Data.Functor.Compat

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. See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or https://github.com/quchen/articles/blob/master/second_functor_law.md for an explanation.

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.

Examples

Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$ Nothing
Nothing

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 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 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 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 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 IO

Since: base-2.1

Defined in GHC.Base

Methods

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

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

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

Functor (ST s)

Since: base-2.1

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

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 (ST s)

Since: base-2.1

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

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 (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 ((,,) 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 ((,,,) 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 ((,,,,) a b c d)

Since: base-4.18.0.0

Defined in GHC.Base

Methods

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

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

Functor ((,,,,,) a b c d e)

Since: base-4.18.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, d, e, a0) -> (a, b, c, d, e, b0)

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

Functor ((,,,,,,) a b c d e f)

Since: base-4.18.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, b0)

(<$) :: a0 -> (a, b, c, d, e, f, b0) -> (a, b, c, d, e, f, a0)

($>) :: 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

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 => f a -> (a -> b) -> f b infixl 1

Flipped version of <$>.

(<&>) = flip fmap

Examples

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)

Generalization of Data.List.unzip.

Since: 4.19.0.0