monoidal (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods zero :: OrderedPolynomial r order n # sinnum :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sumWith :: Foldable f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(Monoidal a, Monoidal b, Monoidal c, Monoidal d, Monoidal e) => Monoidal (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods zero :: (a, b, c, d, e) # sinnum :: Natural -> (a, b, c, d, e) -> (a, b, c, d, e) # sumWith :: Foldable f => (a0 -> (a, b, c, d, e)) -> f a0 -> (a, b, c, d, e) #

class (LeftModule r m, RightModule r m) => Module r m #

Instances

Instances details

(LeftModule r m, RightModule r m) => Module r m
Instance details Defined in Numeric.Algebra.Class

class (Semiring r, Additive m) => LeftModule r m where #

Methods

(.*) :: r -> m -> m #

Instances

Instances details

LeftModule Integer Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int -> Int #
LeftModule Integer Int8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int8 -> Int8 #
LeftModule Integer Int16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int16 -> Int16 #
LeftModule Integer Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int32 -> Int32 #
LeftModule Integer Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Int64 -> Int64 #
LeftModule Integer Integer
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Integer -> Integer #
LeftModule Integer Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word -> Word #
LeftModule Integer Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word8 -> Word8 #
LeftModule Integer Word16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word16 -> Word16 #
LeftModule Integer Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word32 -> Word32 #
LeftModule Integer Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Integer -> Word64 -> Word64 #
LeftModule Natural Bool
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Bool -> Bool #
LeftModule Natural Int
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int -> Int #
LeftModule Natural Int8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int8 -> Int8 #
LeftModule Natural Int16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int16 -> Int16 #
LeftModule Natural Int32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int32 -> Int32 #
LeftModule Natural Int64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Int64 -> Int64 #
LeftModule Natural Integer
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Integer -> Integer #
LeftModule Natural Natural
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Natural -> Natural #
LeftModule Natural Word
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word -> Word #
LeftModule Natural Word8
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word8 -> Word8 #
LeftModule Natural Word16
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word16 -> Word16 #
LeftModule Natural Word32
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word32 -> Word32 #
LeftModule Natural Word64
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: Natural -> Word64 -> Word64 #
Additive m => LeftModule () m
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: () -> m -> m #
Semiring r => LeftModule r ()
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> () -> () #
Num a => LeftModule Integer (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapNum a -> WrapNum a #
Num a => LeftModule Integer (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapFractional a -> WrapFractional a #
Num a => LeftModule Integer (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapIntegral a -> WrapIntegral a #
LeftModule Integer a => LeftModule Integer (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> WrapAlgebra a -> WrapAlgebra a #
LeftModule Integer a => LeftModule Integer (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Integer -> Add a -> Add a #
GCDDomain d => LeftModule Integer (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Integer -> Fraction d -> Fraction d #
LeftModule Integer r => LeftModule Integer (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Integer -> Scalar r -> Scalar r #
(DecidableZero r, LeftModule Integer r) => LeftModule Integer (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Integer -> Unipol r -> Unipol r #
Num a => LeftModule Natural (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapNum a -> WrapNum a #
Num a => LeftModule Natural (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapFractional a -> WrapFractional a #
Num a => LeftModule Natural (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapIntegral a -> WrapIntegral a #
LeftModule Natural a => LeftModule Natural (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> WrapAlgebra a -> WrapAlgebra a #
LeftModule Natural a => LeftModule Natural (Add a)
Instance details Defined in AlgebraicPrelude Methods (.*) :: Natural -> Add a -> Add a #
GCDDomain d => LeftModule Natural (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (.*) :: Natural -> Fraction d -> Fraction d #
LeftModule Natural r => LeftModule Natural (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Natural -> Scalar r -> Scalar r #
(DecidableZero r, LeftModule Natural r) => LeftModule Natural (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Natural -> Unipol r -> Unipol r #
LeftModule r s => LeftModule r (Complex s)
Instance details Defined in Numeric.Algebra.Complex Methods (.*) :: r -> Complex s -> Complex s #
Semiring r => LeftModule r (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: r -> Scalar r -> Scalar r #
(Wraps vars poly, LeftModule Integer poly) => LeftModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Integer -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule Natural poly) => LeftModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars #
LeftModule r m => LeftModule r (e -> m)
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> (e -> m) -> e -> m #
(LeftModule r a, LeftModule r b) => LeftModule r (a, b)
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> (a, b) -> (a, b) #
LeftModule r s => LeftModule r (Covector s m)
Instance details Defined in Numeric.Covector Methods (.*) :: r -> Covector s m -> Covector s m #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> PadPolyL n ord poly -> PadPolyL n ord poly #
Group poly => LeftModule Integer (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Integer -> Quotient poly ideal -> Quotient poly ideal #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly #
Monoidal poly => LeftModule Natural (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Natural -> Quotient poly ideal -> Quotient poly ideal #
(LeftModule r a, LeftModule r b, LeftModule r c) => LeftModule r (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> (a, b, c) -> (a, b, c) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(LeftModule r a, LeftModule r b, LeftModule r c, LeftModule r d) => LeftModule r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> (a, b, c, d) -> (a, b, c, d) #
(LeftModule r a, LeftModule r b, LeftModule r c, LeftModule r d, LeftModule r e) => LeftModule r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods (.*) :: r -> (a, b, c, d, e) -> (a, b, c, d, e) #
Semiring r => LeftModule (Scalar r) (Scalar r)
Instance details Defined in Algebra.Scalar Methods (.*) :: Scalar r -> Scalar r -> Scalar r #
(DecidableZero r, Semiring r) => LeftModule (Scalar r) (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (.*) :: Scalar r -> Unipol r -> Unipol r #
(Commutative r, Rng r) => LeftModule (Complex r) (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods (.*) :: Complex r -> Complex r -> Complex r #
(Wraps vars poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Scalar r -> LabPolynomial poly vars -> LabPolynomial poly vars #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> PadPolyL n ord poly -> PadPolyL n ord poly #
(r ~ Coefficient poly, Field (Coefficient poly), IsOrderedPolynomial poly) => LeftModule (Scalar r) (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (.*) :: Scalar r -> Quotient poly ideal -> Quotient poly ideal #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
Coalgebra r m => LeftModule (Covector r m) (Covector r m)
Instance details Defined in Numeric.Covector Methods (.*) :: Covector r m -> Covector r m -> Covector r m #

class Semiring r => Coalgebra r c where #

Methods

comult :: (c -> r) -> c -> c -> r #

Instances

Instances details

Rng k => Coalgebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods comult :: (ComplexBasis -> k) -> ComplexBasis -> ComplexBasis -> k #
Semiring r => Coalgebra r IntSet
Instance details Defined in Numeric.Algebra.Class Methods comult :: (IntSet -> r) -> IntSet -> IntSet -> r #
Semiring r => Coalgebra r ()
Instance details Defined in Numeric.Algebra.Class Methods comult :: (() -> r) -> () -> () -> r #
Semiring r => Coalgebra r [a]
Instance details Defined in Numeric.Algebra.Class Methods comult :: ([a] -> r) -> [a] -> [a] -> r #
(Semiring r, Ord a) => Coalgebra r (Set a)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Set a -> r) -> Set a -> Set a -> r #
Semiring r => Coalgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Seq a -> r) -> Seq a -> Seq a -> r #
(Semiring r, Additive b) => Coalgebra r (IntMap b)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (IntMap b -> r) -> IntMap b -> IntMap b -> r #
(Semiring r, Ord a, Additive b) => Coalgebra r (Map a b)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Map a b -> r) -> Map a b -> Map a b -> r #
Algebra r m => Coalgebra r (m -> r)
Instance details Defined in Numeric.Algebra.Class Methods comult :: ((m -> r) -> r) -> (m -> r) -> (m -> r) -> r #
(Coalgebra r a, Coalgebra r b) => Coalgebra r (a, b)
Instance details Defined in Numeric.Algebra.Class Methods comult :: ((a, b) -> r) -> (a, b) -> (a, b) -> r #
(Coalgebra r a, Coalgebra r b, Coalgebra r c) => Coalgebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods comult :: ((a, b, c) -> r) -> (a, b, c) -> (a, b, c) -> r #
(Coalgebra r a, Coalgebra r b, Coalgebra r c, Coalgebra r d) => Coalgebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods comult :: ((a, b, c, d) -> r) -> (a, b, c, d) -> (a, b, c, d) -> r #
(Coalgebra r a, Coalgebra r b, Coalgebra r c, Coalgebra r d, Coalgebra r e) => Coalgebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods comult :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> (a, b, c, d, e) -> r #

class Semiring r => Algebra r a where #

Methods

mult :: (a -> a -> r) -> a -> r #

Instances

Instances details

Algebra () a
Instance details Defined in Numeric.Algebra.Class Methods mult :: (a -> a -> ()) -> a -> () #
Rng k => Algebra k ComplexBasis
Instance details Defined in Numeric.Algebra.Complex Methods mult :: (ComplexBasis -> ComplexBasis -> k) -> ComplexBasis -> k #
Semiring r => Algebra r IntSet
Instance details Defined in Numeric.Algebra.Class Methods mult :: (IntSet -> IntSet -> r) -> IntSet -> r #
Semiring r => Algebra r ()
Instance details Defined in Numeric.Algebra.Class Methods mult :: (() -> () -> r) -> () -> r #
Semiring r => Algebra r [a]
Instance details Defined in Numeric.Algebra.Class Methods mult :: ([a] -> [a] -> r) -> [a] -> r #
(Semiring r, Ord a) => Algebra r (Set a)
Instance details Defined in Numeric.Algebra.Class Methods mult :: (Set a -> Set a -> r) -> Set a -> r #
Semiring r => Algebra r (Seq a)
Instance details Defined in Numeric.Algebra.Class Methods mult :: (Seq a -> Seq a -> r) -> Seq a -> r #
(Algebra r a, Algebra r b) => Algebra r (a, b)
Instance details Defined in Numeric.Algebra.Class Methods mult :: ((a, b) -> (a, b) -> r) -> (a, b) -> r #
(Algebra r a, Algebra r b, Algebra r c) => Algebra r (a, b, c)
Instance details Defined in Numeric.Algebra.Class Methods mult :: ((a, b, c) -> (a, b, c) -> r) -> (a, b, c) -> r #
(Algebra r a, Algebra r b, Algebra r c, Algebra r d) => Algebra r (a, b, c, d)
Instance details Defined in Numeric.Algebra.Class Methods mult :: ((a, b, c, d) -> (a, b, c, d) -> r) -> (a, b, c, d) -> r #
(Algebra r a, Algebra r b, Algebra r c, Algebra r d, Algebra r e) => Algebra r (a, b, c, d, e)
Instance details Defined in Numeric.Algebra.Class Methods mult :: ((a, b, c, d, e) -> (a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r #

class (LeftModule Integer r, RightModule Integer r, Monoidal r) => Group r where #

Minimal complete definition

Nothing

Methods

(-) :: r -> r -> r #

negate :: r -> r #

subtract :: r -> r -> r #

times :: Integral n => n -> r -> r #

Instances

Instances details

Group Int
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int -> Int -> Int # negate :: Int -> Int # subtract :: Int -> Int -> Int # times :: Integral n => n -> Int -> Int #
Group Int8
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int8 -> Int8 -> Int8 # negate :: Int8 -> Int8 # subtract :: Int8 -> Int8 -> Int8 # times :: Integral n => n -> Int8 -> Int8 #
Group Int16
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int16 -> Int16 -> Int16 # negate :: Int16 -> Int16 # subtract :: Int16 -> Int16 -> Int16 # times :: Integral n => n -> Int16 -> Int16 #
Group Int32
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # subtract :: Int32 -> Int32 -> Int32 # times :: Integral n => n -> Int32 -> Int32 #
Group Int64
Instance details Defined in Numeric.Additive.Group Methods (-) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # subtract :: Int64 -> Int64 -> Int64 # times :: Integral n => n -> Int64 -> Int64 #
Group Integer
Instance details Defined in Numeric.Additive.Group Methods (-) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # subtract :: Integer -> Integer -> Integer # times :: Integral n => n -> Integer -> Integer #
Group Word
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word -> Word -> Word # negate :: Word -> Word # subtract :: Word -> Word -> Word # times :: Integral n => n -> Word -> Word #
Group Word8
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # subtract :: Word8 -> Word8 -> Word8 # times :: Integral n => n -> Word8 -> Word8 #
Group Word16
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word16 -> Word16 -> Word16 # negate :: Word16 -> Word16 # subtract :: Word16 -> Word16 -> Word16 # times :: Integral n => n -> Word16 -> Word16 #
Group Word32
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # subtract :: Word32 -> Word32 -> Word32 # times :: Integral n => n -> Word32 -> Word32 #
Group Word64
Instance details Defined in Numeric.Additive.Group Methods (-) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # subtract :: Word64 -> Word64 -> Word64 # times :: Integral n => n -> Word64 -> Word64 #
Group ()
Instance details Defined in Numeric.Additive.Group Methods (-) :: () -> () -> () # negate :: () -> () # subtract :: () -> () -> () # times :: Integral n => n -> () -> () #
Num a => Group (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapNum a -> WrapNum a -> WrapNum a # negate :: WrapNum a -> WrapNum a # subtract :: WrapNum a -> WrapNum a -> WrapNum a # times :: Integral n => n -> WrapNum a -> WrapNum a #
Num a => Group (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapFractional a -> WrapFractional a -> WrapFractional a # negate :: WrapFractional a -> WrapFractional a # subtract :: WrapFractional a -> WrapFractional a -> WrapFractional a # times :: Integral n => n -> WrapFractional a -> WrapFractional a #
Num a => Group (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # negate :: WrapIntegral a -> WrapIntegral a # subtract :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # times :: Integral n => n -> WrapIntegral a -> WrapIntegral a #
Group a => Group (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (-) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # negate :: WrapAlgebra a -> WrapAlgebra a # subtract :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # times :: Integral n => n -> WrapAlgebra a -> WrapAlgebra a #
GCDDomain d => Group (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (-) :: Fraction d -> Fraction d -> Fraction d # negate :: Fraction d -> Fraction d # subtract :: Fraction d -> Fraction d -> Fraction d # times :: Integral n => n -> Fraction d -> Fraction d #
Group r => Group (Scalar r)
Instance details Defined in Algebra.Scalar Methods (-) :: Scalar r -> Scalar r -> Scalar r # negate :: Scalar r -> Scalar r # subtract :: Scalar r -> Scalar r -> Scalar r # times :: Integral n => n -> Scalar r -> Scalar r #
Group r => Group (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods (-) :: Complex r -> Complex r -> Complex r # negate :: Complex r -> Complex r # subtract :: Complex r -> Complex r -> Complex r # times :: Integral n => n -> Complex r -> Complex r #
(DecidableZero r, Group r) => Group (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (-) :: Unipol r -> Unipol r -> Unipol r # negate :: Unipol r -> Unipol r # subtract :: Unipol r -> Unipol r -> Unipol r # times :: Integral n => n -> Unipol r -> Unipol r #
Group r => Group (e -> r)
Instance details Defined in Numeric.Additive.Group Methods (-) :: (e -> r) -> (e -> r) -> e -> r # negate :: (e -> r) -> e -> r # subtract :: (e -> r) -> (e -> r) -> e -> r # times :: Integral n => n -> (e -> r) -> e -> r #
(Group a, Group b) => Group (a, b)
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b) -> (a, b) -> (a, b) # negate :: (a, b) -> (a, b) # subtract :: (a, b) -> (a, b) -> (a, b) # times :: Integral n => n -> (a, b) -> (a, b) #
Group s => Group (Covector s a)
Instance details Defined in Numeric.Covector Methods (-) :: Covector s a -> Covector s a -> Covector s a # negate :: Covector s a -> Covector s a # subtract :: Covector s a -> Covector s a -> Covector s a # times :: Integral n => n -> Covector s a -> Covector s a #
(Wraps vars poly, Group poly) => Group (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (-) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # negate :: LabPolynomial poly vars -> LabPolynomial poly vars # subtract :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # times :: Integral n => n -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Group a, Group b, Group c) => Group (a, b, c)
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c) -> (a, b, c) -> (a, b, c) # negate :: (a, b, c) -> (a, b, c) # subtract :: (a, b, c) -> (a, b, c) -> (a, b, c) # times :: Integral n => n -> (a, b, c) -> (a, b, c) #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Group (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (-) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # negate :: PadPolyL n ord poly -> PadPolyL n ord poly # subtract :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # times :: Integral n0 => n0 -> PadPolyL n ord poly -> PadPolyL n ord poly #
Group poly => Group (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (-) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # negate :: Quotient poly ideal -> Quotient poly ideal # subtract :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # times :: Integral n => n -> Quotient poly ideal -> Quotient poly ideal #
(Group a, Group b, Group c, Group d) => Group (a, b, c, d)
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # negate :: (a, b, c, d) -> (a, b, c, d) # subtract :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # times :: Integral n => n -> (a, b, c, d) -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Group (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (-) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # negate :: OrderedPolynomial r order n -> OrderedPolynomial r order n # subtract :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # times :: Integral n0 => n0 -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e)
Instance details Defined in Numeric.Additive.Group Methods (-) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # negate :: (a, b, c, d, e) -> (a, b, c, d, e) # subtract :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # times :: Integral n => n -> (a, b, c, d, e) -> (a, b, c, d, e) #

class Additive m => Partitionable m where #

Methods

partitionWith :: (m -> m -> r) -> m -> NonEmpty r #

Instances

Instances details

Partitionable Bool
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: (Bool -> Bool -> r) -> Bool -> NonEmpty r #
Partitionable Natural
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: (Natural -> Natural -> r) -> Natural -> NonEmpty r #
Partitionable ()
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: (() -> () -> r) -> () -> NonEmpty r #
Partitionable r => Partitionable (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods partitionWith :: (Complex r -> Complex r -> r0) -> Complex r -> NonEmpty r0 #
(Partitionable a, Partitionable b) => Partitionable (a, b)
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: ((a, b) -> (a, b) -> r) -> (a, b) -> NonEmpty r #
(Partitionable a, Partitionable b, Partitionable c) => Partitionable (a, b, c)
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: ((a, b, c) -> (a, b, c) -> r) -> (a, b, c) -> NonEmpty r #
(Partitionable a, Partitionable b, Partitionable c, Partitionable d) => Partitionable (a, b, c, d)
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: ((a, b, c, d) -> (a, b, c, d) -> r) -> (a, b, c, d) -> NonEmpty r #
(Partitionable a, Partitionable b, Partitionable c, Partitionable d, Partitionable e) => Partitionable (a, b, c, d, e)
Instance details Defined in Numeric.Additive.Class Methods partitionWith :: ((a, b, c, d, e) -> (a, b, c, d, e) -> r) -> (a, b, c, d, e) -> NonEmpty r #

class Additive r => Idempotent r #

Instances

Instances details

Idempotent Bool
Instance details Defined in Numeric.Additive.Class
Idempotent ()
Instance details Defined in Numeric.Additive.Class
Idempotent r => Idempotent (Complex r)
Instance details Defined in Numeric.Algebra.Complex
Idempotent r => Idempotent (e -> r)
Instance details Defined in Numeric.Additive.Class
(Idempotent a, Idempotent b) => Idempotent (a, b)
Instance details Defined in Numeric.Additive.Class
Idempotent r => Idempotent (Covector r a)
Instance details Defined in Numeric.Covector
(Idempotent a, Idempotent b, Idempotent c) => Idempotent (a, b, c)
Instance details Defined in Numeric.Additive.Class
(Idempotent a, Idempotent b, Idempotent c, Idempotent d) => Idempotent (a, b, c, d)
Instance details Defined in Numeric.Additive.Class
(Idempotent a, Idempotent b, Idempotent c, Idempotent d, Idempotent e) => Idempotent (a, b, c, d, e)
Instance details Defined in Numeric.Additive.Class

class Additive r where #

Minimal complete definition

(+)

Methods

(+) :: r -> r -> r #

sinnum1p :: Natural -> r -> r #

sumWith1 :: Foldable1 f => (a -> r) -> f a -> r #

Instances

Instances details

Additive Bool
Instance details Defined in Numeric.Additive.Class Methods (+) :: Bool -> Bool -> Bool # sinnum1p :: Natural -> Bool -> Bool # sumWith1 :: Foldable1 f => (a -> Bool) -> f a -> Bool #
Additive Int
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int -> Int -> Int # sinnum1p :: Natural -> Int -> Int # sumWith1 :: Foldable1 f => (a -> Int) -> f a -> Int #
Additive Int8
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int8 -> Int8 -> Int8 # sinnum1p :: Natural -> Int8 -> Int8 # sumWith1 :: Foldable1 f => (a -> Int8) -> f a -> Int8 #
Additive Int16
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int16 -> Int16 -> Int16 # sinnum1p :: Natural -> Int16 -> Int16 # sumWith1 :: Foldable1 f => (a -> Int16) -> f a -> Int16 #
Additive Int32
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int32 -> Int32 -> Int32 # sinnum1p :: Natural -> Int32 -> Int32 # sumWith1 :: Foldable1 f => (a -> Int32) -> f a -> Int32 #
Additive Int64
Instance details Defined in Numeric.Additive.Class Methods (+) :: Int64 -> Int64 -> Int64 # sinnum1p :: Natural -> Int64 -> Int64 # sumWith1 :: Foldable1 f => (a -> Int64) -> f a -> Int64 #
Additive Integer
Instance details Defined in Numeric.Additive.Class Methods (+) :: Integer -> Integer -> Integer # sinnum1p :: Natural -> Integer -> Integer # sumWith1 :: Foldable1 f => (a -> Integer) -> f a -> Integer #
Additive Natural
Instance details Defined in Numeric.Additive.Class Methods (+) :: Natural -> Natural -> Natural # sinnum1p :: Natural -> Natural -> Natural # sumWith1 :: Foldable1 f => (a -> Natural) -> f a -> Natural #
Additive Word
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word -> Word -> Word # sinnum1p :: Natural -> Word -> Word # sumWith1 :: Foldable1 f => (a -> Word) -> f a -> Word #
Additive Word8
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word8 -> Word8 -> Word8 # sinnum1p :: Natural -> Word8 -> Word8 # sumWith1 :: Foldable1 f => (a -> Word8) -> f a -> Word8 #
Additive Word16
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word16 -> Word16 -> Word16 # sinnum1p :: Natural -> Word16 -> Word16 # sumWith1 :: Foldable1 f => (a -> Word16) -> f a -> Word16 #
Additive Word32
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word32 -> Word32 -> Word32 # sinnum1p :: Natural -> Word32 -> Word32 # sumWith1 :: Foldable1 f => (a -> Word32) -> f a -> Word32 #
Additive Word64
Instance details Defined in Numeric.Additive.Class Methods (+) :: Word64 -> Word64 -> Word64 # sinnum1p :: Natural -> Word64 -> Word64 # sumWith1 :: Foldable1 f => (a -> Word64) -> f a -> Word64 #
Additive ()
Instance details Defined in Numeric.Additive.Class Methods (+) :: () -> () -> () # sinnum1p :: Natural -> () -> () # sumWith1 :: Foldable1 f => (a -> ()) -> f a -> () #
Num a => Additive (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapNum a -> WrapNum a -> WrapNum a # sinnum1p :: Natural -> WrapNum a -> WrapNum a # sumWith1 :: Foldable1 f => (a0 -> WrapNum a) -> f a0 -> WrapNum a #
Num a => Additive (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapFractional a -> WrapFractional a -> WrapFractional a # sinnum1p :: Natural -> WrapFractional a -> WrapFractional a # sumWith1 :: Foldable1 f => (a0 -> WrapFractional a) -> f a0 -> WrapFractional a #
Num a => Additive (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapIntegral a -> WrapIntegral a -> WrapIntegral a # sinnum1p :: Natural -> WrapIntegral a -> WrapIntegral a # sumWith1 :: Foldable1 f => (a0 -> WrapIntegral a) -> f a0 -> WrapIntegral a #
Additive a => Additive (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods (+) :: WrapAlgebra a -> WrapAlgebra a -> WrapAlgebra a # sinnum1p :: Natural -> WrapAlgebra a -> WrapAlgebra a # sumWith1 :: Foldable1 f => (a0 -> WrapAlgebra a) -> f a0 -> WrapAlgebra a #
Additive a => Additive (Add a)
Instance details Defined in AlgebraicPrelude Methods (+) :: Add a -> Add a -> Add a # sinnum1p :: Natural -> Add a -> Add a # sumWith1 :: Foldable1 f => (a0 -> Add a) -> f a0 -> Add a #
GCDDomain d => Additive (Fraction d)
Instance details Defined in Numeric.Field.Fraction Methods (+) :: Fraction d -> Fraction d -> Fraction d # sinnum1p :: Natural -> Fraction d -> Fraction d # sumWith1 :: Foldable1 f => (a -> Fraction d) -> f a -> Fraction d #
Additive r => Additive (Scalar r)
Instance details Defined in Algebra.Scalar Methods (+) :: Scalar r -> Scalar r -> Scalar r # sinnum1p :: Natural -> Scalar r -> Scalar r # sumWith1 :: Foldable1 f => (a -> Scalar r) -> f a -> Scalar r #
Additive r => Additive (Complex r)
Instance details Defined in Numeric.Algebra.Complex Methods (+) :: Complex r -> Complex r -> Complex r # sinnum1p :: Natural -> Complex r -> Complex r # sumWith1 :: Foldable1 f => (a -> Complex r) -> f a -> Complex r #
DecidableZero r => Additive (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods (+) :: Unipol r -> Unipol r -> Unipol r # sinnum1p :: Natural -> Unipol r -> Unipol r # sumWith1 :: Foldable1 f => (a -> Unipol r) -> f a -> Unipol r #
Additive r => Additive (b -> r)
Instance details Defined in Numeric.Additive.Class Methods (+) :: (b -> r) -> (b -> r) -> b -> r # sinnum1p :: Natural -> (b -> r) -> b -> r # sumWith1 :: Foldable1 f => (a -> b -> r) -> f a -> b -> r #
(Additive a, Additive b) => Additive (a, b)
Instance details Defined in Numeric.Additive.Class Methods (+) :: (a, b) -> (a, b) -> (a, b) # sinnum1p :: Natural -> (a, b) -> (a, b) # sumWith1 :: Foldable1 f => (a0 -> (a, b)) -> f a0 -> (a, b) #
Additive r => Additive (Covector r a)
Instance details Defined in Numeric.Covector Methods (+) :: Covector r a -> Covector r a -> Covector r a # sinnum1p :: Natural -> Covector r a -> Covector r a # sumWith1 :: Foldable1 f => (a0 -> Covector r a) -> f a0 -> Covector r a #
(Wraps vars poly, Additive poly) => Additive (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (+) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # sinnum1p :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars # sumWith1 :: Foldable1 f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Additive a, Additive b, Additive c) => Additive (a, b, c)
Instance details Defined in Numeric.Additive.Class Methods (+) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sinnum1p :: Natural -> (a, b, c) -> (a, b, c) # sumWith1 :: Foldable1 f => (a0 -> (a, b, c)) -> f a0 -> (a, b, c) #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Additive (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # sinnum1p :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly # sumWith1 :: Foldable1 f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
Additive poly => Additive (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient Methods (+) :: Quotient poly ideal -> Quotient poly ideal -> Quotient poly ideal # sinnum1p :: Natural -> Quotient poly ideal -> Quotient poly ideal # sumWith1 :: Foldable1 f => (a -> Quotient poly ideal) -> f a -> Quotient poly ideal #
(Additive a, Additive b, Additive c, Additive d) => Additive (a, b, c, d)
Instance details Defined in Numeric.Additive.Class Methods (+) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # sinnum1p :: Natural -> (a, b, c, d) -> (a, b, c, d) # sumWith1 :: Foldable1 f => (a0 -> (a, b, c, d)) -> f a0 -> (a, b, c, d) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Additive (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sinnum1p :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sumWith1 :: Foldable1 f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(Additive a, Additive b, Additive c, Additive d, Additive e) => Additive (a, b, c, d, e)
Instance details Defined in Numeric.Additive.Class Methods (+) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # sinnum1p :: Natural -> (a, b, c, d, e) -> (a, b, c, d, e) # sumWith1 :: Foldable1 f => (a0 -> (a, b, c, d, e)) -> f a0 -> (a, b, c, d, e) #

class Additive r => Abelian r #

Instances

Instances details

Abelian Bool
Instance details Defined in Numeric.Additive.Class
Abelian Int
Instance details Defined in Numeric.Additive.Class
Abelian Int8
Instance details Defined in Numeric.Additive.Class
Abelian Int16
Instance details Defined in Numeric.Additive.Class
Abelian Int32
Instance details Defined in Numeric.Additive.Class
Abelian Int64
Instance details Defined in Numeric.Additive.Class
Abelian Integer
Instance details Defined in Numeric.Additive.Class
Abelian Natural
Instance details Defined in Numeric.Additive.Class
Abelian Word
Instance details Defined in Numeric.Additive.Class
Abelian Word8
Instance details Defined in Numeric.Additive.Class
Abelian Word16
Instance details Defined in Numeric.Additive.Class
Abelian Word32
Instance details Defined in Numeric.Additive.Class
Abelian Word64
Instance details Defined in Numeric.Additive.Class
Abelian ()
Instance details Defined in Numeric.Additive.Class
Num a => Abelian (WrapNum a)
Instance details Defined in AlgebraicPrelude
Num a => Abelian (WrapFractional a)
Instance details Defined in AlgebraicPrelude
Num a => Abelian (WrapIntegral a)
Instance details Defined in AlgebraicPrelude
Additive a => Abelian (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude
Additive a => Abelian (Add a)
Instance details Defined in AlgebraicPrelude
GCDDomain d => Abelian (Fraction d)
Instance details Defined in Numeric.Field.Fraction
Abelian r => Abelian (Scalar r)
Instance details Defined in Algebra.Scalar
Abelian r => Abelian (Complex r)
Instance details Defined in Numeric.Algebra.Complex
(DecidableZero r, Abelian r) => Abelian (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate
Abelian r => Abelian (e -> r)
Instance details Defined in Numeric.Additive.Class
(Abelian a, Abelian b) => Abelian (a, b)
Instance details Defined in Numeric.Additive.Class
Abelian s => Abelian (Covector s a)
Instance details Defined in Numeric.Covector
(Wraps vars poly, Abelian poly) => Abelian (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Abelian a, Abelian b, Abelian c) => Abelian (a, b, c)
Instance details Defined in Numeric.Additive.Class
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Abelian (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
Abelian poly => Abelian (Quotient poly ideal) Source #
Instance details Defined in Algebra.Ring.Polynomial.Quotient
(Abelian a, Abelian b, Abelian c, Abelian d) => Abelian (a, b, c, d)
Instance details Defined in Numeric.Additive.Class
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Abelian (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Abelian a, Abelian b, Abelian c, Abelian d, Abelian e) => Abelian (a, b, c, d, e)
Instance details Defined in Numeric.Additive.Class

charWord :: (Integral s, Bounded s) => proxy s -> Natural #

charInt :: (Integral s, Bounded s) => proxy s -> Natural #

zeroRep :: (Applicative m, Monoidal r) => m r #

timesRep :: (Integral n, Functor m, Group r) => n -> m r -> m r #

subtractRep :: (Applicative m, Group r) => m r -> m r -> m r #

sinnumRep :: (Functor m, Monoidal r) => Natural -> m r -> m r #

sinnum1pRep :: (Functor m, Additive r) => Natural -> m r -> m r #

oneRep :: (Representable m, Unital r, UnitalAlgebra r (Rep m)) => m r #

negateRep :: (Functor m, Group r) => m r -> m r #

mulRep :: (Representable m, Algebra r (Rep m)) => m r -> m r -> m r #

minusRep :: (Applicative m, Group r) => m r -> m r -> m r #

fromNaturalRep :: (UnitalAlgebra r (Rep m), Representable m, Rig r) => Natural -> m r #

fromIntegerRep :: (UnitalAlgebra r (Rep m), Representable m, Ring r) => Integer -> m r #

addRep :: (Applicative m, Additive r) => m r -> m r -> m r #

unitM :: CounitalCoalgebra r c => Covector r c #

multM :: Coalgebra r c => c -> c -> Covector r c #

invM :: InvolutiveAlgebra r h => h -> Covector r h #

counitM :: UnitalAlgebra r a => a -> Covector r () #

convolveM :: (Algebra r c, Coalgebra r a) => (c -> Covector r a) -> (c -> Covector r a) -> c -> Covector r a #

comultM :: Algebra r a => a -> Covector r (a, a) #

coinvM :: InvolutiveCoalgebra r h => h -> Covector r h #

antipodeM :: HopfAlgebra r h => h -> Covector r h #

product :: (Foldable f, Unital r) => f r -> r #

powBand :: Unital r => r -> Natural -> r #

pow1pBand :: r -> Natural -> r #

sum :: (Foldable f, Monoidal m) => f m -> m #

sinnumIdempotent :: (Integral n, Idempotent r, Monoidal r) => n -> r -> r #

product1 :: (Foldable1 f, Multiplicative r) => f r -> r #

sum1 :: (Foldable1 f, Additive r) => f r -> r #

sinnum1pIdempotent :: Natural -> r -> r #

class (Vector Vector a, MVector MVector a) => Unbox a #

Instances

Instances details

Unbox Bool
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Char
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Double
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Float
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Int
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Int8
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Int16
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Int32
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Int64
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Word
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Word8
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Word16
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Word32
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Word64
Instance details Defined in Data.Vector.Unboxed.Base
Unbox ()
Instance details Defined in Data.Vector.Unboxed.Base
Unbox All
Instance details Defined in Data.Vector.Unboxed.Base
Unbox Any
Instance details Defined in Data.Vector.Unboxed.Base
Unbox WrapOrdering
Instance details Defined in Algebra.Ring.Polynomial.Monomial
Unbox a => Unbox (Down a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Min a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Max a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (First a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Last a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Identity a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Dual a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Product a)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b) => Unbox (a, b)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b) => Unbox (Arg a b)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b, Unbox c) => Unbox (a, b, c)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox a => Unbox (Const a b)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox (f a) => Unbox (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b, Unbox c, Unbox d) => Unbox (a, b, c, d)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Unbox (a, b, c, d, e)
Instance details Defined in Data.Vector.Unboxed.Base
Unbox (f (g a)) => Unbox (Compose f g a)
Instance details Defined in Data.Vector.Unboxed.Base
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Unbox (a, b, c, d, e, f)
Instance details Defined in Data.Vector.Unboxed.Base

data Vector a #

Instances

Instances details

Monad Vector
Instance details Defined in Data.Vector Methods (>>=) :: Vector a -> (a -> Vector b) -> Vector b # (>>) :: Vector a -> Vector b -> Vector b # return :: a -> Vector a #
Functor Vector
Instance details Defined in Data.Vector Methods fmap :: (a -> b) -> Vector a -> Vector b # (<$) :: a -> Vector b -> Vector a #
MonadFix Vector
Instance details Defined in Data.Vector Methods mfix :: (a -> Vector a) -> Vector a #
MonadFail Vector
Instance details Defined in Data.Vector Methods fail :: String -> Vector a #
Applicative Vector
Instance details Defined in Data.Vector Methods pure :: a -> Vector a # (<>) :: Vector (a -> b) -> Vector a -> Vector b # liftA2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c # (>) :: Vector a -> Vector b -> Vector b # (<*) :: Vector a -> Vector b -> Vector a #
Foldable Vector
Instance details Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldMap' :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # toList :: Vector a -> [a] # null :: Vector a -> Bool # length :: Vector a -> Int # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # sum :: Num a => Vector a -> a # product :: Num a => Vector a -> a #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
MonadPlus Vector
Instance details Defined in Data.Vector Methods mzero :: Vector a # mplus :: Vector a -> Vector a -> Vector a #
Eq1 Vector
Instance details Defined in Data.Vector Methods liftEq :: (a -> b -> Bool) -> Vector a -> Vector b -> Bool #
Ord1 Vector
Instance details Defined in Data.Vector Methods liftCompare :: (a -> b -> Ordering) -> Vector a -> Vector b -> Ordering #
Read1 Vector
Instance details Defined in Data.Vector Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Vector a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Vector a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Vector a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Vector a] #
Show1 Vector
Instance details Defined in Data.Vector Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vector a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vector a] -> ShowS #
MonadZip Vector
Instance details Defined in Data.Vector Methods mzip :: Vector a -> Vector b -> Vector (a, b) # mzipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c # munzip :: Vector (a, b) -> (Vector a, Vector b) #
Alternative Vector
Instance details Defined in Data.Vector Methods empty :: Vector a # (<\|>) :: Vector a -> Vector a -> Vector a # some :: Vector a -> Vector [a] # many :: Vector a -> Vector [a] #
NFData1 Vector
Instance details Defined in Data.Vector Methods liftRnf :: (a -> ()) -> Vector a -> () #
CFreeMonoid Vector
Instance details Defined in Control.Subcategory.Foldable Methods cbasicFromList :: Dom Vector a => [a] -> Vector a ccons :: Dom Vector a => a -> Vector a -> Vector a csnoc :: Dom Vector a => Vector a -> a -> Vector a cfromListN :: Dom Vector a => Int -> [a] -> Vector a ctake :: Dom Vector a => Int -> Vector a -> Vector a cdrop :: Dom Vector a => Int -> Vector a -> Vector a cinit :: Dom Vector a => Vector a -> Vector a ctail :: Dom Vector a => Vector a -> Vector a csplitAt :: Dom Vector a => Int -> Vector a -> (Vector a, Vector a) creplicate :: Dom Vector a => Int -> a -> Vector a cgenerate :: Dom Vector a => Int -> (Int -> a) -> Vector a cgenerateM :: (Dom Vector a, Monad m) => Int -> (Int -> m a) -> m (Vector a) cgenerateA :: (Dom Vector a, Applicative g) => Int -> (Int -> g a) -> g (Vector a) cuncons :: Dom Vector a => Vector a -> Maybe (a, Vector a) cunsnoc :: Dom Vector a => Vector a -> Maybe (Vector a, a) creverse :: Dom Vector a => Vector a -> Vector a cintersperse :: Dom Vector a => a -> Vector a -> Vector a cnub :: (Dom Vector a, Eq a) => Vector a -> Vector a cnubOrd :: (Dom Vector a, Ord a) => Vector a -> Vector a csort :: (Dom Vector a, Ord a) => Vector a -> Vector a csortBy :: Dom Vector a => (a -> a -> Ordering) -> Vector a -> Vector a cinsert :: (Dom Vector a, Ord a) => a -> Vector a -> Vector a cinsertBy :: Dom Vector a => (a -> a -> Ordering) -> a -> Vector a -> Vector a ctakeWhile :: Dom Vector a => (a -> Bool) -> Vector a -> Vector a cdropWhile :: Dom Vector a => (a -> Bool) -> Vector a -> Vector a cspan :: Dom Vector a => (a -> Bool) -> Vector a -> (Vector a, Vector a) cbreak :: Dom Vector a => (a -> Bool) -> Vector a -> (Vector a, Vector a) cfilter :: Dom Vector a => (a -> Bool) -> Vector a -> Vector a cpartition :: Dom Vector a => (a -> Bool) -> Vector a -> (Vector a, Vector a)
CFoldable Vector
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom Vector a, Monoid w) => (a -> w) -> Vector a -> w cfoldMap' :: (Dom Vector a, Monoid m) => (a -> m) -> Vector a -> m cfold :: (Dom Vector w, Monoid w) => Vector w -> w cfoldr :: Dom Vector a => (a -> b -> b) -> b -> Vector a -> b cfoldlM :: (Monad m, Dom Vector b) => (a -> b -> m a) -> a -> Vector b -> m a cfoldlM' :: (Monad m, Dom Vector b) => (a -> b -> m a) -> a -> Vector b -> m a cfoldrM :: (Monad m, Dom Vector a) => (a -> b -> m b) -> b -> Vector a -> m b cfoldrM' :: (Monad m, Dom Vector a) => (a -> b -> m b) -> b -> Vector a -> m b cfoldl :: Dom Vector a => (b -> a -> b) -> b -> Vector a -> b cfoldr' :: Dom Vector a => (a -> b -> b) -> b -> Vector a -> b cfoldl' :: Dom Vector a => (b -> a -> b) -> b -> Vector a -> b cbasicToList :: Dom Vector a => Vector a -> [a] cfoldr1 :: Dom Vector a => (a -> a -> a) -> Vector a -> a cfoldl1 :: Dom Vector a => (a -> a -> a) -> Vector a -> a cindex :: Dom Vector a => Vector a -> Int -> a cnull :: Dom Vector a => Vector a -> Bool clength :: Dom Vector a => Vector a -> Int cany :: Dom Vector a => (a -> Bool) -> Vector a -> Bool call :: Dom Vector a => (a -> Bool) -> Vector a -> Bool celem :: (Eq a, Dom Vector a) => a -> Vector a -> Bool cnotElem :: (Eq a, Dom Vector a) => a -> Vector a -> Bool cminimum :: (Ord a, Dom Vector a) => Vector a -> a cmaximum :: (Ord a, Dom Vector a) => Vector a -> a csum :: (Num a, Dom Vector a) => Vector a -> a cproduct :: (Num a, Dom Vector a) => Vector a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom Vector a, Dom g b) => (a -> g b) -> Vector a -> g () ctraverse_ :: (Applicative g, Dom Vector a) => (a -> g b) -> Vector a -> g () clast :: Dom Vector a => Vector a -> a chead :: Dom Vector a => Vector a -> a cfind :: Dom Vector a => (a -> Bool) -> Vector a -> Maybe a cfindIndex :: Dom Vector a => (a -> Bool) -> Vector a -> Maybe Int cfindIndices :: Dom Vector a => (a -> Bool) -> Vector a -> [Int] celemIndex :: (Dom Vector a, Eq a) => a -> Vector a -> Maybe Int celemIndices :: (Dom Vector a, Eq a) => a -> Vector a -> [Int]
CZip Vector
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom Vector a, Dom Vector b, Dom Vector c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c czip :: (Dom Vector a, Dom Vector b, Dom Vector (a, b)) => Vector a -> Vector b -> Vector (a, b)
CFunctor Vector
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom Vector a, Dom Vector b) => (a -> b) -> Vector a -> Vector b (<$:) :: (Dom Vector a, Dom Vector b) => a -> Vector b -> Vector a
CPointed Vector
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom Vector a => a -> Vector a
CTraversable Vector
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom Vector a, Dom Vector b, Applicative g) => (a -> g b) -> Vector a -> g (Vector b)
CUnzip Vector
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom Vector (a, b), Dom Vector a, Dom Vector b) => Vector (a, b) -> (Vector a, Vector b) cunzipWith :: (Dom Vector c, Dom Vector a, Dom Vector b) => (c -> (a, b)) -> Vector c -> (Vector a, Vector b)
Constrained Vector
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom Vector a
Vector Vector a
Instance details Defined in Data.Vector Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) a -> m (Vector a) basicUnsafeThaw :: PrimMonad m => Vector a -> m (Mutable Vector (PrimState m) a) basicLength :: Vector a -> Int basicUnsafeSlice :: Int -> Int -> Vector a -> Vector a basicUnsafeIndexM :: Monad m => Vector a -> Int -> m a basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) a -> Vector a -> m () elemseq :: Vector a -> a -> b -> b
FoldableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Vector a -> m ifolded :: IndexedFold Int (Vector a) a ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b ifoldl :: (Int -> b -> a -> b) -> b -> Vector a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> Vector a -> b
FunctorWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Vector a -> Vector b imapped :: IndexedSetter Int (Vector a) (Vector b) a b
TraversableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Vector a -> f (Vector b) itraversed :: IndexedTraversal Int (Vector a) (Vector b) a b
IsList (Vector a)
Instance details Defined in Data.Vector Associated Types type Item (Vector a) # Methods fromList :: [Item (Vector a)] -> Vector a # fromListN :: Int -> [Item (Vector a)] -> Vector a # toList :: Vector a -> [Item (Vector a)] #
Eq a => Eq (Vector a)
Instance details Defined in Data.Vector Methods (==) :: Vector a -> Vector a -> Bool # (/=) :: Vector a -> Vector a -> Bool #
Data a => Data (Vector a)
Instance details Defined in Data.Vector Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector a -> c (Vector a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector a) # toConstr :: Vector a -> Constr # dataTypeOf :: Vector a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector a)) # gmapT :: (forall b. Data b => b -> b) -> Vector a -> Vector a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #
Ord a => Ord (Vector a)
Instance details Defined in Data.Vector Methods compare :: Vector a -> Vector a -> Ordering # (<) :: Vector a -> Vector a -> Bool # (<=) :: Vector a -> Vector a -> Bool # (>) :: Vector a -> Vector a -> Bool # (>=) :: Vector a -> Vector a -> Bool # max :: Vector a -> Vector a -> Vector a # min :: Vector a -> Vector a -> Vector a #
Read a => Read (Vector a)
Instance details Defined in Data.Vector Methods readsPrec :: Int -> ReadS (Vector a) # readList :: ReadS [Vector a] # readPrec :: ReadPrec (Vector a) # readListPrec :: ReadPrec [Vector a] #
Show a => Show (Vector a)
Instance details Defined in Data.Vector Methods showsPrec :: Int -> Vector a -> ShowS # show :: Vector a -> String # showList :: [Vector a] -> ShowS #
Semigroup (Vector a)
Instance details Defined in Data.Vector Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Monoid (Vector a)
Instance details Defined in Data.Vector Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
NFData a => NFData (Vector a)
Instance details Defined in Data.Vector Methods rnf :: Vector a -> () #
Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a))
Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a))
AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) ()
Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a
GrowingAppend (Vector a)
Instance details Defined in Data.MonoTraversable
MonoFoldable (Vector a)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Vector a) -> m) -> Vector a -> m ofoldr :: (Element (Vector a) -> b -> b) -> b -> Vector a -> b ofoldl' :: (a0 -> Element (Vector a) -> a0) -> a0 -> Vector a -> a0 otoList :: Vector a -> [Element (Vector a)] oall :: (Element (Vector a) -> Bool) -> Vector a -> Bool oany :: (Element (Vector a) -> Bool) -> Vector a -> Bool onull :: Vector a -> Bool olength :: Vector a -> Int olength64 :: Vector a -> Int64 ocompareLength :: Integral i => Vector a -> i -> Ordering otraverse_ :: Applicative f => (Element (Vector a) -> f b) -> Vector a -> f () ofor_ :: Applicative f => Vector a -> (Element (Vector a) -> f b) -> f () omapM_ :: Applicative m => (Element (Vector a) -> m ()) -> Vector a -> m () oforM_ :: Applicative m => Vector a -> (Element (Vector a) -> m ()) -> m () ofoldlM :: Monad m => (a0 -> Element (Vector a) -> m a0) -> a0 -> Vector a -> m a0 ofoldMap1Ex :: Semigroup m => (Element (Vector a) -> m) -> Vector a -> m ofoldr1Ex :: (Element (Vector a) -> Element (Vector a) -> Element (Vector a)) -> Vector a -> Element (Vector a) ofoldl1Ex' :: (Element (Vector a) -> Element (Vector a) -> Element (Vector a)) -> Vector a -> Element (Vector a) headEx :: Vector a -> Element (Vector a) lastEx :: Vector a -> Element (Vector a) unsafeHead :: Vector a -> Element (Vector a) unsafeLast :: Vector a -> Element (Vector a) maximumByEx :: (Element (Vector a) -> Element (Vector a) -> Ordering) -> Vector a -> Element (Vector a) minimumByEx :: (Element (Vector a) -> Element (Vector a) -> Ordering) -> Vector a -> Element (Vector a) oelem :: Element (Vector a) -> Vector a -> Bool onotElem :: Element (Vector a) -> Vector a -> Bool
MonoFunctor (Vector a)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (Vector a) -> Element (Vector a)) -> Vector a -> Vector a
MonoPointed (Vector a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (Vector a) -> Vector a
MonoTraversable (Vector a)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (Vector a) -> f (Element (Vector a))) -> Vector a -> f (Vector a) omapM :: Applicative m => (Element (Vector a) -> m (Element (Vector a))) -> Vector a -> m (Vector a)
IsSequence (Vector a)
Instance details Defined in Data.Sequences Methods fromList :: [Element (Vector a)] -> Vector a lengthIndex :: Vector a -> Index (Vector a) break :: (Element (Vector a) -> Bool) -> Vector a -> (Vector a, Vector a) span :: (Element (Vector a) -> Bool) -> Vector a -> (Vector a, Vector a) dropWhile :: (Element (Vector a) -> Bool) -> Vector a -> Vector a takeWhile :: (Element (Vector a) -> Bool) -> Vector a -> Vector a splitAt :: Index (Vector a) -> Vector a -> (Vector a, Vector a) unsafeSplitAt :: Index (Vector a) -> Vector a -> (Vector a, Vector a) take :: Index (Vector a) -> Vector a -> Vector a unsafeTake :: Index (Vector a) -> Vector a -> Vector a drop :: Index (Vector a) -> Vector a -> Vector a unsafeDrop :: Index (Vector a) -> Vector a -> Vector a dropEnd :: Index (Vector a) -> Vector a -> Vector a partition :: (Element (Vector a) -> Bool) -> Vector a -> (Vector a, Vector a) uncons :: Vector a -> Maybe (Element (Vector a), Vector a) unsnoc :: Vector a -> Maybe (Vector a, Element (Vector a)) filter :: (Element (Vector a) -> Bool) -> Vector a -> Vector a filterM :: Monad m => (Element (Vector a) -> m Bool) -> Vector a -> m (Vector a) replicate :: Index (Vector a) -> Element (Vector a) -> Vector a replicateM :: Monad m => Index (Vector a) -> m (Element (Vector a)) -> m (Vector a) groupBy :: (Element (Vector a) -> Element (Vector a) -> Bool) -> Vector a -> [Vector a] groupAllOn :: Eq b => (Element (Vector a) -> b) -> Vector a -> [Vector a] subsequences :: Vector a -> [Vector a] permutations :: Vector a -> [Vector a] tailEx :: Vector a -> Vector a tailMay :: Vector a -> Maybe (Vector a) initEx :: Vector a -> Vector a initMay :: Vector a -> Maybe (Vector a) unsafeTail :: Vector a -> Vector a unsafeInit :: Vector a -> Vector a index :: Vector a -> Index (Vector a) -> Maybe (Element (Vector a)) indexEx :: Vector a -> Index (Vector a) -> Element (Vector a) unsafeIndex :: Vector a -> Index (Vector a) -> Element (Vector a) splitWhen :: (Element (Vector a) -> Bool) -> Vector a -> [Vector a]
SemiSequence (Vector a)
Instance details Defined in Data.Sequences Associated Types type Index (Vector a) Methods intersperse :: Element (Vector a) -> Vector a -> Vector a reverse :: Vector a -> Vector a find :: (Element (Vector a) -> Bool) -> Vector a -> Maybe (Element (Vector a)) sortBy :: (Element (Vector a) -> Element (Vector a) -> Ordering) -> Vector a -> Vector a cons :: Element (Vector a) -> Vector a -> Vector a snoc :: Vector a -> Element (Vector a) -> Vector a
t ~ Vector a' => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b)
Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b)
Each (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b
type Mutable Vector
Instance details Defined in Data.Vector type Mutable Vector = MVector
type Key Vector
Instance details Defined in Data.Vector.Instances type Key Vector = Int
type Dom Vector a
Instance details Defined in Control.Subcategory.Functor type Dom Vector a = ()
type Item (Vector a)
Instance details Defined in Data.Vector type Item (Vector a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Unwrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Vector a) = [a]
type Element (Vector a)
Instance details Defined in Data.MonoTraversable type Element (Vector a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type Index (Vector a)
Instance details Defined in Data.Sequences type Index (Vector a) = Int

data HashSet a #

Instances

Instances details

Foldable HashSet
Instance details Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # toList :: HashSet a -> [a] # null :: HashSet a -> Bool # length :: HashSet a -> Int # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # sum :: Num a => HashSet a -> a # product :: Num a => HashSet a -> a #
Eq1 HashSet
Instance details Defined in Data.HashSet.Internal Methods liftEq :: (a -> b -> Bool) -> HashSet a -> HashSet b -> Bool #
Ord1 HashSet
Instance details Defined in Data.HashSet.Internal Methods liftCompare :: (a -> b -> Ordering) -> HashSet a -> HashSet b -> Ordering #
Show1 HashSet
Instance details Defined in Data.HashSet.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashSet a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashSet a] -> ShowS #
NFData1 HashSet
Instance details Defined in Data.HashSet.Internal Methods liftRnf :: (a -> ()) -> HashSet a -> () #
CFoldable HashSet
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom HashSet a, Monoid w) => (a -> w) -> HashSet a -> w cfoldMap' :: (Dom HashSet a, Monoid m) => (a -> m) -> HashSet a -> m cfold :: (Dom HashSet w, Monoid w) => HashSet w -> w cfoldr :: Dom HashSet a => (a -> b -> b) -> b -> HashSet a -> b cfoldlM :: (Monad m, Dom HashSet b) => (a -> b -> m a) -> a -> HashSet b -> m a cfoldlM' :: (Monad m, Dom HashSet b) => (a -> b -> m a) -> a -> HashSet b -> m a cfoldrM :: (Monad m, Dom HashSet a) => (a -> b -> m b) -> b -> HashSet a -> m b cfoldrM' :: (Monad m, Dom HashSet a) => (a -> b -> m b) -> b -> HashSet a -> m b cfoldl :: Dom HashSet a => (b -> a -> b) -> b -> HashSet a -> b cfoldr' :: Dom HashSet a => (a -> b -> b) -> b -> HashSet a -> b cfoldl' :: Dom HashSet a => (b -> a -> b) -> b -> HashSet a -> b cbasicToList :: Dom HashSet a => HashSet a -> [a] cfoldr1 :: Dom HashSet a => (a -> a -> a) -> HashSet a -> a cfoldl1 :: Dom HashSet a => (a -> a -> a) -> HashSet a -> a cindex :: Dom HashSet a => HashSet a -> Int -> a cnull :: Dom HashSet a => HashSet a -> Bool clength :: Dom HashSet a => HashSet a -> Int cany :: Dom HashSet a => (a -> Bool) -> HashSet a -> Bool call :: Dom HashSet a => (a -> Bool) -> HashSet a -> Bool celem :: (Eq a, Dom HashSet a) => a -> HashSet a -> Bool cnotElem :: (Eq a, Dom HashSet a) => a -> HashSet a -> Bool cminimum :: (Ord a, Dom HashSet a) => HashSet a -> a cmaximum :: (Ord a, Dom HashSet a) => HashSet a -> a csum :: (Num a, Dom HashSet a) => HashSet a -> a cproduct :: (Num a, Dom HashSet a) => HashSet a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom HashSet a, Dom g b) => (a -> g b) -> HashSet a -> g () ctraverse_ :: (Applicative g, Dom HashSet a) => (a -> g b) -> HashSet a -> g () clast :: Dom HashSet a => HashSet a -> a chead :: Dom HashSet a => HashSet a -> a cfind :: Dom HashSet a => (a -> Bool) -> HashSet a -> Maybe a cfindIndex :: Dom HashSet a => (a -> Bool) -> HashSet a -> Maybe Int cfindIndices :: Dom HashSet a => (a -> Bool) -> HashSet a -> [Int] celemIndex :: (Dom HashSet a, Eq a) => a -> HashSet a -> Maybe Int celemIndices :: (Dom HashSet a, Eq a) => a -> HashSet a -> [Int]
CFunctor HashSet
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom HashSet a, Dom HashSet b) => (a -> b) -> HashSet a -> HashSet b (<$:) :: (Dom HashSet a, Dom HashSet b) => a -> HashSet b -> HashSet a
CPointed HashSet
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom HashSet a => a -> HashSet a
CTraversable HashSet
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom HashSet a, Dom HashSet b, Applicative g) => (a -> g b) -> HashSet a -> g (HashSet b)
Constrained HashSet
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom HashSet a
Hashable1 HashSet
Instance details Defined in Data.HashSet.Internal Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashSet a -> Int
(Eq a, Hashable a) => IsList (HashSet a)
Instance details Defined in Data.HashSet.Internal Associated Types type Item (HashSet a) # Methods fromList :: [Item (HashSet a)] -> HashSet a # fromListN :: Int -> [Item (HashSet a)] -> HashSet a # toList :: HashSet a -> [Item (HashSet a)] #
Eq a => Eq (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods (==) :: HashSet a -> HashSet a -> Bool # (/=) :: HashSet a -> HashSet a -> Bool #
(Data a, Eq a, Hashable a) => Data (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashSet a -> c (HashSet a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashSet a) # toConstr :: HashSet a -> Constr # dataTypeOf :: HashSet a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashSet a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashSet a)) # gmapT :: (forall b. Data b => b -> b) -> HashSet a -> HashSet a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r # gmapQ :: (forall d. Data d => d -> u) -> HashSet a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HashSet a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) #
Ord a => Ord (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods compare :: HashSet a -> HashSet a -> Ordering # (<) :: HashSet a -> HashSet a -> Bool # (<=) :: HashSet a -> HashSet a -> Bool # (>) :: HashSet a -> HashSet a -> Bool # (>=) :: HashSet a -> HashSet a -> Bool # max :: HashSet a -> HashSet a -> HashSet a # min :: HashSet a -> HashSet a -> HashSet a #
(Eq a, Hashable a, Read a) => Read (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods readsPrec :: Int -> ReadS (HashSet a) # readList :: ReadS [HashSet a] # readPrec :: ReadPrec (HashSet a) # readListPrec :: ReadPrec [HashSet a] #
Show a => Show (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods showsPrec :: Int -> HashSet a -> ShowS # show :: HashSet a -> String # showList :: [HashSet a] -> ShowS #
(Hashable a, Eq a) => Semigroup (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods (<>) :: HashSet a -> HashSet a -> HashSet a # sconcat :: NonEmpty (HashSet a) -> HashSet a # stimes :: Integral b => b -> HashSet a -> HashSet a #
(Hashable a, Eq a) => Monoid (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Hashable a => Hashable (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods hashWithSalt :: Int -> HashSet a -> Int # hash :: HashSet a -> Int #
NFData a => NFData (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods rnf :: HashSet a -> () #
(Hashable a, Eq a) => Wrapped (HashSet a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashSet a) Methods _Wrapped' :: Iso' (HashSet a) (Unwrapped (HashSet a))
(Eq k, Hashable k) => At (HashSet k)
Instance details Defined in Control.Lens.At Methods at :: Index (HashSet k) -> Lens' (HashSet k) (Maybe (IxValue (HashSet k)))
(Eq a, Hashable a) => Contains (HashSet a)
Instance details Defined in Control.Lens.At Methods contains :: Index (HashSet a) -> Lens' (HashSet a) Bool
(Eq k, Hashable k) => Ixed (HashSet k)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashSet k) -> Traversal' (HashSet k) (IxValue (HashSet k))
AsEmpty (HashSet a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashSet a) ()
(Eq v, Hashable v) => GrowingAppend (HashSet v)
Instance details Defined in Data.MonoTraversable
MonoFoldable (HashSet e)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (HashSet e) -> m) -> HashSet e -> m ofoldr :: (Element (HashSet e) -> b -> b) -> b -> HashSet e -> b ofoldl' :: (a -> Element (HashSet e) -> a) -> a -> HashSet e -> a otoList :: HashSet e -> [Element (HashSet e)] oall :: (Element (HashSet e) -> Bool) -> HashSet e -> Bool oany :: (Element (HashSet e) -> Bool) -> HashSet e -> Bool onull :: HashSet e -> Bool olength :: HashSet e -> Int olength64 :: HashSet e -> Int64 ocompareLength :: Integral i => HashSet e -> i -> Ordering otraverse_ :: Applicative f => (Element (HashSet e) -> f b) -> HashSet e -> f () ofor_ :: Applicative f => HashSet e -> (Element (HashSet e) -> f b) -> f () omapM_ :: Applicative m => (Element (HashSet e) -> m ()) -> HashSet e -> m () oforM_ :: Applicative m => HashSet e -> (Element (HashSet e) -> m ()) -> m () ofoldlM :: Monad m => (a -> Element (HashSet e) -> m a) -> a -> HashSet e -> m a ofoldMap1Ex :: Semigroup m => (Element (HashSet e) -> m) -> HashSet e -> m ofoldr1Ex :: (Element (HashSet e) -> Element (HashSet e) -> Element (HashSet e)) -> HashSet e -> Element (HashSet e) ofoldl1Ex' :: (Element (HashSet e) -> Element (HashSet e) -> Element (HashSet e)) -> HashSet e -> Element (HashSet e) headEx :: HashSet e -> Element (HashSet e) lastEx :: HashSet e -> Element (HashSet e) unsafeHead :: HashSet e -> Element (HashSet e) unsafeLast :: HashSet e -> Element (HashSet e) maximumByEx :: (Element (HashSet e) -> Element (HashSet e) -> Ordering) -> HashSet e -> Element (HashSet e) minimumByEx :: (Element (HashSet e) -> Element (HashSet e) -> Ordering) -> HashSet e -> Element (HashSet e) oelem :: Element (HashSet e) -> HashSet e -> Bool onotElem :: Element (HashSet e) -> HashSet e -> Bool
Hashable a => MonoPointed (HashSet a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (HashSet a) -> HashSet a
(Eq element, Hashable element) => IsSet (HashSet element)
Instance details Defined in Data.Containers Methods insertSet :: Element (HashSet element) -> HashSet element -> HashSet element deleteSet :: Element (HashSet element) -> HashSet element -> HashSet element singletonSet :: Element (HashSet element) -> HashSet element setFromList :: [Element (HashSet element)] -> HashSet element setToList :: HashSet element -> [Element (HashSet element)] filterSet :: (Element (HashSet element) -> Bool) -> HashSet element -> HashSet element
(Eq element, Hashable element) => SetContainer (HashSet element)
Instance details Defined in Data.Containers Associated Types type ContainerKey (HashSet element) Methods member :: ContainerKey (HashSet element) -> HashSet element -> Bool notMember :: ContainerKey (HashSet element) -> HashSet element -> Bool union :: HashSet element -> HashSet element -> HashSet element unions :: (MonoFoldable mono, Element mono ~ HashSet element) => mono -> HashSet element difference :: HashSet element -> HashSet element -> HashSet element intersection :: HashSet element -> HashSet element -> HashSet element keys :: HashSet element -> [ContainerKey (HashSet element)]
(t ~ HashSet a', Hashable a, Eq a) => Rewrapped (HashSet a) t
Instance details Defined in Control.Lens.Wrapped
type Dom HashSet a
Instance details Defined in Control.Subcategory.Functor type Dom HashSet a = (Hashable a, Eq a)
type Item (HashSet a)
Instance details Defined in Data.HashSet.Internal type Item (HashSet a) = a
type Index (HashSet a)
Instance details Defined in Control.Lens.At type Index (HashSet a) = a
type Unwrapped (HashSet a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (HashSet a) = [a]
type Element (HashSet e)
Instance details Defined in Data.MonoTraversable type Element (HashSet e) = e
type IxValue (HashSet k)
Instance details Defined in Control.Lens.At type IxValue (HashSet k) = ()
type ContainerKey (HashSet element)
Instance details Defined in Data.Containers type ContainerKey (HashSet element) = element

data HashMap k v #

Instances

Instances details

Bifoldable HashMap
Instance details Defined in Data.HashMap.Internal Methods bifold :: Monoid m => HashMap m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> HashMap a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> HashMap a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> HashMap a b -> c #
Eq2 HashMap
Instance details Defined in Data.HashMap.Internal Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> HashMap a c -> HashMap b d -> Bool #
Ord2 HashMap
Instance details Defined in Data.HashMap.Internal Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> HashMap a c -> HashMap b d -> Ordering #
Show2 HashMap
Instance details Defined in Data.HashMap.Internal Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> HashMap a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [HashMap a b] -> ShowS #
NFData2 HashMap
Instance details Defined in Data.HashMap.Internal Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> HashMap a b -> () #
Hashable2 HashMap
Instance details Defined in Data.HashMap.Internal Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> HashMap a b -> Int
BiPolyMap HashMap
Instance details Defined in Data.Containers Associated Types type BPMKeyConstraint HashMap key Methods mapKeysWith :: (BPMKeyConstraint HashMap k1, BPMKeyConstraint HashMap k2) => (v -> v -> v) -> (k1 -> k2) -> HashMap k1 v -> HashMap k2 v
FoldableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> HashMap k a -> m ifolded :: IndexedFold k (HashMap k a) a ifoldr :: (k -> a -> b -> b) -> b -> HashMap k a -> b ifoldl :: (k -> b -> a -> b) -> b -> HashMap k a -> b ifoldr' :: (k -> a -> b -> b) -> b -> HashMap k a -> b ifoldl' :: (k -> b -> a -> b) -> b -> HashMap k a -> b
FunctorWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> HashMap k a -> HashMap k b imapped :: IndexedSetter k (HashMap k a) (HashMap k b) a b
TraversableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> HashMap k a -> f (HashMap k b) itraversed :: IndexedTraversal k (HashMap k a) (HashMap k b) a b
Functor (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods fmap :: (a -> b) -> HashMap k a -> HashMap k b # (<$) :: a -> HashMap k b -> HashMap k a #
Foldable (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # null :: HashMap k a -> Bool # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # sum :: Num a => HashMap k a -> a # product :: Num a => HashMap k a -> a #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Eq k => Eq1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftEq :: (a -> b -> Bool) -> HashMap k a -> HashMap k b -> Bool #
Ord k => Ord1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftCompare :: (a -> b -> Ordering) -> HashMap k a -> HashMap k b -> Ordering #
(Eq k, Hashable k, Read k) => Read1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (HashMap k a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [HashMap k a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (HashMap k a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [HashMap k a] #
Show k => Show1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashMap k a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashMap k a] -> ShowS #
NFData k => NFData1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftRnf :: (a -> ()) -> HashMap k a -> () #
CFoldable (HashMap k)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (HashMap k) a, Monoid w) => (a -> w) -> HashMap k a -> w cfoldMap' :: (Dom (HashMap k) a, Monoid m) => (a -> m) -> HashMap k a -> m cfold :: (Dom (HashMap k) w, Monoid w) => HashMap k w -> w cfoldr :: Dom (HashMap k) a => (a -> b -> b) -> b -> HashMap k a -> b cfoldlM :: (Monad m, Dom (HashMap k) b) => (a -> b -> m a) -> a -> HashMap k b -> m a cfoldlM' :: (Monad m, Dom (HashMap k) b) => (a -> b -> m a) -> a -> HashMap k b -> m a cfoldrM :: (Monad m, Dom (HashMap k) a) => (a -> b -> m b) -> b -> HashMap k a -> m b cfoldrM' :: (Monad m, Dom (HashMap k) a) => (a -> b -> m b) -> b -> HashMap k a -> m b cfoldl :: Dom (HashMap k) a => (b -> a -> b) -> b -> HashMap k a -> b cfoldr' :: Dom (HashMap k) a => (a -> b -> b) -> b -> HashMap k a -> b cfoldl' :: Dom (HashMap k) a => (b -> a -> b) -> b -> HashMap k a -> b cbasicToList :: Dom (HashMap k) a => HashMap k a -> [a] cfoldr1 :: Dom (HashMap k) a => (a -> a -> a) -> HashMap k a -> a cfoldl1 :: Dom (HashMap k) a => (a -> a -> a) -> HashMap k a -> a cindex :: Dom (HashMap k) a => HashMap k a -> Int -> a cnull :: Dom (HashMap k) a => HashMap k a -> Bool clength :: Dom (HashMap k) a => HashMap k a -> Int cany :: Dom (HashMap k) a => (a -> Bool) -> HashMap k a -> Bool call :: Dom (HashMap k) a => (a -> Bool) -> HashMap k a -> Bool celem :: (Eq a, Dom (HashMap k) a) => a -> HashMap k a -> Bool cnotElem :: (Eq a, Dom (HashMap k) a) => a -> HashMap k a -> Bool cminimum :: (Ord a, Dom (HashMap k) a) => HashMap k a -> a cmaximum :: (Ord a, Dom (HashMap k) a) => HashMap k a -> a csum :: (Num a, Dom (HashMap k) a) => HashMap k a -> a cproduct :: (Num a, Dom (HashMap k) a) => HashMap k a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (HashMap k) a, Dom g b) => (a -> g b) -> HashMap k a -> g () ctraverse_ :: (Applicative g, Dom (HashMap k) a) => (a -> g b) -> HashMap k a -> g () clast :: Dom (HashMap k) a => HashMap k a -> a chead :: Dom (HashMap k) a => HashMap k a -> a cfind :: Dom (HashMap k) a => (a -> Bool) -> HashMap k a -> Maybe a cfindIndex :: Dom (HashMap k) a => (a -> Bool) -> HashMap k a -> Maybe Int cfindIndices :: Dom (HashMap k) a => (a -> Bool) -> HashMap k a -> [Int] celemIndex :: (Dom (HashMap k) a, Eq a) => a -> HashMap k a -> Maybe Int celemIndices :: (Dom (HashMap k) a, Eq a) => a -> HashMap k a -> [Int]
(Eq k, Hashable k) => CZip (HashMap k)
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom (HashMap k) a, Dom (HashMap k) b, Dom (HashMap k) c) => (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c czip :: (Dom (HashMap k) a, Dom (HashMap k) b, Dom (HashMap k) (a, b)) => HashMap k a -> HashMap k b -> HashMap k (a, b)
CFunctor (HashMap k)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (HashMap k) a, Dom (HashMap k) b) => (a -> b) -> HashMap k a -> HashMap k b (<$:) :: (Dom (HashMap k) a, Dom (HashMap k) b) => a -> HashMap k b -> HashMap k a
CTraversable (HashMap k)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (HashMap k) a, Dom (HashMap k) b, Applicative g) => (a -> g b) -> HashMap k a -> g (HashMap k b)
(Eq k, Hashable k) => CUnzip (HashMap k)
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom (HashMap k) (a, b), Dom (HashMap k) a, Dom (HashMap k) b) => HashMap k (a, b) -> (HashMap k a, HashMap k b) cunzipWith :: (Dom (HashMap k) c, Dom (HashMap k) a, Dom (HashMap k) b) => (c -> (a, b)) -> HashMap k c -> (HashMap k a, HashMap k b)
(Hashable k, Eq k) => Apply (HashMap k)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: HashMap k (a -> b) -> HashMap k a -> HashMap k b (.>) :: HashMap k a -> HashMap k b -> HashMap k b (<.) :: HashMap k a -> HashMap k b -> HashMap k a liftF2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c
(Hashable k, Eq k) => Bind (HashMap k)
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: HashMap k a -> (a -> HashMap k b) -> HashMap k b join :: HashMap k (HashMap k a) -> HashMap k a
FoldableWithKey (HashMap k)
Instance details Defined in Data.Key Methods toKeyedList :: HashMap k a -> [(Key (HashMap k), a)] foldMapWithKey :: Monoid m => (Key (HashMap k) -> a -> m) -> HashMap k a -> m foldrWithKey :: (Key (HashMap k) -> a -> b -> b) -> b -> HashMap k a -> b foldlWithKey :: (b -> Key (HashMap k) -> a -> b) -> b -> HashMap k a -> b
(Eq k, Hashable k) => Indexable (HashMap k)
Instance details Defined in Data.Key Methods index :: HashMap k a -> Key (HashMap k) -> a
Keyed (HashMap k)
Instance details Defined in Data.Key Methods mapWithKey :: (Key (HashMap k) -> a -> b) -> HashMap k a -> HashMap k b
(Eq k, Hashable k) => Lookup (HashMap k)
Instance details Defined in Data.Key Methods lookup :: Key (HashMap k) -> HashMap k a -> Maybe a
TraversableWithKey (HashMap k)
Instance details Defined in Data.Key Methods traverseWithKey :: Applicative f => (Key (HashMap k) -> a -> f b) -> HashMap k a -> f (HashMap k b) mapWithKeyM :: Monad m => (Key (HashMap k) -> a -> m b) -> HashMap k a -> m (HashMap k b)
(Eq k, Hashable k) => Zip (HashMap k)
Instance details Defined in Data.Key Methods zipWith :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c zip :: HashMap k a -> HashMap k b -> HashMap k (a, b) zap :: HashMap k (a -> b) -> HashMap k a -> HashMap k b
(Eq k, Hashable k) => ZipWithKey (HashMap k)
Instance details Defined in Data.Key Methods zipWithKey :: (Key (HashMap k) -> a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c zapWithKey :: HashMap k (Key (HashMap k) -> a -> b) -> HashMap k a -> HashMap k b
Constrained (HashMap k)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (HashMap k) a
Hashable k => Hashable1 (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashMap k a -> Int
(Eq key, Hashable key) => PolyMap (HashMap key)
Instance details Defined in Data.Containers Methods differenceMap :: HashMap key value1 -> HashMap key value2 -> HashMap key value1 intersectionMap :: HashMap key value1 -> HashMap key value2 -> HashMap key value1 intersectionWithMap :: (value1 -> value2 -> value3) -> HashMap key value1 -> HashMap key value2 -> HashMap key value3
(Eq k, Hashable k) => IsList (HashMap k v)
Instance details Defined in Data.HashMap.Internal Associated Types type Item (HashMap k v) # Methods fromList :: [Item (HashMap k v)] -> HashMap k v # fromListN :: Int -> [Item (HashMap k v)] -> HashMap k v # toList :: HashMap k v -> [Item (HashMap k v)] #
(Eq k, Eq v) => Eq (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods (==) :: HashMap k v -> HashMap k v -> Bool # (/=) :: HashMap k v -> HashMap k v -> Bool #
(Data k, Data v, Eq k, Hashable k) => Data (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashMap k v -> c (HashMap k v) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashMap k v) # toConstr :: HashMap k v -> Constr # dataTypeOf :: HashMap k v -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashMap k v)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashMap k v)) # gmapT :: (forall b. Data b => b -> b) -> HashMap k v -> HashMap k v # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r # gmapQ :: (forall d. Data d => d -> u) -> HashMap k v -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> HashMap k v -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) #
(Ord k, Ord v) => Ord (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods compare :: HashMap k v -> HashMap k v -> Ordering # (<) :: HashMap k v -> HashMap k v -> Bool # (<=) :: HashMap k v -> HashMap k v -> Bool # (>) :: HashMap k v -> HashMap k v -> Bool # (>=) :: HashMap k v -> HashMap k v -> Bool # max :: HashMap k v -> HashMap k v -> HashMap k v # min :: HashMap k v -> HashMap k v -> HashMap k v #
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e)
Instance details Defined in Data.HashMap.Internal Methods readsPrec :: Int -> ReadS (HashMap k e) # readList :: ReadS [HashMap k e] # readPrec :: ReadPrec (HashMap k e) # readListPrec :: ReadPrec [HashMap k e] #
(Show k, Show v) => Show (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods showsPrec :: Int -> HashMap k v -> ShowS # show :: HashMap k v -> String # showList :: [HashMap k v] -> ShowS #
(Eq k, Hashable k) => Semigroup (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods (<>) :: HashMap k v -> HashMap k v -> HashMap k v # sconcat :: NonEmpty (HashMap k v) -> HashMap k v # stimes :: Integral b => b -> HashMap k v -> HashMap k v #
(Eq k, Hashable k) => Monoid (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods mempty :: HashMap k v # mappend :: HashMap k v -> HashMap k v -> HashMap k v # mconcat :: [HashMap k v] -> HashMap k v #
(Hashable k, Hashable v) => Hashable (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods hashWithSalt :: Int -> HashMap k v -> Int # hash :: HashMap k v -> Int #
(NFData k, NFData v) => NFData (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods rnf :: HashMap k v -> () #
(Hashable k, Eq k) => Wrapped (HashMap k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashMap k a) Methods _Wrapped' :: Iso' (HashMap k a) (Unwrapped (HashMap k a))
(Eq k, Hashable k) => At (HashMap k a)
Instance details Defined in Control.Lens.At Methods at :: Index (HashMap k a) -> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a)))
(Eq k, Hashable k) => Ixed (HashMap k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashMap k a) -> Traversal' (HashMap k a) (IxValue (HashMap k a))
AsEmpty (HashMap k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashMap k a) ()
(Eq k, Hashable k) => GrowingAppend (HashMap k v)
Instance details Defined in Data.MonoTraversable
MonoFoldable (HashMap k v)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (HashMap k v) -> m) -> HashMap k v -> m ofoldr :: (Element (HashMap k v) -> b -> b) -> b -> HashMap k v -> b ofoldl' :: (a -> Element (HashMap k v) -> a) -> a -> HashMap k v -> a otoList :: HashMap k v -> [Element (HashMap k v)] oall :: (Element (HashMap k v) -> Bool) -> HashMap k v -> Bool oany :: (Element (HashMap k v) -> Bool) -> HashMap k v -> Bool onull :: HashMap k v -> Bool olength :: HashMap k v -> Int olength64 :: HashMap k v -> Int64 ocompareLength :: Integral i => HashMap k v -> i -> Ordering otraverse_ :: Applicative f => (Element (HashMap k v) -> f b) -> HashMap k v -> f () ofor_ :: Applicative f => HashMap k v -> (Element (HashMap k v) -> f b) -> f () omapM_ :: Applicative m => (Element (HashMap k v) -> m ()) -> HashMap k v -> m () oforM_ :: Applicative m => HashMap k v -> (Element (HashMap k v) -> m ()) -> m () ofoldlM :: Monad m => (a -> Element (HashMap k v) -> m a) -> a -> HashMap k v -> m a ofoldMap1Ex :: Semigroup m => (Element (HashMap k v) -> m) -> HashMap k v -> m ofoldr1Ex :: (Element (HashMap k v) -> Element (HashMap k v) -> Element (HashMap k v)) -> HashMap k v -> Element (HashMap k v) ofoldl1Ex' :: (Element (HashMap k v) -> Element (HashMap k v) -> Element (HashMap k v)) -> HashMap k v -> Element (HashMap k v) headEx :: HashMap k v -> Element (HashMap k v) lastEx :: HashMap k v -> Element (HashMap k v) unsafeHead :: HashMap k v -> Element (HashMap k v) unsafeLast :: HashMap k v -> Element (HashMap k v) maximumByEx :: (Element (HashMap k v) -> Element (HashMap k v) -> Ordering) -> HashMap k v -> Element (HashMap k v) minimumByEx :: (Element (HashMap k v) -> Element (HashMap k v) -> Ordering) -> HashMap k v -> Element (HashMap k v) oelem :: Element (HashMap k v) -> HashMap k v -> Bool onotElem :: Element (HashMap k v) -> HashMap k v -> Bool
MonoFunctor (HashMap k v)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (HashMap k v) -> Element (HashMap k v)) -> HashMap k v -> HashMap k v
MonoTraversable (HashMap k v)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (HashMap k v) -> f (Element (HashMap k v))) -> HashMap k v -> f (HashMap k v) omapM :: Applicative m => (Element (HashMap k v) -> m (Element (HashMap k v))) -> HashMap k v -> m (HashMap k v)
(Hashable k, Eq k) => HasKeysSet (HashMap k v)
Instance details Defined in Data.Containers Associated Types type KeySet (HashMap k v) Methods keysSet :: HashMap k v -> KeySet (HashMap k v)
(Eq key, Hashable key) => IsMap (HashMap key value)
Instance details Defined in Data.Containers Associated Types type MapValue (HashMap key value) Methods lookup :: ContainerKey (HashMap key value) -> HashMap key value -> Maybe (MapValue (HashMap key value)) insertMap :: ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> HashMap key value -> HashMap key value deleteMap :: ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value singletonMap :: ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> HashMap key value mapFromList :: [(ContainerKey (HashMap key value), MapValue (HashMap key value))] -> HashMap key value mapToList :: HashMap key value -> [(ContainerKey (HashMap key value), MapValue (HashMap key value))] findWithDefault :: MapValue (HashMap key value) -> ContainerKey (HashMap key value) -> HashMap key value -> MapValue (HashMap key value) insertWith :: (MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> HashMap key value -> HashMap key value insertWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> HashMap key value -> HashMap key value insertLookupWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> HashMap key value -> (Maybe (MapValue (HashMap key value)), HashMap key value) adjustMap :: (MapValue (HashMap key value) -> MapValue (HashMap key value)) -> ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value adjustWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value updateMap :: (MapValue (HashMap key value) -> Maybe (MapValue (HashMap key value))) -> ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value updateWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> Maybe (MapValue (HashMap key value))) -> ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value updateLookupWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> Maybe (MapValue (HashMap key value))) -> ContainerKey (HashMap key value) -> HashMap key value -> (Maybe (MapValue (HashMap key value)), HashMap key value) alterMap :: (Maybe (MapValue (HashMap key value)) -> Maybe (MapValue (HashMap key value))) -> ContainerKey (HashMap key value) -> HashMap key value -> HashMap key value unionWith :: (MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> HashMap key value -> HashMap key value -> HashMap key value unionWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> HashMap key value -> HashMap key value -> HashMap key value unionsWith :: (MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> [HashMap key value] -> HashMap key value mapWithKey :: (ContainerKey (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> HashMap key value -> HashMap key value omapKeysWith :: (MapValue (HashMap key value) -> MapValue (HashMap key value) -> MapValue (HashMap key value)) -> (ContainerKey (HashMap key value) -> ContainerKey (HashMap key value)) -> HashMap key value -> HashMap key value filterMap :: (MapValue (HashMap key value) -> Bool) -> HashMap key value -> HashMap key value
(Eq key, Hashable key) => SetContainer (HashMap key value)
Instance details Defined in Data.Containers Associated Types type ContainerKey (HashMap key value) Methods member :: ContainerKey (HashMap key value) -> HashMap key value -> Bool notMember :: ContainerKey (HashMap key value) -> HashMap key value -> Bool union :: HashMap key value -> HashMap key value -> HashMap key value unions :: (MonoFoldable mono, Element mono ~ HashMap key value) => mono -> HashMap key value difference :: HashMap key value -> HashMap key value -> HashMap key value intersection :: HashMap key value -> HashMap key value -> HashMap key value keys :: HashMap key value -> [ContainerKey (HashMap key value)]
(t ~ HashMap k' a', Hashable k, Eq k) => Rewrapped (HashMap k a) t
Instance details Defined in Control.Lens.Wrapped
c ~ d => Each (HashMap c a) (HashMap d b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (HashMap c a) (HashMap d b) a b
type BPMKeyConstraint HashMap key
Instance details Defined in Data.Containers type BPMKeyConstraint HashMap key = (Hashable key, Eq key)
type Key (HashMap k)
Instance details Defined in Data.Key type Key (HashMap k) = k
type Dom (HashMap k) a
Instance details Defined in Control.Subcategory.Functor type Dom (HashMap k) a = ()
type Item (HashMap k v)
Instance details Defined in Data.HashMap.Internal type Item (HashMap k v) = (k, v)
type Index (HashMap k a)
Instance details Defined in Control.Lens.At type Index (HashMap k a) = k
type Unwrapped (HashMap k a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (HashMap k a) = [(k, a)]
type Element (HashMap k v)
Instance details Defined in Data.MonoTraversable type Element (HashMap k v) = v
type IxValue (HashMap k a)
Instance details Defined in Control.Lens.At type IxValue (HashMap k a) = a
type KeySet (HashMap k v)
Instance details Defined in Data.Containers type KeySet (HashMap k v) = HashSet k
type MapValue (HashMap key value)
Instance details Defined in Data.Containers type MapValue (HashMap key value) = value
type ContainerKey (HashMap key value)
Instance details Defined in Data.Containers type ContainerKey (HashMap key value) = key

class Hashable a where #

Minimal complete definition

Nothing

Methods

hashWithSalt :: Int -> a -> Int #

hash :: a -> Int #

Instances

Instances details

Hashable Bool
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Bool -> Int # hash :: Bool -> Int #
Hashable Char
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Char -> Int # hash :: Char -> Int #
Hashable Double
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Double -> Int # hash :: Double -> Int #
Hashable Float
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Float -> Int # hash :: Float -> Int #
Hashable Int
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int -> Int # hash :: Int -> Int #
Hashable Int8
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int8 -> Int # hash :: Int8 -> Int #
Hashable Int16
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int16 -> Int # hash :: Int16 -> Int #
Hashable Int32
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int32 -> Int # hash :: Int32 -> Int #
Hashable Int64
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Int64 -> Int # hash :: Int64 -> Int #
Hashable Integer
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Integer -> Int # hash :: Integer -> Int #
Hashable Natural
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Natural -> Int # hash :: Natural -> Int #
Hashable Ordering
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ordering -> Int # hash :: Ordering -> Int #
Hashable Word
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word -> Int # hash :: Word -> Int #
Hashable Word8
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word8 -> Int # hash :: Word8 -> Int #
Hashable Word16
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word16 -> Int # hash :: Word16 -> Int #
Hashable Word32
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word32 -> Int # hash :: Word32 -> Int #
Hashable Word64
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Word64 -> Int # hash :: Word64 -> Int #
Hashable SomeTypeRep
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> SomeTypeRep -> Int # hash :: SomeTypeRep -> Int #
Hashable ()
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> () -> Int # hash :: () -> Int #
Hashable Text
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Text -> Int # hash :: Text -> Int #
Hashable ByteString
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> ByteString -> Int # hash :: ByteString -> Int #
Hashable Void
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Void -> Int # hash :: Void -> Int #
Hashable Unique
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Unique -> Int # hash :: Unique -> Int #
Hashable Version
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Version -> Int # hash :: Version -> Int #
Hashable ThreadId
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> ThreadId -> Int # hash :: ThreadId -> Int #
Hashable WordPtr
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> WordPtr -> Int # hash :: WordPtr -> Int #
Hashable IntPtr
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> IntPtr -> Int # hash :: IntPtr -> Int #
Hashable Fingerprint
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Fingerprint -> Int # hash :: Fingerprint -> Int #
Hashable ShortByteString
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> ShortByteString -> Int # hash :: ShortByteString -> Int #
Hashable ByteString
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> ByteString -> Int # hash :: ByteString -> Int #
Hashable BigNat
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> BigNat -> Int # hash :: BigNat -> Int #
Hashable Text
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Text -> Int # hash :: Text -> Int #
Hashable a => Hashable [a]
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> [a] -> Int # hash :: [a] -> Int #
Hashable a => Hashable (Maybe a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Maybe a -> Int # hash :: Maybe a -> Int #
Hashable a => Hashable (Ratio a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ratio a -> Int # hash :: Ratio a -> Int #
Hashable (Ptr a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Ptr a -> Int # hash :: Ptr a -> Int #
Hashable (FunPtr a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> FunPtr a -> Int # hash :: FunPtr a -> Int #
Hashable a => Hashable (HashSet a)
Instance details Defined in Data.HashSet.Internal Methods hashWithSalt :: Int -> HashSet a -> Int # hash :: HashSet a -> Int #
Hashable a => Hashable (Complex a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Complex a -> Int # hash :: Complex a -> Int #
Hashable a => Hashable (Min a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Min a -> Int # hash :: Min a -> Int #
Hashable a => Hashable (Max a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Max a -> Int # hash :: Max a -> Int #
Hashable a => Hashable (First a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> First a -> Int # hash :: First a -> Int #
Hashable a => Hashable (Last a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Last a -> Int # hash :: Last a -> Int #
Hashable a => Hashable (WrappedMonoid a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> WrappedMonoid a -> Int # hash :: WrappedMonoid a -> Int #
Hashable a => Hashable (Option a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Option a -> Int # hash :: Option a -> Int #
Hashable (StableName a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> StableName a -> Int # hash :: StableName a -> Int #
Hashable a => Hashable (Identity a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Identity a -> Int # hash :: Identity a -> Int #
Hashable a => Hashable (NonEmpty a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> NonEmpty a -> Int # hash :: NonEmpty a -> Int #
Hashable (Hashed a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Hashed a -> Int # hash :: Hashed a -> Int #
(DecidableZero r, Hashable r) => Hashable (Unipol r) Source #
Instance details Defined in Algebra.Ring.Polynomial.Univariate Methods hashWithSalt :: Int -> Unipol r -> Int # hash :: Unipol r -> Int #
(Hashable a, Hashable b) => Hashable (Either a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Either a b -> Int # hash :: Either a b -> Int #
Hashable (TypeRep a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> TypeRep a -> Int # hash :: TypeRep a -> Int #
(Hashable a1, Hashable a2) => Hashable (a1, a2)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2) -> Int # hash :: (a1, a2) -> Int #
(Hashable k, Hashable v) => Hashable (HashMap k v)
Instance details Defined in Data.HashMap.Internal Methods hashWithSalt :: Int -> HashMap k v -> Int # hash :: HashMap k v -> Int #
Hashable (Fixed a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Fixed a -> Int # hash :: Fixed a -> Int #
Hashable a => Hashable (Arg a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Arg a b -> Int # hash :: Arg a b -> Int #
Hashable (Proxy a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Proxy a -> Int # hash :: Proxy a -> Int #
(Hashable a, Hashable b) => Hashable (These a b)
Instance details Defined in Data.These Methods hashWithSalt :: Int -> These a b -> Int # hash :: These a b -> Int #
(Hashable a1, Hashable a2, Hashable a3) => Hashable (a1, a2, a3)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2, a3) -> Int # hash :: (a1, a2, a3) -> Int #
Hashable a => Hashable (Const a b)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Const a b -> Int # hash :: Const a b -> Int #
Hashable (OrderedMonomial ordering n)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods hashWithSalt :: Int -> OrderedMonomial ordering n -> Int # hash :: OrderedMonomial ordering n -> Int #
Hashable (f a) => Hashable (Sized f n a)
Instance details Defined in Data.Sized.Internal Methods hashWithSalt :: Int -> Sized f n a -> Int # hash :: Sized f n a -> Int #
Hashable (f a) => Hashable (Flipped f a n)
Instance details Defined in Data.Sized.Flipped Methods hashWithSalt :: Int -> Flipped f a n -> Int # hash :: Flipped f a n -> Int #
(Hashable a1, Hashable a2, Hashable a3, Hashable a4) => Hashable (a1, a2, a3, a4)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2, a3, a4) -> Int # hash :: (a1, a2, a3, a4) -> Int #
(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Product f g a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Product f g a -> Int # hash :: Product f g a -> Int #
(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Sum f g a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Sum f g a -> Int # hash :: Sum f g a -> Int #
Hashable r => Hashable (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods hashWithSalt :: Int -> OrderedPolynomial r ord n -> Int # hash :: OrderedPolynomial r ord n -> Int #
(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5) => Hashable (a1, a2, a3, a4, a5)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2, a3, a4, a5) -> Int # hash :: (a1, a2, a3, a4, a5) -> Int #
(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Compose f g a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Compose f g a -> Int # hash :: Compose f g a -> Int #
(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6) => Hashable (a1, a2, a3, a4, a5, a6)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2, a3, a4, a5, a6) -> Int # hash :: (a1, a2, a3, a4, a5, a6) -> Int #
(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6, Hashable a7) => Hashable (a1, a2, a3, a4, a5, a6, a7)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> (a1, a2, a3, a4, a5, a6, a7) -> Int # hash :: (a1, a2, a3, a4, a5, a6, a7) -> Int #

type UVector = Vector #

type SVector = Vector #

type LText = Text #

type LByteString = ByteString #

terror :: HasCallStack => Text -> a #

print :: (MonadIO m, Show a) => a -> m () #

equating :: Eq a => (b -> a) -> b -> b -> Bool #

tshow :: Show a => a -> Text #

textToString :: Text -> String #

readMay :: Read a => Text -> Maybe a #

readLn :: (MonadIO m, Read a) => m a #

readIO :: (MonadIO m, Read a) => Text -> m a #

putChar :: MonadIO m => Char -> m () #

map :: Functor f => (a -> b) -> f a -> f b #

ltextToString :: LText -> String #

intercalate :: Monoid w => w -> [w] -> w #

getChar :: MonadIO m => m Char #

fpToText :: FilePath -> Text #

fpToString :: FilePath -> String #

fpFromText :: Text -> FilePath #

empty :: Monoid w => w #

decodeUtf8 :: ByteString -> Text #

concat :: Monoid w => [w] -> w #

appendFile :: MonadIO m => FilePath -> Text -> m () #

(++) :: Monoid w => w -> w -> w #

data Text #

A space efficient, packed, unboxed Unicode text type.

Instances

Instances details

Hashable Text
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Text -> Int # hash :: Text -> Int #
Ixed Text
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text)
AsEmpty Text
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text ()
Reversing Text
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text
GrowingAppend Text
Instance details Defined in Data.MonoTraversable
MonoFoldable Text
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element Text -> m) -> Text -> m ofoldr :: (Element Text -> b -> b) -> b -> Text -> b ofoldl' :: (a -> Element Text -> a) -> a -> Text -> a otoList :: Text -> [Element Text] oall :: (Element Text -> Bool) -> Text -> Bool oany :: (Element Text -> Bool) -> Text -> Bool onull :: Text -> Bool olength :: Text -> Int olength64 :: Text -> Int64 ocompareLength :: Integral i => Text -> i -> Ordering otraverse_ :: Applicative f => (Element Text -> f b) -> Text -> f () ofor_ :: Applicative f => Text -> (Element Text -> f b) -> f () omapM_ :: Applicative m => (Element Text -> m ()) -> Text -> m () oforM_ :: Applicative m => Text -> (Element Text -> m ()) -> m () ofoldlM :: Monad m => (a -> Element Text -> m a) -> a -> Text -> m a ofoldMap1Ex :: Semigroup m => (Element Text -> m) -> Text -> m ofoldr1Ex :: (Element Text -> Element Text -> Element Text) -> Text -> Element Text ofoldl1Ex' :: (Element Text -> Element Text -> Element Text) -> Text -> Element Text headEx :: Text -> Element Text lastEx :: Text -> Element Text unsafeHead :: Text -> Element Text unsafeLast :: Text -> Element Text maximumByEx :: (Element Text -> Element Text -> Ordering) -> Text -> Element Text minimumByEx :: (Element Text -> Element Text -> Ordering) -> Text -> Element Text oelem :: Element Text -> Text -> Bool onotElem :: Element Text -> Text -> Bool
MonoFunctor Text
Instance details Defined in Data.MonoTraversable Methods omap :: (Element Text -> Element Text) -> Text -> Text
MonoPointed Text
Instance details Defined in Data.MonoTraversable Methods opoint :: Element Text -> Text
MonoTraversable Text
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element Text -> f (Element Text)) -> Text -> f Text omapM :: Applicative m => (Element Text -> m (Element Text)) -> Text -> m Text
MonoZip Text
Instance details Defined in Data.Containers Methods ozipWith :: (Element Text -> Element Text -> Element Text) -> Text -> Text -> Text ozip :: Text -> Text -> [(Element Text, Element Text)] ounzip :: [(Element Text, Element Text)] -> (Text, Text)
IsSequence Text
Instance details Defined in Data.Sequences Methods fromList :: [Element Text] -> Text lengthIndex :: Text -> Index Text break :: (Element Text -> Bool) -> Text -> (Text, Text) span :: (Element Text -> Bool) -> Text -> (Text, Text) dropWhile :: (Element Text -> Bool) -> Text -> Text takeWhile :: (Element Text -> Bool) -> Text -> Text splitAt :: Index Text -> Text -> (Text, Text) unsafeSplitAt :: Index Text -> Text -> (Text, Text) take :: Index Text -> Text -> Text unsafeTake :: Index Text -> Text -> Text drop :: Index Text -> Text -> Text unsafeDrop :: Index Text -> Text -> Text dropEnd :: Index Text -> Text -> Text partition :: (Element Text -> Bool) -> Text -> (Text, Text) uncons :: Text -> Maybe (Element Text, Text) unsnoc :: Text -> Maybe (Text, Element Text) filter :: (Element Text -> Bool) -> Text -> Text filterM :: Monad m => (Element Text -> m Bool) -> Text -> m Text replicate :: Index Text -> Element Text -> Text replicateM :: Monad m => Index Text -> m (Element Text) -> m Text groupBy :: (Element Text -> Element Text -> Bool) -> Text -> [Text] groupAllOn :: Eq b => (Element Text -> b) -> Text -> [Text] subsequences :: Text -> [Text] permutations :: Text -> [Text] tailEx :: Text -> Text tailMay :: Text -> Maybe Text initEx :: Text -> Text initMay :: Text -> Maybe Text unsafeTail :: Text -> Text unsafeInit :: Text -> Text index :: Text -> Index Text -> Maybe (Element Text) indexEx :: Text -> Index Text -> Element Text unsafeIndex :: Text -> Index Text -> Element Text splitWhen :: (Element Text -> Bool) -> Text -> [Text]
SemiSequence Text
Instance details Defined in Data.Sequences Associated Types type Index Text Methods intersperse :: Element Text -> Text -> Text reverse :: Text -> Text find :: (Element Text -> Bool) -> Text -> Maybe (Element Text) sortBy :: (Element Text -> Element Text -> Ordering) -> Text -> Text cons :: Element Text -> Text -> Text snoc :: Text -> Element Text -> Text
Textual Text
Instance details Defined in Data.Sequences Methods words :: Text -> [Text] unwords :: (Element seq ~ Text, MonoFoldable seq) => seq -> Text lines :: Text -> [Text] unlines :: (Element seq ~ Text, MonoFoldable seq) => seq -> Text toLower :: Text -> Text toUpper :: Text -> Text toCaseFold :: Text -> Text breakWord :: Text -> (Text, Text) breakLine :: Text -> (Text, Text)
Strict Text Text
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' Text Text0
LazySequence Text Text
Instance details Defined in Data.Sequences Methods toChunks :: Text -> [Text0] fromChunks :: [Text0] -> Text toStrict :: Text -> Text0 fromStrict :: Text0 -> Text
Utf8 Text ByteString
Instance details Defined in Data.Sequences Methods encodeUtf8 :: Text -> ByteString decodeUtf8 :: ByteString -> Text
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text)
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char)
(a ~ Char, b ~ Char) => Each Text Text a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b
type Item Text
Instance details Defined in Data.Text type Item Text = Char
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int
type Element Text
Instance details Defined in Data.MonoTraversable type Element Text = Char
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type Index Text
Instance details Defined in Data.Sequences type Index Text = Int

encodeUtf8 :: Text -> ByteString #

Encode text using UTF-8 encoding.

(<.>) :: FilePath -> String -> FilePath infixr 7 #

Add an extension, even if there is already one there, equivalent to addExtension.

"/directory/path" <.> "ext" == "/directory/path.ext"
"/directory/path" <.> ".ext" == "/directory/path.ext"

(</>) :: FilePath -> FilePath -> FilePath infixr 5 #

Combine two paths with a path separator. If the second path starts with a path separator or a drive letter, then it returns the second. The intention is that readFile (dir </> file) will access the same file as setCurrentDirectory dir; readFile file.

Posix:   "/directory" </> "file.ext" == "/directory/file.ext"
Windows: "/directory" </> "file.ext" == "/directory\\file.ext"
         "directory" </> "/file.ext" == "/file.ext"
Valid x => (takeDirectory x </> takeFileName x) `equalFilePath` x

Combined:

Posix:   "/" </> "test" == "/test"
Posix:   "home" </> "bob" == "home/bob"
Posix:   "x:" </> "foo" == "x:/foo"
Windows: "C:\\foo" </> "bar" == "C:\\foo\\bar"
Windows: "home" </> "bob" == "home\\bob"

Not combined:

Posix:   "home" </> "/bob" == "/bob"
Windows: "home" </> "C:\\bob" == "C:\\bob"

Not combined (tricky):

On Windows, if a filepath starts with a single slash, it is relative to the root of the current drive. In [1], this is (confusingly) referred to as an absolute path. The current behavior of </> is to never combine these forms.

Windows: "home" </> "/bob" == "/bob"
Windows: "home" </> "\\bob" == "\\bob"
Windows: "C:\\home" </> "\\bob" == "\\bob"

On Windows, from [1]: "If a file name begins with only a disk designator but not the backslash after the colon, it is interpreted as a relative path to the current directory on the drive with the specified letter." The current behavior of </> is to never combine these forms.

Windows: "D:\\foo" </> "C:bar" == "C:bar"
Windows: "C:\\foo" </> "C:bar" == "C:bar"

data Set a #

A set of values a.

Instances

Instances details

Foldable Set	Folds in order of increasing key.
Instance details Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # toList :: Set a -> [a] # null :: Set a -> Bool # length :: Set a -> Int # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # minimum :: Ord a => Set a -> a # sum :: Num a => Set a -> a # product :: Num a => Set a -> a #
Eq1 Set	Since: containers-0.5.9
Instance details Defined in Data.Set.Internal Methods liftEq :: (a -> b -> Bool) -> Set a -> Set b -> Bool #
Ord1 Set	Since: containers-0.5.9
Instance details Defined in Data.Set.Internal Methods liftCompare :: (a -> b -> Ordering) -> Set a -> Set b -> Ordering #
Show1 Set	Since: containers-0.5.9
Instance details Defined in Data.Set.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Set a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Set a] -> ShowS #
CFoldable Set
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom Set a, Monoid w) => (a -> w) -> Set a -> w cfoldMap' :: (Dom Set a, Monoid m) => (a -> m) -> Set a -> m cfold :: (Dom Set w, Monoid w) => Set w -> w cfoldr :: Dom Set a => (a -> b -> b) -> b -> Set a -> b cfoldlM :: (Monad m, Dom Set b) => (a -> b -> m a) -> a -> Set b -> m a cfoldlM' :: (Monad m, Dom Set b) => (a -> b -> m a) -> a -> Set b -> m a cfoldrM :: (Monad m, Dom Set a) => (a -> b -> m b) -> b -> Set a -> m b cfoldrM' :: (Monad m, Dom Set a) => (a -> b -> m b) -> b -> Set a -> m b cfoldl :: Dom Set a => (b -> a -> b) -> b -> Set a -> b cfoldr' :: Dom Set a => (a -> b -> b) -> b -> Set a -> b cfoldl' :: Dom Set a => (b -> a -> b) -> b -> Set a -> b cbasicToList :: Dom Set a => Set a -> [a] cfoldr1 :: Dom Set a => (a -> a -> a) -> Set a -> a cfoldl1 :: Dom Set a => (a -> a -> a) -> Set a -> a cindex :: Dom Set a => Set a -> Int -> a cnull :: Dom Set a => Set a -> Bool clength :: Dom Set a => Set a -> Int cany :: Dom Set a => (a -> Bool) -> Set a -> Bool call :: Dom Set a => (a -> Bool) -> Set a -> Bool celem :: (Eq a, Dom Set a) => a -> Set a -> Bool cnotElem :: (Eq a, Dom Set a) => a -> Set a -> Bool cminimum :: (Ord a, Dom Set a) => Set a -> a cmaximum :: (Ord a, Dom Set a) => Set a -> a csum :: (Num a, Dom Set a) => Set a -> a cproduct :: (Num a, Dom Set a) => Set a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom Set a, Dom g b) => (a -> g b) -> Set a -> g () ctraverse_ :: (Applicative g, Dom Set a) => (a -> g b) -> Set a -> g () clast :: Dom Set a => Set a -> a chead :: Dom Set a => Set a -> a cfind :: Dom Set a => (a -> Bool) -> Set a -> Maybe a cfindIndex :: Dom Set a => (a -> Bool) -> Set a -> Maybe Int cfindIndices :: Dom Set a => (a -> Bool) -> Set a -> [Int] celemIndex :: (Dom Set a, Eq a) => a -> Set a -> Maybe Int celemIndices :: (Dom Set a, Eq a) => a -> Set a -> [Int]
CFunctor Set
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom Set a, Dom Set b) => (a -> b) -> Set a -> Set b (<$:) :: (Dom Set a, Dom Set b) => a -> Set b -> Set a
CPointed Set
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom Set a => a -> Set a
CTraversable Set
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom Set a, Dom Set b, Applicative g) => (a -> g b) -> Set a -> g (Set b)
Constrained Set
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom Set a
(Semiring r, Band r, Ord a) => IdempotentAlgebra r (Set a)
Instance details Defined in Numeric.Algebra.Idempotent
(Commutative r, Semiring r, Ord a) => CommutativeAlgebra r (Set a)
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a) => CocommutativeCoalgebra r (Set a)
Instance details Defined in Numeric.Algebra.Commutative
(Semiring r, Ord a) => Coalgebra r (Set a)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Set a -> r) -> Set a -> Set a -> r #
(Semiring r, Ord a) => Algebra r (Set a)
Instance details Defined in Numeric.Algebra.Class Methods mult :: (Set a -> Set a -> r) -> Set a -> r #
(Semiring r, Band r, Ord c) => IdempotentCoalgebra r (Set c)
Instance details Defined in Numeric.Algebra.Idempotent
Ord a => IsList (Set a)	Since: containers-0.5.6.2
Instance details Defined in Data.Set.Internal Associated Types type Item (Set a) # Methods fromList :: [Item (Set a)] -> Set a # fromListN :: Int -> [Item (Set a)] -> Set a # toList :: Set a -> [Item (Set a)] #
Eq a => Eq (Set a)
Instance details Defined in Data.Set.Internal Methods (==) :: Set a -> Set a -> Bool # (/=) :: Set a -> Set a -> Bool #
(Data a, Ord a) => Data (Set a)
Instance details Defined in Data.Set.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Set a -> c (Set a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Set a) # toConstr :: Set a -> Constr # dataTypeOf :: Set a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Set a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Set a)) # gmapT :: (forall b. Data b => b -> b) -> Set a -> Set a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r # gmapQ :: (forall d. Data d => d -> u) -> Set a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Set a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) #
Ord a => Ord (Set a)
Instance details Defined in Data.Set.Internal Methods compare :: Set a -> Set a -> Ordering # (<) :: Set a -> Set a -> Bool # (<=) :: Set a -> Set a -> Bool # (>) :: Set a -> Set a -> Bool # (>=) :: Set a -> Set a -> Bool # max :: Set a -> Set a -> Set a # min :: Set a -> Set a -> Set a #
(Read a, Ord a) => Read (Set a)
Instance details Defined in Data.Set.Internal Methods readsPrec :: Int -> ReadS (Set a) # readList :: ReadS [Set a] # readPrec :: ReadPrec (Set a) # readListPrec :: ReadPrec [Set a] #
Show a => Show (Set a)
Instance details Defined in Data.Set.Internal Methods showsPrec :: Int -> Set a -> ShowS # show :: Set a -> String # showList :: [Set a] -> ShowS #
Ord a => Semigroup (Set a)	Since: containers-0.5.7
Instance details Defined in Data.Set.Internal Methods (<>) :: Set a -> Set a -> Set a # sconcat :: NonEmpty (Set a) -> Set a # stimes :: Integral b => b -> Set a -> Set a #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Ord a => LocallyFiniteOrder (Set a)
Instance details Defined in Numeric.Order.LocallyFinite Methods range :: Set a -> Set a -> [Set a] rangeSize :: Set a -> Set a -> Natural moebiusInversion :: Ring r => Set a -> Set a -> r
NFData a => NFData (Set a)
Instance details Defined in Data.Set.Internal Methods rnf :: Set a -> () #
Ord a => Wrapped (Set a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Set a) Methods _Wrapped' :: Iso' (Set a) (Unwrapped (Set a))
Ord k => At (Set k)
Instance details Defined in Control.Lens.At Methods at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k)))
Ord a => Contains (Set a)
Instance details Defined in Control.Lens.At Methods contains :: Index (Set a) -> Lens' (Set a) Bool
Ord k => Ixed (Set k)
Instance details Defined in Control.Lens.At Methods ix :: Index (Set k) -> Traversal' (Set k) (IxValue (Set k))
AsEmpty (Set a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Set a) ()
Ord v => GrowingAppend (Set v)
Instance details Defined in Data.MonoTraversable
Ord e => MonoFoldable (Set e)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Set e) -> m) -> Set e -> m ofoldr :: (Element (Set e) -> b -> b) -> b -> Set e -> b ofoldl' :: (a -> Element (Set e) -> a) -> a -> Set e -> a otoList :: Set e -> [Element (Set e)] oall :: (Element (Set e) -> Bool) -> Set e -> Bool oany :: (Element (Set e) -> Bool) -> Set e -> Bool onull :: Set e -> Bool olength :: Set e -> Int olength64 :: Set e -> Int64 ocompareLength :: Integral i => Set e -> i -> Ordering otraverse_ :: Applicative f => (Element (Set e) -> f b) -> Set e -> f () ofor_ :: Applicative f => Set e -> (Element (Set e) -> f b) -> f () omapM_ :: Applicative m => (Element (Set e) -> m ()) -> Set e -> m () oforM_ :: Applicative m => Set e -> (Element (Set e) -> m ()) -> m () ofoldlM :: Monad m => (a -> Element (Set e) -> m a) -> a -> Set e -> m a ofoldMap1Ex :: Semigroup m => (Element (Set e) -> m) -> Set e -> m ofoldr1Ex :: (Element (Set e) -> Element (Set e) -> Element (Set e)) -> Set e -> Element (Set e) ofoldl1Ex' :: (Element (Set e) -> Element (Set e) -> Element (Set e)) -> Set e -> Element (Set e) headEx :: Set e -> Element (Set e) lastEx :: Set e -> Element (Set e) unsafeHead :: Set e -> Element (Set e) unsafeLast :: Set e -> Element (Set e) maximumByEx :: (Element (Set e) -> Element (Set e) -> Ordering) -> Set e -> Element (Set e) minimumByEx :: (Element (Set e) -> Element (Set e) -> Ordering) -> Set e -> Element (Set e) oelem :: Element (Set e) -> Set e -> Bool onotElem :: Element (Set e) -> Set e -> Bool
MonoPointed (Set a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (Set a) -> Set a
Ord element => IsSet (Set element)
Instance details Defined in Data.Containers Methods insertSet :: Element (Set element) -> Set element -> Set element deleteSet :: Element (Set element) -> Set element -> Set element singletonSet :: Element (Set element) -> Set element setFromList :: [Element (Set element)] -> Set element setToList :: Set element -> [Element (Set element)] filterSet :: (Element (Set element) -> Bool) -> Set element -> Set element
Ord element => SetContainer (Set element)
Instance details Defined in Data.Containers Associated Types type ContainerKey (Set element) Methods member :: ContainerKey (Set element) -> Set element -> Bool notMember :: ContainerKey (Set element) -> Set element -> Bool union :: Set element -> Set element -> Set element unions :: (MonoFoldable mono, Element mono ~ Set element) => mono -> Set element difference :: Set element -> Set element -> Set element intersection :: Set element -> Set element -> Set element keys :: Set element -> [ContainerKey (Set element)]
(t ~ Set a', Ord a) => Rewrapped (Set a) t
Instance details Defined in Control.Lens.Wrapped
type Dom Set a
Instance details Defined in Control.Subcategory.Functor type Dom Set a = Ord a
type Item (Set a)
Instance details Defined in Data.Set.Internal type Item (Set a) = a
type Index (Set a)
Instance details Defined in Control.Lens.At type Index (Set a) = a
type Unwrapped (Set a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Set a) = [a]
type Element (Set e)
Instance details Defined in Data.MonoTraversable type Element (Set e) = e
type IxValue (Set k)
Instance details Defined in Control.Lens.At type IxValue (Set k) = ()
type ContainerKey (Set element)
Instance details Defined in Data.Containers type ContainerKey (Set element) = element

data Seq a #

General-purpose finite sequences.

Instances

Instances details

Monad Seq
Instance details Defined in Data.Sequence.Internal Methods (>>=) :: Seq a -> (a -> Seq b) -> Seq b # (>>) :: Seq a -> Seq b -> Seq b # return :: a -> Seq a #
Functor Seq
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b # (<$) :: a -> Seq b -> Seq a #
MonadFix Seq	Since: containers-0.5.11
Instance details Defined in Data.Sequence.Internal Methods mfix :: (a -> Seq a) -> Seq a #
Applicative Seq	Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods pure :: a -> Seq a # (<>) :: Seq (a -> b) -> Seq a -> Seq b # liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # (>) :: Seq a -> Seq b -> Seq b # (<*) :: Seq a -> Seq b -> Seq a #
Foldable Seq
Instance details Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # toList :: Seq a -> [a] # null :: Seq a -> Bool # length :: Seq a -> Int # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # minimum :: Ord a => Seq a -> a # sum :: Num a => Seq a -> a # product :: Num a => Seq a -> a #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
MonadPlus Seq
Instance details Defined in Data.Sequence.Internal Methods mzero :: Seq a # mplus :: Seq a -> Seq a -> Seq a #
Eq1 Seq	Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftEq :: (a -> b -> Bool) -> Seq a -> Seq b -> Bool #
Ord1 Seq	Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftCompare :: (a -> b -> Ordering) -> Seq a -> Seq b -> Ordering #
Read1 Seq	Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Seq a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Seq a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Seq a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Seq a] #
Show1 Seq	Since: containers-0.5.9
Instance details Defined in Data.Sequence.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Seq a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Seq a] -> ShowS #
MonadZip Seq	`mzipWith` = `zipWith` `munzip` = `unzip`
Instance details Defined in Data.Sequence.Internal Methods mzip :: Seq a -> Seq b -> Seq (a, b) # mzipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # munzip :: Seq (a, b) -> (Seq a, Seq b) #
Alternative Seq	Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods empty :: Seq a # (<\|>) :: Seq a -> Seq a -> Seq a # some :: Seq a -> Seq [a] # many :: Seq a -> Seq [a] #
CFreeMonoid Seq
Instance details Defined in Control.Subcategory.Foldable Methods cbasicFromList :: Dom Seq a => [a] -> Seq a ccons :: Dom Seq a => a -> Seq a -> Seq a csnoc :: Dom Seq a => Seq a -> a -> Seq a cfromListN :: Dom Seq a => Int -> [a] -> Seq a ctake :: Dom Seq a => Int -> Seq a -> Seq a cdrop :: Dom Seq a => Int -> Seq a -> Seq a cinit :: Dom Seq a => Seq a -> Seq a ctail :: Dom Seq a => Seq a -> Seq a csplitAt :: Dom Seq a => Int -> Seq a -> (Seq a, Seq a) creplicate :: Dom Seq a => Int -> a -> Seq a cgenerate :: Dom Seq a => Int -> (Int -> a) -> Seq a cgenerateM :: (Dom Seq a, Monad m) => Int -> (Int -> m a) -> m (Seq a) cgenerateA :: (Dom Seq a, Applicative g) => Int -> (Int -> g a) -> g (Seq a) cuncons :: Dom Seq a => Seq a -> Maybe (a, Seq a) cunsnoc :: Dom Seq a => Seq a -> Maybe (Seq a, a) creverse :: Dom Seq a => Seq a -> Seq a cintersperse :: Dom Seq a => a -> Seq a -> Seq a cnub :: (Dom Seq a, Eq a) => Seq a -> Seq a cnubOrd :: (Dom Seq a, Ord a) => Seq a -> Seq a csort :: (Dom Seq a, Ord a) => Seq a -> Seq a csortBy :: Dom Seq a => (a -> a -> Ordering) -> Seq a -> Seq a cinsert :: (Dom Seq a, Ord a) => a -> Seq a -> Seq a cinsertBy :: Dom Seq a => (a -> a -> Ordering) -> a -> Seq a -> Seq a ctakeWhile :: Dom Seq a => (a -> Bool) -> Seq a -> Seq a cdropWhile :: Dom Seq a => (a -> Bool) -> Seq a -> Seq a cspan :: Dom Seq a => (a -> Bool) -> Seq a -> (Seq a, Seq a) cbreak :: Dom Seq a => (a -> Bool) -> Seq a -> (Seq a, Seq a) cfilter :: Dom Seq a => (a -> Bool) -> Seq a -> Seq a cpartition :: Dom Seq a => (a -> Bool) -> Seq a -> (Seq a, Seq a)
CFoldable Seq
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom Seq a, Monoid w) => (a -> w) -> Seq a -> w cfoldMap' :: (Dom Seq a, Monoid m) => (a -> m) -> Seq a -> m cfold :: (Dom Seq w, Monoid w) => Seq w -> w cfoldr :: Dom Seq a => (a -> b -> b) -> b -> Seq a -> b cfoldlM :: (Monad m, Dom Seq b) => (a -> b -> m a) -> a -> Seq b -> m a cfoldlM' :: (Monad m, Dom Seq b) => (a -> b -> m a) -> a -> Seq b -> m a cfoldrM :: (Monad m, Dom Seq a) => (a -> b -> m b) -> b -> Seq a -> m b cfoldrM' :: (Monad m, Dom Seq a) => (a -> b -> m b) -> b -> Seq a -> m b cfoldl :: Dom Seq a => (b -> a -> b) -> b -> Seq a -> b cfoldr' :: Dom Seq a => (a -> b -> b) -> b -> Seq a -> b cfoldl' :: Dom Seq a => (b -> a -> b) -> b -> Seq a -> b cbasicToList :: Dom Seq a => Seq a -> [a] cfoldr1 :: Dom Seq a => (a -> a -> a) -> Seq a -> a cfoldl1 :: Dom Seq a => (a -> a -> a) -> Seq a -> a cindex :: Dom Seq a => Seq a -> Int -> a cnull :: Dom Seq a => Seq a -> Bool clength :: Dom Seq a => Seq a -> Int cany :: Dom Seq a => (a -> Bool) -> Seq a -> Bool call :: Dom Seq a => (a -> Bool) -> Seq a -> Bool celem :: (Eq a, Dom Seq a) => a -> Seq a -> Bool cnotElem :: (Eq a, Dom Seq a) => a -> Seq a -> Bool cminimum :: (Ord a, Dom Seq a) => Seq a -> a cmaximum :: (Ord a, Dom Seq a) => Seq a -> a csum :: (Num a, Dom Seq a) => Seq a -> a cproduct :: (Num a, Dom Seq a) => Seq a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom Seq a, Dom g b) => (a -> g b) -> Seq a -> g () ctraverse_ :: (Applicative g, Dom Seq a) => (a -> g b) -> Seq a -> g () clast :: Dom Seq a => Seq a -> a chead :: Dom Seq a => Seq a -> a cfind :: Dom Seq a => (a -> Bool) -> Seq a -> Maybe a cfindIndex :: Dom Seq a => (a -> Bool) -> Seq a -> Maybe Int cfindIndices :: Dom Seq a => (a -> Bool) -> Seq a -> [Int] celemIndex :: (Dom Seq a, Eq a) => a -> Seq a -> Maybe Int celemIndices :: (Dom Seq a, Eq a) => a -> Seq a -> [Int]
CZip Seq
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom Seq a, Dom Seq b, Dom Seq c) => (a -> b -> c) -> Seq a -> Seq b -> Seq c czip :: (Dom Seq a, Dom Seq b, Dom Seq (a, b)) => Seq a -> Seq b -> Seq (a, b)
CFunctor Seq
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom Seq a, Dom Seq b) => (a -> b) -> Seq a -> Seq b (<$:) :: (Dom Seq a, Dom Seq b) => a -> Seq b -> Seq a
CPointed Seq
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom Seq a => a -> Seq a
CTraversable Seq
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom Seq a, Dom Seq b, Applicative g) => (a -> g b) -> Seq a -> g (Seq b)
CUnzip Seq
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom Seq (a, b), Dom Seq a, Dom Seq b) => Seq (a, b) -> (Seq a, Seq b) cunzipWith :: (Dom Seq c, Dom Seq a, Dom Seq b) => (c -> (a, b)) -> Seq c -> (Seq a, Seq b)
Adjustable Seq
Instance details Defined in Data.Key Methods adjust :: (a -> a) -> Key Seq -> Seq a -> Seq a replace :: Key Seq -> a -> Seq a -> Seq a
Apply Seq
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Seq (a -> b) -> Seq a -> Seq b (.>) :: Seq a -> Seq b -> Seq b (<.) :: Seq a -> Seq b -> Seq a liftF2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c
Bind Seq
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Seq a -> (a -> Seq b) -> Seq b join :: Seq (Seq a) -> Seq a
FoldableWithKey Seq
Instance details Defined in Data.Key Methods toKeyedList :: Seq a -> [(Key Seq, a)] foldMapWithKey :: Monoid m => (Key Seq -> a -> m) -> Seq a -> m foldrWithKey :: (Key Seq -> a -> b -> b) -> b -> Seq a -> b foldlWithKey :: (b -> Key Seq -> a -> b) -> b -> Seq a -> b
Indexable Seq
Instance details Defined in Data.Key Methods index :: Seq a -> Key Seq -> a
Keyed Seq
Instance details Defined in Data.Key Methods mapWithKey :: (Key Seq -> a -> b) -> Seq a -> Seq b
Lookup Seq
Instance details Defined in Data.Key Methods lookup :: Key Seq -> Seq a -> Maybe a
TraversableWithKey Seq
Instance details Defined in Data.Key Methods traverseWithKey :: Applicative f => (Key Seq -> a -> f b) -> Seq a -> f (Seq b) mapWithKeyM :: Monad m => (Key Seq -> a -> m b) -> Seq a -> m (Seq b)
Zip Seq
Instance details Defined in Data.Key Methods zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c zip :: Seq a -> Seq b -> Seq (a, b) zap :: Seq (a -> b) -> Seq a -> Seq b
ZipWithKey Seq
Instance details Defined in Data.Key Methods zipWithKey :: (Key Seq -> a -> b -> c) -> Seq a -> Seq b -> Seq c zapWithKey :: Seq (Key Seq -> a -> b) -> Seq a -> Seq b
Constrained Seq
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom Seq a
UnzipWith Seq
Instance details Defined in Data.Sequence.Internal Methods unzipWith' :: (x -> (a, b)) -> Seq x -> (Seq a, Seq b)
FoldableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Seq a -> m ifolded :: IndexedFold Int (Seq a) a ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> Seq a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> Seq a -> b
FunctorWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Seq a -> Seq b imapped :: IndexedSetter Int (Seq a) (Seq b) a b
TraversableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) itraversed :: IndexedTraversal Int (Seq a) (Seq b) a b
(Monoidal r, Semiring r) => UnitalAlgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital Methods unit :: r -> Seq a -> r #
Semiring r => CounitalCoalgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital Methods counit :: (Seq a -> r) -> r #
(Monoidal r, Semiring r) => Bialgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Unital
Semiring r => Coalgebra r (Seq a)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Seq a -> r) -> Seq a -> Seq a -> r #
Semiring r => Algebra r (Seq a)
Instance details Defined in Numeric.Algebra.Class Methods mult :: (Seq a -> Seq a -> r) -> Seq a -> r #
IsList (Seq a)
Instance details Defined in Data.Sequence.Internal Associated Types type Item (Seq a) # Methods fromList :: [Item (Seq a)] -> Seq a # fromListN :: Int -> [Item (Seq a)] -> Seq a # toList :: Seq a -> [Item (Seq a)] #
Eq a => Eq (Seq a)
Instance details Defined in Data.Sequence.Internal Methods (==) :: Seq a -> Seq a -> Bool # (/=) :: Seq a -> Seq a -> Bool #
Data a => Data (Seq a)
Instance details Defined in Data.Sequence.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Seq a -> c (Seq a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Seq a) # toConstr :: Seq a -> Constr # dataTypeOf :: Seq a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Seq a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Seq a)) # gmapT :: (forall b. Data b => b -> b) -> Seq a -> Seq a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r # gmapQ :: (forall d. Data d => d -> u) -> Seq a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Seq a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) #
Ord a => Ord (Seq a)
Instance details Defined in Data.Sequence.Internal Methods compare :: Seq a -> Seq a -> Ordering # (<) :: Seq a -> Seq a -> Bool # (<=) :: Seq a -> Seq a -> Bool # (>) :: Seq a -> Seq a -> Bool # (>=) :: Seq a -> Seq a -> Bool # max :: Seq a -> Seq a -> Seq a # min :: Seq a -> Seq a -> Seq a #
Read a => Read (Seq a)
Instance details Defined in Data.Sequence.Internal Methods readsPrec :: Int -> ReadS (Seq a) # readList :: ReadS [Seq a] # readPrec :: ReadPrec (Seq a) # readListPrec :: ReadPrec [Seq a] #
Show a => Show (Seq a)
Instance details Defined in Data.Sequence.Internal Methods showsPrec :: Int -> Seq a -> ShowS # show :: Seq a -> String # showList :: [Seq a] -> ShowS #
a ~ Char => IsString (Seq a)	Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods fromString :: String -> Seq a #
Semigroup (Seq a)	Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods (<>) :: Seq a -> Seq a -> Seq a # sconcat :: NonEmpty (Seq a) -> Seq a # stimes :: Integral b => b -> Seq a -> Seq a #
Monoid (Seq a)
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
NFData a => NFData (Seq a)
Instance details Defined in Data.Sequence.Internal Methods rnf :: Seq a -> () #
Wrapped (Seq a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Seq a) Methods _Wrapped' :: Iso' (Seq a) (Unwrapped (Seq a))
Ixed (Seq a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Seq a) -> Traversal' (Seq a) (IxValue (Seq a))
AsEmpty (Seq a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Seq a) ()
Reversing (Seq a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Seq a -> Seq a
GrowingAppend (Seq a)
Instance details Defined in Data.MonoTraversable
MonoFoldable (Seq a)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Seq a) -> m) -> Seq a -> m ofoldr :: (Element (Seq a) -> b -> b) -> b -> Seq a -> b ofoldl' :: (a0 -> Element (Seq a) -> a0) -> a0 -> Seq a -> a0 otoList :: Seq a -> [Element (Seq a)] oall :: (Element (Seq a) -> Bool) -> Seq a -> Bool oany :: (Element (Seq a) -> Bool) -> Seq a -> Bool onull :: Seq a -> Bool olength :: Seq a -> Int olength64 :: Seq a -> Int64 ocompareLength :: Integral i => Seq a -> i -> Ordering otraverse_ :: Applicative f => (Element (Seq a) -> f b) -> Seq a -> f () ofor_ :: Applicative f => Seq a -> (Element (Seq a) -> f b) -> f () omapM_ :: Applicative m => (Element (Seq a) -> m ()) -> Seq a -> m () oforM_ :: Applicative m => Seq a -> (Element (Seq a) -> m ()) -> m () ofoldlM :: Monad m => (a0 -> Element (Seq a) -> m a0) -> a0 -> Seq a -> m a0 ofoldMap1Ex :: Semigroup m => (Element (Seq a) -> m) -> Seq a -> m ofoldr1Ex :: (Element (Seq a) -> Element (Seq a) -> Element (Seq a)) -> Seq a -> Element (Seq a) ofoldl1Ex' :: (Element (Seq a) -> Element (Seq a) -> Element (Seq a)) -> Seq a -> Element (Seq a) headEx :: Seq a -> Element (Seq a) lastEx :: Seq a -> Element (Seq a) unsafeHead :: Seq a -> Element (Seq a) unsafeLast :: Seq a -> Element (Seq a) maximumByEx :: (Element (Seq a) -> Element (Seq a) -> Ordering) -> Seq a -> Element (Seq a) minimumByEx :: (Element (Seq a) -> Element (Seq a) -> Ordering) -> Seq a -> Element (Seq a) oelem :: Element (Seq a) -> Seq a -> Bool onotElem :: Element (Seq a) -> Seq a -> Bool
MonoFunctor (Seq a)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (Seq a) -> Element (Seq a)) -> Seq a -> Seq a
MonoPointed (Seq a)
Instance details Defined in Data.MonoTraversable Methods opoint :: Element (Seq a) -> Seq a
MonoTraversable (Seq a)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (Seq a) -> f (Element (Seq a))) -> Seq a -> f (Seq a) omapM :: Applicative m => (Element (Seq a) -> m (Element (Seq a))) -> Seq a -> m (Seq a)
IsSequence (Seq a)
Instance details Defined in Data.Sequences Methods fromList :: [Element (Seq a)] -> Seq a lengthIndex :: Seq a -> Index (Seq a) break :: (Element (Seq a) -> Bool) -> Seq a -> (Seq a, Seq a) span :: (Element (Seq a) -> Bool) -> Seq a -> (Seq a, Seq a) dropWhile :: (Element (Seq a) -> Bool) -> Seq a -> Seq a takeWhile :: (Element (Seq a) -> Bool) -> Seq a -> Seq a splitAt :: Index (Seq a) -> Seq a -> (Seq a, Seq a) unsafeSplitAt :: Index (Seq a) -> Seq a -> (Seq a, Seq a) take :: Index (Seq a) -> Seq a -> Seq a unsafeTake :: Index (Seq a) -> Seq a -> Seq a drop :: Index (Seq a) -> Seq a -> Seq a unsafeDrop :: Index (Seq a) -> Seq a -> Seq a dropEnd :: Index (Seq a) -> Seq a -> Seq a partition :: (Element (Seq a) -> Bool) -> Seq a -> (Seq a, Seq a) uncons :: Seq a -> Maybe (Element (Seq a), Seq a) unsnoc :: Seq a -> Maybe (Seq a, Element (Seq a)) filter :: (Element (Seq a) -> Bool) -> Seq a -> Seq a filterM :: Monad m => (Element (Seq a) -> m Bool) -> Seq a -> m (Seq a) replicate :: Index (Seq a) -> Element (Seq a) -> Seq a replicateM :: Monad m => Index (Seq a) -> m (Element (Seq a)) -> m (Seq a) groupBy :: (Element (Seq a) -> Element (Seq a) -> Bool) -> Seq a -> [Seq a] groupAllOn :: Eq b => (Element (Seq a) -> b) -> Seq a -> [Seq a] subsequences :: Seq a -> [Seq a] permutations :: Seq a -> [Seq a] tailEx :: Seq a -> Seq a tailMay :: Seq a -> Maybe (Seq a) initEx :: Seq a -> Seq a initMay :: Seq a -> Maybe (Seq a) unsafeTail :: Seq a -> Seq a unsafeInit :: Seq a -> Seq a index :: Seq a -> Index (Seq a) -> Maybe (Element (Seq a)) indexEx :: Seq a -> Index (Seq a) -> Element (Seq a) unsafeIndex :: Seq a -> Index (Seq a) -> Element (Seq a) splitWhen :: (Element (Seq a) -> Bool) -> Seq a -> [Seq a]
SemiSequence (Seq a)
Instance details Defined in Data.Sequences Associated Types type Index (Seq a) Methods intersperse :: Element (Seq a) -> Seq a -> Seq a reverse :: Seq a -> Seq a find :: (Element (Seq a) -> Bool) -> Seq a -> Maybe (Element (Seq a)) sortBy :: (Element (Seq a) -> Element (Seq a) -> Ordering) -> Seq a -> Seq a cons :: Element (Seq a) -> Seq a -> Seq a snoc :: Seq a -> Element (Seq a) -> Seq a
t ~ Seq a' => Rewrapped (Seq a) t
Instance details Defined in Control.Lens.Wrapped
Cons (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b)
Snoc (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b)
Each (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Seq a) (Seq b) a b
type Key Seq
Instance details Defined in Data.Key type Key Seq = Int
type Dom Seq a
Instance details Defined in Control.Subcategory.Functor type Dom Seq a = ()
type Item (Seq a)
Instance details Defined in Data.Sequence.Internal type Item (Seq a) = a
type Index (Seq a)
Instance details Defined in Control.Lens.At type Index (Seq a) = Int
type Unwrapped (Seq a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Seq a) = [a]
type Element (Seq a)
Instance details Defined in Data.MonoTraversable type Element (Seq a) = a
type IxValue (Seq a)
Instance details Defined in Control.Lens.At type IxValue (Seq a) = a
type Index (Seq a)
Instance details Defined in Data.Sequences type Index (Seq a) = Int

data Map k a #

A Map from keys k to values a.

The Semigroup operation for Map is union, which prefers values from the left operand. If m1 maps a key k to a value a1, and m2 maps the same key to a different value a2, then their union m1 <> m2 maps k to a1.

Instances

Instances details

Bifoldable Map	Since: containers-0.6.3.1
Instance details Defined in Data.Map.Internal Methods bifold :: Monoid m => Map m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Map a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Map a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Map a b -> c #
Eq2 Map	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Map a c -> Map b d -> Bool #
Ord2 Map	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Map a c -> Map b d -> Ordering #
Show2 Map	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Map a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Map a b] -> ShowS #
BiPolyMap Map
Instance details Defined in Data.Containers Associated Types type BPMKeyConstraint Map key Methods mapKeysWith :: (BPMKeyConstraint Map k1, BPMKeyConstraint Map k2) => (v -> v -> v) -> (k1 -> k2) -> Map k1 v -> Map k2 v
FoldableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> Map k a -> m ifolded :: IndexedFold k (Map k a) a ifoldr :: (k -> a -> b -> b) -> b -> Map k a -> b ifoldl :: (k -> b -> a -> b) -> b -> Map k a -> b ifoldr' :: (k -> a -> b -> b) -> b -> Map k a -> b ifoldl' :: (k -> b -> a -> b) -> b -> Map k a -> b
FunctorWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> Map k a -> Map k b imapped :: IndexedSetter k (Map k a) (Map k b) a b
TraversableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> Map k a -> f (Map k b) itraversed :: IndexedTraversal k (Map k a) (Map k b) a b
Ord k => TraverseMax k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' k (Map k v) v
Ord k => TraverseMin k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' k (Map k v) v
(Commutative r, Semiring r, Ord a, Abelian b) => CocommutativeCoalgebra r (Map a b)
Instance details Defined in Numeric.Algebra.Commutative
(Semiring r, Ord a, Additive b) => Coalgebra r (Map a b)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (Map a b -> r) -> Map a b -> Map a b -> r #
Functor (Map k)
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b # (<$) :: a -> Map k b -> Map k a #
Foldable (Map k)	Folds in order of increasing key.
Instance details Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # toList :: Map k a -> [a] # null :: Map k a -> Bool # length :: Map k a -> Int # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # sum :: Num a => Map k a -> a # product :: Num a => Map k a -> a #
Traversable (Map k)	Traverses in order of increasing key.
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Eq k => Eq1 (Map k)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftEq :: (a -> b -> Bool) -> Map k a -> Map k b -> Bool #
Ord k => Ord1 (Map k)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftCompare :: (a -> b -> Ordering) -> Map k a -> Map k b -> Ordering #
(Ord k, Read k) => Read1 (Map k)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Map k a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Map k a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Map k a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Map k a] #
Show k => Show1 (Map k)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Map k a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Map k a] -> ShowS #
CFoldable (Map k)
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom (Map k) a, Monoid w) => (a -> w) -> Map k a -> w cfoldMap' :: (Dom (Map k) a, Monoid m) => (a -> m) -> Map k a -> m cfold :: (Dom (Map k) w, Monoid w) => Map k w -> w cfoldr :: Dom (Map k) a => (a -> b -> b) -> b -> Map k a -> b cfoldlM :: (Monad m, Dom (Map k) b) => (a -> b -> m a) -> a -> Map k b -> m a cfoldlM' :: (Monad m, Dom (Map k) b) => (a -> b -> m a) -> a -> Map k b -> m a cfoldrM :: (Monad m, Dom (Map k) a) => (a -> b -> m b) -> b -> Map k a -> m b cfoldrM' :: (Monad m, Dom (Map k) a) => (a -> b -> m b) -> b -> Map k a -> m b cfoldl :: Dom (Map k) a => (b -> a -> b) -> b -> Map k a -> b cfoldr' :: Dom (Map k) a => (a -> b -> b) -> b -> Map k a -> b cfoldl' :: Dom (Map k) a => (b -> a -> b) -> b -> Map k a -> b cbasicToList :: Dom (Map k) a => Map k a -> [a] cfoldr1 :: Dom (Map k) a => (a -> a -> a) -> Map k a -> a cfoldl1 :: Dom (Map k) a => (a -> a -> a) -> Map k a -> a cindex :: Dom (Map k) a => Map k a -> Int -> a cnull :: Dom (Map k) a => Map k a -> Bool clength :: Dom (Map k) a => Map k a -> Int cany :: Dom (Map k) a => (a -> Bool) -> Map k a -> Bool call :: Dom (Map k) a => (a -> Bool) -> Map k a -> Bool celem :: (Eq a, Dom (Map k) a) => a -> Map k a -> Bool cnotElem :: (Eq a, Dom (Map k) a) => a -> Map k a -> Bool cminimum :: (Ord a, Dom (Map k) a) => Map k a -> a cmaximum :: (Ord a, Dom (Map k) a) => Map k a -> a csum :: (Num a, Dom (Map k) a) => Map k a -> a cproduct :: (Num a, Dom (Map k) a) => Map k a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom (Map k) a, Dom g b) => (a -> g b) -> Map k a -> g () ctraverse_ :: (Applicative g, Dom (Map k) a) => (a -> g b) -> Map k a -> g () clast :: Dom (Map k) a => Map k a -> a chead :: Dom (Map k) a => Map k a -> a cfind :: Dom (Map k) a => (a -> Bool) -> Map k a -> Maybe a cfindIndex :: Dom (Map k) a => (a -> Bool) -> Map k a -> Maybe Int cfindIndices :: Dom (Map k) a => (a -> Bool) -> Map k a -> [Int] celemIndex :: (Dom (Map k) a, Eq a) => a -> Map k a -> Maybe Int celemIndices :: (Dom (Map k) a, Eq a) => a -> Map k a -> [Int]
Ord k => CZip (Map k)
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom (Map k) a, Dom (Map k) b, Dom (Map k) c) => (a -> b -> c) -> Map k a -> Map k b -> Map k c czip :: (Dom (Map k) a, Dom (Map k) b, Dom (Map k) (a, b)) => Map k a -> Map k b -> Map k (a, b)
Ord k => CFunctor (Map k)
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom (Map k) a, Dom (Map k) b) => (a -> b) -> Map k a -> Map k b (<$:) :: (Dom (Map k) a, Dom (Map k) b) => a -> Map k b -> Map k a
Ord k => CTraversable (Map k)
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom (Map k) a, Dom (Map k) b, Applicative g) => (a -> g b) -> Map k a -> g (Map k b)
Ord k => CUnzip (Map k)
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom (Map k) (a, b), Dom (Map k) a, Dom (Map k) b) => Map k (a, b) -> (Map k a, Map k b) cunzipWith :: (Dom (Map k) c, Dom (Map k) a, Dom (Map k) b) => (c -> (a, b)) -> Map k c -> (Map k a, Map k b)
Ord k => Adjustable (Map k)
Instance details Defined in Data.Key Methods adjust :: (a -> a) -> Key (Map k) -> Map k a -> Map k a replace :: Key (Map k) -> a -> Map k a -> Map k a
Ord k => Apply (Map k)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Map k (a -> b) -> Map k a -> Map k b (.>) :: Map k a -> Map k b -> Map k b (<.) :: Map k a -> Map k b -> Map k a liftF2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c
Ord k => Bind (Map k)
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Map k a -> (a -> Map k b) -> Map k b join :: Map k (Map k a) -> Map k a
FoldableWithKey (Map k)
Instance details Defined in Data.Key Methods toKeyedList :: Map k a -> [(Key (Map k), a)] foldMapWithKey :: Monoid m => (Key (Map k) -> a -> m) -> Map k a -> m foldrWithKey :: (Key (Map k) -> a -> b -> b) -> b -> Map k a -> b foldlWithKey :: (b -> Key (Map k) -> a -> b) -> b -> Map k a -> b
Ord k => Indexable (Map k)
Instance details Defined in Data.Key Methods index :: Map k a -> Key (Map k) -> a
Keyed (Map k)
Instance details Defined in Data.Key Methods mapWithKey :: (Key (Map k) -> a -> b) -> Map k a -> Map k b
Ord k => Lookup (Map k)
Instance details Defined in Data.Key Methods lookup :: Key (Map k) -> Map k a -> Maybe a
TraversableWithKey (Map k)
Instance details Defined in Data.Key Methods traverseWithKey :: Applicative f => (Key (Map k) -> a -> f b) -> Map k a -> f (Map k b) mapWithKeyM :: Monad m => (Key (Map k) -> a -> m b) -> Map k a -> m (Map k b)
Ord k => Zip (Map k)
Instance details Defined in Data.Key Methods zipWith :: (a -> b -> c) -> Map k a -> Map k b -> Map k c zip :: Map k a -> Map k b -> Map k (a, b) zap :: Map k (a -> b) -> Map k a -> Map k b
Ord k => ZipWithKey (Map k)
Instance details Defined in Data.Key Methods zipWithKey :: (Key (Map k) -> a -> b -> c) -> Map k a -> Map k b -> Map k c zapWithKey :: Map k (Key (Map k) -> a -> b) -> Map k a -> Map k b
Constrained (Map k)
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom (Map k) a
Ord key => PolyMap (Map key)
Instance details Defined in Data.Containers Methods differenceMap :: Map key value1 -> Map key value2 -> Map key value1 intersectionMap :: Map key value1 -> Map key value2 -> Map key value1 intersectionWithMap :: (value1 -> value2 -> value3) -> Map key value1 -> Map key value2 -> Map key value3
Ord k => IsList (Map k v)	Since: containers-0.5.6.2
Instance details Defined in Data.Map.Internal Associated Types type Item (Map k v) # Methods fromList :: [Item (Map k v)] -> Map k v # fromListN :: Int -> [Item (Map k v)] -> Map k v # toList :: Map k v -> [Item (Map k v)] #
(Eq k, Eq a) => Eq (Map k a)
Instance details Defined in Data.Map.Internal Methods (==) :: Map k a -> Map k a -> Bool # (/=) :: Map k a -> Map k a -> Bool #
(Data k, Data a, Ord k) => Data (Map k a)
Instance details Defined in Data.Map.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) # toConstr :: Map k a -> Constr # dataTypeOf :: Map k a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) # gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r # gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #
(Ord k, Ord v) => Ord (Map k v)
Instance details Defined in Data.Map.Internal Methods compare :: Map k v -> Map k v -> Ordering # (<) :: Map k v -> Map k v -> Bool # (<=) :: Map k v -> Map k v -> Bool # (>) :: Map k v -> Map k v -> Bool # (>=) :: Map k v -> Map k v -> Bool # max :: Map k v -> Map k v -> Map k v # min :: Map k v -> Map k v -> Map k v #
(Ord k, Read k, Read e) => Read (Map k e)
Instance details Defined in Data.Map.Internal Methods readsPrec :: Int -> ReadS (Map k e) # readList :: ReadS [Map k e] # readPrec :: ReadPrec (Map k e) # readListPrec :: ReadPrec [Map k e] #
(Show k, Show a) => Show (Map k a)
Instance details Defined in Data.Map.Internal Methods showsPrec :: Int -> Map k a -> ShowS # show :: Map k a -> String # showList :: [Map k a] -> ShowS #
Ord k => Semigroup (Map k v)
Instance details Defined in Data.Map.Internal Methods (<>) :: Map k v -> Map k v -> Map k v # sconcat :: NonEmpty (Map k v) -> Map k v # stimes :: Integral b => b -> Map k v -> Map k v #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
(NFData k, NFData a) => NFData (Map k a)
Instance details Defined in Data.Map.Internal Methods rnf :: Map k a -> () #
Ord k => Wrapped (Map k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Map k a) Methods _Wrapped' :: Iso' (Map k a) (Unwrapped (Map k a))
Ord k => At (Map k a)
Instance details Defined in Control.Lens.At Methods at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a)))
Ord k => Ixed (Map k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Map k a) -> Traversal' (Map k a) (IxValue (Map k a))
AsEmpty (Map k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Map k a) ()
Ord k => GrowingAppend (Map k v)
Instance details Defined in Data.MonoTraversable
MonoFoldable (Map k v)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (Map k v) -> m) -> Map k v -> m ofoldr :: (Element (Map k v) -> b -> b) -> b -> Map k v -> b ofoldl' :: (a -> Element (Map k v) -> a) -> a -> Map k v -> a otoList :: Map k v -> [Element (Map k v)] oall :: (Element (Map k v) -> Bool) -> Map k v -> Bool oany :: (Element (Map k v) -> Bool) -> Map k v -> Bool onull :: Map k v -> Bool olength :: Map k v -> Int olength64 :: Map k v -> Int64 ocompareLength :: Integral i => Map k v -> i -> Ordering otraverse_ :: Applicative f => (Element (Map k v) -> f b) -> Map k v -> f () ofor_ :: Applicative f => Map k v -> (Element (Map k v) -> f b) -> f () omapM_ :: Applicative m => (Element (Map k v) -> m ()) -> Map k v -> m () oforM_ :: Applicative m => Map k v -> (Element (Map k v) -> m ()) -> m () ofoldlM :: Monad m => (a -> Element (Map k v) -> m a) -> a -> Map k v -> m a ofoldMap1Ex :: Semigroup m => (Element (Map k v) -> m) -> Map k v -> m ofoldr1Ex :: (Element (Map k v) -> Element (Map k v) -> Element (Map k v)) -> Map k v -> Element (Map k v) ofoldl1Ex' :: (Element (Map k v) -> Element (Map k v) -> Element (Map k v)) -> Map k v -> Element (Map k v) headEx :: Map k v -> Element (Map k v) lastEx :: Map k v -> Element (Map k v) unsafeHead :: Map k v -> Element (Map k v) unsafeLast :: Map k v -> Element (Map k v) maximumByEx :: (Element (Map k v) -> Element (Map k v) -> Ordering) -> Map k v -> Element (Map k v) minimumByEx :: (Element (Map k v) -> Element (Map k v) -> Ordering) -> Map k v -> Element (Map k v) oelem :: Element (Map k v) -> Map k v -> Bool onotElem :: Element (Map k v) -> Map k v -> Bool
MonoFunctor (Map k v)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (Map k v) -> Element (Map k v)) -> Map k v -> Map k v
MonoTraversable (Map k v)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (Map k v) -> f (Element (Map k v))) -> Map k v -> f (Map k v) omapM :: Applicative m => (Element (Map k v) -> m (Element (Map k v))) -> Map k v -> m (Map k v)
Ord k => HasKeysSet (Map k v)
Instance details Defined in Data.Containers Associated Types type KeySet (Map k v) Methods keysSet :: Map k v -> KeySet (Map k v)
Ord key => IsMap (Map key value)
Instance details Defined in Data.Containers Associated Types type MapValue (Map key value) Methods lookup :: ContainerKey (Map key value) -> Map key value -> Maybe (MapValue (Map key value)) insertMap :: ContainerKey (Map key value) -> MapValue (Map key value) -> Map key value -> Map key value deleteMap :: ContainerKey (Map key value) -> Map key value -> Map key value singletonMap :: ContainerKey (Map key value) -> MapValue (Map key value) -> Map key value mapFromList :: [(ContainerKey (Map key value), MapValue (Map key value))] -> Map key value mapToList :: Map key value -> [(ContainerKey (Map key value), MapValue (Map key value))] findWithDefault :: MapValue (Map key value) -> ContainerKey (Map key value) -> Map key value -> MapValue (Map key value) insertWith :: (MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> ContainerKey (Map key value) -> MapValue (Map key value) -> Map key value -> Map key value insertWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> ContainerKey (Map key value) -> MapValue (Map key value) -> Map key value -> Map key value insertLookupWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> ContainerKey (Map key value) -> MapValue (Map key value) -> Map key value -> (Maybe (MapValue (Map key value)), Map key value) adjustMap :: (MapValue (Map key value) -> MapValue (Map key value)) -> ContainerKey (Map key value) -> Map key value -> Map key value adjustWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> ContainerKey (Map key value) -> Map key value -> Map key value updateMap :: (MapValue (Map key value) -> Maybe (MapValue (Map key value))) -> ContainerKey (Map key value) -> Map key value -> Map key value updateWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> Maybe (MapValue (Map key value))) -> ContainerKey (Map key value) -> Map key value -> Map key value updateLookupWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> Maybe (MapValue (Map key value))) -> ContainerKey (Map key value) -> Map key value -> (Maybe (MapValue (Map key value)), Map key value) alterMap :: (Maybe (MapValue (Map key value)) -> Maybe (MapValue (Map key value))) -> ContainerKey (Map key value) -> Map key value -> Map key value unionWith :: (MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> Map key value -> Map key value -> Map key value unionWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> Map key value -> Map key value -> Map key value unionsWith :: (MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> [Map key value] -> Map key value mapWithKey :: (ContainerKey (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> Map key value -> Map key value omapKeysWith :: (MapValue (Map key value) -> MapValue (Map key value) -> MapValue (Map key value)) -> (ContainerKey (Map key value) -> ContainerKey (Map key value)) -> Map key value -> Map key value filterMap :: (MapValue (Map key value) -> Bool) -> Map key value -> Map key value
Ord k => SetContainer (Map k v)
Instance details Defined in Data.Containers Associated Types type ContainerKey (Map k v) Methods member :: ContainerKey (Map k v) -> Map k v -> Bool notMember :: ContainerKey (Map k v) -> Map k v -> Bool union :: Map k v -> Map k v -> Map k v unions :: (MonoFoldable mono, Element mono ~ Map k v) => mono -> Map k v difference :: Map k v -> Map k v -> Map k v intersection :: Map k v -> Map k v -> Map k v keys :: Map k v -> [ContainerKey (Map k v)]
(t ~ Map k' a', Ord k) => Rewrapped (Map k a) t
Instance details Defined in Control.Lens.Wrapped
c ~ d => Each (Map c a) (Map d b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Map c a) (Map d b) a b
type BPMKeyConstraint Map key
Instance details Defined in Data.Containers type BPMKeyConstraint Map key = Ord key
type Key (Map k)
Instance details Defined in Data.Key type Key (Map k) = k
type Dom (Map k) a
Instance details Defined in Control.Subcategory.Functor type Dom (Map k) a = ()
type Item (Map k v)
Instance details Defined in Data.Map.Internal type Item (Map k v) = (k, v)
type Index (Map k a)
Instance details Defined in Control.Lens.At type Index (Map k a) = k
type Unwrapped (Map k a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Map k a) = [(k, a)]
type Element (Map k v)
Instance details Defined in Data.MonoTraversable type Element (Map k v) = v
type IxValue (Map k a)
Instance details Defined in Control.Lens.At type IxValue (Map k a) = a
type KeySet (Map k v)
Instance details Defined in Data.Containers type KeySet (Map k v) = Set k
type MapValue (Map key value)
Instance details Defined in Data.Containers type MapValue (Map key value) = value
type ContainerKey (Map k v)
Instance details Defined in Data.Containers type ContainerKey (Map k v) = k

data IntSet #

A set of integers.

Instances

Instances details

IsList IntSet	Since: containers-0.5.6.2
Instance details Defined in Data.IntSet.Internal Associated Types type Item IntSet # Methods fromList :: [Item IntSet] -> IntSet # fromListN :: Int -> [Item IntSet] -> IntSet # toList :: IntSet -> [Item IntSet] #
Eq IntSet
Instance details Defined in Data.IntSet.Internal Methods (==) :: IntSet -> IntSet -> Bool # (/=) :: IntSet -> IntSet -> Bool #
Data IntSet
Instance details Defined in Data.IntSet.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IntSet -> c IntSet # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c IntSet # toConstr :: IntSet -> Constr # dataTypeOf :: IntSet -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c IntSet) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c IntSet) # gmapT :: (forall b. Data b => b -> b) -> IntSet -> IntSet # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IntSet -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IntSet -> r # gmapQ :: (forall d. Data d => d -> u) -> IntSet -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> IntSet -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet #
Ord IntSet
Instance details Defined in Data.IntSet.Internal Methods compare :: IntSet -> IntSet -> Ordering # (<) :: IntSet -> IntSet -> Bool # (<=) :: IntSet -> IntSet -> Bool # (>) :: IntSet -> IntSet -> Bool # (>=) :: IntSet -> IntSet -> Bool # max :: IntSet -> IntSet -> IntSet # min :: IntSet -> IntSet -> IntSet #
Read IntSet
Instance details Defined in Data.IntSet.Internal Methods readsPrec :: Int -> ReadS IntSet # readList :: ReadS [IntSet] # readPrec :: ReadPrec IntSet # readListPrec :: ReadPrec [IntSet] #
Show IntSet
Instance details Defined in Data.IntSet.Internal Methods showsPrec :: Int -> IntSet -> ShowS # show :: IntSet -> String # showList :: [IntSet] -> ShowS #
Semigroup IntSet	Since: containers-0.5.7
Instance details Defined in Data.IntSet.Internal Methods (<>) :: IntSet -> IntSet -> IntSet # sconcat :: NonEmpty IntSet -> IntSet # stimes :: Integral b => b -> IntSet -> IntSet #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
NFData IntSet
Instance details Defined in Data.IntSet.Internal Methods rnf :: IntSet -> () #
Wrapped IntSet
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped IntSet Methods _Wrapped' :: Iso' IntSet (Unwrapped IntSet)
At IntSet
Instance details Defined in Control.Lens.At Methods at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet))
Contains IntSet
Instance details Defined in Control.Lens.At Methods contains :: Index IntSet -> Lens' IntSet Bool
Ixed IntSet
Instance details Defined in Control.Lens.At Methods ix :: Index IntSet -> Traversal' IntSet (IxValue IntSet)
AsEmpty IntSet
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' IntSet ()
GrowingAppend IntSet
Instance details Defined in Data.MonoTraversable
MonoFoldable IntSet
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element IntSet -> m) -> IntSet -> m ofoldr :: (Element IntSet -> b -> b) -> b -> IntSet -> b ofoldl' :: (a -> Element IntSet -> a) -> a -> IntSet -> a otoList :: IntSet -> [Element IntSet] oall :: (Element IntSet -> Bool) -> IntSet -> Bool oany :: (Element IntSet -> Bool) -> IntSet -> Bool onull :: IntSet -> Bool olength :: IntSet -> Int olength64 :: IntSet -> Int64 ocompareLength :: Integral i => IntSet -> i -> Ordering otraverse_ :: Applicative f => (Element IntSet -> f b) -> IntSet -> f () ofor_ :: Applicative f => IntSet -> (Element IntSet -> f b) -> f () omapM_ :: Applicative m => (Element IntSet -> m ()) -> IntSet -> m () oforM_ :: Applicative m => IntSet -> (Element IntSet -> m ()) -> m () ofoldlM :: Monad m => (a -> Element IntSet -> m a) -> a -> IntSet -> m a ofoldMap1Ex :: Semigroup m => (Element IntSet -> m) -> IntSet -> m ofoldr1Ex :: (Element IntSet -> Element IntSet -> Element IntSet) -> IntSet -> Element IntSet ofoldl1Ex' :: (Element IntSet -> Element IntSet -> Element IntSet) -> IntSet -> Element IntSet headEx :: IntSet -> Element IntSet lastEx :: IntSet -> Element IntSet unsafeHead :: IntSet -> Element IntSet unsafeLast :: IntSet -> Element IntSet maximumByEx :: (Element IntSet -> Element IntSet -> Ordering) -> IntSet -> Element IntSet minimumByEx :: (Element IntSet -> Element IntSet -> Ordering) -> IntSet -> Element IntSet oelem :: Element IntSet -> IntSet -> Bool onotElem :: Element IntSet -> IntSet -> Bool
MonoPointed IntSet
Instance details Defined in Data.MonoTraversable Methods opoint :: Element IntSet -> IntSet
IsSet IntSet
Instance details Defined in Data.Containers Methods insertSet :: Element IntSet -> IntSet -> IntSet deleteSet :: Element IntSet -> IntSet -> IntSet singletonSet :: Element IntSet -> IntSet setFromList :: [Element IntSet] -> IntSet setToList :: IntSet -> [Element IntSet] filterSet :: (Element IntSet -> Bool) -> IntSet -> IntSet
SetContainer IntSet
Instance details Defined in Data.Containers Associated Types type ContainerKey IntSet Methods member :: ContainerKey IntSet -> IntSet -> Bool notMember :: ContainerKey IntSet -> IntSet -> Bool union :: IntSet -> IntSet -> IntSet unions :: (MonoFoldable mono, Element mono ~ IntSet) => mono -> IntSet difference :: IntSet -> IntSet -> IntSet intersection :: IntSet -> IntSet -> IntSet keys :: IntSet -> [ContainerKey IntSet]
(Semiring r, Band r) => IdempotentAlgebra r IntSet
Instance details Defined in Numeric.Algebra.Idempotent
(Commutative r, Semiring r) => CommutativeAlgebra r IntSet
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r) => CocommutativeCoalgebra r IntSet
Instance details Defined in Numeric.Algebra.Commutative
Semiring r => Coalgebra r IntSet
Instance details Defined in Numeric.Algebra.Class Methods comult :: (IntSet -> r) -> IntSet -> IntSet -> r #
Semiring r => Algebra r IntSet
Instance details Defined in Numeric.Algebra.Class Methods mult :: (IntSet -> IntSet -> r) -> IntSet -> r #
t ~ IntSet => Rewrapped IntSet t
Instance details Defined in Control.Lens.Wrapped
(Semiring r, Band r) => IdempotentCoalgebra r IntSet
Instance details Defined in Numeric.Algebra.Idempotent
CPointed (WrapMono IntSet :: Type -> Type)
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom (WrapMono IntSet) a => a -> WrapMono IntSet a
type Item IntSet
Instance details Defined in Data.IntSet.Internal type Item IntSet = Key
type Index IntSet
Instance details Defined in Control.Lens.At type Index IntSet = Int
type Unwrapped IntSet
Instance details Defined in Control.Lens.Wrapped type Unwrapped IntSet = [Int]
type Element IntSet
Instance details Defined in Data.MonoTraversable type Element IntSet = Int
type IxValue IntSet
Instance details Defined in Control.Lens.At type IxValue IntSet = ()
type ContainerKey IntSet
Instance details Defined in Data.Containers type ContainerKey IntSet = Int

data IntMap a #

A map of integers to values a.

Instances

Instances details

Functor IntMap
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> IntMap a -> IntMap b # (<$) :: a -> IntMap b -> IntMap a #
Foldable IntMap	Folds in order of increasing key.
Instance details Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # toList :: IntMap a -> [a] # null :: IntMap a -> Bool # length :: IntMap a -> Int # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # sum :: Num a => IntMap a -> a # product :: Num a => IntMap a -> a #
Traversable IntMap	Traverses in order of increasing key.
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Eq1 IntMap	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods liftEq :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool #
Ord1 IntMap	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods liftCompare :: (a -> b -> Ordering) -> IntMap a -> IntMap b -> Ordering #
Read1 IntMap	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (IntMap a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [IntMap a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (IntMap a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [IntMap a] #
Show1 IntMap	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> IntMap a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [IntMap a] -> ShowS #
CFoldable IntMap
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom IntMap a, Monoid w) => (a -> w) -> IntMap a -> w cfoldMap' :: (Dom IntMap a, Monoid m) => (a -> m) -> IntMap a -> m cfold :: (Dom IntMap w, Monoid w) => IntMap w -> w cfoldr :: Dom IntMap a => (a -> b -> b) -> b -> IntMap a -> b cfoldlM :: (Monad m, Dom IntMap b) => (a -> b -> m a) -> a -> IntMap b -> m a cfoldlM' :: (Monad m, Dom IntMap b) => (a -> b -> m a) -> a -> IntMap b -> m a cfoldrM :: (Monad m, Dom IntMap a) => (a -> b -> m b) -> b -> IntMap a -> m b cfoldrM' :: (Monad m, Dom IntMap a) => (a -> b -> m b) -> b -> IntMap a -> m b cfoldl :: Dom IntMap a => (b -> a -> b) -> b -> IntMap a -> b cfoldr' :: Dom IntMap a => (a -> b -> b) -> b -> IntMap a -> b cfoldl' :: Dom IntMap a => (b -> a -> b) -> b -> IntMap a -> b cbasicToList :: Dom IntMap a => IntMap a -> [a] cfoldr1 :: Dom IntMap a => (a -> a -> a) -> IntMap a -> a cfoldl1 :: Dom IntMap a => (a -> a -> a) -> IntMap a -> a cindex :: Dom IntMap a => IntMap a -> Int -> a cnull :: Dom IntMap a => IntMap a -> Bool clength :: Dom IntMap a => IntMap a -> Int cany :: Dom IntMap a => (a -> Bool) -> IntMap a -> Bool call :: Dom IntMap a => (a -> Bool) -> IntMap a -> Bool celem :: (Eq a, Dom IntMap a) => a -> IntMap a -> Bool cnotElem :: (Eq a, Dom IntMap a) => a -> IntMap a -> Bool cminimum :: (Ord a, Dom IntMap a) => IntMap a -> a cmaximum :: (Ord a, Dom IntMap a) => IntMap a -> a csum :: (Num a, Dom IntMap a) => IntMap a -> a cproduct :: (Num a, Dom IntMap a) => IntMap a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom IntMap a, Dom g b) => (a -> g b) -> IntMap a -> g () ctraverse_ :: (Applicative g, Dom IntMap a) => (a -> g b) -> IntMap a -> g () clast :: Dom IntMap a => IntMap a -> a chead :: Dom IntMap a => IntMap a -> a cfind :: Dom IntMap a => (a -> Bool) -> IntMap a -> Maybe a cfindIndex :: Dom IntMap a => (a -> Bool) -> IntMap a -> Maybe Int cfindIndices :: Dom IntMap a => (a -> Bool) -> IntMap a -> [Int] celemIndex :: (Dom IntMap a, Eq a) => a -> IntMap a -> Maybe Int celemIndices :: (Dom IntMap a, Eq a) => a -> IntMap a -> [Int]
CZip IntMap
Instance details Defined in Control.Subcategory.Zip Methods czipWith :: (Dom IntMap a, Dom IntMap b, Dom IntMap c) => (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c czip :: (Dom IntMap a, Dom IntMap b, Dom IntMap (a, b)) => IntMap a -> IntMap b -> IntMap (a, b)
CFunctor IntMap
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom IntMap a, Dom IntMap b) => (a -> b) -> IntMap a -> IntMap b (<$:) :: (Dom IntMap a, Dom IntMap b) => a -> IntMap b -> IntMap a
CTraversable IntMap
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom IntMap a, Dom IntMap b, Applicative g) => (a -> g b) -> IntMap a -> g (IntMap b)
CUnzip IntMap
Instance details Defined in Control.Subcategory.Zip Methods cunzip :: (Dom IntMap (a, b), Dom IntMap a, Dom IntMap b) => IntMap (a, b) -> (IntMap a, IntMap b) cunzipWith :: (Dom IntMap c, Dom IntMap a, Dom IntMap b) => (c -> (a, b)) -> IntMap c -> (IntMap a, IntMap b)
Adjustable IntMap
Instance details Defined in Data.Key Methods adjust :: (a -> a) -> Key IntMap -> IntMap a -> IntMap a replace :: Key IntMap -> a -> IntMap a -> IntMap a
Apply IntMap
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b (.>) :: IntMap a -> IntMap b -> IntMap b (<.) :: IntMap a -> IntMap b -> IntMap a liftF2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
Bind IntMap
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: IntMap a -> (a -> IntMap b) -> IntMap b join :: IntMap (IntMap a) -> IntMap a
FoldableWithKey IntMap
Instance details Defined in Data.Key Methods toKeyedList :: IntMap a -> [(Key IntMap, a)] foldMapWithKey :: Monoid m => (Key IntMap -> a -> m) -> IntMap a -> m foldrWithKey :: (Key IntMap -> a -> b -> b) -> b -> IntMap a -> b foldlWithKey :: (b -> Key IntMap -> a -> b) -> b -> IntMap a -> b
Indexable IntMap
Instance details Defined in Data.Key Methods index :: IntMap a -> Key IntMap -> a
Keyed IntMap
Instance details Defined in Data.Key Methods mapWithKey :: (Key IntMap -> a -> b) -> IntMap a -> IntMap b
Lookup IntMap
Instance details Defined in Data.Key Methods lookup :: Key IntMap -> IntMap a -> Maybe a
TraversableWithKey IntMap
Instance details Defined in Data.Key Methods traverseWithKey :: Applicative f => (Key IntMap -> a -> f b) -> IntMap a -> f (IntMap b) mapWithKeyM :: Monad m => (Key IntMap -> a -> m b) -> IntMap a -> m (IntMap b)
Zip IntMap
Instance details Defined in Data.Key Methods zipWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c zip :: IntMap a -> IntMap b -> IntMap (a, b) zap :: IntMap (a -> b) -> IntMap a -> IntMap b
ZipWithKey IntMap
Instance details Defined in Data.Key Methods zipWithKey :: (Key IntMap -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c zapWithKey :: IntMap (Key IntMap -> a -> b) -> IntMap a -> IntMap b
Constrained IntMap
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom IntMap a
PolyMap IntMap
Instance details Defined in Data.Containers Methods differenceMap :: IntMap value1 -> IntMap value2 -> IntMap value1 intersectionMap :: IntMap value1 -> IntMap value2 -> IntMap value1 intersectionWithMap :: (value1 -> value2 -> value3) -> IntMap value1 -> IntMap value2 -> IntMap value3
FoldableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> IntMap a -> m ifolded :: IndexedFold Int (IntMap a) a ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b ifoldl :: (Int -> b -> a -> b) -> b -> IntMap a -> b ifoldr' :: (Int -> a -> b -> b) -> b -> IntMap a -> b ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b
FunctorWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> IntMap a -> IntMap b imapped :: IndexedSetter Int (IntMap a) (IntMap b) a b
TraversableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) itraversed :: IndexedTraversal Int (IntMap a) (IntMap b) a b
TraverseMax Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v
TraverseMin Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v
(Commutative r, Semiring r, Abelian b) => CocommutativeCoalgebra r (IntMap b)
Instance details Defined in Numeric.Algebra.Commutative
(Semiring r, Additive b) => Coalgebra r (IntMap b)
Instance details Defined in Numeric.Algebra.Class Methods comult :: (IntMap b -> r) -> IntMap b -> IntMap b -> r #
IsList (IntMap a)	Since: containers-0.5.6.2
Instance details Defined in Data.IntMap.Internal Associated Types type Item (IntMap a) # Methods fromList :: [Item (IntMap a)] -> IntMap a # fromListN :: Int -> [Item (IntMap a)] -> IntMap a # toList :: IntMap a -> [Item (IntMap a)] #
Eq a => Eq (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods (==) :: IntMap a -> IntMap a -> Bool # (/=) :: IntMap a -> IntMap a -> Bool #
Data a => Data (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IntMap a -> c (IntMap a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (IntMap a) # toConstr :: IntMap a -> Constr # dataTypeOf :: IntMap a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (IntMap a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (IntMap a)) # gmapT :: (forall b. Data b => b -> b) -> IntMap a -> IntMap a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IntMap a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IntMap a -> r # gmapQ :: (forall d. Data d => d -> u) -> IntMap a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> IntMap a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) #
Ord a => Ord (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods compare :: IntMap a -> IntMap a -> Ordering # (<) :: IntMap a -> IntMap a -> Bool # (<=) :: IntMap a -> IntMap a -> Bool # (>) :: IntMap a -> IntMap a -> Bool # (>=) :: IntMap a -> IntMap a -> Bool # max :: IntMap a -> IntMap a -> IntMap a # min :: IntMap a -> IntMap a -> IntMap a #
Read e => Read (IntMap e)
Instance details Defined in Data.IntMap.Internal Methods readsPrec :: Int -> ReadS (IntMap e) # readList :: ReadS [IntMap e] # readPrec :: ReadPrec (IntMap e) # readListPrec :: ReadPrec [IntMap e] #
Show a => Show (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods showsPrec :: Int -> IntMap a -> ShowS # show :: IntMap a -> String # showList :: [IntMap a] -> ShowS #
Semigroup (IntMap a)	Since: containers-0.5.7
Instance details Defined in Data.IntMap.Internal Methods (<>) :: IntMap a -> IntMap a -> IntMap a # sconcat :: NonEmpty (IntMap a) -> IntMap a # stimes :: Integral b => b -> IntMap a -> IntMap a #
Monoid (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
NFData a => NFData (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods rnf :: IntMap a -> () #
Wrapped (IntMap a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IntMap a) Methods _Wrapped' :: Iso' (IntMap a) (Unwrapped (IntMap a))
At (IntMap a)
Instance details Defined in Control.Lens.At Methods at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a)))
Ixed (IntMap a)
Instance details Defined in Control.Lens.At Methods ix :: Index (IntMap a) -> Traversal' (IntMap a) (IxValue (IntMap a))
AsEmpty (IntMap a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (IntMap a) ()
GrowingAppend (IntMap v)
Instance details Defined in Data.MonoTraversable
MonoFoldable (IntMap a)
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element (IntMap a) -> m) -> IntMap a -> m ofoldr :: (Element (IntMap a) -> b -> b) -> b -> IntMap a -> b ofoldl' :: (a0 -> Element (IntMap a) -> a0) -> a0 -> IntMap a -> a0 otoList :: IntMap a -> [Element (IntMap a)] oall :: (Element (IntMap a) -> Bool) -> IntMap a -> Bool oany :: (Element (IntMap a) -> Bool) -> IntMap a -> Bool onull :: IntMap a -> Bool olength :: IntMap a -> Int olength64 :: IntMap a -> Int64 ocompareLength :: Integral i => IntMap a -> i -> Ordering otraverse_ :: Applicative f => (Element (IntMap a) -> f b) -> IntMap a -> f () ofor_ :: Applicative f => IntMap a -> (Element (IntMap a) -> f b) -> f () omapM_ :: Applicative m => (Element (IntMap a) -> m ()) -> IntMap a -> m () oforM_ :: Applicative m => IntMap a -> (Element (IntMap a) -> m ()) -> m () ofoldlM :: Monad m => (a0 -> Element (IntMap a) -> m a0) -> a0 -> IntMap a -> m a0 ofoldMap1Ex :: Semigroup m => (Element (IntMap a) -> m) -> IntMap a -> m ofoldr1Ex :: (Element (IntMap a) -> Element (IntMap a) -> Element (IntMap a)) -> IntMap a -> Element (IntMap a) ofoldl1Ex' :: (Element (IntMap a) -> Element (IntMap a) -> Element (IntMap a)) -> IntMap a -> Element (IntMap a) headEx :: IntMap a -> Element (IntMap a) lastEx :: IntMap a -> Element (IntMap a) unsafeHead :: IntMap a -> Element (IntMap a) unsafeLast :: IntMap a -> Element (IntMap a) maximumByEx :: (Element (IntMap a) -> Element (IntMap a) -> Ordering) -> IntMap a -> Element (IntMap a) minimumByEx :: (Element (IntMap a) -> Element (IntMap a) -> Ordering) -> IntMap a -> Element (IntMap a) oelem :: Element (IntMap a) -> IntMap a -> Bool onotElem :: Element (IntMap a) -> IntMap a -> Bool
MonoFunctor (IntMap a)
Instance details Defined in Data.MonoTraversable Methods omap :: (Element (IntMap a) -> Element (IntMap a)) -> IntMap a -> IntMap a
MonoTraversable (IntMap a)
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element (IntMap a) -> f (Element (IntMap a))) -> IntMap a -> f (IntMap a) omapM :: Applicative m => (Element (IntMap a) -> m (Element (IntMap a))) -> IntMap a -> m (IntMap a)
HasKeysSet (IntMap v)
Instance details Defined in Data.Containers Associated Types type KeySet (IntMap v) Methods keysSet :: IntMap v -> KeySet (IntMap v)
IsMap (IntMap value)
Instance details Defined in Data.Containers Associated Types type MapValue (IntMap value) Methods lookup :: ContainerKey (IntMap value) -> IntMap value -> Maybe (MapValue (IntMap value)) insertMap :: ContainerKey (IntMap value) -> MapValue (IntMap value) -> IntMap value -> IntMap value deleteMap :: ContainerKey (IntMap value) -> IntMap value -> IntMap value singletonMap :: ContainerKey (IntMap value) -> MapValue (IntMap value) -> IntMap value mapFromList :: [(ContainerKey (IntMap value), MapValue (IntMap value))] -> IntMap value mapToList :: IntMap value -> [(ContainerKey (IntMap value), MapValue (IntMap value))] findWithDefault :: MapValue (IntMap value) -> ContainerKey (IntMap value) -> IntMap value -> MapValue (IntMap value) insertWith :: (MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> ContainerKey (IntMap value) -> MapValue (IntMap value) -> IntMap value -> IntMap value insertWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> ContainerKey (IntMap value) -> MapValue (IntMap value) -> IntMap value -> IntMap value insertLookupWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> ContainerKey (IntMap value) -> MapValue (IntMap value) -> IntMap value -> (Maybe (MapValue (IntMap value)), IntMap value) adjustMap :: (MapValue (IntMap value) -> MapValue (IntMap value)) -> ContainerKey (IntMap value) -> IntMap value -> IntMap value adjustWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> ContainerKey (IntMap value) -> IntMap value -> IntMap value updateMap :: (MapValue (IntMap value) -> Maybe (MapValue (IntMap value))) -> ContainerKey (IntMap value) -> IntMap value -> IntMap value updateWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> Maybe (MapValue (IntMap value))) -> ContainerKey (IntMap value) -> IntMap value -> IntMap value updateLookupWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> Maybe (MapValue (IntMap value))) -> ContainerKey (IntMap value) -> IntMap value -> (Maybe (MapValue (IntMap value)), IntMap value) alterMap :: (Maybe (MapValue (IntMap value)) -> Maybe (MapValue (IntMap value))) -> ContainerKey (IntMap value) -> IntMap value -> IntMap value unionWith :: (MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> IntMap value -> IntMap value -> IntMap value unionWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> IntMap value -> IntMap value -> IntMap value unionsWith :: (MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> [IntMap value] -> IntMap value mapWithKey :: (ContainerKey (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> IntMap value -> IntMap value omapKeysWith :: (MapValue (IntMap value) -> MapValue (IntMap value) -> MapValue (IntMap value)) -> (ContainerKey (IntMap value) -> ContainerKey (IntMap value)) -> IntMap value -> IntMap value filterMap :: (MapValue (IntMap value) -> Bool) -> IntMap value -> IntMap value
SetContainer (IntMap value)
Instance details Defined in Data.Containers Associated Types type ContainerKey (IntMap value) Methods member :: ContainerKey (IntMap value) -> IntMap value -> Bool notMember :: ContainerKey (IntMap value) -> IntMap value -> Bool union :: IntMap value -> IntMap value -> IntMap value unions :: (MonoFoldable mono, Element mono ~ IntMap value) => mono -> IntMap value difference :: IntMap value -> IntMap value -> IntMap value intersection :: IntMap value -> IntMap value -> IntMap value keys :: IntMap value -> [ContainerKey (IntMap value)]
t ~ IntMap a' => Rewrapped (IntMap a) t
Instance details Defined in Control.Lens.Wrapped
Each (IntMap a) (IntMap b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (IntMap a) (IntMap b) a b
type Key IntMap
Instance details Defined in Data.Key type Key IntMap = Int
type Dom IntMap a
Instance details Defined in Control.Subcategory.Functor type Dom IntMap a = ()
type Item (IntMap a)
Instance details Defined in Data.IntMap.Internal type Item (IntMap a) = (Key, a)
type Index (IntMap a)
Instance details Defined in Control.Lens.At type Index (IntMap a) = Int
type Unwrapped (IntMap a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (IntMap a) = [(Int, a)]
type Element (IntMap a)
Instance details Defined in Data.MonoTraversable type Element (IntMap a) = a
type IxValue (IntMap a)
Instance details Defined in Control.Lens.At type IxValue (IntMap a) = a
type KeySet (IntMap v)
Instance details Defined in Data.Containers type KeySet (IntMap v) = IntSet
type MapValue (IntMap value)
Instance details Defined in Data.Containers type MapValue (IntMap value) = value
type ContainerKey (IntMap value)
Instance details Defined in Data.Containers type ContainerKey (IntMap value) = Int

data ByteString #

A space-efficient representation of a Word8 vector, supporting many efficient operations.

A ByteString contains 8-bit bytes, or by using the operations from Data.ByteString.Char8 it can be interpreted as containing 8-bit characters.

Instances

Instances details

IsList ByteString	Since: bytestring-0.10.12.0
Instance details Defined in Data.ByteString.Internal Associated Types type Item ByteString # Methods fromList :: [Item ByteString] -> ByteString # fromListN :: Int -> [Item ByteString] -> ByteString # toList :: ByteString -> [Item ByteString] #
Eq ByteString
Instance details Defined in Data.ByteString.Internal Methods (==) :: ByteString -> ByteString -> Bool # (/=) :: ByteString -> ByteString -> Bool #
Data ByteString
Instance details Defined in Data.ByteString.Internal Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ByteString -> c ByteString # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ByteString # toConstr :: ByteString -> Constr # dataTypeOf :: ByteString -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c ByteString) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ByteString) # gmapT :: (forall b. Data b => b -> b) -> ByteString -> ByteString # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ByteString -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ByteString -> r # gmapQ :: (forall d. Data d => d -> u) -> ByteString -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ByteString -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString #
Ord ByteString
Instance details Defined in Data.ByteString.Internal Methods compare :: ByteString -> ByteString -> Ordering # (<) :: ByteString -> ByteString -> Bool # (<=) :: ByteString -> ByteString -> Bool # (>) :: ByteString -> ByteString -> Bool # (>=) :: ByteString -> ByteString -> Bool # max :: ByteString -> ByteString -> ByteString # min :: ByteString -> ByteString -> ByteString #
Read ByteString
Instance details Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] #
Show ByteString
Instance details Defined in Data.ByteString.Internal Methods showsPrec :: Int -> ByteString -> ShowS # show :: ByteString -> String # showList :: [ByteString] -> ShowS #
IsString ByteString	Beware: `fromString` truncates multi-byte characters to octets. e.g. "枯朶に烏のとまりけり秋の暮" becomes �6k�nh~�Q��n�
Instance details Defined in Data.ByteString.Internal Methods fromString :: String -> ByteString #
Semigroup ByteString
Instance details Defined in Data.ByteString.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Hashable ByteString
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> ByteString -> Int # hash :: ByteString -> Int #
NFData ByteString
Instance details Defined in Data.ByteString.Internal Methods rnf :: ByteString -> () #
Ixed ByteString
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString)
AsEmpty ByteString
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString ()
Reversing ByteString
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString
GrowingAppend ByteString
Instance details Defined in Data.MonoTraversable
MonoFoldable ByteString
Instance details Defined in Data.MonoTraversable Methods ofoldMap :: Monoid m => (Element ByteString -> m) -> ByteString -> m ofoldr :: (Element ByteString -> b -> b) -> b -> ByteString -> b ofoldl' :: (a -> Element ByteString -> a) -> a -> ByteString -> a otoList :: ByteString -> [Element ByteString] oall :: (Element ByteString -> Bool) -> ByteString -> Bool oany :: (Element ByteString -> Bool) -> ByteString -> Bool onull :: ByteString -> Bool olength :: ByteString -> Int olength64 :: ByteString -> Int64 ocompareLength :: Integral i => ByteString -> i -> Ordering otraverse_ :: Applicative f => (Element ByteString -> f b) -> ByteString -> f () ofor_ :: Applicative f => ByteString -> (Element ByteString -> f b) -> f () omapM_ :: Applicative m => (Element ByteString -> m ()) -> ByteString -> m () oforM_ :: Applicative m => ByteString -> (Element ByteString -> m ()) -> m () ofoldlM :: Monad m => (a -> Element ByteString -> m a) -> a -> ByteString -> m a ofoldMap1Ex :: Semigroup m => (Element ByteString -> m) -> ByteString -> m ofoldr1Ex :: (Element ByteString -> Element ByteString -> Element ByteString) -> ByteString -> Element ByteString ofoldl1Ex' :: (Element ByteString -> Element ByteString -> Element ByteString) -> ByteString -> Element ByteString headEx :: ByteString -> Element ByteString lastEx :: ByteString -> Element ByteString unsafeHead :: ByteString -> Element ByteString unsafeLast :: ByteString -> Element ByteString maximumByEx :: (Element ByteString -> Element ByteString -> Ordering) -> ByteString -> Element ByteString minimumByEx :: (Element ByteString -> Element ByteString -> Ordering) -> ByteString -> Element ByteString oelem :: Element ByteString -> ByteString -> Bool onotElem :: Element ByteString -> ByteString -> Bool
MonoFunctor ByteString
Instance details Defined in Data.MonoTraversable Methods omap :: (Element ByteString -> Element ByteString) -> ByteString -> ByteString
MonoPointed ByteString
Instance details Defined in Data.MonoTraversable Methods opoint :: Element ByteString -> ByteString
MonoTraversable ByteString
Instance details Defined in Data.MonoTraversable Methods otraverse :: Applicative f => (Element ByteString -> f (Element ByteString)) -> ByteString -> f ByteString omapM :: Applicative m => (Element ByteString -> m (Element ByteString)) -> ByteString -> m ByteString
MonoZip ByteString
Instance details Defined in Data.Containers Methods ozipWith :: (Element ByteString -> Element ByteString -> Element ByteString) -> ByteString -> ByteString -> ByteString ozip :: ByteString -> ByteString -> [(Element ByteString, Element ByteString)] ounzip :: [(Element ByteString, Element ByteString)] -> (ByteString, ByteString)
IsSequence ByteString
Instance details Defined in Data.Sequences Methods fromList :: [Element ByteString] -> ByteString lengthIndex :: ByteString -> Index ByteString break :: (Element ByteString -> Bool) -> ByteString -> (ByteString, ByteString) span :: (Element ByteString -> Bool) -> ByteString -> (ByteString, ByteString) dropWhile :: (Element ByteString -> Bool) -> ByteString -> ByteString takeWhile :: (Element ByteString -> Bool) -> ByteString -> ByteString splitAt :: Index ByteString -> ByteString -> (ByteString, ByteString) unsafeSplitAt :: Index ByteString -> ByteString -> (ByteString, ByteString) take :: Index ByteString -> ByteString -> ByteString unsafeTake :: Index ByteString -> ByteString -> ByteString drop :: Index ByteString -> ByteString -> ByteString unsafeDrop :: Index ByteString -> ByteString -> ByteString dropEnd :: Index ByteString -> ByteString -> ByteString partition :: (Element ByteString -> Bool) -> ByteString -> (ByteString, ByteString) uncons :: ByteString -> Maybe (Element ByteString, ByteString) unsnoc :: ByteString -> Maybe (ByteString, Element ByteString) filter :: (Element ByteString -> Bool) -> ByteString -> ByteString filterM :: Monad m => (Element ByteString -> m Bool) -> ByteString -> m ByteString replicate :: Index ByteString -> Element ByteString -> ByteString replicateM :: Monad m => Index ByteString -> m (Element ByteString) -> m ByteString groupBy :: (Element ByteString -> Element ByteString -> Bool) -> ByteString -> [ByteString] groupAllOn :: Eq b => (Element ByteString -> b) -> ByteString -> [ByteString] subsequences :: ByteString -> [ByteString] permutations :: ByteString -> [ByteString] tailEx :: ByteString -> ByteString tailMay :: ByteString -> Maybe ByteString initEx :: ByteString -> ByteString initMay :: ByteString -> Maybe ByteString unsafeTail :: ByteString -> ByteString unsafeInit :: ByteString -> ByteString index :: ByteString -> Index ByteString -> Maybe (Element ByteString) indexEx :: ByteString -> Index ByteString -> Element ByteString unsafeIndex :: ByteString -> Index ByteString -> Element ByteString splitWhen :: (Element ByteString -> Bool) -> ByteString -> [ByteString]
SemiSequence ByteString
Instance details Defined in Data.Sequences Associated Types type Index ByteString Methods intersperse :: Element ByteString -> ByteString -> ByteString reverse :: ByteString -> ByteString find :: (Element ByteString -> Bool) -> ByteString -> Maybe (Element ByteString) sortBy :: (Element ByteString -> Element ByteString -> Ordering) -> ByteString -> ByteString cons :: Element ByteString -> ByteString -> ByteString snoc :: ByteString -> Element ByteString -> ByteString
Strict ByteString ByteString
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' ByteString ByteString0
LazySequence ByteString ByteString
Instance details Defined in Data.Sequences Methods toChunks :: ByteString -> [ByteString0] fromChunks :: [ByteString0] -> ByteString toStrict :: ByteString -> ByteString0 fromStrict :: ByteString0 -> ByteString
Utf8 Text ByteString
Instance details Defined in Data.Sequences Methods encodeUtf8 :: Text -> ByteString decodeUtf8 :: ByteString -> Text
Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString)
Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8)
(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b
type Item ByteString
Instance details Defined in Data.ByteString.Internal type Item ByteString = Word8
type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int
type Element ByteString
Instance details Defined in Data.MonoTraversable type Element ByteString = Word8
type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type Index ByteString
Instance details Defined in Data.Sequences type Index ByteString = Int

not :: Bool -> Bool #

Boolean "not"

(||) :: Bool -> Bool -> Bool infixr 2 #

Boolean "or", lazy in the second argument

(&&) :: Bool -> Bool -> Bool infixr 3 #

Boolean "and", lazy in the second argument

data SomeException #

The SomeException type is the root of the exception type hierarchy. When an exception of type e is thrown, behind the scenes it is encapsulated in a SomeException.

Instances

Instances details

Show SomeException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods showsPrec :: Int -> SomeException -> ShowS # show :: SomeException -> String # showList :: [SomeException] -> ShowS #
Exception SomeException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods toException :: SomeException -> SomeException # fromException :: SomeException -> Maybe SomeException # displayException :: SomeException -> String #

error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #

error stops execution and displays an error message.

undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

type String = [Char] #

A String is a list of characters. String constants in Haskell are values of type String.

See Data.List for operations on lists.

class (Alternative m, Monad m) => MonadPlus (m :: Type -> Type) where #

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a #

The identity of mplus. It should also satisfy the equations

mzero >>= f  =  mzero
v >> mzero   =  mzero

The default definition is

mzero = empty

mplus :: m a -> m a -> m a #

An associative operation. The default definition is

mplus = (<|>)

Instances

Instances details

MonadPlus []	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: [a] # mplus :: [a] -> [a] -> [a] #
MonadPlus Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a # mplus :: Maybe a -> Maybe a -> Maybe a #
MonadPlus IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a # mplus :: IO a -> IO a -> IO a #
MonadPlus Vector
Instance details Defined in Data.Vector Methods mzero :: Vector a # mplus :: Vector a -> Vector a -> Vector a #
MonadPlus Seq
Instance details Defined in Data.Sequence.Internal Methods mzero :: Seq a # mplus :: Seq a -> Seq a -> Seq a #
MonadPlus Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mzero :: Option a # mplus :: Option a -> Option a -> Option a #
MonadPlus STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods mzero :: STM a # mplus :: STM a -> STM a -> STM a #
MonadPlus ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods mzero :: ReadPrec a # mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a #
MonadPlus ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods mzero :: ReadP a # mplus :: ReadP a -> ReadP a -> ReadP a #
MonadPlus P	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods mzero :: P a # mplus :: P a -> P a -> P a #
MonadPlus Array
Instance details Defined in Data.Primitive.Array Methods mzero :: Array a # mplus :: Array a -> Array a -> Array a #
MonadPlus SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods mzero :: SmallArray a # mplus :: SmallArray a -> SmallArray a -> SmallArray a #
MonadPlus (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: U1 a # mplus :: U1 a -> U1 a -> U1 a #
Monoidal r => MonadPlus (Covector r)
Instance details Defined in Numeric.Covector Methods mzero :: Covector r a # mplus :: Covector r a -> Covector r a -> Covector r a #
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods mzero :: ArrowMonad a a0 # mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 #
MonadPlus (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a # mplus :: Proxy a -> Proxy a -> Proxy a #
Monad m => MonadPlus (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods mzero :: MaybeT m a # mplus :: MaybeT m a -> MaybeT m a -> MaybeT m a #
Monad m => MonadPlus (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods mzero :: CatchT m a # mplus :: CatchT m a -> CatchT m a -> CatchT m a #
Monad m => MonadPlus (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods mzero :: ListT m a # mplus :: ListT m a -> ListT m a -> ListT m a #
MonadPlus (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods mzero :: ReifiedFold s a # mplus :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #
MonadPlus f => MonadPlus (WrapFunctor f)
Instance details Defined in Control.Subcategory.Wrapper.Internal Methods mzero :: WrapFunctor f a # mplus :: WrapFunctor f a -> WrapFunctor f a -> WrapFunctor f a #
Monad m => MonadPlus (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods mzero :: IterT m a # mplus :: IterT m a -> IterT m a -> IterT m a #
(Functor v, MonadPlus v) => MonadPlus (Free v)
Instance details Defined in Control.Monad.Free Methods mzero :: Free v a # mplus :: Free v a -> Free v a -> Free v a #
MonadPlus m => MonadPlus (Yoneda m)
Instance details Defined in Data.Functor.Yoneda Methods mzero :: Yoneda m a # mplus :: Yoneda m a -> Yoneda m a -> Yoneda m a #
MonadPlus f => MonadPlus (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: Rec1 f a # mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a #
MonadPlus m => MonadPlus (Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods mzero :: Kleisli m a a0 # mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 #
MonadPlus f => MonadPlus (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a # mplus :: Ap f a -> Ap f a -> Ap f a #
MonadPlus f => MonadPlus (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a # mplus :: Alt f a -> Alt f a -> Alt f a #
(Monad m, Monoid e) => MonadPlus (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods mzero :: ExceptT e m a # mplus :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #
MonadPlus m => MonadPlus (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods mzero :: IdentityT m a # mplus :: IdentityT m a -> IdentityT m a -> IdentityT m a #
(Monad m, Error e) => MonadPlus (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods mzero :: ErrorT e m a # mplus :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #
MonadPlus m => MonadPlus (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods mzero :: ReaderT r m a # mplus :: ReaderT r m a -> ReaderT r m a -> ReaderT r m a #
MonadPlus m => MonadPlus (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods mzero :: StateT s m a # mplus :: StateT s m a -> StateT s m a -> StateT s m a #
MonadPlus m => MonadPlus (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods mzero :: StateT s m a # mplus :: StateT s m a -> StateT s m a -> StateT s m a #
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods mzero :: WriterT w m a # mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #
(Monoid w, MonadPlus m) => MonadPlus (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods mzero :: WriterT w m a # mplus :: WriterT w m a -> WriterT w m a -> WriterT w m a #
MonadPlus m => MonadPlus (Reverse m)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods mzero :: Reverse m a # mplus :: Reverse m a -> Reverse m a -> Reverse m a #
(Functor f, MonadPlus m) => MonadPlus (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods mzero :: FreeT f m a # mplus :: FreeT f m a -> FreeT f m a -> FreeT f m a #
MonadPlus m => MonadPlus (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods mzero :: RandT g m a # mplus :: RandT g m a -> RandT g m a -> RandT g m a #
MonadPlus m => MonadPlus (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods mzero :: RandT g m a # mplus :: RandT g m a -> RandT g m a -> RandT g m a #
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: (f :: g) a # mplus :: (f :: g) a -> (f :: g) a -> (f :: g) a #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a # mplus :: Product f g a -> Product f g a -> Product f g a #
MonadPlus f => MonadPlus (Star f a)
Instance details Defined in Data.Profunctor.Types Methods mzero :: Star f a a0 # mplus :: Star f a a0 -> Star f a a0 -> Star f a a0 #
MonadPlus f => MonadPlus (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: M1 i c f a # mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a #
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods mzero :: RWST r w s m a # mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #
(Monoid w, MonadPlus m) => MonadPlus (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods mzero :: RWST r w s m a # mplus :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a #

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

when :: Applicative f => Bool -> f () -> f () #

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

will output the string Debugging if the Boolean value debug is True, and otherwise do nothing.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r #

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

liftM2 (+) [0,1] [0,2] = [0,2,1,3]
liftM2 (+) (Just 1) Nothing = Nothing

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

ap :: Monad m => m (a -> b) -> m a -> m b #

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

return f `ap` x1 `ap` ... `ap` xn

is equivalent to

liftMn f x1 x2 ... xn

id :: a -> a #

Identity function.

id x = x

const :: a -> b -> a #

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 #

Function composition.

flip :: (a -> b -> c) -> b -> a -> c #

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

until :: (a -> Bool) -> (a -> a) -> a -> a #

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

curry :: ((a, b) -> c) -> a -> b -> c #

curry converts an uncurried function to a curried function.

Examples

Expand

>>> curry fst 1 2
1

uncurry :: (a -> b -> c) -> (a, b) -> c #

uncurry converts a curried function to a function on pairs.

Examples

Expand

>>> uncurry (+) (1,2)
3

>>> uncurry ($) (show, 1)
"1"

>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

swap :: (a, b) -> (b, a) #

Swap the components of a pair.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Expand

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

void :: Functor f => f a -> f () #

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Using ApplicativeDo: 'void as' can be understood as the do expression

do as
   pure ()

with an inferred Functor constraint.

Examples

Expand

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an Either Int ():

>>> void (Left 8675309)
Left 8675309
>>> void (Right 8675309)
Right ()

Replace every element of a list with unit:

>>> void [1,2,3]
[(),(),()]

Replace the second element of a pair with unit:

>>> void (1,2)
(1,())

Discard the result of an IO action:

>>> mapM print [1,2]
1
2
[(),()]
>>> void $ mapM print [1,2]
1
2

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0 #

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `on` f) x y = f x + f y

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

(*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})

```
((*) `on` f) `on` g = (*) `on` (f . g)
```
```
flip on f . flip on g = flip on (g . f)
```

bool :: a -> a -> Bool -> a #

Case analysis for the Bool type. bool x y p evaluates to x when p is False, and evaluates to y when p is True.

This is equivalent to if p then y else x; that is, one can think of it as an if-then-else construct with its arguments reordered.

Examples

Expand

Basic usage:

>>> bool "foo" "bar" True
"bar"
>>> bool "foo" "bar" False
"foo"

Confirm that bool x y p and if p then y else x are equivalent:

>>> let p = True; x = "bar"; y = "foo"
>>> bool x y p == if p then y else x
True
>>> let p = False
>>> bool x y p == if p then y else x
True

Since: base-4.7.0.0

maybe :: b -> (a -> b) -> Maybe a -> b #

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Expand

Basic usage:

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

isJust :: Maybe a -> Bool #

The isJust function returns True iff its argument is of the form Just _.

Examples

Expand

Basic usage:

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)
True

isNothing :: Maybe a -> Bool #

The isNothing function returns True iff its argument is Nothing.

Examples

Expand

Basic usage:

>>> isNothing (Just 3)
False

>>> isNothing (Just ())
False

>>> isNothing Nothing
True

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)
False

fromMaybe :: a -> Maybe a -> a #

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

Examples

Expand

Basic usage:

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"

>>> fromMaybe "" Nothing
""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

maybeToList :: Maybe a -> [a] #

The maybeToList function returns an empty list when given Nothing or a singleton list when given Just.

Examples

Expand

Basic usage:

>>> maybeToList (Just 7)
[7]

>>> maybeToList Nothing
[]

One can use maybeToList to avoid pattern matching when combined with a function that (safely) works on lists:

>>> import Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

listToMaybe :: [a] -> Maybe a #

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

Examples

Expand

Basic usage:

>>> listToMaybe []
Nothing

>>> listToMaybe [9]
Just 9

>>> listToMaybe [1,2,3]
Just 1

Composing maybeToList with listToMaybe should be the identity on singleton/empty lists:

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

But not on lists with more than one element:

>>> maybeToList $ listToMaybe [1,2,3]
[1]

catMaybes :: [Maybe a] -> [a] #

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

Examples

Expand

Basic usage:

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

When constructing a list of Maybe values, catMaybes can be used to return all of the "success" results (if the list is the result of a map, then mapMaybe would be more appropriate):

>>> import Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

mapMaybe :: (a -> Maybe b) -> [a] -> [b] #

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

Examples

Expand

Using mapMaybe f x is a shortcut for catMaybes $ map f x in most cases:

>>> import Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

If we map the Just constructor, the entire list should be returned:

>>> mapMaybe Just [1,2,3]
[1,2,3]

head :: [a] -> a #

$\mathcal{O}(1)$. Extract the first element of a list, which must be non-empty.

uncons :: [a] -> Maybe (a, [a]) #

$\mathcal{O}(1)$. Decompose a list into its head and tail. If the list is empty, returns Nothing. If the list is non-empty, returns Just (x, xs), where x is the head of the list and xs its tail.

Since: base-4.8.0.0

tail :: [a] -> [a] #

$\mathcal{O}(1)$. Extract the elements after the head of a list, which must be non-empty.

last :: [a] -> a #

$\mathcal{O}(n)$. Extract the last element of a list, which must be finite and non-empty.

init :: [a] -> [a] #

$\mathcal{O}(n)$. Return all the elements of a list except the last one. The list must be non-empty.

foldl1' :: (a -> a -> a) -> [a] -> a #

A strict version of foldl1

scanl :: (b -> a -> b) -> b -> [a] -> [b] #

$\mathcal{O}(n)$. scanl is similar to foldl, but returns a list of successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a] #

$\mathcal{O}(n)$. scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanl' :: (b -> a -> b) -> b -> [a] -> [b] #

$\mathcal{O}(n)$. A strictly accumulating version of scanl

scanr :: (a -> b -> b) -> b -> [a] -> [b] #

$\mathcal{O}(n)$. scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a] #

$\mathcal{O}(n)$. scanr1 is a variant of scanr that has no starting value argument.

iterate :: (a -> a) -> a -> [a] #

iterate f x returns an infinite list of repeated applications of f to x:

iterate f x == [x, f x, f (f x), ...]

Note that iterate is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See iterate' for a strict variant of this function.

iterate' :: (a -> a) -> a -> [a] #

iterate' is the strict version of iterate.

It ensures that the result of each application of force to weak head normal form before proceeding.

repeat :: a -> [a] #

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a] #

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

cycle :: [a] -> [a] #

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

takeWhile :: (a -> Bool) -> [a] -> [a] #

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
takeWhile (< 9) [1,2,3] == [1,2,3]
takeWhile (< 0) [1,2,3] == []

dropWhile :: (a -> Bool) -> [a] -> [a] #

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

take :: Int -> [a] -> [a] #

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

take 5 "Hello World!" == "Hello"
take 3 [1,2,3,4,5] == [1,2,3]
take 3 [1,2] == [1,2]
take 3 [] == []
take (-1) [1,2] == []
take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

drop :: Int -> [a] -> [a] #

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

drop 6 "Hello World!" == "World!"
drop 3 [1,2,3,4,5] == [4,5]
drop 3 [1,2] == []
drop 3 [] == []
drop (-1) [1,2] == [1,2]
drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

splitAt :: Int -> [a] -> ([a], [a]) #

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

span :: (a -> Bool) -> [a] -> ([a], [a]) #

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
span (< 9) [1,2,3] == ([1,2,3],[])
span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

break :: (a -> Bool) -> [a] -> ([a], [a]) #

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
break (< 9) [1,2,3] == ([],[1,2,3])
break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

reverse :: [a] -> [a] #

reverse xs returns the elements of xs in reverse order. xs must be finite.

lookup :: Eq a => a -> [(a, b)] -> Maybe b #

$\mathcal{O}(n)$. lookup key assocs looks up a key in an association list.

>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

(!!) :: [a] -> Int -> a infixl 9 #

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] #

zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #

$\mathcal{O}(\min(m,n))$. zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

unzip :: [(a, b)] -> ([a], [b]) #

unzip transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) #

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

type ShowS = String -> String #

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

shows :: Show a => a -> ShowS #

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowS #

utility function converting a Char to a show function that simply prepends the character unchanged.

showString :: String -> ShowS #

utility function converting a String to a show function that simply prepends the string unchanged.

showParen :: Bool -> ShowS -> ShowS #

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

even :: Integral a => a -> Bool #

odd :: Integral a => a -> Bool #

type ReadS a = String -> [(a, String)] #

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

readParen :: Bool -> ReadS a -> ReadS a #

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

class Storable a #

The member functions of this class facilitate writing values of primitive types to raw memory (which may have been allocated with the above mentioned routines) and reading values from blocks of raw memory. The class, furthermore, includes support for computing the storage requirements and alignment restrictions of storable types.

Memory addresses are represented as values of type Ptr a, for some a which is an instance of class Storable. The type argument to Ptr helps provide some valuable type safety in FFI code (you can't mix pointers of different types without an explicit cast), while helping the Haskell type system figure out which marshalling method is needed for a given pointer.

All marshalling between Haskell and a foreign language ultimately boils down to translating Haskell data structures into the binary representation of a corresponding data structure of the foreign language and vice versa. To code this marshalling in Haskell, it is necessary to manipulate primitive data types stored in unstructured memory blocks. The class Storable facilitates this manipulation on all types for which it is instantiated, which are the standard basic types of Haskell, the fixed size Int types (Int8, Int16, Int32, Int64), the fixed size Word types (Word8, Word16, Word32, Word64), StablePtr, all types from Foreign.C.Types, as well as Ptr.

Minimal complete definition

sizeOf, alignment, (peek | peekElemOff | peekByteOff), (poke | pokeElemOff | pokeByteOff)

Instances

Instances details

Storable Bool	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Bool -> Int # alignment :: Bool -> Int # peekElemOff :: Ptr Bool -> Int -> IO Bool # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () # peekByteOff :: Ptr b -> Int -> IO Bool # pokeByteOff :: Ptr b -> Int -> Bool -> IO () # peek :: Ptr Bool -> IO Bool # poke :: Ptr Bool -> Bool -> IO () #
Storable Char	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Char -> Int # alignment :: Char -> Int # peekElemOff :: Ptr Char -> Int -> IO Char # pokeElemOff :: Ptr Char -> Int -> Char -> IO () # peekByteOff :: Ptr b -> Int -> IO Char # pokeByteOff :: Ptr b -> Int -> Char -> IO () # peek :: Ptr Char -> IO Char # poke :: Ptr Char -> Char -> IO () #
Storable Double	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Double -> Int # alignment :: Double -> Int # peekElemOff :: Ptr Double -> Int -> IO Double # pokeElemOff :: Ptr Double -> Int -> Double -> IO () # peekByteOff :: Ptr b -> Int -> IO Double # pokeByteOff :: Ptr b -> Int -> Double -> IO () # peek :: Ptr Double -> IO Double # poke :: Ptr Double -> Double -> IO () #
Storable Float	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Float -> Int # alignment :: Float -> Int # peekElemOff :: Ptr Float -> Int -> IO Float # pokeElemOff :: Ptr Float -> Int -> Float -> IO () # peekByteOff :: Ptr b -> Int -> IO Float # pokeByteOff :: Ptr b -> Int -> Float -> IO () # peek :: Ptr Float -> IO Float # poke :: Ptr Float -> Float -> IO () #
Storable Int	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int -> Int # alignment :: Int -> Int # peekElemOff :: Ptr Int -> Int -> IO Int # pokeElemOff :: Ptr Int -> Int -> Int -> IO () # peekByteOff :: Ptr b -> Int -> IO Int # pokeByteOff :: Ptr b -> Int -> Int -> IO () # peek :: Ptr Int -> IO Int # poke :: Ptr Int -> Int -> IO () #
Storable Int8	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int8 -> Int # alignment :: Int8 -> Int # peekElemOff :: Ptr Int8 -> Int -> IO Int8 # pokeElemOff :: Ptr Int8 -> Int -> Int8 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int8 # pokeByteOff :: Ptr b -> Int -> Int8 -> IO () # peek :: Ptr Int8 -> IO Int8 # poke :: Ptr Int8 -> Int8 -> IO () #
Storable Int16	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int16 -> Int # alignment :: Int16 -> Int # peekElemOff :: Ptr Int16 -> Int -> IO Int16 # pokeElemOff :: Ptr Int16 -> Int -> Int16 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int16 # pokeByteOff :: Ptr b -> Int -> Int16 -> IO () # peek :: Ptr Int16 -> IO Int16 # poke :: Ptr Int16 -> Int16 -> IO () #
Storable Int32	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int32 -> Int # alignment :: Int32 -> Int # peekElemOff :: Ptr Int32 -> Int -> IO Int32 # pokeElemOff :: Ptr Int32 -> Int -> Int32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int32 # pokeByteOff :: Ptr b -> Int -> Int32 -> IO () # peek :: Ptr Int32 -> IO Int32 # poke :: Ptr Int32 -> Int32 -> IO () #
Storable Int64	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int64 -> Int # alignment :: Int64 -> Int # peekElemOff :: Ptr Int64 -> Int -> IO Int64 # pokeElemOff :: Ptr Int64 -> Int -> Int64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int64 # pokeByteOff :: Ptr b -> Int -> Int64 -> IO () # peek :: Ptr Int64 -> IO Int64 # poke :: Ptr Int64 -> Int64 -> IO () #
Storable Word	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word -> Int # alignment :: Word -> Int # peekElemOff :: Ptr Word -> Int -> IO Word # pokeElemOff :: Ptr Word -> Int -> Word -> IO () # peekByteOff :: Ptr b -> Int -> IO Word # pokeByteOff :: Ptr b -> Int -> Word -> IO () # peek :: Ptr Word -> IO Word # poke :: Ptr Word -> Word -> IO () #
Storable Word8	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word8 -> Int # alignment :: Word8 -> Int # peekElemOff :: Ptr Word8 -> Int -> IO Word8 # pokeElemOff :: Ptr Word8 -> Int -> Word8 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word8 # pokeByteOff :: Ptr b -> Int -> Word8 -> IO () # peek :: Ptr Word8 -> IO Word8 # poke :: Ptr Word8 -> Word8 -> IO () #
Storable Word16	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word16 -> Int # alignment :: Word16 -> Int # peekElemOff :: Ptr Word16 -> Int -> IO Word16 # pokeElemOff :: Ptr Word16 -> Int -> Word16 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word16 # pokeByteOff :: Ptr b -> Int -> Word16 -> IO () # peek :: Ptr Word16 -> IO Word16 # poke :: Ptr Word16 -> Word16 -> IO () #
Storable Word32	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word32 -> Int # alignment :: Word32 -> Int # peekElemOff :: Ptr Word32 -> Int -> IO Word32 # pokeElemOff :: Ptr Word32 -> Int -> Word32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word32 # pokeByteOff :: Ptr b -> Int -> Word32 -> IO () # peek :: Ptr Word32 -> IO Word32 # poke :: Ptr Word32 -> Word32 -> IO () #
Storable Word64	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Word64 -> Int # alignment :: Word64 -> Int # peekElemOff :: Ptr Word64 -> Int -> IO Word64 # pokeElemOff :: Ptr Word64 -> Int -> Word64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word64 # pokeByteOff :: Ptr b -> Int -> Word64 -> IO () # peek :: Ptr Word64 -> IO Word64 # poke :: Ptr Word64 -> Word64 -> IO () #
Storable ()	Since: base-4.9.0.0
Instance details Defined in Foreign.Storable Methods sizeOf :: () -> Int # alignment :: () -> Int # peekElemOff :: Ptr () -> Int -> IO () # pokeElemOff :: Ptr () -> Int -> () -> IO () # peekByteOff :: Ptr b -> Int -> IO () # pokeByteOff :: Ptr b -> Int -> () -> IO () # peek :: Ptr () -> IO () # poke :: Ptr () -> () -> IO () #
Storable CDev
Instance details Defined in System.Posix.Types Methods sizeOf :: CDev -> Int # alignment :: CDev -> Int # peekElemOff :: Ptr CDev -> Int -> IO CDev # pokeElemOff :: Ptr CDev -> Int -> CDev -> IO () # peekByteOff :: Ptr b -> Int -> IO CDev # pokeByteOff :: Ptr b -> Int -> CDev -> IO () # peek :: Ptr CDev -> IO CDev # poke :: Ptr CDev -> CDev -> IO () #
Storable CIno
Instance details Defined in System.Posix.Types Methods sizeOf :: CIno -> Int # alignment :: CIno -> Int # peekElemOff :: Ptr CIno -> Int -> IO CIno # pokeElemOff :: Ptr CIno -> Int -> CIno -> IO () # peekByteOff :: Ptr b -> Int -> IO CIno # pokeByteOff :: Ptr b -> Int -> CIno -> IO () # peek :: Ptr CIno -> IO CIno # poke :: Ptr CIno -> CIno -> IO () #
Storable CMode
Instance details Defined in System.Posix.Types Methods sizeOf :: CMode -> Int # alignment :: CMode -> Int # peekElemOff :: Ptr CMode -> Int -> IO CMode # pokeElemOff :: Ptr CMode -> Int -> CMode -> IO () # peekByteOff :: Ptr b -> Int -> IO CMode # pokeByteOff :: Ptr b -> Int -> CMode -> IO () # peek :: Ptr CMode -> IO CMode # poke :: Ptr CMode -> CMode -> IO () #
Storable COff
Instance details Defined in System.Posix.Types Methods sizeOf :: COff -> Int # alignment :: COff -> Int # peekElemOff :: Ptr COff -> Int -> IO COff # pokeElemOff :: Ptr COff -> Int -> COff -> IO () # peekByteOff :: Ptr b -> Int -> IO COff # pokeByteOff :: Ptr b -> Int -> COff -> IO () # peek :: Ptr COff -> IO COff # poke :: Ptr COff -> COff -> IO () #
Storable CPid
Instance details Defined in System.Posix.Types Methods sizeOf :: CPid -> Int # alignment :: CPid -> Int # peekElemOff :: Ptr CPid -> Int -> IO CPid # pokeElemOff :: Ptr CPid -> Int -> CPid -> IO () # peekByteOff :: Ptr b -> Int -> IO CPid # pokeByteOff :: Ptr b -> Int -> CPid -> IO () # peek :: Ptr CPid -> IO CPid # poke :: Ptr CPid -> CPid -> IO () #
Storable CSsize
Instance details Defined in System.Posix.Types Methods sizeOf :: CSsize -> Int # alignment :: CSsize -> Int # peekElemOff :: Ptr CSsize -> Int -> IO CSsize # pokeElemOff :: Ptr CSsize -> Int -> CSsize -> IO () # peekByteOff :: Ptr b -> Int -> IO CSsize # pokeByteOff :: Ptr b -> Int -> CSsize -> IO () # peek :: Ptr CSsize -> IO CSsize # poke :: Ptr CSsize -> CSsize -> IO () #
Storable CGid
Instance details Defined in System.Posix.Types Methods sizeOf :: CGid -> Int # alignment :: CGid -> Int # peekElemOff :: Ptr CGid -> Int -> IO CGid # pokeElemOff :: Ptr CGid -> Int -> CGid -> IO () # peekByteOff :: Ptr b -> Int -> IO CGid # pokeByteOff :: Ptr b -> Int -> CGid -> IO () # peek :: Ptr CGid -> IO CGid # poke :: Ptr CGid -> CGid -> IO () #
Storable CNlink
Instance details Defined in System.Posix.Types Methods sizeOf :: CNlink -> Int # alignment :: CNlink -> Int # peekElemOff :: Ptr CNlink -> Int -> IO CNlink # pokeElemOff :: Ptr CNlink -> Int -> CNlink -> IO () # peekByteOff :: Ptr b -> Int -> IO CNlink # pokeByteOff :: Ptr b -> Int -> CNlink -> IO () # peek :: Ptr CNlink -> IO CNlink # poke :: Ptr CNlink -> CNlink -> IO () #
Storable CUid
Instance details Defined in System.Posix.Types Methods sizeOf :: CUid -> Int # alignment :: CUid -> Int # peekElemOff :: Ptr CUid -> Int -> IO CUid # pokeElemOff :: Ptr CUid -> Int -> CUid -> IO () # peekByteOff :: Ptr b -> Int -> IO CUid # pokeByteOff :: Ptr b -> Int -> CUid -> IO () # peek :: Ptr CUid -> IO CUid # poke :: Ptr CUid -> CUid -> IO () #
Storable CCc
Instance details Defined in System.Posix.Types Methods sizeOf :: CCc -> Int # alignment :: CCc -> Int # peekElemOff :: Ptr CCc -> Int -> IO CCc # pokeElemOff :: Ptr CCc -> Int -> CCc -> IO () # peekByteOff :: Ptr b -> Int -> IO CCc # pokeByteOff :: Ptr b -> Int -> CCc -> IO () # peek :: Ptr CCc -> IO CCc # poke :: Ptr CCc -> CCc -> IO () #
Storable CSpeed
Instance details Defined in System.Posix.Types Methods sizeOf :: CSpeed -> Int # alignment :: CSpeed -> Int # peekElemOff :: Ptr CSpeed -> Int -> IO CSpeed # pokeElemOff :: Ptr CSpeed -> Int -> CSpeed -> IO () # peekByteOff :: Ptr b -> Int -> IO CSpeed # pokeByteOff :: Ptr b -> Int -> CSpeed -> IO () # peek :: Ptr CSpeed -> IO CSpeed # poke :: Ptr CSpeed -> CSpeed -> IO () #
Storable CTcflag
Instance details Defined in System.Posix.Types Methods sizeOf :: CTcflag -> Int # alignment :: CTcflag -> Int # peekElemOff :: Ptr CTcflag -> Int -> IO CTcflag # pokeElemOff :: Ptr CTcflag -> Int -> CTcflag -> IO () # peekByteOff :: Ptr b -> Int -> IO CTcflag # pokeByteOff :: Ptr b -> Int -> CTcflag -> IO () # peek :: Ptr CTcflag -> IO CTcflag # poke :: Ptr CTcflag -> CTcflag -> IO () #
Storable CRLim
Instance details Defined in System.Posix.Types Methods sizeOf :: CRLim -> Int # alignment :: CRLim -> Int # peekElemOff :: Ptr CRLim -> Int -> IO CRLim # pokeElemOff :: Ptr CRLim -> Int -> CRLim -> IO () # peekByteOff :: Ptr b -> Int -> IO CRLim # pokeByteOff :: Ptr b -> Int -> CRLim -> IO () # peek :: Ptr CRLim -> IO CRLim # poke :: Ptr CRLim -> CRLim -> IO () #
Storable CBlkSize
Instance details Defined in System.Posix.Types Methods sizeOf :: CBlkSize -> Int # alignment :: CBlkSize -> Int # peekElemOff :: Ptr CBlkSize -> Int -> IO CBlkSize # pokeElemOff :: Ptr CBlkSize -> Int -> CBlkSize -> IO () # peekByteOff :: Ptr b -> Int -> IO CBlkSize # pokeByteOff :: Ptr b -> Int -> CBlkSize -> IO () # peek :: Ptr CBlkSize -> IO CBlkSize # poke :: Ptr CBlkSize -> CBlkSize -> IO () #
Storable CBlkCnt
Instance details Defined in System.Posix.Types Methods sizeOf :: CBlkCnt -> Int # alignment :: CBlkCnt -> Int # peekElemOff :: Ptr CBlkCnt -> Int -> IO CBlkCnt # pokeElemOff :: Ptr CBlkCnt -> Int -> CBlkCnt -> IO () # peekByteOff :: Ptr b -> Int -> IO CBlkCnt # pokeByteOff :: Ptr b -> Int -> CBlkCnt -> IO () # peek :: Ptr CBlkCnt -> IO CBlkCnt # poke :: Ptr CBlkCnt -> CBlkCnt -> IO () #
Storable CClockId
Instance details Defined in System.Posix.Types Methods sizeOf :: CClockId -> Int # alignment :: CClockId -> Int # peekElemOff :: Ptr CClockId -> Int -> IO CClockId # pokeElemOff :: Ptr CClockId -> Int -> CClockId -> IO () # peekByteOff :: Ptr b -> Int -> IO CClockId # pokeByteOff :: Ptr b -> Int -> CClockId -> IO () # peek :: Ptr CClockId -> IO CClockId # poke :: Ptr CClockId -> CClockId -> IO () #
Storable CFsBlkCnt
Instance details Defined in System.Posix.Types Methods sizeOf :: CFsBlkCnt -> Int # alignment :: CFsBlkCnt -> Int # peekElemOff :: Ptr CFsBlkCnt -> Int -> IO CFsBlkCnt # pokeElemOff :: Ptr CFsBlkCnt -> Int -> CFsBlkCnt -> IO () # peekByteOff :: Ptr b -> Int -> IO CFsBlkCnt # pokeByteOff :: Ptr b -> Int -> CFsBlkCnt -> IO () # peek :: Ptr CFsBlkCnt -> IO CFsBlkCnt # poke :: Ptr CFsBlkCnt -> CFsBlkCnt -> IO () #
Storable CFsFilCnt
Instance details Defined in System.Posix.Types Methods sizeOf :: CFsFilCnt -> Int # alignment :: CFsFilCnt -> Int # peekElemOff :: Ptr CFsFilCnt -> Int -> IO CFsFilCnt # pokeElemOff :: Ptr CFsFilCnt -> Int -> CFsFilCnt -> IO () # peekByteOff :: Ptr b -> Int -> IO CFsFilCnt # pokeByteOff :: Ptr b -> Int -> CFsFilCnt -> IO () # peek :: Ptr CFsFilCnt -> IO CFsFilCnt # poke :: Ptr CFsFilCnt -> CFsFilCnt -> IO () #
Storable CId
Instance details Defined in System.Posix.Types Methods sizeOf :: CId -> Int # alignment :: CId -> Int # peekElemOff :: Ptr CId -> Int -> IO CId # pokeElemOff :: Ptr CId -> Int -> CId -> IO () # peekByteOff :: Ptr b -> Int -> IO CId # pokeByteOff :: Ptr b -> Int -> CId -> IO () # peek :: Ptr CId -> IO CId # poke :: Ptr CId -> CId -> IO () #
Storable CKey
Instance details Defined in System.Posix.Types Methods sizeOf :: CKey -> Int # alignment :: CKey -> Int # peekElemOff :: Ptr CKey -> Int -> IO CKey # pokeElemOff :: Ptr CKey -> Int -> CKey -> IO () # peekByteOff :: Ptr b -> Int -> IO CKey # pokeByteOff :: Ptr b -> Int -> CKey -> IO () # peek :: Ptr CKey -> IO CKey # poke :: Ptr CKey -> CKey -> IO () #
Storable CTimer
Instance details Defined in System.Posix.Types Methods sizeOf :: CTimer -> Int # alignment :: CTimer -> Int # peekElemOff :: Ptr CTimer -> Int -> IO CTimer # pokeElemOff :: Ptr CTimer -> Int -> CTimer -> IO () # peekByteOff :: Ptr b -> Int -> IO CTimer # pokeByteOff :: Ptr b -> Int -> CTimer -> IO () # peek :: Ptr CTimer -> IO CTimer # poke :: Ptr CTimer -> CTimer -> IO () #
Storable CSocklen
Instance details Defined in System.Posix.Types Methods sizeOf :: CSocklen -> Int # alignment :: CSocklen -> Int # peekElemOff :: Ptr CSocklen -> Int -> IO CSocklen # pokeElemOff :: Ptr CSocklen -> Int -> CSocklen -> IO () # peekByteOff :: Ptr b -> Int -> IO CSocklen # pokeByteOff :: Ptr b -> Int -> CSocklen -> IO () # peek :: Ptr CSocklen -> IO CSocklen # poke :: Ptr CSocklen -> CSocklen -> IO () #
Storable CNfds
Instance details Defined in System.Posix.Types Methods sizeOf :: CNfds -> Int # alignment :: CNfds -> Int # peekElemOff :: Ptr CNfds -> Int -> IO CNfds # pokeElemOff :: Ptr CNfds -> Int -> CNfds -> IO () # peekByteOff :: Ptr b -> Int -> IO CNfds # pokeByteOff :: Ptr b -> Int -> CNfds -> IO () # peek :: Ptr CNfds -> IO CNfds # poke :: Ptr CNfds -> CNfds -> IO () #
Storable Fd
Instance details Defined in System.Posix.Types Methods sizeOf :: Fd -> Int # alignment :: Fd -> Int # peekElemOff :: Ptr Fd -> Int -> IO Fd # pokeElemOff :: Ptr Fd -> Int -> Fd -> IO () # peekByteOff :: Ptr b -> Int -> IO Fd # pokeByteOff :: Ptr b -> Int -> Fd -> IO () # peek :: Ptr Fd -> IO Fd # poke :: Ptr Fd -> Fd -> IO () #
Storable CChar
Instance details Defined in Foreign.C.Types Methods sizeOf :: CChar -> Int # alignment :: CChar -> Int # peekElemOff :: Ptr CChar -> Int -> IO CChar # pokeElemOff :: Ptr CChar -> Int -> CChar -> IO () # peekByteOff :: Ptr b -> Int -> IO CChar # pokeByteOff :: Ptr b -> Int -> CChar -> IO () # peek :: Ptr CChar -> IO CChar # poke :: Ptr CChar -> CChar -> IO () #
Storable CSChar
Instance details Defined in Foreign.C.Types Methods sizeOf :: CSChar -> Int # alignment :: CSChar -> Int # peekElemOff :: Ptr CSChar -> Int -> IO CSChar # pokeElemOff :: Ptr CSChar -> Int -> CSChar -> IO () # peekByteOff :: Ptr b -> Int -> IO CSChar # pokeByteOff :: Ptr b -> Int -> CSChar -> IO () # peek :: Ptr CSChar -> IO CSChar # poke :: Ptr CSChar -> CSChar -> IO () #
Storable CUChar
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUChar -> Int # alignment :: CUChar -> Int # peekElemOff :: Ptr CUChar -> Int -> IO CUChar # pokeElemOff :: Ptr CUChar -> Int -> CUChar -> IO () # peekByteOff :: Ptr b -> Int -> IO CUChar # pokeByteOff :: Ptr b -> Int -> CUChar -> IO () # peek :: Ptr CUChar -> IO CUChar # poke :: Ptr CUChar -> CUChar -> IO () #
Storable CShort
Instance details Defined in Foreign.C.Types Methods sizeOf :: CShort -> Int # alignment :: CShort -> Int # peekElemOff :: Ptr CShort -> Int -> IO CShort # pokeElemOff :: Ptr CShort -> Int -> CShort -> IO () # peekByteOff :: Ptr b -> Int -> IO CShort # pokeByteOff :: Ptr b -> Int -> CShort -> IO () # peek :: Ptr CShort -> IO CShort # poke :: Ptr CShort -> CShort -> IO () #
Storable CUShort
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUShort -> Int # alignment :: CUShort -> Int # peekElemOff :: Ptr CUShort -> Int -> IO CUShort # pokeElemOff :: Ptr CUShort -> Int -> CUShort -> IO () # peekByteOff :: Ptr b -> Int -> IO CUShort # pokeByteOff :: Ptr b -> Int -> CUShort -> IO () # peek :: Ptr CUShort -> IO CUShort # poke :: Ptr CUShort -> CUShort -> IO () #
Storable CInt
Instance details Defined in Foreign.C.Types Methods sizeOf :: CInt -> Int # alignment :: CInt -> Int # peekElemOff :: Ptr CInt -> Int -> IO CInt # pokeElemOff :: Ptr CInt -> Int -> CInt -> IO () # peekByteOff :: Ptr b -> Int -> IO CInt # pokeByteOff :: Ptr b -> Int -> CInt -> IO () # peek :: Ptr CInt -> IO CInt # poke :: Ptr CInt -> CInt -> IO () #
Storable CUInt
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUInt -> Int # alignment :: CUInt -> Int # peekElemOff :: Ptr CUInt -> Int -> IO CUInt # pokeElemOff :: Ptr CUInt -> Int -> CUInt -> IO () # peekByteOff :: Ptr b -> Int -> IO CUInt # pokeByteOff :: Ptr b -> Int -> CUInt -> IO () # peek :: Ptr CUInt -> IO CUInt # poke :: Ptr CUInt -> CUInt -> IO () #
Storable CLong
Instance details Defined in Foreign.C.Types Methods sizeOf :: CLong -> Int # alignment :: CLong -> Int # peekElemOff :: Ptr CLong -> Int -> IO CLong # pokeElemOff :: Ptr CLong -> Int -> CLong -> IO () # peekByteOff :: Ptr b -> Int -> IO CLong # pokeByteOff :: Ptr b -> Int -> CLong -> IO () # peek :: Ptr CLong -> IO CLong # poke :: Ptr CLong -> CLong -> IO () #
Storable CULong
Instance details Defined in Foreign.C.Types Methods sizeOf :: CULong -> Int # alignment :: CULong -> Int # peekElemOff :: Ptr CULong -> Int -> IO CULong # pokeElemOff :: Ptr CULong -> Int -> CULong -> IO () # peekByteOff :: Ptr b -> Int -> IO CULong # pokeByteOff :: Ptr b -> Int -> CULong -> IO () # peek :: Ptr CULong -> IO CULong # poke :: Ptr CULong -> CULong -> IO () #
Storable CLLong
Instance details Defined in Foreign.C.Types Methods sizeOf :: CLLong -> Int # alignment :: CLLong -> Int # peekElemOff :: Ptr CLLong -> Int -> IO CLLong # pokeElemOff :: Ptr CLLong -> Int -> CLLong -> IO () # peekByteOff :: Ptr b -> Int -> IO CLLong # pokeByteOff :: Ptr b -> Int -> CLLong -> IO () # peek :: Ptr CLLong -> IO CLLong # poke :: Ptr CLLong -> CLLong -> IO () #
Storable CULLong
Instance details Defined in Foreign.C.Types Methods sizeOf :: CULLong -> Int # alignment :: CULLong -> Int # peekElemOff :: Ptr CULLong -> Int -> IO CULLong # pokeElemOff :: Ptr CULLong -> Int -> CULLong -> IO () # peekByteOff :: Ptr b -> Int -> IO CULLong # pokeByteOff :: Ptr b -> Int -> CULLong -> IO () # peek :: Ptr CULLong -> IO CULLong # poke :: Ptr CULLong -> CULLong -> IO () #
Storable CBool
Instance details Defined in Foreign.C.Types Methods sizeOf :: CBool -> Int # alignment :: CBool -> Int # peekElemOff :: Ptr CBool -> Int -> IO CBool # pokeElemOff :: Ptr CBool -> Int -> CBool -> IO () # peekByteOff :: Ptr b -> Int -> IO CBool # pokeByteOff :: Ptr b -> Int -> CBool -> IO () # peek :: Ptr CBool -> IO CBool # poke :: Ptr CBool -> CBool -> IO () #
Storable CFloat
Instance details Defined in Foreign.C.Types Methods sizeOf :: CFloat -> Int # alignment :: CFloat -> Int # peekElemOff :: Ptr CFloat -> Int -> IO CFloat # pokeElemOff :: Ptr CFloat -> Int -> CFloat -> IO () # peekByteOff :: Ptr b -> Int -> IO CFloat # pokeByteOff :: Ptr b -> Int -> CFloat -> IO () # peek :: Ptr CFloat -> IO CFloat # poke :: Ptr CFloat -> CFloat -> IO () #
Storable CDouble
Instance details Defined in Foreign.C.Types Methods sizeOf :: CDouble -> Int # alignment :: CDouble -> Int # peekElemOff :: Ptr CDouble -> Int -> IO CDouble # pokeElemOff :: Ptr CDouble -> Int -> CDouble -> IO () # peekByteOff :: Ptr b -> Int -> IO CDouble # pokeByteOff :: Ptr b -> Int -> CDouble -> IO () # peek :: Ptr CDouble -> IO CDouble # poke :: Ptr CDouble -> CDouble -> IO () #
Storable CPtrdiff
Instance details Defined in Foreign.C.Types Methods sizeOf :: CPtrdiff -> Int # alignment :: CPtrdiff -> Int # peekElemOff :: Ptr CPtrdiff -> Int -> IO CPtrdiff # pokeElemOff :: Ptr CPtrdiff -> Int -> CPtrdiff -> IO () # peekByteOff :: Ptr b -> Int -> IO CPtrdiff # pokeByteOff :: Ptr b -> Int -> CPtrdiff -> IO () # peek :: Ptr CPtrdiff -> IO CPtrdiff # poke :: Ptr CPtrdiff -> CPtrdiff -> IO () #
Storable CSize
Instance details Defined in Foreign.C.Types Methods sizeOf :: CSize -> Int # alignment :: CSize -> Int # peekElemOff :: Ptr CSize -> Int -> IO CSize # pokeElemOff :: Ptr CSize -> Int -> CSize -> IO () # peekByteOff :: Ptr b -> Int -> IO CSize # pokeByteOff :: Ptr b -> Int -> CSize -> IO () # peek :: Ptr CSize -> IO CSize # poke :: Ptr CSize -> CSize -> IO () #
Storable CWchar
Instance details Defined in Foreign.C.Types Methods sizeOf :: CWchar -> Int # alignment :: CWchar -> Int # peekElemOff :: Ptr CWchar -> Int -> IO CWchar # pokeElemOff :: Ptr CWchar -> Int -> CWchar -> IO () # peekByteOff :: Ptr b -> Int -> IO CWchar # pokeByteOff :: Ptr b -> Int -> CWchar -> IO () # peek :: Ptr CWchar -> IO CWchar # poke :: Ptr CWchar -> CWchar -> IO () #
Storable CSigAtomic
Instance details Defined in Foreign.C.Types Methods sizeOf :: CSigAtomic -> Int # alignment :: CSigAtomic -> Int # peekElemOff :: Ptr CSigAtomic -> Int -> IO CSigAtomic # pokeElemOff :: Ptr CSigAtomic -> Int -> CSigAtomic -> IO () # peekByteOff :: Ptr b -> Int -> IO CSigAtomic # pokeByteOff :: Ptr b -> Int -> CSigAtomic -> IO () # peek :: Ptr CSigAtomic -> IO CSigAtomic # poke :: Ptr CSigAtomic -> CSigAtomic -> IO () #
Storable CClock
Instance details Defined in Foreign.C.Types Methods sizeOf :: CClock -> Int # alignment :: CClock -> Int # peekElemOff :: Ptr CClock -> Int -> IO CClock # pokeElemOff :: Ptr CClock -> Int -> CClock -> IO () # peekByteOff :: Ptr b -> Int -> IO CClock # pokeByteOff :: Ptr b -> Int -> CClock -> IO () # peek :: Ptr CClock -> IO CClock # poke :: Ptr CClock -> CClock -> IO () #
Storable CTime
Instance details Defined in Foreign.C.Types Methods sizeOf :: CTime -> Int # alignment :: CTime -> Int # peekElemOff :: Ptr CTime -> Int -> IO CTime # pokeElemOff :: Ptr CTime -> Int -> CTime -> IO () # peekByteOff :: Ptr b -> Int -> IO CTime # pokeByteOff :: Ptr b -> Int -> CTime -> IO () # peek :: Ptr CTime -> IO CTime # poke :: Ptr CTime -> CTime -> IO () #
Storable CUSeconds
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUSeconds -> Int # alignment :: CUSeconds -> Int # peekElemOff :: Ptr CUSeconds -> Int -> IO CUSeconds # pokeElemOff :: Ptr CUSeconds -> Int -> CUSeconds -> IO () # peekByteOff :: Ptr b -> Int -> IO CUSeconds # pokeByteOff :: Ptr b -> Int -> CUSeconds -> IO () # peek :: Ptr CUSeconds -> IO CUSeconds # poke :: Ptr CUSeconds -> CUSeconds -> IO () #
Storable CSUSeconds
Instance details Defined in Foreign.C.Types Methods sizeOf :: CSUSeconds -> Int # alignment :: CSUSeconds -> Int # peekElemOff :: Ptr CSUSeconds -> Int -> IO CSUSeconds # pokeElemOff :: Ptr CSUSeconds -> Int -> CSUSeconds -> IO () # peekByteOff :: Ptr b -> Int -> IO CSUSeconds # pokeByteOff :: Ptr b -> Int -> CSUSeconds -> IO () # peek :: Ptr CSUSeconds -> IO CSUSeconds # poke :: Ptr CSUSeconds -> CSUSeconds -> IO () #
Storable CIntPtr
Instance details Defined in Foreign.C.Types Methods sizeOf :: CIntPtr -> Int # alignment :: CIntPtr -> Int # peekElemOff :: Ptr CIntPtr -> Int -> IO CIntPtr # pokeElemOff :: Ptr CIntPtr -> Int -> CIntPtr -> IO () # peekByteOff :: Ptr b -> Int -> IO CIntPtr # pokeByteOff :: Ptr b -> Int -> CIntPtr -> IO () # peek :: Ptr CIntPtr -> IO CIntPtr # poke :: Ptr CIntPtr -> CIntPtr -> IO () #
Storable CUIntPtr
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUIntPtr -> Int # alignment :: CUIntPtr -> Int # peekElemOff :: Ptr CUIntPtr -> Int -> IO CUIntPtr # pokeElemOff :: Ptr CUIntPtr -> Int -> CUIntPtr -> IO () # peekByteOff :: Ptr b -> Int -> IO CUIntPtr # pokeByteOff :: Ptr b -> Int -> CUIntPtr -> IO () # peek :: Ptr CUIntPtr -> IO CUIntPtr # poke :: Ptr CUIntPtr -> CUIntPtr -> IO () #
Storable CIntMax
Instance details Defined in Foreign.C.Types Methods sizeOf :: CIntMax -> Int # alignment :: CIntMax -> Int # peekElemOff :: Ptr CIntMax -> Int -> IO CIntMax # pokeElemOff :: Ptr CIntMax -> Int -> CIntMax -> IO () # peekByteOff :: Ptr b -> Int -> IO CIntMax # pokeByteOff :: Ptr b -> Int -> CIntMax -> IO () # peek :: Ptr CIntMax -> IO CIntMax # poke :: Ptr CIntMax -> CIntMax -> IO () #
Storable CUIntMax
Instance details Defined in Foreign.C.Types Methods sizeOf :: CUIntMax -> Int # alignment :: CUIntMax -> Int # peekElemOff :: Ptr CUIntMax -> Int -> IO CUIntMax # pokeElemOff :: Ptr CUIntMax -> Int -> CUIntMax -> IO () # peekByteOff :: Ptr b -> Int -> IO CUIntMax # pokeByteOff :: Ptr b -> Int -> CUIntMax -> IO () # peek :: Ptr CUIntMax -> IO CUIntMax # poke :: Ptr CUIntMax -> CUIntMax -> IO () #
Storable Fingerprint	Since: base-4.4.0.0
Instance details Defined in Foreign.Storable Methods sizeOf :: Fingerprint -> Int # alignment :: Fingerprint -> Int # peekElemOff :: Ptr Fingerprint -> Int -> IO Fingerprint # pokeElemOff :: Ptr Fingerprint -> Int -> Fingerprint -> IO () # peekByteOff :: Ptr b -> Int -> IO Fingerprint # pokeByteOff :: Ptr b -> Int -> Fingerprint -> IO () # peek :: Ptr Fingerprint -> IO Fingerprint # poke :: Ptr Fingerprint -> Fingerprint -> IO () #
Storable CodePoint
Instance details Defined in Data.Text.Encoding Methods sizeOf :: CodePoint -> Int # alignment :: CodePoint -> Int # peekElemOff :: Ptr CodePoint -> Int -> IO CodePoint # pokeElemOff :: Ptr CodePoint -> Int -> CodePoint -> IO () # peekByteOff :: Ptr b -> Int -> IO CodePoint # pokeByteOff :: Ptr b -> Int -> CodePoint -> IO () # peek :: Ptr CodePoint -> IO CodePoint # poke :: Ptr CodePoint -> CodePoint -> IO () #
Storable DecoderState
Instance details Defined in Data.Text.Encoding Methods sizeOf :: DecoderState -> Int # alignment :: DecoderState -> Int # peekElemOff :: Ptr DecoderState -> Int -> IO DecoderState # pokeElemOff :: Ptr DecoderState -> Int -> DecoderState -> IO () # peekByteOff :: Ptr b -> Int -> IO DecoderState # pokeByteOff :: Ptr b -> Int -> DecoderState -> IO () # peek :: Ptr DecoderState -> IO DecoderState # poke :: Ptr DecoderState -> DecoderState -> IO () #
(Storable a, Integral a) => Storable (Ratio a)	Since: base-4.8.0.0
Instance details Defined in Foreign.Storable Methods sizeOf :: Ratio a -> Int # alignment :: Ratio a -> Int # peekElemOff :: Ptr (Ratio a) -> Int -> IO (Ratio a) # pokeElemOff :: Ptr (Ratio a) -> Int -> Ratio a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Ratio a) # pokeByteOff :: Ptr b -> Int -> Ratio a -> IO () # peek :: Ptr (Ratio a) -> IO (Ratio a) # poke :: Ptr (Ratio a) -> Ratio a -> IO () #
Storable (StablePtr a)	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: StablePtr a -> Int # alignment :: StablePtr a -> Int # peekElemOff :: Ptr (StablePtr a) -> Int -> IO (StablePtr a) # pokeElemOff :: Ptr (StablePtr a) -> Int -> StablePtr a -> IO () # peekByteOff :: Ptr b -> Int -> IO (StablePtr a) # pokeByteOff :: Ptr b -> Int -> StablePtr a -> IO () # peek :: Ptr (StablePtr a) -> IO (StablePtr a) # poke :: Ptr (StablePtr a) -> StablePtr a -> IO () #
Storable (Ptr a)	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Ptr a -> Int # alignment :: Ptr a -> Int # peekElemOff :: Ptr (Ptr a) -> Int -> IO (Ptr a) # pokeElemOff :: Ptr (Ptr a) -> Int -> Ptr a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Ptr a) # pokeByteOff :: Ptr b -> Int -> Ptr a -> IO () # peek :: Ptr (Ptr a) -> IO (Ptr a) # poke :: Ptr (Ptr a) -> Ptr a -> IO () #
Storable (FunPtr a)	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: FunPtr a -> Int # alignment :: FunPtr a -> Int # peekElemOff :: Ptr (FunPtr a) -> Int -> IO (FunPtr a) # pokeElemOff :: Ptr (FunPtr a) -> Int -> FunPtr a -> IO () # peekByteOff :: Ptr b -> Int -> IO (FunPtr a) # pokeByteOff :: Ptr b -> Int -> FunPtr a -> IO () # peek :: Ptr (FunPtr a) -> IO (FunPtr a) # poke :: Ptr (FunPtr a) -> FunPtr a -> IO () #
Storable a => Storable (WrapNum a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapNum a -> Int # alignment :: WrapNum a -> Int # peekElemOff :: Ptr (WrapNum a) -> Int -> IO (WrapNum a) # pokeElemOff :: Ptr (WrapNum a) -> Int -> WrapNum a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapNum a) # pokeByteOff :: Ptr b -> Int -> WrapNum a -> IO () # peek :: Ptr (WrapNum a) -> IO (WrapNum a) # poke :: Ptr (WrapNum a) -> WrapNum a -> IO () #
Storable a => Storable (WrapFractional a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapFractional a -> Int # alignment :: WrapFractional a -> Int # peekElemOff :: Ptr (WrapFractional a) -> Int -> IO (WrapFractional a) # pokeElemOff :: Ptr (WrapFractional a) -> Int -> WrapFractional a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapFractional a) # pokeByteOff :: Ptr b -> Int -> WrapFractional a -> IO () # peek :: Ptr (WrapFractional a) -> IO (WrapFractional a) # poke :: Ptr (WrapFractional a) -> WrapFractional a -> IO () #
Storable a => Storable (WrapIntegral a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapIntegral a -> Int # alignment :: WrapIntegral a -> Int # peekElemOff :: Ptr (WrapIntegral a) -> Int -> IO (WrapIntegral a) # pokeElemOff :: Ptr (WrapIntegral a) -> Int -> WrapIntegral a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapIntegral a) # pokeByteOff :: Ptr b -> Int -> WrapIntegral a -> IO () # peek :: Ptr (WrapIntegral a) -> IO (WrapIntegral a) # poke :: Ptr (WrapIntegral a) -> WrapIntegral a -> IO () #
Storable a => Storable (WrapAlgebra a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: WrapAlgebra a -> Int # alignment :: WrapAlgebra a -> Int # peekElemOff :: Ptr (WrapAlgebra a) -> Int -> IO (WrapAlgebra a) # pokeElemOff :: Ptr (WrapAlgebra a) -> Int -> WrapAlgebra a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrapAlgebra a) # pokeByteOff :: Ptr b -> Int -> WrapAlgebra a -> IO () # peek :: Ptr (WrapAlgebra a) -> IO (WrapAlgebra a) # poke :: Ptr (WrapAlgebra a) -> WrapAlgebra a -> IO () #
Storable a => Storable (Add a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: Add a -> Int # alignment :: Add a -> Int # peekElemOff :: Ptr (Add a) -> Int -> IO (Add a) # pokeElemOff :: Ptr (Add a) -> Int -> Add a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Add a) # pokeByteOff :: Ptr b -> Int -> Add a -> IO () # peek :: Ptr (Add a) -> IO (Add a) # poke :: Ptr (Add a) -> Add a -> IO () #
Storable a => Storable (Mult a)
Instance details Defined in AlgebraicPrelude Methods sizeOf :: Mult a -> Int # alignment :: Mult a -> Int # peekElemOff :: Ptr (Mult a) -> Int -> IO (Mult a) # pokeElemOff :: Ptr (Mult a) -> Int -> Mult a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Mult a) # pokeByteOff :: Ptr b -> Int -> Mult a -> IO () # peek :: Ptr (Mult a) -> IO (Mult a) # poke :: Ptr (Mult a) -> Mult a -> IO () #
Storable a => Storable (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods sizeOf :: Down a -> Int # alignment :: Down a -> Int # peekElemOff :: Ptr (Down a) -> Int -> IO (Down a) # pokeElemOff :: Ptr (Down a) -> Int -> Down a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Down a) # pokeByteOff :: Ptr b -> Int -> Down a -> IO () # peek :: Ptr (Down a) -> IO (Down a) # poke :: Ptr (Down a) -> Down a -> IO () #
Storable a => Storable (Complex a)	Since: base-4.8.0.0
Instance details Defined in Data.Complex Methods sizeOf :: Complex a -> Int # alignment :: Complex a -> Int # peekElemOff :: Ptr (Complex a) -> Int -> IO (Complex a) # pokeElemOff :: Ptr (Complex a) -> Int -> Complex a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Complex a) # pokeByteOff :: Ptr b -> Int -> Complex a -> IO () # peek :: Ptr (Complex a) -> IO (Complex a) # poke :: Ptr (Complex a) -> Complex a -> IO () #
Storable a => Storable (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods sizeOf :: Identity a -> Int # alignment :: Identity a -> Int # peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) # pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Identity a) # pokeByteOff :: Ptr b -> Int -> Identity a -> IO () # peek :: Ptr (Identity a) -> IO (Identity a) # poke :: Ptr (Identity a) -> Identity a -> IO () #
Storable g => Storable (StateGen g)
Instance details Defined in System.Random.Internal Methods sizeOf :: StateGen g -> Int # alignment :: StateGen g -> Int # peekElemOff :: Ptr (StateGen g) -> Int -> IO (StateGen g) # pokeElemOff :: Ptr (StateGen g) -> Int -> StateGen g -> IO () # peekByteOff :: Ptr b -> Int -> IO (StateGen g) # pokeByteOff :: Ptr b -> Int -> StateGen g -> IO () # peek :: Ptr (StateGen g) -> IO (StateGen g) # poke :: Ptr (StateGen g) -> StateGen g -> IO () #
Storable g => Storable (AtomicGen g)
Instance details Defined in System.Random.Stateful Methods sizeOf :: AtomicGen g -> Int # alignment :: AtomicGen g -> Int # peekElemOff :: Ptr (AtomicGen g) -> Int -> IO (AtomicGen g) # pokeElemOff :: Ptr (AtomicGen g) -> Int -> AtomicGen g -> IO () # peekByteOff :: Ptr b -> Int -> IO (AtomicGen g) # pokeByteOff :: Ptr b -> Int -> AtomicGen g -> IO () # peek :: Ptr (AtomicGen g) -> IO (AtomicGen g) # poke :: Ptr (AtomicGen g) -> AtomicGen g -> IO () #
Storable g => Storable (IOGen g)
Instance details Defined in System.Random.Stateful Methods sizeOf :: IOGen g -> Int # alignment :: IOGen g -> Int # peekElemOff :: Ptr (IOGen g) -> Int -> IO (IOGen g) # pokeElemOff :: Ptr (IOGen g) -> Int -> IOGen g -> IO () # peekByteOff :: Ptr b -> Int -> IO (IOGen g) # pokeByteOff :: Ptr b -> Int -> IOGen g -> IO () # peek :: Ptr (IOGen g) -> IO (IOGen g) # poke :: Ptr (IOGen g) -> IOGen g -> IO () #
Storable g => Storable (STGen g)
Instance details Defined in System.Random.Stateful Methods sizeOf :: STGen g -> Int # alignment :: STGen g -> Int # peekElemOff :: Ptr (STGen g) -> Int -> IO (STGen g) # pokeElemOff :: Ptr (STGen g) -> Int -> STGen g -> IO () # peekByteOff :: Ptr b -> Int -> IO (STGen g) # pokeByteOff :: Ptr b -> Int -> STGen g -> IO () # peek :: Ptr (STGen g) -> IO (STGen g) # poke :: Ptr (STGen g) -> STGen g -> IO () #
Prim a => Storable (PrimStorable a)
Instance details Defined in Data.Primitive.Types Methods sizeOf :: PrimStorable a -> Int # alignment :: PrimStorable a -> Int # peekElemOff :: Ptr (PrimStorable a) -> Int -> IO (PrimStorable a) # pokeElemOff :: Ptr (PrimStorable a) -> Int -> PrimStorable a -> IO () # peekByteOff :: Ptr b -> Int -> IO (PrimStorable a) # pokeByteOff :: Ptr b -> Int -> PrimStorable a -> IO () # peek :: Ptr (PrimStorable a) -> IO (PrimStorable a) # poke :: Ptr (PrimStorable a) -> PrimStorable a -> IO () #
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int # alignment :: Const a b -> Int # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () # peek :: Ptr (Const a b) -> IO (Const a b) # poke :: Ptr (Const a b) -> Const a b -> IO () #
Storable a => Storable (Tagged s a)
Instance details Defined in Data.Tagged Methods sizeOf :: Tagged s a -> Int # alignment :: Tagged s a -> Int # peekElemOff :: Ptr (Tagged s a) -> Int -> IO (Tagged s a) # pokeElemOff :: Ptr (Tagged s a) -> Int -> Tagged s a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Tagged s a) # pokeByteOff :: Ptr b -> Int -> Tagged s a -> IO () # peek :: Ptr (Tagged s a) -> IO (Tagged s a) # poke :: Ptr (Tagged s a) -> Tagged s a -> IO () #

newtype Down a #

The Down type allows you to reverse sort order conveniently. A value of type Down a contains a value of type a (represented as Down a). If a has an Ord instance associated with it then comparing two values thus wrapped will give you the opposite of their normal sort order. This is particularly useful when sorting in generalised list comprehensions, as in: then sortWith by Down x

Since: base-4.6.0.0

Constructors

Down
Fields getDown :: a Since: base-4.14.0.0

Instances

Instances details

Monad Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b # (>>) :: Down a -> Down b -> Down b # return :: a -> Down a #
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b # (<$) :: a -> Down b -> Down a #
Applicative Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a # (<>) :: Down (a -> b) -> Down a -> Down b # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c # (>) :: Down a -> Down b -> Down b # (<*) :: Down a -> Down b -> Down a #
Foldable Down	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # toList :: Down a -> [a] # null :: Down a -> Bool # length :: Down a -> Int # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # minimum :: Ord a => Down a -> a # sum :: Num a => Down a -> a # product :: Num a => Down a -> a #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Eq1 Down	Since: base-4.12.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Down a -> Down b -> Bool #
Ord1 Down	Since: base-4.12.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Down a -> Down b -> Ordering #
Read1 Down	Since: base-4.12.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Down a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Down a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Down a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Down a] #
Show1 Down	Since: base-4.12.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Down a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Down a] -> ShowS #
NFData1 Down	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Down a -> () #
CFoldable Down
Instance details Defined in Control.Subcategory.Foldable Methods cfoldMap :: (Dom Down a, Monoid w) => (a -> w) -> Down a -> w cfoldMap' :: (Dom Down a, Monoid m) => (a -> m) -> Down a -> m cfold :: (Dom Down w, Monoid w) => Down w -> w cfoldr :: Dom Down a => (a -> b -> b) -> b -> Down a -> b cfoldlM :: (Monad m, Dom Down b) => (a -> b -> m a) -> a -> Down b -> m a cfoldlM' :: (Monad m, Dom Down b) => (a -> b -> m a) -> a -> Down b -> m a cfoldrM :: (Monad m, Dom Down a) => (a -> b -> m b) -> b -> Down a -> m b cfoldrM' :: (Monad m, Dom Down a) => (a -> b -> m b) -> b -> Down a -> m b cfoldl :: Dom Down a => (b -> a -> b) -> b -> Down a -> b cfoldr' :: Dom Down a => (a -> b -> b) -> b -> Down a -> b cfoldl' :: Dom Down a => (b -> a -> b) -> b -> Down a -> b cbasicToList :: Dom Down a => Down a -> [a] cfoldr1 :: Dom Down a => (a -> a -> a) -> Down a -> a cfoldl1 :: Dom Down a => (a -> a -> a) -> Down a -> a cindex :: Dom Down a => Down a -> Int -> a cnull :: Dom Down a => Down a -> Bool clength :: Dom Down a => Down a -> Int cany :: Dom Down a => (a -> Bool) -> Down a -> Bool call :: Dom Down a => (a -> Bool) -> Down a -> Bool celem :: (Eq a, Dom Down a) => a -> Down a -> Bool cnotElem :: (Eq a, Dom Down a) => a -> Down a -> Bool cminimum :: (Ord a, Dom Down a) => Down a -> a cmaximum :: (Ord a, Dom Down a) => Down a -> a csum :: (Num a, Dom Down a) => Down a -> a cproduct :: (Num a, Dom Down a) => Down a -> a cctraverse_ :: (CApplicative g, CPointed g, Dom g (), Dom Down a, Dom g b) => (a -> g b) -> Down a -> g () ctraverse_ :: (Applicative g, Dom Down a) => (a -> g b) -> Down a -> g () clast :: Dom Down a => Down a -> a chead :: Dom Down a => Down a -> a cfind :: Dom Down a => (a -> Bool) -> Down a -> Maybe a cfindIndex :: Dom Down a => (a -> Bool) -> Down a -> Maybe Int cfindIndices :: Dom Down a => (a -> Bool) -> Down a -> [Int] celemIndex :: (Dom Down a, Eq a) => a -> Down a -> Maybe Int celemIndices :: (Dom Down a, Eq a) => a -> Down a -> [Int]
CFunctor Down
Instance details Defined in Control.Subcategory.Functor Methods cmap :: (Dom Down a, Dom Down b) => (a -> b) -> Down a -> Down b (<$:) :: (Dom Down a, Dom Down b) => a -> Down b -> Down a
CPointed Down
Instance details Defined in Control.Subcategory.Pointed Methods cpure :: Dom Down a => a -> Down a
CTraversable Down
Instance details Defined in Control.Subcategory.Foldable Methods ctraverse :: (Dom Down a, Dom Down b, Applicative g) => (a -> g b) -> Down a -> g (Down b)
Apply Down
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Down (a -> b) -> Down a -> Down b (.>) :: Down a -> Down b -> Down b (<.) :: Down a -> Down b -> Down a liftF2 :: (a -> b -> c) -> Down a -> Down b -> Down c
Bind Down
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Down a -> (a -> Down b) -> Down b join :: Down (Down a) -> Down a
Constrained Down
Instance details Defined in Control.Subcategory.Functor Associated Types type Dom Down a
Unbox a => MVector MVector (Down a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Down a) -> Int basicUnsafeSlice :: Int -> Int -> MVector s (Down a) -> MVector s (Down a) basicOverlaps :: MVector s (Down a) -> MVector s (Down a) -> Bool basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Down a)) basicInitialize :: PrimMonad m => MVector (PrimState m) (Down a) -> m () basicUnsafeReplicate :: PrimMonad m => Int -> Down a -> m (MVector (PrimState m) (Down a)) basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> m (Down a) basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> Down a -> m () basicClear :: PrimMonad m => MVector (PrimState m) (Down a) -> m () basicSet :: PrimMonad m => MVector (PrimState m) (Down a) -> Down a -> m () basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Down a) -> MVector (PrimState m) (Down a) -> m () basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Down a) -> MVector (PrimState m) (Down a) -> m () basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> m (MVector (PrimState m) (Down a))
Unbox a => Vector Vector (Down a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> m (Vector (Down a)) basicUnsafeThaw :: PrimMonad m => Vector (Down a) -> m (Mutable Vector (PrimState m) (Down a)) basicLength :: Vector (Down a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (Down a) -> Vector (Down a) basicUnsafeIndexM :: Monad m => Vector (Down a) -> Int -> m (Down a) basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> Vector (Down a) -> m () elemseq :: Vector (Down a) -> Down a -> b -> b
Bounded a => Bounded (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods minBound :: Down a # maxBound :: Down a #
Enum a => Enum (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods succ :: Down a -> Down a # pred :: Down a -> Down a # toEnum :: Int -> Down a # fromEnum :: Down a -> Int # enumFrom :: Down a -> [Down a] # enumFromThen :: Down a -> Down a -> [Down a] # enumFromTo :: Down a -> Down a -> [Down a] # enumFromThenTo :: Down a -> Down a -> Down a -> [Down a] #
Eq a => Eq (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods (==) :: Down a -> Down a -> Bool # (/=) :: Down a -> Down a -> Bool #
Floating a => Floating (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods pi :: Down a # exp :: Down a -> Down a # log :: Down a -> Down a # sqrt :: Down a -> Down a # (**) :: Down a -> Down a -> Down a # logBase :: Down a -> Down a -> Down a # sin :: Down a -> Down a # cos :: Down a -> Down a # tan :: Down a -> Down a # asin :: Down a -> Down a # acos :: Down a -> Down a # atan :: Down a -> Down a # sinh :: Down a -> Down a # cosh :: Down a -> Down a # tanh :: Down a -> Down a # asinh :: Down a -> Down a # acosh :: Down a -> Down a # atanh :: Down a -> Down a # log1p :: Down a -> Down a # expm1 :: Down a -> Down a # log1pexp :: Down a -> Down a # log1mexp :: Down a -> Down a #
Fractional a => Fractional (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods (/) :: Down a -> Down a -> Down a # recip :: Down a -> Down a # fromRational :: Rational -> Down a #
Integral a => Integral (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods quot :: Down a -> Down a -> Down a # rem :: Down a -> Down a -> Down a # div :: Down a -> Down a -> Down a # mod :: Down a -> Down a -> Down a # quotRem :: Down a -> Down a -> (Down a, Down a) # divMod :: Down a -> Down a -> (Down a, Down a) # toInteger :: Down a -> Integer #
Num a => Num (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (+) :: Down a -> Down a -> Down a # (-) :: Down a -> Down a -> Down a # (*) :: Down a -> Down a -> Down a # negate :: Down a -> Down a # abs :: Down a -> Down a # signum :: Down a -> Down a # fromInteger :: Integer -> Down a #
Ord a => Ord (Down a)	Since: base-4.6.0.0
Instance details Defined in Data.Ord Methods compare :: Down a -> Down a -> Ordering # (<) :: Down a -> Down a -> Bool # (<=) :: Down a -> Down a -> Bool # (>) :: Down a -> Down a -> Bool # (>=) :: Down a -> Down a -> Bool # max :: Down a -> Down a -> Down a # min :: Down a -> Down a -> Down a #
Read a => Read (Down a)	This instance would be equivalent to the derived instances of the `Down` newtype if the `getDown` field were removed Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods readsPrec :: Int -> ReadS (Down a) # readList :: ReadS [Down a] # readPrec :: ReadPrec (Down a) # readListPrec :: ReadPrec [Down a] #
Real a => Real (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods toRational :: Down a -> Rational #
RealFloat a => RealFloat (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods floatRadix :: Down a -> Integer # floatDigits :: Down a -> Int # floatRange :: Down a -> (Int, Int) # decodeFloat :: Down a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Down a # exponent :: Down a -> Int # significand :: Down a -> Down a # scaleFloat :: Int -> Down a -> Down a # isNaN :: Down a -> Bool # isInfinite :: Down a -> Bool # isDenormalized :: Down a -> Bool # isNegativeZero :: Down a -> Bool # isIEEE :: Down a -> Bool # atan2 :: Down a -> Down a -> Down a #
RealFrac a => RealFrac (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods properFraction :: Integral b => Down a -> (b, Down a) # truncate :: Integral b => Down a -> b # round :: Integral b => Down a -> b # ceiling :: Integral b => Down a -> b # floor :: Integral b => Down a -> b #
Show a => Show (Down a)	This instance would be equivalent to the derived instances of the `Down` newtype if the `getDown` field were removed Since: base-4.7.0.0
Instance details Defined in Data.Ord Methods showsPrec :: Int -> Down a -> ShowS # show :: Down a -> String # showList :: [Down a] -> ShowS #
Ix a => Ix (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods range :: (Down a, Down a) -> [Down a] # index :: (Down a, Down a) -> Down a -> Int # unsafeIndex :: (Down a, Down a) -> Down a -> Int # inRange :: (Down a, Down a) -> Down a -> Bool # rangeSize :: (Down a, Down a) -> Int # unsafeRangeSize :: (Down a, Down a) -> Int #
Generic (Down a)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (Down a) :: Type -> Type # Methods from :: Down a -> Rep (Down a) x # to :: Rep (Down a) x -> Down a #
Semigroup a => Semigroup (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a # sconcat :: NonEmpty (Down a) -> Down a # stimes :: Integral b => b -> Down a -> Down a #
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
Unbox a => Unbox (Down a)
Instance details Defined in Data.Vector.Unboxed.Base
Storable a => Storable (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods sizeOf :: Down a -> Int # alignment :: Down a -> Int # peekElemOff :: Ptr (Down a) -> Int -> IO (Down a) # pokeElemOff :: Ptr (Down a) -> Int -> Down a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Down a) # pokeByteOff :: Ptr b -> Int -> Down a -> IO () # peek :: Ptr (Down a) -> IO (Down a) # poke :: Ptr (Down a) -> Down a -> IO () #
Bits a => Bits (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods (.&.) :: Down a -> Down a -> Down a # (.\|.) :: Down a -> Down a -> Down a # xor :: Down a -> Down a -> Down a # complement :: Down a -> Down a # shift :: Down a -> Int -> Down a # rotate :: Down a -> Int -> Down a # zeroBits :: Down a # bit :: Int -> Down a # setBit :: Down a -> Int -> Down a # clearBit :: Down a -> Int -> Down a # complementBit :: Down a -> Int -> Down a # testBit :: Down a -> Int -> Bool # bitSizeMaybe :: Down a -> Maybe Int # bitSize :: Down a -> Int # isSigned :: Down a -> Bool # shiftL :: Down a -> Int -> Down a # unsafeShiftL :: Down a -> Int -> Down a # shiftR :: Down a -> Int -> Down a # unsafeShiftR :: Down a -> Int -> Down a # rotateL :: Down a -> Int -> Down a # rotateR :: Down a -> Int -> Down a # popCount :: Down a -> Int #
FiniteBits a => FiniteBits (Down a)	Since: base-4.14.0.0
Instance details Defined in Data.Ord Methods finiteBitSize :: Down a -> Int # countLeadingZeros :: Down a -> Int # countTrailingZeros :: Down a -> Int #
NFData a => NFData (Down a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Down a -> () #
Wrapped (Down a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Down a) Methods _Wrapped' :: Iso' (Down a) (Unwrapped (Down a))
SMonoid a => SMonoid (Down a)
Instance details Defined in Data.Singletons.Prelude.Monoid Methods sMempty :: Sing MemptySym0 sMappend :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MappendSym0 t1) t2) sMconcat :: forall (t :: [Down a]). Sing t -> Sing (Apply MconcatSym0 t)
SSemigroup a => SSemigroup (Down a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%<>) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<>@#@$) t1) t2) sSconcat :: forall (t :: NonEmpty (Down a)). Sing t -> Sing (Apply SconcatSym0 t)
SNum a => SNum (Down a)
Instance details Defined in Data.Singletons.Prelude.Num Methods (%+) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (+@#@$) t1) t2) (%-) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (-@#@$) t1) t2) (%) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (@#@$) t1) t2) sNegate :: forall (t :: Down a). Sing t -> Sing (Apply NegateSym0 t) sAbs :: forall (t :: Down a). Sing t -> Sing (Apply AbsSym0 t) sSignum :: forall (t :: Down a). Sing t -> Sing (Apply SignumSym0 t) sFromInteger :: forall (t :: Nat). Sing t -> Sing (Apply FromIntegerSym0 t)
SOrd a => SOrd (Down a)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sCompare :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply CompareSym0 t1) t2) (%<) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<@#@$) t1) t2) (%<=) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<=@#@$) t1) t2) (%>) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>@#@$) t1) t2) (%>=) :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>=@#@$) t1) t2) sMax :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MaxSym0 t1) t2) sMin :: forall (t1 :: Down a) (t2 :: Down a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MinSym0 t1) t2)
PSemigroup (Down a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Associated Types type arg <> arg1 :: a type Sconcat arg :: a
PMonoid (Down a)
Instance details Defined in Data.Singletons.Prelude.Monoid Associated Types type Mempty :: a type Mappend arg arg1 :: a type Mconcat arg :: a
PNum (Down a)
Instance details Defined in Data.Singletons.Prelude.Num Associated Types type arg + arg1 :: a type arg - arg1 :: a type arg * arg1 :: a type Negate arg :: a type Abs arg :: a type Signum arg :: a type FromInteger arg :: a
POrd (Down a)
Instance details Defined in Data.Singletons.Prelude.Ord Associated Types type Compare arg arg1 :: Ordering type arg < arg1 :: Bool type arg <= arg1 :: Bool type arg > arg1 :: Bool type arg >= arg1 :: Bool type Max arg arg1 :: a type Min arg arg1 :: a
Prim a => Prim (Down a)
Instance details Defined in Data.Primitive.Types Methods sizeOf# :: Down a -> Int# alignment# :: Down a -> Int# indexByteArray# :: ByteArray# -> Int# -> Down a readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Down a #) writeByteArray# :: MutableByteArray# s -> Int# -> Down a -> State# s -> State# s setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Down a -> State# s -> State# s indexOffAddr# :: Addr# -> Int# -> Down a readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Down a #) writeOffAddr# :: Addr# -> Int# -> Down a -> State# s -> State# s setOffAddr# :: Addr# -> Int# -> Int# -> Down a -> State# s -> State# s
Generic1 Down	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 Down :: k -> Type # Methods from1 :: forall (a :: k). Down a -> Rep1 Down a # to1 :: forall (a :: k). Rep1 Down a -> Down a #
t ~ Down b => Rewrapped (Down a) t
Instance details Defined in Control.Lens.Wrapped
SDecide a => TestCoercion (SDown :: Down a -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods testCoercion :: forall (a0 :: k) (b :: k). SDown a0 -> SDown b -> Maybe (Coercion a0 b) #
SDecide a => TestEquality (SDown :: Down a -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods testEquality :: forall (a0 :: k) (b :: k). SDown a0 -> SDown b -> Maybe (a0 :~: b) #
SingI (DownSym0 :: TyFun a (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing DownSym0 #
SingI (GetDownSym0 :: TyFun (Down a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods sing :: Sing GetDownSym0 #
SuppressUnusedWarnings (FromInteger_6989586621679976084Sym0 :: TyFun Nat (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (DownSym0 :: TyFun a (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Pure_6989586621681492787Sym0 :: TyFun a (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Applicative Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976053Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976042Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976031Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Signum_6989586621679976077Sym0 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Negate_6989586621679976063Sym0 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Abs_6989586621679976070Sym0 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (GetDownSym0 :: TyFun (Down a) a -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240867Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680158242Sym0 :: TyFun a (Down b ~> Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Functor Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976053Sym1 a6989586621679976058 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976042Sym1 a6989586621679976047 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621679976031Sym1 a6989586621679976036 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type)
Instance details Defined in Data.Singletons.Prelude.Ord Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680240867Sym1 a6989586621680240872 :: TyFun (Down a) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681501451Sym0 :: TyFun (Down a) ((a ~> Down b) ~> Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681492797Sym0 :: TyFun (Down (a ~> b)) (Down a ~> Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Applicative Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680158231Sym0 :: TyFun (a ~> b) (Down a ~> Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Functor Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621680158242Sym1 a6989586621680158247 :: TyFun (Down b) (Down a) -> Type)
Instance details Defined in Data.Singletons.Prelude.Functor Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (Fmap_6989586621680158231Sym1 a6989586621680158236 :: TyFun (Down a) (Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Functor Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681492797Sym1 a6989586621681492802 :: TyFun (Down a) (Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Applicative Methods suppressUnusedWarnings :: ()
SuppressUnusedWarnings (TFHelper_6989586621681501451Sym1 a6989586621681501456 :: TyFun (a ~> Down b) (Down b) -> Type)
Instance details Defined in Data.Singletons.Prelude.Monad Methods suppressUnusedWarnings :: ()
type Dom Down a
Instance details Defined in Control.Subcategory.Functor type Dom Down a = ()
type Return (arg :: a)
Instance details Defined in Data.Singletons.Prelude.Monad type Return (arg :: a) = Apply (Return_6989586621680012055Sym0 :: TyFun a (Down a) -> Type) arg
type Pure (a :: k1)
Instance details Defined in Data.Singletons.Prelude.Applicative type Pure (a :: k1) = Apply (Pure_6989586621681492787Sym0 :: TyFun k1 (Down k1) -> Type) a
type Fmap (a2 :: a1 ~> b) (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Functor type Fmap (a2 :: a1 ~> b) (a3 :: Down a1) = Apply (Apply (Fmap_6989586621680158231Sym0 :: TyFun (a1 ~> b) (Down a1 ~> Down b) -> Type) a2) a3
type (arg1 :: Down a) >> (arg2 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Monad type (arg1 :: Down a) >> (arg2 :: Down b) = Apply (Apply (TFHelper_6989586621680012038Sym0 :: TyFun (Down a) (Down b ~> Down b) -> Type) arg1) arg2
type (a2 :: Down a1) >>= (a3 :: a1 ~> Down b)
Instance details Defined in Data.Singletons.Prelude.Monad type (a2 :: Down a1) >>= (a3 :: a1 ~> Down b) = Apply (Apply (TFHelper_6989586621681501451Sym0 :: TyFun (Down a1) ((a1 ~> Down b) ~> Down b) -> Type) a2) a3
type (arg1 :: Down a) *> (arg2 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Applicative type (arg1 :: Down a) *> (arg2 :: Down b) = Apply (Apply (TFHelper_6989586621680011999Sym0 :: TyFun (Down a) (Down b ~> Down b) -> Type) arg1) arg2
type (arg1 :: Down a) <* (arg2 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Applicative type (arg1 :: Down a) <* (arg2 :: Down b) = Apply (Apply (TFHelper_6989586621680012010Sym0 :: TyFun (Down a) (Down b ~> Down a) -> Type) arg1) arg2
type (a2 :: Down (a1 ~> b)) <*> (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Applicative type (a2 :: Down (a1 ~> b)) <*> (a3 :: Down a1) = Apply (Apply (TFHelper_6989586621681492797Sym0 :: TyFun (Down (a1 ~> b)) (Down a1 ~> Down b) -> Type) a2) a3
type (a1 :: k1) <$ (a2 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Functor type (a1 :: k1) <$ (a2 :: Down b) = Apply (Apply (TFHelper_6989586621680158242Sym0 :: TyFun k1 (Down b ~> Down k1) -> Type) a1) a2
type LiftA2 (arg1 :: a ~> (b ~> c)) (arg2 :: Down a) (arg3 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Applicative type LiftA2 (arg1 :: a ~> (b ~> c)) (arg2 :: Down a) (arg3 :: Down b) = Apply (Apply (Apply (LiftA2_6989586621680011983Sym0 :: TyFun (a ~> (b ~> c)) (Down a ~> (Down b ~> Down c)) -> Type) arg1) arg2) arg3
newtype MVector s (Down a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Down a) = MV_Down (MVector s a)
type Apply (FromInteger_6989586621679976084Sym0 :: TyFun Nat (Down a) -> Type) (a6989586621679976088 :: Nat)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (FromInteger_6989586621679976084Sym0 :: TyFun Nat (Down a) -> Type) (a6989586621679976088 :: Nat) = FromInteger_6989586621679976084Sym1 a6989586621679976088 :: Down a
type Apply (DownSym0 :: TyFun a (Down a) -> Type) (a6989586621679846569 :: a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (DownSym0 :: TyFun a (Down a) -> Type) (a6989586621679846569 :: a) = DownSym1 a6989586621679846569
type Apply (Pure_6989586621681492787Sym0 :: TyFun a (Down a) -> Type) (a6989586621681492793 :: a)
Instance details Defined in Data.Singletons.Prelude.Applicative type Apply (Pure_6989586621681492787Sym0 :: TyFun a (Down a) -> Type) (a6989586621681492793 :: a) = Pure_6989586621681492787Sym1 a6989586621681492793
type Apply (TFHelper_6989586621680158242Sym0 :: TyFun a (Down b ~> Down a) -> Type) (a6989586621680158247 :: a)
Instance details Defined in Data.Singletons.Prelude.Functor type Apply (TFHelper_6989586621680158242Sym0 :: TyFun a (Down b ~> Down a) -> Type) (a6989586621680158247 :: a) = TFHelper_6989586621680158242Sym1 a6989586621680158247 :: TyFun (Down b) (Down a) -> Type
type Rep (Down a)
Instance details Defined in GHC.Generics type Rep (Down a) = D1 ('MetaData "Down" "Data.Ord" "base" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Sing
Instance details Defined in Data.Singletons.Prelude.Ord type Sing = SDown :: Down a -> Type
type Demote (Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Demote (Down a) = Down (Demote a)
newtype Vector (Down a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Down a) = V_Down (Vector a)
type Unwrapped (Down a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Down a) = a
type Mempty
Instance details Defined in Data.Singletons.Prelude.Monoid type Mempty = Mempty_6989586621680700997Sym0 :: Down a
type Rep1 Down
Instance details Defined in GHC.Generics type Rep1 Down = D1 ('MetaData "Down" "Data.Ord" "base" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Abs (a2 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type Abs (a2 :: Down a1) = Apply (Abs_6989586621679976070Sym0 :: TyFun (Down a1) (Down a1) -> Type) a2
type FromInteger a2
Instance details Defined in Data.Singletons.Prelude.Num type FromInteger a2 = Apply (FromInteger_6989586621679976084Sym0 :: TyFun Nat (Down a1) -> Type) a2
type Negate (a2 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type Negate (a2 :: Down a1) = Apply (Negate_6989586621679976063Sym0 :: TyFun (Down a1) (Down a1) -> Type) a2
type Signum (a2 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type Signum (a2 :: Down a1) = Apply (Signum_6989586621679976077Sym0 :: TyFun (Down a1) (Down a1) -> Type) a2
type Sconcat (arg :: NonEmpty (Down a))
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sconcat (arg :: NonEmpty (Down a)) = Apply (Sconcat_6989586621680240682Sym0 :: TyFun (NonEmpty (Down a)) (Down a) -> Type) arg
type Mconcat (arg :: [Down a])
Instance details Defined in Data.Singletons.Prelude.Monoid type Mconcat (arg :: [Down a]) = Apply (Mconcat_6989586621680691385Sym0 :: TyFun [Down a] (Down a) -> Type) arg
type (x :: Down a) /= (y :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type (x :: Down a) /= (y :: Down a) = Not (x == y)
type (a2 :: Down a1) == (b :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Ord type (a2 :: Down a1) == (b :: Down a1) = Equals_6989586621679847283 a2 b
type (a2 :: Down a1) <> (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type (a2 :: Down a1) <> (a3 :: Down a1) = Apply (Apply (TFHelper_6989586621680240867Sym0 :: TyFun (Down a1) (Down a1 ~> Down a1) -> Type) a2) a3
type (a2 :: Down a1) * (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type (a2 :: Down a1) * (a3 :: Down a1) = Apply (Apply (TFHelper_6989586621679976053Sym0 :: TyFun (Down a1) (Down a1 ~> Down a1) -> Type) a2) a3
type (a2 :: Down a1) + (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type (a2 :: Down a1) + (a3 :: Down a1) = Apply (Apply (TFHelper_6989586621679976031Sym0 :: TyFun (Down a1) (Down a1 ~> Down a1) -> Type) a2) a3
type (a2 :: Down a1) - (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Num type (a2 :: Down a1) - (a3 :: Down a1) = Apply (Apply (TFHelper_6989586621679976042Sym0 :: TyFun (Down a1) (Down a1 ~> Down a1) -> Type) a2) a3
type Mappend (arg1 :: Down a) (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Monoid type Mappend (arg1 :: Down a) (arg2 :: Down a) = Apply (Apply (Mappend_6989586621680691371Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) arg1) arg2
type Max (arg1 :: Down a) (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Max (arg1 :: Down a) (arg2 :: Down a) = Apply (Apply (Max_6989586621679837511Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) arg1) arg2
type Min (arg1 :: Down a) (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Min (arg1 :: Down a) (arg2 :: Down a) = Apply (Apply (Min_6989586621679837527Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) arg1) arg2
type Compare (a2 :: Down a1) (a3 :: Down a1)
Instance details Defined in Data.Singletons.Prelude.Ord type Compare (a2 :: Down a1) (a3 :: Down a1) = Apply (Apply (Compare_6989586621679847274Sym0 :: TyFun (Down a1) (Down a1 ~> Ordering) -> Type) a2) a3
type (arg1 :: Down a) <= (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Down a) <= (arg2 :: Down a) = Apply (Apply (TFHelper_6989586621679837463Sym0 :: TyFun (Down a) (Down a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Down a) < (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Down a) < (arg2 :: Down a) = Apply (Apply (TFHelper_6989586621679837447Sym0 :: TyFun (Down a) (Down a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Down a) >= (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Down a) >= (arg2 :: Down a) = Apply (Apply (TFHelper_6989586621679837495Sym0 :: TyFun (Down a) (Down a ~> Bool) -> Type) arg1) arg2
type (arg1 :: Down a) > (arg2 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type (arg1 :: Down a) > (arg2 :: Down a) = Apply (Apply (TFHelper_6989586621679837479Sym0 :: TyFun (Down a) (Down a ~> Bool) -> Type) arg1) arg2
type Apply (GetDownSym0 :: TyFun (Down a) a -> Type) (a6989586621679846572 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (GetDownSym0 :: TyFun (Down a) a -> Type) (a6989586621679846572 :: Down a) = GetDownSym1 a6989586621679846572
type Apply (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type) (a6989586621679847280 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679847274Sym1 a6989586621679847279 :: TyFun (Down a) Ordering -> Type) (a6989586621679847280 :: Down a) = Compare_6989586621679847274Sym2 a6989586621679847279 a6989586621679847280
type Apply (Negate_6989586621679976063Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976067 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (Negate_6989586621679976063Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976067 :: Down a) = Negate_6989586621679976063Sym1 a6989586621679976067
type Apply (Abs_6989586621679976070Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976074 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (Abs_6989586621679976070Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976074 :: Down a) = Abs_6989586621679976070Sym1 a6989586621679976074
type Apply (Signum_6989586621679976077Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976081 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (Signum_6989586621679976077Sym0 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976081 :: Down a) = Signum_6989586621679976077Sym1 a6989586621679976081
type Apply (TFHelper_6989586621679976031Sym1 a6989586621679976036 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976037 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976031Sym1 a6989586621679976036 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976037 :: Down a) = TFHelper_6989586621679976031Sym2 a6989586621679976036 a6989586621679976037
type Apply (TFHelper_6989586621679976042Sym1 a6989586621679976047 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976048 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976042Sym1 a6989586621679976047 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976048 :: Down a) = TFHelper_6989586621679976042Sym2 a6989586621679976047 a6989586621679976048
type Apply (TFHelper_6989586621679976053Sym1 a6989586621679976058 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976059 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976053Sym1 a6989586621679976058 :: TyFun (Down a) (Down a) -> Type) (a6989586621679976059 :: Down a) = TFHelper_6989586621679976053Sym2 a6989586621679976058 a6989586621679976059
type Apply (TFHelper_6989586621680240867Sym1 a6989586621680240872 :: TyFun (Down a) (Down a) -> Type) (a6989586621680240873 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240867Sym1 a6989586621680240872 :: TyFun (Down a) (Down a) -> Type) (a6989586621680240873 :: Down a) = TFHelper_6989586621680240867Sym2 a6989586621680240872 a6989586621680240873
type Apply (Fmap_6989586621680158231Sym1 a6989586621680158236 :: TyFun (Down a) (Down b) -> Type) (a6989586621680158237 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Functor type Apply (Fmap_6989586621680158231Sym1 a6989586621680158236 :: TyFun (Down a) (Down b) -> Type) (a6989586621680158237 :: Down a) = Fmap_6989586621680158231Sym2 a6989586621680158236 a6989586621680158237
type Apply (TFHelper_6989586621680158242Sym1 a6989586621680158247 :: TyFun (Down b) (Down a) -> Type) (a6989586621680158248 :: Down b)
Instance details Defined in Data.Singletons.Prelude.Functor type Apply (TFHelper_6989586621680158242Sym1 a6989586621680158247 :: TyFun (Down b) (Down a) -> Type) (a6989586621680158248 :: Down b) = TFHelper_6989586621680158242Sym2 a6989586621680158247 a6989586621680158248
type Apply (TFHelper_6989586621681492797Sym1 a6989586621681492802 :: TyFun (Down a) (Down b) -> Type) (a6989586621681492803 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Applicative type Apply (TFHelper_6989586621681492797Sym1 a6989586621681492802 :: TyFun (Down a) (Down b) -> Type) (a6989586621681492803 :: Down a) = TFHelper_6989586621681492797Sym2 a6989586621681492802 a6989586621681492803
type Apply (TFHelper_6989586621679976031Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976036 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976031Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976036 :: Down a) = TFHelper_6989586621679976031Sym1 a6989586621679976036
type Apply (TFHelper_6989586621679976042Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976047 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976042Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976047 :: Down a) = TFHelper_6989586621679976042Sym1 a6989586621679976047
type Apply (TFHelper_6989586621679976053Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976058 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Num type Apply (TFHelper_6989586621679976053Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621679976058 :: Down a) = TFHelper_6989586621679976053Sym1 a6989586621679976058
type Apply (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type) (a6989586621679847279 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Ord type Apply (Compare_6989586621679847274Sym0 :: TyFun (Down a) (Down a ~> Ordering) -> Type) (a6989586621679847279 :: Down a) = Compare_6989586621679847274Sym1 a6989586621679847279
type Apply (TFHelper_6989586621680240867Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621680240872 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Apply (TFHelper_6989586621680240867Sym0 :: TyFun (Down a) (Down a ~> Down a) -> Type) (a6989586621680240872 :: Down a) = TFHelper_6989586621680240867Sym1 a6989586621680240872
type Apply (TFHelper_6989586621681501451Sym0 :: TyFun (Down a) ((a ~> Down b) ~> Down b) -> Type) (a6989586621681501456 :: Down a)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (TFHelper_6989586621681501451Sym0 :: TyFun (Down a) ((a ~> Down b) ~> Down b) -> Type) (a6989586621681501456 :: Down a) = TFHelper_6989586621681501451Sym1 a6989586621681501456 :: TyFun (a ~> Down b) (Down b) -> Type
type Apply (TFHelper_6989586621681492797Sym0 :: TyFun (Down (a ~> b)) (Down a ~> Down b) -> Type) (a6989586621681492802 :: Down (a ~> b))
Instance details Defined in Data.Singletons.Prelude.Applicative type Apply (TFHelper_6989586621681492797Sym0 :: TyFun (Down (a ~> b)) (Down a ~> Down b) -> Type) (a6989586621681492802 :: Down (a ~> b)) = TFHelper_6989586621681492797Sym1 a6989586621681492802
type Apply (TFHelper_6989586621681501451Sym1 a6989586621681501456 :: TyFun (a ~> Down b) (Down b) -> Type) (a6989586621681501457 :: a ~> Down b)
Instance details Defined in Data.Singletons.Prelude.Monad type Apply (TFHelper_6989586621681501451Sym1 a6989586621681501456 :: TyFun (a ~> Down b) (Down b) -> Type) (a6989586621681501457 :: a ~> Down b) = TFHelper_6989586621681501451Sym2 a6989586621681501456 a6989586621681501457
type Apply (Fmap_6989586621680158231Sym0 :: TyFun (a ~> b) (Down a ~> Down b) -> Type) (a6989586621680158236 :: a ~> b)
Instance details Defined in Data.Singletons.Prelude.Functor type Apply (Fmap_6989586621680158231Sym0 :: TyFun (a ~> b) (Down a ~> Down b) -> Type) (a6989586621680158236 :: a ~> b) = Fmap_6989586621680158231Sym1 a6989586621680158236

comparing :: Ord a => (b -> a) -> b -> b -> Ordering #

comparing p x y = compare (p x) (p y)

Useful combinator for use in conjunction with the xxxBy family of functions from Data.List, for example:

  ... sortBy (comparing fst) ...

either :: (a -> c) -> (b -> c) -> Either a b -> c #

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

Expand

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

lefts :: [Either a b] -> [a] #

Extracts from a list of Either all the Left elements. All the Left elements are extracted in order.

Examples

Expand

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> lefts list
["foo","bar","baz"]

rights :: [Either a b] -> [b] #

Extracts from a list of Either all the Right elements. All the Right elements are extracted in order.

Examples

Expand

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> rights list
[3,7]

partitionEithers :: [Either a b] -> ([a], [b]) #

Partitions a list of Either into two lists. All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

Examples

Expand

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list
(["foo","bar","baz"],[3,7])

The pair returned by partitionEithers x should be the same pair as (lefts x, rights x):

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list == (lefts list, rights list)
True

reads :: Read a => ReadS a #

equivalent to readsPrec with a precedence of 0.

dropWhileEnd :: (a -> Bool) -> [a] -> [a] #

The dropWhileEnd function drops the largest suffix of a list in which the given predicate holds for all elements. For example:

>>> dropWhileEnd isSpace "foo\n"
"foo"

>>> dropWhileEnd isSpace "foo bar"
"foo bar"

dropWhileEnd isSpace ("foo\n" ++ undefined) == "foo" ++ undefined

Since: base-4.5.0.0

stripPrefix :: Eq a => [a] -> [a] -> Maybe [a] #

$\mathcal{O}(\min(m,n))$. The stripPrefix function drops the given prefix from a list. It returns Nothing if the list did not start with the prefix given, or Just the list after the prefix, if it does.

>>> stripPrefix "foo" "foobar"
Just "bar"

>>> stripPrefix "foo" "foo"
Just ""

>>> stripPrefix "foo" "barfoo"
Nothing

>>> stripPrefix "foo" "barfoobaz"
Nothing

elemIndex :: Eq a => a -> [a] -> Maybe Int #

The elemIndex function returns the index of the first element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.

>>> elemIndex 4 [0..]
Just 4

elemIndices :: Eq a => a -> [a] -> [Int] #

The elemIndices function extends elemIndex, by returning the indices of all elements equal to the query element, in ascending order.

>>> elemIndices 'o' "Hello World"
[4,7]

findIndex :: (a -> Bool) -> [a] -> Maybe Int #

The findIndex function takes a predicate and a list and returns the index of the first element in the list satisfying the predicate, or Nothing if there is no such element.

>>> findIndex isSpace "Hello World!"
Just 5

findIndices :: (a -> Bool) -> [a] -> [Int] #

The findIndices function extends findIndex, by returning the indices of all elements satisfying the predicate, in ascending order.

>>> findIndices (`elem` "aeiou") "Hello World!"
[1,4,7]

isPrefixOf :: Eq a => [a] -> [a] -> Bool #

$\mathcal{O}(\min(m,n))$. The isPrefixOf function takes two lists and returns True iff the first list is a prefix of the second.

>>> "Hello" `isPrefixOf` "Hello World!"
True

>>> "Hello" `isPrefixOf` "Wello Horld!"
False

isSuffixOf :: Eq a => [a] -> [a] -> Bool #

The isSuffixOf function takes two lists and returns True iff the first list is a suffix of the second. The second list must be finite.

>>> "ld!" `isSuffixOf` "Hello World!"
True

>>> "World" `isSuffixOf` "Hello World!"
False

isInfixOf :: Eq a => [a] -> [a] -> Bool #

The isInfixOf function takes two lists and returns True iff the first list is contained, wholly and intact, anywhere within the second.

>>> isInfixOf "Haskell" "I really like Haskell."
True

>>> isInfixOf "Ial" "I really like Haskell."
False

nub :: Eq a => [a] -> [a] #

$\mathcal{O}(n^2)$. The nub function removes duplicate elements from a list. In particular, it keeps only the first occurrence of each element. (The name nub means `essence'.) It is a special case of nubBy, which allows the programmer to supply their own equality test.

>>> nub [1,2,3,4,3,2,1,2,4,3,5]
[1,2,3,4,5]

nubBy :: (a -> a -> Bool) -> [a] -> [a] #

The nubBy function behaves just like nub, except it uses a user-supplied equality predicate instead of the overloaded == function.

>>> nubBy (\x y -> mod x 3 == mod y 3) [1,2,4,5,6]
[1,2,6]

delete :: Eq a => a -> [a] -> [a] #

$\mathcal{O}(n)$. delete x removes the first occurrence of x from its list argument. For example,

>>> delete 'a' "banana"
"bnana"

It is a special case of deleteBy, which allows the programmer to supply their own equality test.

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a] #

$\mathcal{O}(n)$. The deleteBy function behaves like delete, but takes a user-supplied equality predicate.

>>> deleteBy (<=) 4 [1..10]
[1,2,3,5,6,7,8,9,10]

union :: Eq a => [a] -> [a] -> [a] #

The union function returns the list union of the two lists. For example,

>>> "dog" `union` "cow"
"dogcw"

Duplicates, and elements of the first list, are removed from the the second list, but if the first list contains duplicates, so will the result. It is a special case of unionBy, which allows the programmer to supply their own equality test.

unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] #

The unionBy function is the non-overloaded version of union.

intersect :: Eq a => [a] -> [a] -> [a] #

The intersect function takes the list intersection of two lists. For example,

>>> [1,2,3,4] `intersect` [2,4,6,8]
[2,4]

If the first list contains duplicates, so will the result.

>>> [1,2,2,3,4] `intersect` [6,4,4,2]
[2,2,4]

It is a special case of intersectBy, which allows the programmer to supply their own equality test. If the element is found in both the first and the second list, the element from the first list will be used.

intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] #

The intersectBy function is the non-overloaded version of intersect.

intersperse :: a -> [a] -> [a] #

$\mathcal{O}(n)$. The intersperse function takes an element and a list and `intersperses' that element between the elements of the list. For example,

>>> intersperse ',' "abcde"
"a,b,c,d,e"

transpose :: [[a]] -> [[a]] #

The transpose function transposes the rows and columns of its argument. For example,

>>> transpose [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

If some of the rows are shorter than the following rows, their elements are skipped:

>>> transpose [[10,11],[20],[],[30,31,32]]
[[10,20,30],[11,31],[32]]

partition :: (a -> Bool) -> [a] -> ([a], [a]) #

The partition function takes a predicate a list and returns the pair of lists of elements which do and do not satisfy the predicate, respectively; i.e.,

partition p xs == (filter p xs, filter (not . p) xs)

>>> partition (`elem` "aeiou") "Hello World!"
("eoo","Hll Wrld!")

insert :: Ord a => a -> [a] -> [a] #

$\mathcal{O}(n)$. The insert function takes an element and a list and inserts the element into the list at the first position where it is less than or equal to the next element. In particular, if the list is sorted before the call, the result will also be sorted. It is a special case of insertBy, which allows the programmer to supply their own comparison function.

>>> insert 4 [1,2,3,5,6,7]
[1,2,3,4,5,6,7]

insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a] #

$\mathcal{O}(n)$. The non-overloaded version of insert.

genericLength :: Num i => [a] -> i #

$\mathcal{O}(n)$. The genericLength function is an overloaded version of length. In particular, instead of returning an Int, it returns any type which is an instance of Num. It is, however, less efficient than length.

>>> genericLength [1, 2, 3] :: Int
3
>>> genericLength [1, 2, 3] :: Float
3.0

genericTake :: Integral i => i -> [a] -> [a] #

The genericTake function is an overloaded version of take, which accepts any Integral value as the number of elements to take.

genericDrop :: Integral i => i -> [a] -> [a] #

The genericDrop function is an overloaded version of drop, which accepts any Integral value as the number of elements to drop.

genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) #

The genericSplitAt function is an overloaded version of splitAt, which accepts any Integral value as the position at which to split.

genericIndex :: Integral i => [a] -> i -> a #

The genericIndex function is an overloaded version of !!, which accepts any Integral value as the index.

genericReplicate :: Integral i => i -> a -> [a] #

The genericReplicate function is an overloaded version of replicate, which accepts any Integral value as the number of repetitions to make.

zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)] #

The zip4 function takes four lists and returns a list of quadruples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)] #

The zip5 function takes five lists and returns a list of five-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)] #

The zip6 function takes six lists and returns a list of six-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)] #

The zip7 function takes seven lists and returns a list of seven-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e] #

The zipWith4 function takes a function which combines four elements, as well as four lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] #

The zipWith5 function takes a function which combines five elements, as well as five lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] #

The zipWith6 function takes a function which combines six elements, as well as six lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h] #

The zipWith7 function takes a function which combines seven elements, as well as seven lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d]) #

The unzip4 function takes a list of quadruples and returns four lists, analogous to unzip.

unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e]) #

The unzip5 function takes a list of five-tuples and returns five lists, analogous to unzip.

unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f]) #

The unzip6 function takes a list of six-tuples and returns six lists, analogous to unzip.

unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g]) #

The unzip7 function takes a list of seven-tuples and returns seven lists, analogous to unzip.

deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] #

The deleteFirstsBy function takes a predicate and two lists and returns the first list with the first occurrence of each element of the second list removed.

group :: Eq a => [a] -> [[a]] #

The group function takes a list and returns a list of lists such that the concatenation of the result is equal to the argument. Moreover, each sublist in the result contains only equal elements. For example,

>>> group "Mississippi"
["M","i","ss","i","ss","i","pp","i"]

It is a special case of groupBy, which allows the programmer to supply their own equality test.

groupBy :: (a -> a -> Bool) -> [a] -> [[a]] #

The groupBy function is the non-overloaded version of group.

inits :: [a] -> [[a]] #

The inits function returns all initial segments of the argument, shortest first. For example,

>>> inits "abc"
["","a","ab","abc"]

Note that inits has the following strictness property: inits (xs ++ _|_) = inits xs ++ _|_

In particular, inits _|_ = [] : _|_

tails :: [a] -> [[a]] #

$\mathcal{O}(n)$. The tails function returns all final segments of the argument, longest first. For example,

>>> tails "abc"
["abc","bc","c",""]

Note that tails has the following strictness property: tails _|_ = _|_ : _|_

subsequences :: [a] -> [[a]] #

The subsequences function returns the list of all subsequences of the argument.

>>> subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]

permutations :: [a] -> [[a]] #

The permutations function returns the list of all permutations of the argument.

>>> permutations "abc"
["abc","bac","cba","bca","cab","acb"]

sort :: Ord a => [a] -> [a] #

The sort function implements a stable sorting algorithm. It is a special case of sortBy, which allows the programmer to supply their own comparison function.

Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.

>>> sort [1,6,4,3,2,5]
[1,2,3,4,5,6]

sortBy :: (a -> a -> Ordering) -> [a] -> [a] #

The sortBy function is the non-overloaded version of sort.

>>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

sortOn :: Ord b => (a -> b) -> [a] -> [a] #

Sort a list by comparing the results of a key function applied to each element. sortOn f is equivalent to sortBy (comparing f), but has the performance advantage of only evaluating f once for each element in the input list. This is called the decorate-sort-undecorate paradigm, or Schwartzian transform.

Elements are arranged from from lowest to highest, keeping duplicates in the order they appeared in the input.

>>> sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

Since: base-4.8.0.0

unfoldr :: (b -> Maybe (a, b)) -> b -> [a] #

The unfoldr function is a `dual' to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. The function takes the element and returns Nothing if it is done producing the list or returns Just (a,b), in which case, a is a prepended to the list and b is used as the next element in a recursive call. For example,

iterate f == unfoldr (\x -> Just (x, f x))

In some cases, unfoldr can undo a foldr operation:

unfoldr f' (foldr f z xs) == xs

if the following holds:

f' (f x y) = Just (x,y)
f' z       = Nothing

A simple use of unfoldr:

>>> unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
[10,9,8,7,6,5,4,3,2,1]

lines :: String -> [String] #

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]

>>> lines "\n"
[""]

>>> lines "one"
["one"]

>>> lines "one\n"
["one"]

>>> lines "one\n\n"
["one",""]

>>> lines "one\ntwo"
["one","two"]

>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

unlines :: [String] -> String #

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

words :: String -> [String] #

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

unwords :: [String] -> String #

unwords is an inverse operation to words. It joins words with separating spaces.

>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"

traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #

Map each element of a structure to an action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see traverse.

for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for.

>>> for_ [1..4] print
1
2
3
4

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m () #

forM_ is mapM_ with its arguments flipped. For a version that doesn't ignore the results see forM.

As of base 4.8.0.0, forM_ is just for_, specialized to Monad.

sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f () #

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequenceA.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

asum :: (Foldable t, Alternative f) => t (f a) -> f a #

The sum of a collection of actions, generalizing concat.

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"

msum :: (Foldable t, MonadPlus m) => t (m a) -> m a #

The sum of a collection of actions, generalizing concat. As of base 4.8.0.0, msum is just asum, specialized to MonadPlus.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #

Map a function over all the elements of a container and concatenate the resulting lists.

and :: Foldable t => t Bool -> Bool #

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

or :: Foldable t => t Bool -> Bool #

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

any :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether any element of the structure satisfies the predicate.

all :: Foldable t => (a -> Bool) -> t a -> Bool #

Determines whether all elements of the structure satisfy the predicate.

maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #

The largest element of a non-empty structure with respect to the given comparison function.

minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #

The least element of a non-empty structure with respect to the given comparison function.

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

notElem is the negation of elem.

find :: Foldable t => (a -> Bool) -> t a -> Maybe a #

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

class (Typeable e, Show e) => Exception e where #

Any type that you wish to throw or catch as an exception must be an instance of the Exception class. The simplest case is a new exception type directly below the root:

data MyException = ThisException | ThatException
    deriving Show

instance Exception MyException

The default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:

*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException

In more complicated examples, you may wish to define a whole hierarchy of exceptions:

---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler

data SomeCompilerException = forall e . Exception e => SomeCompilerException e

instance Show SomeCompilerException where
    show (SomeCompilerException e) = show e

instance Exception SomeCompilerException

compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException

compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
    SomeCompilerException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler

data SomeFrontendException = forall e . Exception e => SomeFrontendException e

instance Show SomeFrontendException where
    show (SomeFrontendException e) = show e

instance Exception SomeFrontendException where
    toException = compilerExceptionToException
    fromException = compilerExceptionFromException

frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException

frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
    SomeFrontendException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception

data MismatchedParentheses = MismatchedParentheses
    deriving Show

instance Exception MismatchedParentheses where
    toException   = frontendExceptionToException
    fromException = frontendExceptionFromException

We can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:

*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: IOException))
*** Exception: MismatchedParentheses

Minimal complete definition

Nothing

Methods

toException :: e -> SomeException #

fromException :: SomeException -> Maybe e #

displayException :: e -> String #

Render this exception value in a human-friendly manner.

Default implementation: show.

Since: base-4.8.0.0

Instances

Instances details

Exception SomeException	Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods toException :: SomeException -> SomeException # fromException :: SomeException -> Maybe SomeException # displayException :: SomeException -> String #
Exception IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: IOException -> SomeException # fromException :: SomeException -> Maybe IOException # displayException :: IOException -> String #
Exception Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods toException :: Void -> SomeException # fromException :: SomeException -> Maybe Void # displayException :: Void -> String #
Exception PatternMatchFail	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: PatternMatchFail -> SomeException # fromException :: SomeException -> Maybe PatternMatchFail # displayException :: PatternMatchFail -> String #
Exception RecSelError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: RecSelError -> SomeException # fromException :: SomeException -> Maybe RecSelError # displayException :: RecSelError -> String #
Exception RecConError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: RecConError -> SomeException # fromException :: SomeException -> Maybe RecConError # displayException :: RecConError -> String #
Exception RecUpdError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: RecUpdError -> SomeException # fromException :: SomeException -> Maybe RecUpdError # displayException :: RecUpdError -> String #
Exception NoMethodError	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: NoMethodError -> SomeException # fromException :: SomeException -> Maybe NoMethodError # displayException :: NoMethodError -> String #
Exception TypeError	Since: base-4.9.0.0
Instance details Defined in Control.Exception.Base Methods toException :: TypeError -> SomeException # fromException :: SomeException -> Maybe TypeError # displayException :: TypeError -> String #
Exception NonTermination	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: NonTermination -> SomeException # fromException :: SomeException -> Maybe NonTermination # displayException :: NonTermination -> String #
Exception NestedAtomically	Since: base-4.0
Instance details Defined in Control.Exception.Base Methods toException :: NestedAtomically -> SomeException # fromException :: SomeException -> Maybe NestedAtomically # displayException :: NestedAtomically -> String #
Exception BlockedIndefinitelyOnMVar	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: BlockedIndefinitelyOnMVar -> SomeException # fromException :: SomeException -> Maybe BlockedIndefinitelyOnMVar # displayException :: BlockedIndefinitelyOnMVar -> String #
Exception BlockedIndefinitelyOnSTM	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: BlockedIndefinitelyOnSTM -> SomeException # fromException :: SomeException -> Maybe BlockedIndefinitelyOnSTM # displayException :: BlockedIndefinitelyOnSTM -> String #
Exception Deadlock	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: Deadlock -> SomeException # fromException :: SomeException -> Maybe Deadlock # displayException :: Deadlock -> String #
Exception AllocationLimitExceeded	Since: base-4.8.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: AllocationLimitExceeded -> SomeException # fromException :: SomeException -> Maybe AllocationLimitExceeded # displayException :: AllocationLimitExceeded -> String #
Exception CompactionFailed	Since: base-4.10.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: CompactionFailed -> SomeException # fromException :: SomeException -> Maybe CompactionFailed # displayException :: CompactionFailed -> String #
Exception AssertionFailed	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: AssertionFailed -> SomeException # fromException :: SomeException -> Maybe AssertionFailed # displayException :: AssertionFailed -> String #
Exception SomeAsyncException	Since: base-4.7.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: SomeAsyncException -> SomeException # fromException :: SomeException -> Maybe SomeAsyncException # displayException :: SomeAsyncException -> String #
Exception AsyncException	Since: base-4.7.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: AsyncException -> SomeException # fromException :: SomeException -> Maybe AsyncException # displayException :: AsyncException -> String #
Exception ArrayException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: ArrayException -> SomeException # fromException :: SomeException -> Maybe ArrayException # displayException :: ArrayException -> String #
Exception FixIOException	Since: base-4.11.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: FixIOException -> SomeException # fromException :: SomeException -> Maybe FixIOException # displayException :: FixIOException -> String #
Exception ExitCode	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: ExitCode -> SomeException # fromException :: SomeException -> Maybe ExitCode # displayException :: ExitCode -> String #
Exception ErrorCall	Since: base-4.0.0.0
Instance details Defined in GHC.Exception Methods toException :: ErrorCall -> SomeException # fromException :: SomeException -> Maybe ErrorCall # displayException :: ErrorCall -> String #
Exception ArithException	Since: base-4.0.0.0
Instance details Defined in GHC.Exception.Type Methods toException :: ArithException -> SomeException # fromException :: SomeException -> Maybe ArithException # displayException :: ArithException -> String #
Exception BothBottom
Instance details Defined in Data.Unamb Methods toException :: BothBottom -> SomeException # fromException :: SomeException -> Maybe BothBottom # displayException :: BothBottom -> String #
Exception DontBother
Instance details Defined in Data.Unamb Methods toException :: DontBother -> SomeException # fromException :: SomeException -> Maybe DontBother # displayException :: DontBother -> String #

type IOError = IOException #

The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

data IOException #

Exceptions that occur in the IO monad. An IOException records a more specific error type, a descriptive string and maybe the handle that was used when the error was flagged.

Instances

Instances details

Eq IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOException -> IOException -> Bool # (/=) :: IOException -> IOException -> Bool #
Show IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOException -> ShowS # show :: IOException -> String # showList :: [IOException] -> ShowS #
Exception IOException	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods toException :: IOException -> SomeException # fromException :: SomeException -> Maybe IOException # displayException :: IOException -> String #
Error IOException
Instance details Defined in Control.Monad.Trans.Error Methods noMsg :: IOException # strMsg :: String -> IOException #

userError :: String -> IOError #

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)

type FilePath = String #

File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.

data IOErrorType #

An abstract type that contains a value for each variant of IOError.

Instances

Instances details

Eq IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool # (/=) :: IOErrorType -> IOErrorType -> Bool #
Show IOErrorType	Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOErrorType -> ShowS # show :: IOErrorType -> String # showList :: [IOErrorType] -> ShowS #

ioError :: IOError -> IO a #

Raise an IOError in the IO monad.

tryIOError :: IO a -> IO (Either IOError a) #

The construct tryIOError comp exposes IO errors which occur within a computation, and which are not fully handled.

Non-I/O exceptions are not caught by this variant; to catch all exceptions, use try from Control.Exception.

Since: base-4.4.0.0

mkIOError :: IOErrorType -> String -> Maybe Handle -> Maybe FilePath -> IOError #

Construct an IOError of the given type where the second argument describes the error location and the third and fourth argument contain the file handle and file path of the file involved in the error if applicable.

isAlreadyExistsError :: IOError -> Bool #

An error indicating that an IO operation failed because one of its arguments already exists.

isDoesNotExistError :: IOError -> Bool #

An error indicating that an IO operation failed because one of its arguments does not exist.

isAlreadyInUseError :: IOError -> Bool #

An error indicating that an IO operation failed because one of its arguments is a single-use resource, which is already being used (for example, opening the same file twice for writing might give this error).

isFullError :: IOError -> Bool #

An error indicating that an IO operation failed because the device is full.

isEOFError :: IOError -> Bool #

An error indicating that an IO operation failed because the end of file has been reached.

isIllegalOperation :: IOError -> Bool #

An error indicating that an IO operation failed because the operation was not possible. Any computation which returns an IO result may fail with isIllegalOperation. In some cases, an implementation will not be able to distinguish between the possible error causes. In this case it should fail with isIllegalOperation.

isPermissionError :: IOError -> Bool #

An error indicating that an IO operation failed because the user does not have sufficient operating system privilege to perform that operation.

isUserError :: IOError -> Bool #

A programmer-defined error value constructed using userError.

isResourceVanishedError :: IOError -> Bool #

An error indicating that the operation failed because the resource vanished. See resourceVanishedErrorType.

Since: base-4.14.0.0

alreadyExistsErrorType :: IOErrorType #

I/O error where the operation failed because one of its arguments already exists.

doesNotExistErrorType :: IOErrorType #

I/O error where the operation failed because one of its arguments does not exist.

alreadyInUseErrorType :: IOErrorType #

I/O error where the operation failed because one of its arguments is a single-use resource, which is already being used.

fullErrorType :: IOErrorType #

I/O error where the operation failed because the device is full.

eofErrorType :: IOErrorType #

I/O error where the operation failed because the end of file has been reached.

illegalOperationErrorType :: IOErrorType #

I/O error where the operation is not possible.

permissionErrorType :: IOErrorType #

I/O error where the operation failed because the user does not have sufficient operating system privilege to perform that operation.

userErrorType :: IOErrorType #

I/O error that is programmer-defined.

resourceVanishedErrorType :: IOErrorType #

I/O error where the operation failed because the resource vanished. This happens when, for example, attempting to write to a closed socket or attempting to write to a named pipe that was deleted.

Since: base-4.14.0.0

isAlreadyExistsErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because one of its arguments already exists.

isDoesNotExistErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because one of its arguments does not exist.

isAlreadyInUseErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because one of its arguments is a single-use resource, which is already being used.

isFullErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because the device is full.

isEOFErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because the end of file has been reached.

isIllegalOperationErrorType :: IOErrorType -> Bool #

I/O error where the operation is not possible.

isPermissionErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because the user does not have sufficient operating system privilege to perform that operation.

isUserErrorType :: IOErrorType -> Bool #

I/O error that is programmer-defined.

isResourceVanishedErrorType :: IOErrorType -> Bool #

I/O error where the operation failed because the resource vanished. See resourceVanishedErrorType.

Since: base-4.14.0.0

ioeGetErrorType :: IOError -> IOErrorType #

ioeGetErrorString :: IOError -> String #

ioeGetLocation :: IOError -> String #

ioeGetHandle :: IOError -> Maybe Handle #

ioeGetFileName :: IOError -> Maybe FilePath #

ioeSetErrorType :: IOError -> IOErrorType -> IOError #

ioeSetErrorString :: IOError -> String -> IOError #

ioeSetLocation :: IOError -> String -> IOError #

ioeSetHandle :: IOError -> Handle -> IOError #

ioeSetFileName :: IOError -> FilePath -> IOError #

modifyIOError :: (IOError -> IOError) -> IO a -> IO a #

Catch any IOError that occurs in the computation and throw a modified version.

annotateIOError :: IOError -> String -> Maybe Handle -> Maybe FilePath -> IOError #

Adds a location description and maybe a file path and file handle to an IOError. If any of the file handle or file path is not given the corresponding value in the IOError remains unaltered.

catchIOError :: IO a -> (IOError -> IO a) -> IO a #

The catchIOError function establishes a handler that receives any IOError raised in the action protected by catchIOError. An IOError is caught by the most recent handler established by one of the exception handling functions. These handlers are not selective: all IOErrors are caught. Exception propagation must be explicitly provided in a handler by re-raising any unwanted exceptions. For example, in

f = catchIOError g (\e -> if IO.isEOFError e then return [] else ioError e)

the function f returns [] when an end-of-file exception (cf. isEOFError) occurs in g; otherwise, the exception is propagated to the next outer handler.

When an exception propagates outside the main program, the Haskell system prints the associated IOError value and exits the program.

Non-I/O exceptions are not caught by this variant; to catch all exceptions, use catch from Control.Exception.

Since: base-4.4.0.0

putStr :: String -> IO () #

Write a string to the standard output device (same as hPutStr stdout).

putStrLn :: String -> IO () #

The same as putStr, but adds a newline character.

getLine :: IO String #

Read a line from the standard input device (same as hGetLine stdin).

getContents :: IO String #

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

interact :: (String -> String) -> IO () #

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

readFile :: FilePath -> IO String #

The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.

writeFile :: FilePath -> String -> IO () #

The computation writeFile file str function writes the string str, to the file file.

for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b) #

for is traverse with its arguments flipped. For a version that ignores the results see for_.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) #

forM is mapM with its arguments flipped. For a version that ignores the results see forM_.

mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) #

The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) #

The mapAccumR function behaves like a combination of fmap and foldr; it applies a function to each element of a structure, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new structure.

isSubsequenceOf :: Eq a => [a] -> [a] -> Bool #

The isSubsequenceOf function takes two lists and returns True if all the elements of the first list occur, in order, in the second. The elements do not have to occur consecutively.

isSubsequenceOf x y is equivalent to elem x (subsequences y).

Examples

Expand

>>> isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
True
>>> isSubsequenceOf ['a','d'..'z'] ['a'..'z']
True
>>> isSubsequenceOf [1..10] [10,9..0]
False

Since: base-4.8.0.0

filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a] #

This generalizes the list-based filter function.

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #

Left-to-right composition of Kleisli arrows.

'(bs >=> cs) a' can be understood as the do expression

do b <- bs a
   cs b

(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1 #

Right-to-left composition of Kleisli arrows. (>=>), with the arguments flipped.

Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

forever :: Applicative f => f a -> f b #

Repeat an action indefinitely.

Using ApplicativeDo: 'forever as' can be understood as the pseudo-do expression

do as
   as
   ..

with as repeating.

Examples

Expand

A common use of forever is to process input from network sockets, Handles, and channels (e.g. MVar and Chan).

For example, here is how we might implement an echo server, using forever both to listen for client connections on a network socket and to echo client input on client connection handles:

echoServer :: Socket -> IO ()
echoServer socket = forever $ do
  client <- accept socket
  forkFinally (echo client) (\_ -> hClose client)
  where
    echo :: Handle -> IO ()
    echo client = forever $
      hGetLine client >>= hPutStrLn client

mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) #

The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state monad.

zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c] #

The zipWithM function generalizes zipWith to arbitrary applicative functors.

zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () #

zipWithM_ is the extension of zipWithM which ignores the final result.

foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the `folded function' are not commutative.

foldM f a1 [x1, x2, ..., xm]

==

do
  a2 <- f a1 x1
  a3 <- f a2 x2
  ...
  f am xm

If right-to-left evaluation is required, the input list should be reversed.

Note: foldM is the same as foldlM

foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () #

Like foldM, but discards the result.

replicateM :: Applicative m => Int -> m a -> m [a] #

replicateM n act performs the action n times, gathering the results.

Using ApplicativeDo: 'replicateM 5 as' can be understood as the do expression

do a1 <- as
   a2 <- as
   a3 <- as
   a4 <- as
   a5 <- as
   pure [a1,a2,a3,a4,a5]

Note the Applicative constraint.

replicateM_ :: Applicative m => Int -> m a -> m () #

Like replicateM, but discards the result.

unless :: Applicative f => Bool -> f () -> f () #

The reverse of when.

(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4 #

Strict version of <$>.

Since: base-4.8.0.0

mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a #

Direct MonadPlus equivalent of filter.

Examples

Expand

The filter function is just mfilter specialized to the list monad:

filter = ( mfilter :: (a -> Bool) -> [a] -> [a] )

An example using mfilter with the Maybe monad:

>>> mfilter odd (Just 1)
Just 1
>>> mfilter odd (Just 2)
Nothing

class Monad m => MonadIO (m :: Type -> Type) where #

Monads in which IO computations may be embedded. Any monad built by applying a sequence of monad transformers to the IO monad will be an instance of this class.

Instances should satisfy the following laws, which state that liftIO is a transformer of monads:

```
liftIO . return = return
```

liftIO (m >>= f) = liftIO m >>= (liftIO . f)

Methods

liftIO :: IO a -> m a #

Lift a computation from the IO monad.

Instances

Instances details

MonadIO IO	Since: base-4.9.0.0
Instance details Defined in Control.Monad.IO.Class Methods liftIO :: IO a -> IO a #
MonadIO Q
Instance details Defined in Language.Haskell.TH.Syntax Methods liftIO :: IO a -> Q a #
MonadIO m => MonadIO (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods liftIO :: IO a -> MaybeT m a #
MonadIO m => MonadIO (CatchT m)
Instance details Defined in Control.Monad.Catch.Pure Methods liftIO :: IO a -> CatchT m a #
MonadIO m => MonadIO (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods liftIO :: IO a -> ListT m a #
MonadIO m => MonadIO (IterT m)
Instance details Defined in Control.Monad.Trans.Iter Methods liftIO :: IO a -> IterT m a #
MonadIO m => MonadIO (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods liftIO :: IO a -> ExceptT e m a #
MonadIO m => MonadIO (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods liftIO :: IO a -> IdentityT m a #
(Error e, MonadIO m) => MonadIO (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods liftIO :: IO a -> ErrorT e m a #
MonadIO m => MonadIO (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods liftIO :: IO a -> ReaderT r m a #
MonadIO m => MonadIO (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods liftIO :: IO a -> StateT s m a #
MonadIO m => MonadIO (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods liftIO :: IO a -> StateT s m a #
(Monoid w, MonadIO m) => MonadIO (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods liftIO :: IO a -> WriterT w m a #
(Monoid w, MonadIO m) => MonadIO (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods liftIO :: IO a -> WriterT w m a #
(Functor f, MonadIO m) => MonadIO (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods liftIO :: IO a -> FreeT f m a #
MonadIO m => MonadIO (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods liftIO :: IO a -> RandT g m a #
MonadIO m => MonadIO (RandT g m)
Instance details Defined in Control.Monad.Trans.Random.Strict Methods liftIO :: IO a -> RandT g m a #
MonadIO m => MonadIO (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods liftIO :: IO a -> ContT r m a #
(Monoid w, MonadIO m) => MonadIO (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods liftIO :: IO a -> RWST r w s m a #
(Monoid w, MonadIO m) => MonadIO (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods liftIO :: IO a -> RWST r w s m a #

second :: Arrow a => a b c -> a (d, b) (d, c) #

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c') infixr 3 #

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

first :: Arrow a => a b c -> a (b, d) (c, d) #

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c') infixr 3 #

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

(<|>) :: Alternative f => f a -> f a -> f a infixl 3 #

An associative binary operation

lift :: (MonadTrans t, Monad m) => m a -> t m a #

Lift a computation from the argument monad to the constructed monad.

module Algebra.Ring.Polynomial.Monomial

module Algebra.Ring.Polynomial.Class

type Polynomial r = OrderedPolynomial r Grevlex Source #

transformMonomial :: (IsMonomialOrder m o', CoeffRing k, KnownNat m) => (USized n Int -> USized m Int) -> OrderedPolynomial k o n -> OrderedPolynomial k o' m Source #

castPolynomial :: forall r n m o o'. (CoeffRing r, KnownNat n, KnownNat m, IsMonomialOrder n o, IsMonomialOrder m o') => OrderedPolynomial r o n -> OrderedPolynomial r o' m Source #

changeOrder :: forall k n o o'. (CoeffRing k, Eq (Monomial n), IsMonomialOrder n o, IsMonomialOrder n o', KnownNat n) => o' -> OrderedPolynomial k o n -> OrderedPolynomial k o' n Source #

changeOrderProxy :: forall k n o o'. (CoeffRing k, Eq (Monomial n), IsMonomialOrder n o, IsMonomialOrder n o', KnownNat n) => Proxy o' -> OrderedPolynomial k o n -> OrderedPolynomial k o' n Source #

scastPolynomial :: (IsMonomialOrder n o, IsMonomialOrder m o', KnownNat m, CoeffRing r, KnownNat n) => SNat m -> OrderedPolynomial r o n -> OrderedPolynomial r o' m Source #

newtype OrderedPolynomial r order n Source #

n-ary polynomial ring over some noetherian ring R.

Constructors

Polynomial
Fields _terms :: Map (OrderedMonomial order n) r

Instances

Instances details

(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Integer -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Integer (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule Natural (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => RightModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: OrderedPolynomial r order n -> Scalar r -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => LeftModule (Scalar r) (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
Eq r => Eq (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (==) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> Bool # (/=) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> Bool #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Num (OrderedPolynomial r order n) Source #	We provide Num instance to use trivial injection R into R[X]. Do not use signum or abs.
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # (-) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # (*) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # negate :: OrderedPolynomial r order n -> OrderedPolynomial r order n # abs :: OrderedPolynomial r order n -> OrderedPolynomial r order n # signum :: OrderedPolynomial r order n -> OrderedPolynomial r order n # fromInteger :: Integer -> OrderedPolynomial r order n #
(CoeffRing r, IsOrder n ord, Ord r) => Ord (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods compare :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Ordering # (<) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (<=) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (>) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # (>=) :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # max :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # min :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #
(KnownNat n, CoeffRing r, IsMonomialOrder n order, PrettyCoeff r) => Show (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods showsPrec :: Int -> OrderedPolynomial r order n -> ShowS # show :: OrderedPolynomial r order n -> String # showList :: [OrderedPolynomial r order n] -> ShowS #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => UFD (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(KnownNat n, Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => UFD (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => PID (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods egcd :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => GCDDomain (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods gcd :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 # reduceFraction :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) # lcm :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 #
(KnownNat n, Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => GCDDomain (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial Methods gcd :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # reduceFraction :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> (OrderedPolynomial r ord n, OrderedPolynomial r ord n) # lcm :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #
(Eq r, DecidableUnits r, DecidableZero r, KnownNat n, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => IntegralDomain (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods divides :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool # maybeQuot :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Maybe (OrderedPolynomial r ord n) #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => IntegralDomain (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods divides :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> Bool # maybeQuot :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> Maybe (OrderedPolynomial r ord 1) #
(Eq r, DecidableUnits r, DecidableZero r, Field r, IsMonomialOrder 1 ord, ZeroProductSemiring r) => Euclidean (OrderedPolynomial r ord 1) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods degree :: OrderedPolynomial r ord 1 -> Maybe Natural # divide :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> (OrderedPolynomial r ord 1, OrderedPolynomial r ord 1) # quot :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 # rem :: OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 -> OrderedPolynomial r ord 1 #
(Eq r, DecidableUnits r, DecidableZero r, KnownNat n, Field r, IsMonomialOrder n ord, ZeroProductSemiring r) => ZeroProductSemiring (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(Eq r, Euclidean r, KnownNat n, IsMonomialOrder n ord) => UnitNormalForm (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods splitUnit :: OrderedPolynomial r ord n -> (OrderedPolynomial r ord n, OrderedPolynomial r ord n) #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Ring (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromInteger :: Integer -> OrderedPolynomial r order n
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Rig (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromNatural :: Natural -> OrderedPolynomial r order n #
(IsMonomialOrder n ord, Characteristic r, KnownNat n, CoeffRing r) => Characteristic (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods char :: proxy (OrderedPolynomial r ord n) -> Natural #
(CoeffRing r, KnownNat n, IsMonomialOrder n ord) => DecidableZero (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isZero :: OrderedPolynomial r ord n -> Bool #
(CoeffRing r, IsMonomialOrder n ord, DecidableUnits r, KnownNat n) => DecidableUnits (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods recipUnit :: OrderedPolynomial r ord n -> Maybe (OrderedPolynomial r ord n) # isUnit :: OrderedPolynomial r ord n -> Bool # (^?) :: Integral n0 => OrderedPolynomial r ord n -> n0 -> Maybe (OrderedPolynomial r ord n) #
(Eq r, KnownNat n, Euclidean r, IsMonomialOrder n ord) => DecidableAssociates (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isAssociate :: OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> Bool #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Unital (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods one :: OrderedPolynomial r order n # pow :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n # productWith :: Foldable f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Commutative (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Semiring (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Multiplicative (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # pow1p :: OrderedPolynomial r order n -> Natural -> OrderedPolynomial r order n # productWith1 :: Foldable1 f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Monoidal (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods zero :: OrderedPolynomial r order n # sinnum :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sumWith :: Foldable f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Group (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (-) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # negate :: OrderedPolynomial r order n -> OrderedPolynomial r order n # subtract :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # times :: Integral n0 => n0 -> OrderedPolynomial r order n -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Additive (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: OrderedPolynomial r order n -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sinnum1p :: Natural -> OrderedPolynomial r order n -> OrderedPolynomial r order n # sumWith1 :: Foldable1 f => (a -> OrderedPolynomial r order n) -> f a -> OrderedPolynomial r order n #
(IsMonomialOrder n order, CoeffRing r, KnownNat n) => Abelian (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
Hashable r => Hashable (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods hashWithSalt :: Int -> OrderedPolynomial r ord n -> Int # hash :: OrderedPolynomial r ord n -> Int #
NFData r => NFData (OrderedPolynomial r order n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods rnf :: OrderedPolynomial r order n -> () #
(KnownNat n, IsMonomialOrder n ord, CoeffRing r) => IsPolynomial (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Associated Types type Coefficient (OrderedPolynomial r ord n) # type Arity (OrderedPolynomial r ord n) :: Nat # Methods liftMap :: (Module (Scalar (Coefficient (OrderedPolynomial r ord n))) alg, Ring alg, Commutative alg) => (Ordinal (Arity (OrderedPolynomial r ord n)) -> alg) -> OrderedPolynomial r ord n -> alg # subst :: (Ring alg, Commutative alg, Module (Scalar (Coefficient (OrderedPolynomial r ord n))) alg) => Sized (Arity (OrderedPolynomial r ord n)) alg -> OrderedPolynomial r ord n -> alg # substWith :: Ring m => (Coefficient (OrderedPolynomial r ord n) -> m -> m) -> Sized (Arity (OrderedPolynomial r ord n)) m -> OrderedPolynomial r ord n -> m # sArity' :: OrderedPolynomial r ord n -> SNat (Arity (OrderedPolynomial r ord n)) # sArity :: proxy (OrderedPolynomial r ord n) -> SNat (Arity (OrderedPolynomial r ord n)) # arity :: proxy (OrderedPolynomial r ord n) -> Integer # injectCoeff :: Coefficient (OrderedPolynomial r ord n) -> OrderedPolynomial r ord n # injectCoeff' :: proxy (OrderedPolynomial r ord n) -> Coefficient (OrderedPolynomial r ord n) -> OrderedPolynomial r ord n # monomials :: OrderedPolynomial r ord n -> HashSet (Monomial (Arity (OrderedPolynomial r ord n))) # terms' :: OrderedPolynomial r ord n -> Map (Monomial (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n)) # coeff' :: Monomial (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> Coefficient (OrderedPolynomial r ord n) # constantTerm :: OrderedPolynomial r ord n -> Coefficient (OrderedPolynomial r ord n) # fromMonomial :: Monomial (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # toPolynomial' :: (Coefficient (OrderedPolynomial r ord n), Monomial (Arity (OrderedPolynomial r ord n))) -> OrderedPolynomial r ord n # polynomial' :: Map (Monomial (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # totalDegree' :: OrderedPolynomial r ord n -> Int # var :: Ordinal (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # mapCoeff' :: (Coefficient (OrderedPolynomial r ord n) -> Coefficient (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # (>\|) :: Monomial (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # (\|<) :: OrderedPolynomial r ord n -> Monomial (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # (!*) :: Coefficient (OrderedPolynomial r ord n) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # _Terms' :: Iso' (OrderedPolynomial r ord n) (Map (Monomial (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n))) # mapMonomial :: (Monomial (Arity (OrderedPolynomial r ord n)) -> Monomial (Arity (OrderedPolynomial r ord n))) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #
(KnownNat n, CoeffRing r, IsMonomialOrder n ord) => IsOrderedPolynomial (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Associated Types type MOrder (OrderedPolynomial r ord n) # Methods coeff :: OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> Coefficient (OrderedPolynomial r ord n) # terms :: OrderedPolynomial r ord n -> Map (OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n)) # leadingTerm :: OrderedPolynomial r ord n -> (Coefficient (OrderedPolynomial r ord n), OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) # leadingMonomial :: OrderedPolynomial r ord n -> OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) # leadingCoeff :: OrderedPolynomial r ord n -> Coefficient (OrderedPolynomial r ord n) # splitLeadingTerm :: OrderedPolynomial r ord n -> (Term (OrderedPolynomial r ord n), OrderedPolynomial r ord n) # orderedMonomials :: OrderedPolynomial r ord n -> Set (OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) # fromOrderedMonomial :: OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # toPolynomial :: (Coefficient (OrderedPolynomial r ord n), OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) -> OrderedPolynomial r ord n # polynomial :: Map (OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # (>) :: OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # (<) :: OrderedPolynomial r ord n -> OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n # _Terms :: Iso' (OrderedPolynomial r ord n) (Map (OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) (Coefficient (OrderedPolynomial r ord n))) # diff :: Ordinal (Arity (OrderedPolynomial r ord n)) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n # mapMonomialMonotonic :: (OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n)) -> OrderedMonomial (MOrder (OrderedPolynomial r ord n)) (Arity (OrderedPolynomial r ord n))) -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n #
type Arity (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type Arity (OrderedPolynomial r ord n) = n
type Coefficient (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type Coefficient (OrderedPolynomial r ord n) = r
type MOrder (OrderedPolynomial r ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type MOrder (OrderedPolynomial r ord n) = ord

allVars :: forall k ord n. (IsMonomialOrder n ord, CoeffRing k, KnownNat n) => Sized n (OrderedPolynomial k ord n) Source #

substVar :: (CoeffRing r, KnownNat n, IsMonomialOrder n ord, 1 <= n) => Ordinal n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n -> OrderedPolynomial r ord n Source #

substVar n f substitutes n-th variable with polynomial f, without changing arity.

homogenize :: forall k ord n. (CoeffRing k, KnownNat n, IsMonomialOrder (n + 1) ord, IsMonomialOrder n ord) => OrderedPolynomial k ord n -> OrderedPolynomial k ord (n + 1) Source #

Calculate the homogenized polynomial of given one, with additional variable is the last variable.

unhomogenize :: forall k ord n. (CoeffRing k, KnownNat n, IsMonomialOrder n ord, IsMonomialOrder (n + 1) ord) => OrderedPolynomial k ord (n + 1) -> OrderedPolynomial k ord n Source #

normalize :: DecidableZero r => OrderedPolynomial r order n -> OrderedPolynomial r order n Source #

varX :: forall r n order. (CoeffRing r, KnownNat n, IsMonomialOrder n order, 0 < n) => OrderedPolynomial r order n Source #

getTerms :: OrderedPolynomial k order n -> [(k, OrderedMonomial order n)] Source #

shiftR :: forall k r n ord. (CoeffRing r, KnownNat n, IsMonomialOrder n ord, IsMonomialOrder (k + n) ord) => SNat k -> OrderedPolynomial r ord n -> OrderedPolynomial r ord (k + n) Source #

orderedBy :: OrderedPolynomial k o n -> o -> OrderedPolynomial k o n Source #

mapCoeff :: (KnownNat n, CoeffRing b, IsMonomialOrder n ord) => (a -> b) -> OrderedPolynomial a ord n -> OrderedPolynomial b ord n Source #

reversal :: (CoeffRing k, IsMonomialOrder 1 o) => Int -> OrderedPolynomial k o 1 -> OrderedPolynomial k o 1 Source #

padeApprox :: (Field r, DecidableUnits r, CoeffRing r, ZeroProductSemiring r, IsMonomialOrder 1 order) => Natural -> Natural -> OrderedPolynomial r order 1 -> (OrderedPolynomial r order 1, OrderedPolynomial r order 1) Source #

eval :: (CoeffRing r, IsMonomialOrder n order, KnownNat n) => Sized n r -> OrderedPolynomial r order n -> r Source #

Evaluate polynomial at some point.

evalUnivariate :: (CoeffRing b, IsMonomialOrder 1 order) => b -> OrderedPolynomial b order 1 -> b Source #

substUnivariate :: (Module (Scalar r) b, Unital b, CoeffRing r, IsMonomialOrder 1 order) => b -> OrderedPolynomial r order 1 -> b Source #

Substitute univariate polynomial using Horner's rule

minpolRecurrent :: forall k. (Eq k, ZeroProductSemiring k, DecidableUnits k, DecidableZero k, Field k) => Natural -> [k] -> Polynomial k 1 Source #

class IsOrder (n :: Nat) ordering where #

Class to lookup ordering from its (type-level) name.

Methods

cmpMonomial :: Proxy ordering -> MonomialOrder n #

Instances

Instances details

KnownNat n => IsOrder n Revlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Revlex -> MonomialOrder n #
KnownNat n => IsOrder n Lex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Lex -> MonomialOrder n #
KnownNat n => IsOrder n Grlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grlex -> MonomialOrder n #
KnownNat n => IsOrder n Grevlex
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grevlex -> MonomialOrder n #
IsOrder n ord => IsOrder n (Graded ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (Graded ord) -> MonomialOrder n #
(KnownNat n, IsOrder n ord, SingI ws) => IsOrder n (WeightOrder ws ord)
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (WeightOrder ws ord) -> MonomialOrder n #
(IsOrder n ord, IsOrder m ord', KnownNat m, KnownNat n, k ~ (n + m)) => IsOrder k (ProductOrder n m ord ord')
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (ProductOrder n m ord ord') -> MonomialOrder k #

newtype PadPolyL n ord poly Source #

Constructors

PadPolyL
Fields runPadPolyL :: OrderedPolynomial poly (Graded ord) n

Instances

Instances details

(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Integer -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => RightModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Integer (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Integer -> PadPolyL n ord poly -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => LeftModule Natural (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*.) :: PadPolyL n ord poly -> Scalar r -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (.*) :: Scalar r -> PadPolyL n ord poly -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Eq (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (==) :: PadPolyL n ord poly -> PadPolyL n ord poly -> Bool # (/=) :: PadPolyL n ord poly -> PadPolyL n ord poly -> Bool #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Num (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # (-) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # (*) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # negate :: PadPolyL n ord poly -> PadPolyL n ord poly # abs :: PadPolyL n ord poly -> PadPolyL n ord poly # signum :: PadPolyL n ord poly -> PadPolyL n ord poly # fromInteger :: Integer -> PadPolyL n ord poly #
(r ~ Coefficient poly, IsOrderedPolynomial poly, SingI (Replicate n 1), KnownNat n, CoeffRing r, IsMonomialOrder n order, PrettyCoeff r) => Show (PadPolyL n order poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods showsPrec :: Int -> PadPolyL n order poly -> ShowS # show :: PadPolyL n order poly -> String # showList :: [PadPolyL n order poly] -> ShowS #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Ring (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromInteger :: Integer -> PadPolyL n ord poly
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Rig (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods fromNatural :: Natural -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => DecidableZero (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods isZero :: PadPolyL n ord poly -> Bool #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Unital (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods one :: PadPolyL n ord poly # pow :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly # productWith :: Foldable f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Commutative (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Semiring (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Multiplicative (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (*) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # pow1p :: PadPolyL n ord poly -> Natural -> PadPolyL n ord poly # productWith1 :: Foldable1 f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Monoidal (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods zero :: PadPolyL n ord poly # sinnum :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly # sumWith :: Foldable f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Group (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (-) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # negate :: PadPolyL n ord poly -> PadPolyL n ord poly # subtract :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # times :: Integral n0 => n0 -> PadPolyL n ord poly -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Additive (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Methods (+) :: PadPolyL n ord poly -> PadPolyL n ord poly -> PadPolyL n ord poly # sinnum1p :: Natural -> PadPolyL n ord poly -> PadPolyL n ord poly # sumWith1 :: Foldable1 f => (a -> PadPolyL n ord poly) -> f a -> PadPolyL n ord poly #
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => Abelian (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal
(KnownNat n, IsMonomialOrder n ord, IsPolynomial poly) => IsPolynomial (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Associated Types type Coefficient (PadPolyL n ord poly) # type Arity (PadPolyL n ord poly) :: Nat # Methods liftMap :: (Module (Scalar (Coefficient (PadPolyL n ord poly))) alg, Ring alg, Commutative alg) => (Ordinal (Arity (PadPolyL n ord poly)) -> alg) -> PadPolyL n ord poly -> alg # subst :: (Ring alg, Commutative alg, Module (Scalar (Coefficient (PadPolyL n ord poly))) alg) => Sized (Arity (PadPolyL n ord poly)) alg -> PadPolyL n ord poly -> alg # substWith :: Ring m => (Coefficient (PadPolyL n ord poly) -> m -> m) -> Sized (Arity (PadPolyL n ord poly)) m -> PadPolyL n ord poly -> m # sArity' :: PadPolyL n ord poly -> SNat (Arity (PadPolyL n ord poly)) # sArity :: proxy (PadPolyL n ord poly) -> SNat (Arity (PadPolyL n ord poly)) # arity :: proxy (PadPolyL n ord poly) -> Integer # injectCoeff :: Coefficient (PadPolyL n ord poly) -> PadPolyL n ord poly # injectCoeff' :: proxy (PadPolyL n ord poly) -> Coefficient (PadPolyL n ord poly) -> PadPolyL n ord poly # monomials :: PadPolyL n ord poly -> HashSet (Monomial (Arity (PadPolyL n ord poly))) # terms' :: PadPolyL n ord poly -> Map (Monomial (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly)) # coeff' :: Monomial (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly -> Coefficient (PadPolyL n ord poly) # constantTerm :: PadPolyL n ord poly -> Coefficient (PadPolyL n ord poly) # fromMonomial :: Monomial (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly # toPolynomial' :: (Coefficient (PadPolyL n ord poly), Monomial (Arity (PadPolyL n ord poly))) -> PadPolyL n ord poly # polynomial' :: Map (Monomial (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly)) -> PadPolyL n ord poly # totalDegree' :: PadPolyL n ord poly -> Int # var :: Ordinal (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly # mapCoeff' :: (Coefficient (PadPolyL n ord poly) -> Coefficient (PadPolyL n ord poly)) -> PadPolyL n ord poly -> PadPolyL n ord poly # (>\|) :: Monomial (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly -> PadPolyL n ord poly # (\|<) :: PadPolyL n ord poly -> Monomial (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly # (!*) :: Coefficient (PadPolyL n ord poly) -> PadPolyL n ord poly -> PadPolyL n ord poly # _Terms' :: Iso' (PadPolyL n ord poly) (Map (Monomial (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly))) # mapMonomial :: (Monomial (Arity (PadPolyL n ord poly)) -> Monomial (Arity (PadPolyL n ord poly))) -> PadPolyL n ord poly -> PadPolyL n ord poly #
(SingI (Replicate n 1), KnownNat n, IsMonomialOrder n ord, IsOrderedPolynomial poly) => IsOrderedPolynomial (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal Associated Types type MOrder (PadPolyL n ord poly) # Methods coeff :: OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly -> Coefficient (PadPolyL n ord poly) # terms :: PadPolyL n ord poly -> Map (OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly)) # leadingTerm :: PadPolyL n ord poly -> (Coefficient (PadPolyL n ord poly), OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) # leadingMonomial :: PadPolyL n ord poly -> OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) # leadingCoeff :: PadPolyL n ord poly -> Coefficient (PadPolyL n ord poly) # splitLeadingTerm :: PadPolyL n ord poly -> (Term (PadPolyL n ord poly), PadPolyL n ord poly) # orderedMonomials :: PadPolyL n ord poly -> Set (OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) # fromOrderedMonomial :: OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly # toPolynomial :: (Coefficient (PadPolyL n ord poly), OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) -> PadPolyL n ord poly # polynomial :: Map (OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly)) -> PadPolyL n ord poly # (>) :: OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly -> PadPolyL n ord poly # (<) :: PadPolyL n ord poly -> OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly # _Terms :: Iso' (PadPolyL n ord poly) (Map (OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) (Coefficient (PadPolyL n ord poly))) # diff :: Ordinal (Arity (PadPolyL n ord poly)) -> PadPolyL n ord poly -> PadPolyL n ord poly # mapMonomialMonotonic :: (OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly)) -> OrderedMonomial (MOrder (PadPolyL n ord poly)) (Arity (PadPolyL n ord poly))) -> PadPolyL n ord poly -> PadPolyL n ord poly #
type Arity (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type Arity (PadPolyL n ord poly) = n + Arity poly
type Coefficient (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type Coefficient (PadPolyL n ord poly) = Coefficient poly
type MOrder (PadPolyL n ord poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Internal type MOrder (PadPolyL n ord poly) = ProductOrder n (Arity poly) (Graded ord) (MOrder poly)

padLeftPoly :: (IsMonomialOrder n ord, IsPolynomial poly) => SNat n -> ord -> poly -> PadPolyL n ord poly Source #

module Algebra.Ring.Ideal

module Algebra.Normed

module Algebra.Internal