Relude.Functor.Reexport

Reexports functionality regarding Functor and Bifunctor typeclasses.

Documentation

class Bifunctor (p :: Type -> Type -> Type) where

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with Functor, a type constructor such as Either does not need to be partially applied for a Bifunctor instance, and the methods in this class permit mapping functions over the Left value or the Right value, or both at the same time.

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4

first :: (a -> b) -> p a c -> p b c

Map covariantly over the first argument.

first f ≡ bimap f id

Examples

>>> first toUpper ('j', 3)
('J',3)

>>> first toUpper (Left 'j')
Left 'J'

second :: (b -> c) -> p a b -> p a c

Map covariantly over the second argument.

second ≡ bimap id

Examples

>>> second (+1) ('j', 3)
('j',4)

>>> second (+1) (Right 3)
Right 4

Instances

Bifunctor Either

Since: base-4.8.0.0

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

Bifunctor Arg

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d

first :: (a -> b) -> Arg a c -> Arg b c

second :: (b -> c) -> Arg a b -> Arg a c

Bifunctor (,)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)

first :: (a -> b) -> (a, c) -> (b, c)

second :: (b -> c) -> (a, b) -> (a, c)

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d

first :: (a -> b) -> Const a c -> Const b c

second :: (b -> c) -> Const a b -> Const a c

Bifunctor ((,,) x1)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d)

first :: (a -> b) -> (x1, a, c) -> (x1, b, c)

second :: (b -> c) -> (x1, a, b) -> (x1, a, c)

Bifunctor (K1 i :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d

first :: (a -> b) -> K1 i a c -> K1 i b c

second :: (b -> c) -> K1 i a b -> K1 i a c

Bifunctor ((,,,) x1 x2)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d)

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c)

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c)

Bifunctor ((,,,,) x1 x2 x3)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d)

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c)

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c)

Bifunctor ((,,,,,) x1 x2 x3 x4)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c)

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c)

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

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

Examples

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

>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"

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

>>> fmap show (Left 17)
Left 17
>>> fmap show (Right 17)
Right "17"

Double each element of a list:

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

Apply even to the second element of a pair:

>>> fmap even (2,2)
(2,True)

It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap).

It explains why fmap can be used with tuples containing values of different types as in the following example:

>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)

(<$) :: 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.

Instances

Functor ZipList

Since: base-2.1

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b

(<$) :: a -> ZipList b -> ZipList a

Functor Handler

Since: base-4.6.0.0

Defined in Control.Exception

Methods

fmap :: (a -> b) -> Handler a -> Handler b

(<$) :: a -> Handler b -> Handler a

Functor Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Functor First

Since: base-4.8.0.0

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

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

fmap :: (a -> b) -> Down a -> Down b

(<$) :: a -> Down b -> Down a

Functor First

Since: base-4.9.0.0

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

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Functor STM

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

fmap :: (a -> b) -> STM a -> STM b

(<$) :: a -> STM b -> STM a

Functor Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 a

Functor P

Since: base-4.8.0.0

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> P a -> P b

(<$) :: a -> P b -> P a

Functor ReadP

Since: base-2.1

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b

(<$) :: a -> ReadP b -> ReadP a

Functor ReadPrec

Since: base-2.1

Defined in Text.ParserCombinators.ReadPrec

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b

(<$) :: a -> ReadPrec b -> ReadPrec a

Functor Put

Defined in Data.ByteString.Builder.Internal

Methods

fmap :: (a -> b) -> Put a -> Put b

(<$) :: a -> Put b -> Put a

Functor IntMap

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> IntMap a -> IntMap b

(<$) :: a -> IntMap b -> IntMap a

Functor Digit

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Digit a -> Digit b

(<$) :: a -> Digit b -> Digit a

Functor Elem

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Elem a -> Elem b

(<$) :: a -> Elem b -> Elem a

Functor FingerTree

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> FingerTree a -> FingerTree b

(<$) :: a -> FingerTree b -> FingerTree a

Functor Node

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Node a -> Node b

(<$) :: a -> Node b -> Node a

Functor Seq

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> Seq a -> Seq b

(<$) :: a -> Seq b -> Seq a

Functor ViewL

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> ViewL a -> ViewL b

(<$) :: a -> ViewL b -> ViewL a

Functor ViewR

Defined in Data.Sequence.Internal

Methods

fmap :: (a -> b) -> ViewR a -> ViewR b

(<$) :: a -> ViewR b -> ViewR a

Functor Tree

Defined in Data.Tree

Methods

fmap :: (a -> b) -> Tree a -> Tree b

(<$) :: a -> Tree b -> Tree a

Functor IO

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor Q

Defined in Language.Haskell.TH.Syntax

Methods

fmap :: (a -> b) -> Q a -> Q b

(<$) :: a -> Q b -> Q a

Functor TyVarBndr

Defined in Language.Haskell.TH.Syntax

Methods

fmap :: (a -> b) -> TyVarBndr a -> TyVarBndr b

(<$) :: a -> TyVarBndr b -> TyVarBndr a

Functor NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor Maybe

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor Solo

Since: base-4.15

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Solo a -> Solo b

(<$) :: a -> Solo b -> Solo a

Functor []

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Monad m => Functor (WrappedMonad m)

Since: base-2.1

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

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0

Functor (Either a)

Since: base-3.0

Defined in Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b

(<$) :: a0 -> Either a b -> Either a a0

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b

(<$) :: a -> Proxy b -> Proxy a

Functor (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b

(<$) :: a0 -> Arg a b -> Arg a a0

Functor (Array i)

Since: base-2.1

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b

(<$) :: a -> Array i b -> Array i a

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b

(<$) :: a -> U1 b -> U1 a

Functor (V1 :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Functor (Map k)

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> Map k a -> Map k b

(<$) :: a -> Map k b -> Map k a

Functor m => Functor (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

fmap :: (a -> b) -> MaybeT m a -> MaybeT m b

(<$) :: a -> MaybeT m b -> MaybeT m a

Functor (HashMap k)

Defined in Data.HashMap.Internal

Methods

fmap :: (a -> b) -> HashMap k a -> HashMap k b

(<$) :: a -> HashMap k b -> HashMap k a

Functor ((,) a)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b)

(<$) :: a0 -> (a, b) -> (a, a0)

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

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

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

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

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

Defined in Data.Semigroup.Internal

Methods

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

(<$) :: a -> Alt f b -> Alt f a

Functor f => Functor (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b

(<$) :: a -> Rec1 f b -> Rec1 f a

Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a

Functor (URec Char :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

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 LiftedRep -> Type)

Since: base-4.9.0.0

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 LiftedRep -> Type)

Since: base-4.9.0.0

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 LiftedRep -> Type)

Since: base-4.9.0.0

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 LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b

(<$) :: a -> URec Word b -> URec Word a

(Applicative f, Monad f) => Functor (WhenMissing f x)

Since: containers-0.5.9

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 (ErrorT e m)

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 (ExceptT e m)

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)

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 (ReaderT r m)

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)

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 ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0)

(<$) :: a0 -> (a, b, b0) -> (a, b, a0)

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

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

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 g) => Functor (f :*: g)

Since: base-4.9.0.0

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

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b

(<$) :: a -> (f :+: g) b -> (f :+: g) a

Functor (K1 i c :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

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 (WhenMatched f x y)

Since: containers-0.5.9

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

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 ((,,,) a b c)

Since: base-4.14.0.0

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 ((->) r)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b

(<$) :: a -> (r -> b) -> r -> a

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

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 g) => Functor (f :.: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b

(<$) :: a -> (f :.: g) b -> (f :.: g) a

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

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 (WhenMatched f k x y)

Since: containers-0.5.9

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

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

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

Examples

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

(<$>) :: 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

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)

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

Flipped version of <$.

Examples

Replace the contents of a Maybe Int with a constant String:

>>> Nothing $> "foo"
Nothing
>>> Just 90210 $> "foo"
Just "foo"

Replace the contents of an Either Int Int with a constant String, resulting in an Either Int String:

>>> Left 8675309 $> "foo"
Left 8675309
>>> Right 8675309 $> "foo"
Right "foo"

Replace each element of a list with a constant String:

>>> [1,2,3] $> "foo"
["foo","foo","foo"]

Replace the second element of a pair with a constant String:

>>> (1,2) $> "foo"
(1,"foo")

Since: base-4.7.0.0

newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) infixr 9

Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.

Constructors

Compose infixr 9

Fields

• getCompose :: f (g a)

Instances

TestEquality f => TestEquality (Compose f g :: k2 -> Type)

The deduction (via generativity) that if g x :~: g y then x :~: y.

Since: base-4.14.0.0

Defined in Data.Functor.Compose

Methods

testEquality :: forall (a :: k) (b :: k). Compose f g a -> Compose f g b -> Maybe (a :~: b)

Functor f => Generic1 (Compose f g :: k -> Type)

Defined in Data.Functor.Compose

Associated Types

type Rep1 (Compose f g) :: k -> Type

Methods

from1 :: forall (a :: k0). Compose f g a -> Rep1 (Compose f g) a

to1 :: forall (a :: k0). Rep1 (Compose f g) a -> Compose f g a

(Foldable f, Foldable g) => Foldable (Compose f g)

Since: base-4.9.0.0

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

(Eq1 f, Eq1 g) => Eq1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftEq :: (a -> b -> Bool) -> Compose f g a -> Compose f g b -> Bool

(Ord1 f, Ord1 g) => Ord1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftCompare :: (a -> b -> Ordering) -> Compose f g a -> Compose f g b -> Ordering

(Read1 f, Read1 g) => Read1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose f g a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a]

(Show1 f, Show1 g) => Show1 (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose f g a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose f g a] -> ShowS

(Functor f, Contravariant g) => Contravariant (Compose f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Compose f g a -> Compose f g a'

(>$) :: b -> Compose f g b -> Compose f g a

(Traversable f, Traversable g) => Traversable (Compose f g)

Since: base-4.9.0.0

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)

(Alternative f, Applicative g) => Alternative (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a

(<|>) :: Compose f g a -> Compose f g a -> Compose f g a

some :: Compose f g a -> Compose f g [a]

many :: Compose f g a -> Compose f g [a]

(Applicative f, Applicative g) => Applicative (Compose f g)

Since: base-4.9.0.0

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

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

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

(NFData1 f, NFData1 g) => NFData1 (Compose f g)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Compose f g a -> ()

(Hashable1 f, Hashable1 g) => Hashable1 (Compose f g)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Compose f g a -> Int

(Foldable1 f, Foldable1 g) => Foldable1 (Compose f g)

Since: 0.3.0

Defined in Relude.Extra.Foldable1

Methods

foldMap1 :: Semigroup m => (a -> m) -> Compose f g a -> m

fold1 :: Semigroup m => Compose f g m -> m

foldr1 :: (a -> b -> b) -> b -> Compose f g a -> b

toNonEmpty :: Compose f g a -> NonEmpty a

head1 :: Compose f g a -> a

last1 :: Compose f g a -> a

maximum1 :: Ord a => Compose f g a -> a

minimum1 :: Ord a => Compose f g a -> a

maximumOn1 :: Ord b => (a -> b) -> Compose f g a -> a

minimumOn1 :: Ord b => (a -> b) -> Compose f g a -> a

(Typeable a, Typeable f, Typeable g, Typeable k1, Typeable k2, Data (f (g a))) => Data (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Compose f g a -> c (Compose f g a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a)

toConstr :: Compose f g a -> Constr

dataTypeOf :: Compose f g a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a))

gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r

gmapQ :: (forall d. Data d => d -> u) -> Compose f g a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose f g a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)

Monoid (f (g a)) => Monoid (Compose f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a

mappend :: Compose f g a -> Compose f g a -> Compose f g a

mconcat :: [Compose f g a] -> Compose f g a

Semigroup (f (g a)) => Semigroup (Compose f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a

sconcat :: NonEmpty (Compose f g a) -> Compose f g a

stimes :: Integral b => b -> Compose f g a -> Compose f g a

Generic (Compose f g a)

Defined in Data.Functor.Compose

Associated Types

type Rep (Compose f g a) :: Type -> Type

Methods

from :: Compose f g a -> Rep (Compose f g a) x

to :: Rep (Compose f g a) x -> Compose f g a

(Read1 f, Read1 g, Read a) => Read (Compose f g a)

Since: base-4.9.0.0

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]

(Show1 f, Show1 g, Show a) => Show (Compose f g a)

Since: base-4.9.0.0

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

(NFData1 f, NFData1 g, NFData a) => NFData (Compose f g a)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

rnf :: Compose f g a -> ()

(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool

(/=) :: Compose f g a -> Compose f g a -> Bool

(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a)

Since: base-4.9.0.0

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

(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Compose f g a)

In general, hash (Compose x) ≠ hash x. However, hashWithSalt satisfies its variant of this equivalence.

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Compose f g a -> Int

hash :: Compose f g a -> Int

type Rep1 (Compose f g :: k -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

type Rep1 (Compose f g :: k -> Type) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (f :.: Rec1 g)))

type Rep (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

type Rep (Compose f g a) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g a)))))

newtype Identity a

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity

Fields

• runIdentity :: a

Instances

MonadFix Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

mfix :: (a -> Identity a) -> Identity a

Foldable Identity

Since: base-4.8.0.0

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

Eq1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool

Ord1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering

Read1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a]

Show1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS

Traversable Identity

Since: base-4.9.0.0

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)

Applicative Identity

Since: base-4.8.0.0

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

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Monad Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b

(>>) :: Identity a -> Identity b -> Identity b

return :: a -> Identity a

NFData1 Identity

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Identity a -> ()

Hashable1 Identity

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Identity a -> Int

Foldable1 Identity

Since: 0.3.0

Defined in Relude.Extra.Foldable1

Methods

foldMap1 :: Semigroup m => (a -> m) -> Identity a -> m

fold1 :: Semigroup m => Identity m -> m

foldr1 :: (a -> b -> b) -> b -> Identity a -> b

toNonEmpty :: Identity a -> NonEmpty a

head1 :: Identity a -> a

last1 :: Identity a -> a

maximum1 :: Ord a => Identity a -> a

minimum1 :: Ord a => Identity a -> a

maximumOn1 :: Ord b => (a -> b) -> Identity a -> a

minimumOn1 :: Ord b => (a -> b) -> Identity a -> a

Generic1 Identity

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type

Methods

from1 :: forall (a :: k). Identity a -> Rep1 Identity a

to1 :: forall (a :: k). Rep1 Identity a -> Identity a

Data a => Data (Identity a)

Since: base-4.9.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Identity a -> c (Identity a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Identity a)

toConstr :: Identity a -> Constr

dataTypeOf :: Identity a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Identity a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Identity a))

gmapT :: (forall b. Data b => b -> b) -> Identity a -> Identity a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQ :: (forall d. Data d => d -> u) -> Identity a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Identity a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

IsString a => IsString (Identity a)

Since: base-4.9.0.0

Defined in Data.String

Methods

fromString :: String -> Identity a

Storable a => Storable (Identity a)

Since: base-4.9.0.0

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 ()

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(.&.) :: Identity a -> Identity a -> Identity a

(.|.) :: Identity a -> Identity a -> Identity a

xor :: Identity a -> Identity a -> Identity a

complement :: Identity a -> Identity a

shift :: Identity a -> Int -> Identity a

rotate :: Identity a -> Int -> Identity a

zeroBits :: Identity a

bit :: Int -> Identity a

setBit :: Identity a -> Int -> Identity a

clearBit :: Identity a -> Int -> Identity a

complementBit :: Identity a -> Int -> Identity a

testBit :: Identity a -> Int -> Bool

bitSizeMaybe :: Identity a -> Maybe Int

bitSize :: Identity a -> Int

isSigned :: Identity a -> Bool

shiftL :: Identity a -> Int -> Identity a

unsafeShiftL :: Identity a -> Int -> Identity a

shiftR :: Identity a -> Int -> Identity a

unsafeShiftR :: Identity a -> Int -> Identity a

rotateL :: Identity a -> Int -> Identity a

rotateR :: Identity a -> Int -> Identity a

popCount :: Identity a -> Int

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

finiteBitSize :: Identity a -> Int

countLeadingZeros :: Identity a -> Int

countTrailingZeros :: Identity a -> Int

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

minBound :: Identity a

maxBound :: Identity a

Enum a => Enum (Identity a)

Since: base-4.9.0.0

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]

Floating a => Floating (Identity a)

Since: base-4.9.0.0

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

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

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

Generic (Identity a)

Defined in Data.Functor.Identity

Associated Types

type Rep (Identity a) :: Type -> Type

Methods

from :: Identity a -> Rep (Identity a) x

to :: Rep (Identity a) x -> Identity a

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

range :: (Identity a, Identity a) -> [Identity a]

index :: (Identity a, Identity a) -> Identity a -> Int

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

inRange :: (Identity a, Identity a) -> Identity a -> Bool

rangeSize :: (Identity a, Identity a) -> Int

unsafeRangeSize :: (Identity a, Identity a) -> Int

Num a => Num (Identity a)

Since: base-4.9.0.0

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

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

Defined in Data.Functor.Identity

Methods

readsPrec :: Int -> ReadS (Identity a)

readList :: ReadS [Identity a]

readPrec :: ReadPrec (Identity a)

readListPrec :: ReadPrec [Identity a]

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Integral a => Integral (Identity a)

Since: base-4.9.0.0

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

Real a => Real (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

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

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

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS

show :: Identity a -> String

showList :: [Identity a] -> ShowS

NFData a => NFData (Identity a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Identity a -> ()

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool

(/=) :: Identity a -> Identity a -> Bool

Ord a => Ord (Identity a)

Since: base-4.8.0.0

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

Hashable a => Hashable (Identity a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Identity a -> Int

hash :: Identity a -> Int

type Rep1 Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

type Rep1 Identity = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

type Rep (Identity a) = D1 ('MetaData "Identity" "Data.Functor.Identity" "base" 'True) (C1 ('MetaCons "Identity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Predicate a

Constructors

Predicate

Fields

• getPredicate :: a -> Bool

Instances

Contravariant Predicate

A Predicate is a Contravariant Functor, because contramap can apply its function argument to the input of the predicate.

Without newtypes contramap f equals precomposing with f (= (. f)).

contramap :: (a' -> a) -> (Predicate a -> Predicate a')
contramap f (Predicate g) = Predicate (g . f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Predicate a -> Predicate a'

(>$) :: b -> Predicate b -> Predicate a

Monoid (Predicate a)

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Predicate a

mappend :: Predicate a -> Predicate a -> Predicate a

mconcat :: [Predicate a] -> Predicate a

Semigroup (Predicate a)

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a

Defined in Data.Functor.Contravariant

Methods

(<>) :: Predicate a -> Predicate a -> Predicate a

sconcat :: NonEmpty (Predicate a) -> Predicate a

stimes :: Integral b => b -> Predicate a -> Predicate a

newtype Op a b

Dual function arrows.

Constructors

Op

Fields

• getOp :: b -> a

Instances

Category Op

Defined in Data.Functor.Contravariant

Methods

id :: forall (a :: k). Op a a

(.) :: forall (b :: k) (c :: k) (a :: k). Op b c -> Op a b -> Op a c

Contravariant (Op a)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Op a a0 -> Op a a'

(>$) :: b -> Op a b -> Op a a0

Monoid a => Monoid (Op a b)

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty

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

Semigroup a => Semigroup (Op a b)

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a

Defined in Data.Functor.Contravariant

Methods

(<>) :: Op a b -> Op a b -> Op a b

sconcat :: NonEmpty (Op a b) -> Op a b

stimes :: Integral b0 => b0 -> Op a b -> Op a b

Floating a => Floating (Op a b)

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

Num a => Num (Op a b)

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

Fractional a => Fractional (Op a b)

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

newtype Equivalence a

This data type represents an equivalence relation.

Equivalence relations are expected to satisfy three laws:

Reflexivity

getEquivalence f a a = True

Symmetry

getEquivalence f a b = getEquivalence f b a

Transitivity

If getEquivalence f a b and getEquivalence f b c are both True then so is getEquivalence f a c.

The types alone do not enforce these laws, so you'll have to check them yourself.

Constructors

Equivalence

Fields

• getEquivalence :: a -> a -> Bool

Instances

Contravariant Equivalence

Equivalence relations are Contravariant, because you can apply the contramapped function to each input to the equivalence relation.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Equivalence a -> Equivalence a'

(>$) :: b -> Equivalence b -> Equivalence a

Monoid (Equivalence a)

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Equivalence a

mappend :: Equivalence a -> Equivalence a -> Equivalence a

mconcat :: [Equivalence a] -> Equivalence a

Semigroup (Equivalence a)

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv a b

Defined in Data.Functor.Contravariant

Methods

(<>) :: Equivalence a -> Equivalence a -> Equivalence a

sconcat :: NonEmpty (Equivalence a) -> Equivalence a

stimes :: Integral b => b -> Equivalence a -> Equivalence a

class Contravariant (f :: Type -> Type) where

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap :: (a' -> a) -> (Predicate a -> Predicate a')
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

Identity

contramap id = id

Composition

contramap (g . f) = contramap f . contramap g

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

Minimal complete definition

contramap

Methods

contramap :: (a' -> a) -> f a -> f a'

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

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

Instances

Contravariant Comparison

A Comparison is a Contravariant Functor, because contramap can apply its function argument to each input of the comparison function.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Comparison a -> Comparison a'

(>$) :: b -> Comparison b -> Comparison a

Contravariant Equivalence

Equivalence relations are Contravariant, because you can apply the contramapped function to each input to the equivalence relation.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Equivalence a -> Equivalence a'

(>$) :: b -> Equivalence b -> Equivalence a

Contravariant Predicate

A Predicate is a Contravariant Functor, because contramap can apply its function argument to the input of the predicate.

Without newtypes contramap f equals precomposing with f (= (. f)).

contramap :: (a' -> a) -> (Predicate a -> Predicate a')
contramap f (Predicate g) = Predicate (g . f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Predicate a -> Predicate a'

(>$) :: b -> Predicate b -> Predicate a

Contravariant (Op a)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Op a a0 -> Op a a'

(>$) :: b -> Op a b -> Op a a0

Contravariant (Proxy :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Proxy a -> Proxy a'

(>$) :: b -> Proxy b -> Proxy a

Contravariant (U1 :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> U1 a -> U1 a'

(>$) :: b -> U1 b -> U1 a

Contravariant (V1 :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> V1 a -> V1 a'

(>$) :: b -> V1 b -> V1 a

Contravariant m => Contravariant (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

contramap :: (a' -> a) -> MaybeT m a -> MaybeT m a'

(>$) :: b -> MaybeT m b -> MaybeT m a

Contravariant (Const a :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Const a a0 -> Const a a'

(>$) :: b -> Const a b -> Const a a0

Contravariant f => Contravariant (Alt f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Alt f a -> Alt f a'

(>$) :: b -> Alt f b -> Alt f a

Contravariant f => Contravariant (Rec1 f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Rec1 f a -> Rec1 f a'

(>$) :: b -> Rec1 f b -> Rec1 f a

Contravariant m => Contravariant (ErrorT e m)

Defined in Control.Monad.Trans.Error

Methods

contramap :: (a' -> a) -> ErrorT e m a -> ErrorT e m a'

(>$) :: b -> ErrorT e m b -> ErrorT e m a

Contravariant m => Contravariant (ExceptT e m)

Defined in Control.Monad.Trans.Except

Methods

contramap :: (a' -> a) -> ExceptT e m a -> ExceptT e m a'

(>$) :: b -> ExceptT e m b -> ExceptT e m a

Contravariant f => Contravariant (IdentityT f)

Defined in Control.Monad.Trans.Identity

Methods

contramap :: (a' -> a) -> IdentityT f a -> IdentityT f a'

(>$) :: b -> IdentityT f b -> IdentityT f a

Contravariant m => Contravariant (ReaderT r m)

Defined in Control.Monad.Trans.Reader

Methods

contramap :: (a' -> a) -> ReaderT r m a -> ReaderT r m a'

(>$) :: b -> ReaderT r m b -> ReaderT r m a

Contravariant m => Contravariant (StateT s m)

Defined in Control.Monad.Trans.State.Strict

Methods

contramap :: (a' -> a) -> StateT s m a -> StateT s m a'

(>$) :: b -> StateT s m b -> StateT s m a

(Contravariant f, Contravariant g) => Contravariant (Product f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Product f g a -> Product f g a'

(>$) :: b -> Product f g b -> Product f g a

(Contravariant f, Contravariant g) => Contravariant (Sum f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Sum f g a -> Sum f g a'

(>$) :: b -> Sum f g b -> Sum f g a

(Contravariant f, Contravariant g) => Contravariant (f :*: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :*: g) a -> (f :*: g) a'

(>$) :: b -> (f :*: g) b -> (f :*: g) a

(Contravariant f, Contravariant g) => Contravariant (f :+: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :+: g) a -> (f :+: g) a'

(>$) :: b -> (f :+: g) b -> (f :+: g) a

Contravariant (K1 i c :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> K1 i c a -> K1 i c a'

(>$) :: b -> K1 i c b -> K1 i c a

(Functor f, Contravariant g) => Contravariant (Compose f g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Compose f g a -> Compose f g a'

(>$) :: b -> Compose f g b -> Compose f g a

(Functor f, Contravariant g) => Contravariant (f :.: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> (f :.: g) a -> (f :.: g) a'

(>$) :: b -> (f :.: g) b -> (f :.: g) a

Contravariant f => Contravariant (M1 i c f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> M1 i c f a -> M1 i c f a'

(>$) :: b -> M1 i c f b -> M1 i c f a

newtype Comparison a

Defines a total ordering on a type as per compare.

This condition is not checked by the types. You must ensure that the supplied values are valid total orderings yourself.

Constructors

Comparison

Fields

• getComparison :: a -> a -> Ordering

Instances

Contravariant Comparison

A Comparison is a Contravariant Functor, because contramap can apply its function argument to each input of the comparison function.

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Comparison a -> Comparison a'

(>$) :: b -> Comparison b -> Comparison a

Monoid (Comparison a)

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ

Defined in Data.Functor.Contravariant

Methods

mempty :: Comparison a

mappend :: Comparison a -> Comparison a -> Comparison a

mconcat :: [Comparison a] -> Comparison a

Semigroup (Comparison a)

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'

Defined in Data.Functor.Contravariant

Methods

(<>) :: Comparison a -> Comparison a -> Comparison a

sconcat :: NonEmpty (Comparison a) -> Comparison a

stimes :: Integral b => b -> Comparison a -> Comparison a

phantom :: (Functor f, Contravariant f) => f a -> f b

If f is both Functor and Contravariant then by the time you factor in the laws of each of those classes, it can't actually use its argument in any meaningful capacity.

This method is surprisingly useful. Where both instances exist and are lawful we have the following laws:

fmap      f ≡ phantom
contramap f ≡ phantom

defaultEquivalence :: Eq a => Equivalence a

Check for equivalence with ==.

Note: The instances for Double and Float violate reflexivity for NaN.

defaultComparison :: Ord a => Comparison a

Compare using compare.

comparisonEquivalence :: Comparison a -> Equivalence a

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

This is an infix alias for contramap.

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

This is an infix version of contramap with the arguments flipped.

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

This is >$ with its arguments flipped.