Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Functor.Compat

Synopsis

module Data.Functor
class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- (<$) :: a -> f b -> f a
($>) :: Functor f => f a -> b -> f b
void :: Functor f => f a -> f ()
(<&>) :: Functor f => f a -> (a -> b) -> f b
unzip :: Functor f => f (a, b) -> (f a, f b)

Documentation

module Data.Functor

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

Expand

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

Instances details

Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b # (<$) :: a -> ZipList b -> ZipList a #
Functor Handler	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b # (<$) :: a -> Handler b -> Handler a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
Functor 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 Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b # (<$) :: a -> Down b -> Down a #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b # (<$) :: 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 # (<$) :: a -> Last b -> Last a #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b # (<$) :: a -> Max b -> Max a #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b # (<$) :: a -> Min b -> Min a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Functor STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b # (<$) :: a -> STM b -> STM a #
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b # (<$) :: a -> Par1 b -> Par1 a #
Functor P	Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b # (<$) :: a -> P b -> P a #
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b # (<$) :: a -> ReadP b -> ReadP a #
Functor ReadPrec	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods fmap :: (a -> b) -> ReadPrec a -> ReadPrec b # (<$) :: a -> ReadPrec b -> ReadPrec a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b # (<$) :: a -> NonEmpty b -> NonEmpty a #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Functor Solo	Since: base-4.15
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Solo a -> Solo b # (<$) :: a -> Solo b -> Solo a #
Functor []	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] # (<$) :: a -> [b] -> [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 # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a #
Functor (ST s)	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fmap :: (a -> b) -> ST s a -> ST s b # (<$) :: a -> ST s b -> ST s a #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Functor (Array i)	Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b # (<$) :: a -> Array i b -> Array i a #
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b # (<$) :: a -> U1 b -> U1 a #
Functor (V1 :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
Functor (ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b # (<$) :: a -> ST s b -> ST s a #
Functor ((,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) # (<$) :: a0 -> (a, b) -> (a, a0) #
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: 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 #
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 # (<$) :: a -> Rec1 f b -> Rec1 f a #
Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b # (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #
Functor (URec Char :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b # (<$) :: a -> URec Char b -> URec Char a #
Functor (URec Double :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Functor (URec Float :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Functor (URec Int :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Functor (URec Word :: TYPE LiftedRep -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b # (<$) :: a -> URec Word b -> URec Word a #
Functor ((,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) # (<$) :: a0 -> (a, b, b0) -> (a, b, a0) #
(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 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 (K1 i c :: TYPE LiftedRep -> 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 # (<$) :: a -> K1 i c b -> K1 i c a #
Functor ((,,,) a b c)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) # (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) #
Functor ((->) r)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b # (<$) :: a -> (r -> b) -> r -> a #
(Functor f, Functor g) => Functor (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b # (<$) :: a -> Compose f g b -> Compose f g a #
(Functor f, Functor 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 # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b # (<$) :: a -> M1 i c f b -> M1 i c f a #

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

Flipped version of <$.

Examples

Expand

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

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

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

(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 #

Flipped version of <$>.

(<&>) = flip fmap

Examples

Expand

Apply (+1) to a list, a Just and a Right:

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0

unzip :: Functor f => f (a, b) -> (f a, f b) Source #

Generalization of Data.List.unzip.

Since: 4.19.0.0