base-4.20.0.0: Core data structures and operations

Data.Functor

Description

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

Synopsis

# Documentation

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

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 these articles by School of Haskell or David Luposchainsky for an explanation.

Minimal complete definition

fmap

Methods

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

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)


(<$) :: a -> f b -> f a infixl 4 Source # Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version. #### Examples Expand Perform a computation with Maybe and replace the result with a constant value if it is Just: >>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$Nothing Nothing  #### Instances Instances details  Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodsfmap :: (a -> b) -> Complex a -> Complex b Source #(<$) :: a -> Complex b -> Complex a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Max a -> Max b Source #(<$) :: a -> Max b -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Min a -> Min b Source #(<$) :: a -> Min b -> Min a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source #(<$) :: a -> ArgDescr b -> ArgDescr a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source #(<$) :: a -> ArgOrder b -> ArgOrder a Source # Source # Since: base-4.7.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b Source #(<$) :: a -> OptDescr b -> OptDescr a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source #(<$) :: a -> NonEmpty b -> NonEmpty a Source # Source # Since: base-4.3.0.0 Instance detailsDefined in GHC.Internal.Conc.Sync Methodsfmap :: (a -> b) -> STM a -> STM b Source #(<$) :: a -> STM b -> STM a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Exception Methodsfmap :: (a -> b) -> Handler a -> Handler b Source #(<$) :: a -> Handler b -> Handler a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity Methodsfmap :: (a -> b) -> Identity a -> Identity b Source #(<$) :: a -> Identity b -> Identity a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Since: base-4.11.0.0 Instance detailsDefined in GHC.Internal.Data.Ord Methodsfmap :: (a -> b) -> Down a -> Down b Source #(<$) :: a -> Down b -> Down a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b Source #(<$) :: a -> Dual b -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b Source #(<$) :: a -> Product b -> Product a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b Source #(<$) :: a -> Sum b -> Sum a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Functor.ZipList Methodsfmap :: (a -> b) -> ZipList a -> ZipList b Source #(<$) :: a -> ZipList b -> ZipList a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.GHCi Methodsfmap :: (a -> b) -> NoIO a -> NoIO b Source #(<$) :: a -> NoIO b -> NoIO a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Par1 a -> Par1 b Source #(<$) :: a -> Par1 b -> Par1 a Source # Source # Instance detailsDefined in GHC.Internal.TH.Syntax Methodsfmap :: (a -> b) -> Q a -> Q b Source #(<$) :: a -> Q b -> Q a Source # Source # Instance detailsDefined in GHC.Internal.TH.Syntax Methodsfmap :: (a -> b) -> TyVarBndr a -> TyVarBndr b Source #(<$) :: a -> TyVarBndr b -> TyVarBndr a Source # Source # Since: base-4.8.0.0 Instance details Methodsfmap :: (a -> b) -> P a -> P b Source #(<$) :: a -> P b -> P a Source # Source # Since: base-2.1 Instance details Methodsfmap :: (a -> b) -> ReadP a -> ReadP b Source #(<$) :: a -> ReadP b -> ReadP a Source # Source # Since: base-2.1 Instance details Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source #(<$) :: a -> ReadPrec b -> ReadPrec a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> IO a -> IO b Source #(<$) :: a -> IO b -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b Source #(<$) :: a -> Maybe b -> Maybe a Source # Source # Since: base-4.15 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> Solo a -> Solo b Source #(<$) :: a -> Solo b -> Solo a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> [a] -> [b] Source #(<$) :: a -> [b] -> [a] Source # Monad m => Functor (WrappedMonad m) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # Functor (Arg a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source #(<$) :: a0 -> Arg a b -> Arg a a0 Source # Functor (Array i) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Arr Methodsfmap :: (a -> b) -> Array i a -> Array i b Source #(<$) :: a -> Array i b -> Array i a Source # Arrow a => Functor (ArrowMonad a) Source # Since: base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # Functor (ST s) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.ST.Lazy.Imp Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Source # Since: base-3.0 Instance detailsDefined in GHC.Internal.Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b Source #(<$) :: a0 -> Either a b -> Either a a0 Source # Source # Since: base-4.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateL s a -> StateL s b Source #(<$) :: a -> StateL s b -> StateL s a Source # Source # Since: base-4.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateR s a -> StateR s b Source #(<$) :: a -> StateR s b -> StateR s a Source # Functor (Proxy :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in GHC.Internal.Data.Proxy Methodsfmap :: (a -> b) -> Proxy a -> Proxy b Source #(<$) :: a -> Proxy b -> Proxy a Source # Functor (U1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> U1 a -> U1 b Source #(<$) :: a -> U1 b -> U1 a Source # Functor (V1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> V1 a -> V1 b Source #(<$) :: a -> V1 b -> V1 a Source # Functor (ST s) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.ST Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Functor ((,) a) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) Source #(<$) :: a0 -> (a, b) -> (a, a0) Source # Arrow a => Functor (WrappedArrow a b) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source #(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # Functor m => Functor (Kleisli m a) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsfmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source # Functor (Const m :: Type -> Type) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b Source #(<$) :: a -> Const m b -> Const m a Source # Monad m => Functor (StateT s m) Source # Since: base-4.18.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Utils Methodsfmap :: (a -> b) -> StateT s m a -> StateT s m b Source #(<$) :: a -> StateT s m b -> StateT s m a Source # Functor f => Functor (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Internal.Data.Monoid Methodsfmap :: (a -> b) -> Ap f a -> Ap f b Source #(<$) :: a -> Ap f b -> Ap f a Source # Functor f => Functor (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Alt f a -> Alt f b Source #(<$) :: a -> Alt f b -> Alt f a Source # (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source # Since: base-4.17.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source #(<$) :: a -> Generically1 f b -> Generically1 f a Source # Functor f => Functor (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source #(<$) :: a -> Rec1 f b -> Rec1 f a Source # Functor (URec (Ptr ()) :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source # Functor (URec Char :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Char a -> URec Char b Source #(<$) :: a -> URec Char b -> URec Char a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Double a -> URec Double b Source #(<$) :: a -> URec Double b -> URec Double a Source # Functor (URec Float :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Float a -> URec Float b Source #(<$) :: a -> URec Float b -> URec Float a Source # Functor (URec Int :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Int a -> URec Int b Source #(<$) :: a -> URec Int b -> URec Int a Source # Functor (URec Word :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> URec Word a -> URec Word b Source #(<$) :: a -> URec Word b -> URec Word a Source # Functor ((,,) a b) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source #(<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source # (Functor f, Functor g) => Functor (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodsfmap :: (a -> b) -> Product f g a -> Product f g b Source #(<$) :: a -> Product f g b -> Product f g a Source # (Functor f, Functor g) => Functor (Sum f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Sum Methodsfmap :: (a -> b) -> Sum f g a -> Sum f g b Source #(<$) :: a -> Sum f g b -> Sum f g a Source # (Functor f, Functor g) => Functor (f :*: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source #(<$) :: a -> (f :*: g) b -> (f :*: g) a Source # (Functor f, Functor g) => Functor (f :+: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source #(<$) :: a -> (f :+: g) b -> (f :+: g) a Source # Functor (K1 i c :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b Source #(<$) :: a -> K1 i c b -> K1 i c a Source # Functor ((,,,) a b c) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source #(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source # Functor ((->) r) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b Source #(<$) :: a -> (r -> b) -> r -> a Source # (Functor f, Functor g) => Functor (Compose f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Compose Methodsfmap :: (a -> b) -> Compose f g a -> Compose f g b Source #(<$) :: a -> Compose f g b -> Compose f g a Source # (Functor f, Functor g) => Functor (f :.: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source #(<$) :: a -> (f :.: g) b -> (f :.: g) a Source # Functor f => Functor (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Generics Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source #(<$) :: a -> M1 i c f b -> M1 i c f a Source # Functor ((,,,,) a b c d) Source # Since: base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, a0) -> (a, b, c, d, b0) Source #(<$) :: a0 -> (a, b, c, d, b0) -> (a, b, c, d, a0) Source # Functor ((,,,,,) a b c d e) Source # Since: base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, e, a0) -> (a, b, c, d, e, b0) Source #(<$) :: a0 -> (a, b, c, d, e, b0) -> (a, b, c, d, e, a0) Source # Functor ((,,,,,,) a b c d e f) Source # Since: base-4.18.0.0 Instance detailsDefined in GHC.Internal.Base Methodsfmap :: (a0 -> b0) -> (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, b0) Source #(<$) :: a0 -> (a, b, c, d, e, f, b0) -> (a, b, c, d, e, f, a0) Source #

($>) :: Functor f => f a -> b -> f b infixl 4 Source # Flipped version of <$.

#### 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

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


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

Flipped version of <$>. (<&>) = flip fmap  #### Examples Expand Apply (+1) to a list, a Just and a Right: >>> Just 2 <&> (+1) Just 3  >>> [1,2,3] <&> (+1) [2,3,4]  >>> Right 3 <&> (+1) Right 4  Since: base-4.11.0.0 unzip :: Functor f => f (a, b) -> (f a, f b) Source # Generalization of Data.List.unzip. #### Examples Expand >>> unzip (Just ("Hello", "World")) (Just "Hello",Just "World")  >>> unzip [("I", "love"), ("really", "haskell")] (["I","really"],["love","haskell"])  Since: base-4.19.0.0 void :: Functor f => f a -> f () Source # void value discards or ignores the result of evaluation, such as the return value of an IO action. #### Examples Expand Replace the contents of a Maybe Int with unit: >>> void Nothing Nothing  >>> void (Just 3) Just ()  Replace the contents of an Either Int Int with unit, resulting in an Either Int (): >>> void (Left 8675309) Left 8675309  >>> void (Right 8675309) Right ()  Replace every element of a list with unit: >>> void [1,2,3] [(),(),()]  Replace the second element of a pair with unit: >>> void (1,2) (1,())  Discard the result of an IO action: >>> mapM print [1,2] 1 2 [(),()]  >>> void$ mapM print [1,2]
1
2