base-4.13.0.0: Basic libraries

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.

#### Examples

Expand
>>> fmap show (Just 1)  --  (a   -> b)      -> f a       -> f b
Just "1"                --  (Int -> String) -> Maybe Int -> Maybe String

>>> fmap show Nothing   --  (a   -> b)      -> f a       -> f b
Nothing                 --  (Int -> String) -> Maybe Int -> Maybe String

>>> fmap show [1,2,3]   --  (a   -> b)      -> f a       -> f b
["1", "2", "3"]         --  (Int -> String) -> [Int]     -> [String]

>>> fmap show []        --  (a   -> b)      -> f a       -> f b
[]                      --  (Int -> String) -> [Int]     -> [String]


The fmap function is also available as the infix operator <$>: >>> fmap show (Just 1) -- (Int -> String) -> Maybe Int -> Maybe String Just "1" >>> show <$> (Just 1)  --  (Int -> String) -> Maybe Int -> Maybe String
Just "1"

Synopsis

# Documentation

class Functor f 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.

Methods

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

#### Instances

Instances details
 Functor [] # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> [a] -> [b] #(<$) :: a -> [b] -> [a] # # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Par1 a -> Par1 b #(<$) :: a -> Par1 b -> Par1 a # # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b #(<$) :: a -> NonEmpty b -> NonEmpty a # # Since: base-4.8.0.0 Instance detailsDefined in GHC.GHCi Methodsfmap :: (a -> b) -> NoIO a -> NoIO b #(<$) :: a -> NoIO b -> NoIO a # # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> ReadP a -> ReadP b #(<$) :: a -> ReadP b -> ReadP a # # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b #(<$) :: a -> ReadPrec b -> ReadPrec a # # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methodsfmap :: (a -> b) -> Down a -> Down b #(<$) :: a -> Down b -> Down a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b #(<$) :: a -> Product b -> Product a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b #(<$) :: a -> Sum b -> Sum a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b #(<$) :: a -> Dual b -> Dual a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Since: base-4.3.0.0 Instance detailsDefined in GHC.Conc.Sync Methodsfmap :: (a -> b) -> STM a -> STM b #(<$) :: a -> STM b -> STM a # # Since: base-4.6.0.0 Instance detailsDefined in Control.Exception Methodsfmap :: (a -> b) -> Handler a -> Handler b #(<$) :: a -> Handler b -> Handler a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Functor.Identity Methodsfmap :: (a -> b) -> Identity a -> Identity b #(<$) :: a -> Identity b -> Identity a # # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> ZipList a -> ZipList b #(<$) :: a -> ZipList b -> ZipList a # # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b #(<$) :: a -> ArgDescr b -> ArgDescr a # # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b #(<$) :: a -> OptDescr b -> OptDescr a # # Since: base-4.6.0.0 Instance detailsDefined in System.Console.GetOpt Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b #(<$) :: a -> ArgOrder b -> ArgOrder a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Option a -> Option b #(<$) :: a -> Option b -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Max a -> Max b #(<$) :: a -> Max b -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Min a -> Min b #(<$) :: a -> Min b -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodsfmap :: (a -> b) -> Complex a -> Complex b #(<$) :: a -> Complex b -> Complex a # # Since: base-3.0 Instance detailsDefined in Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b #(<$) :: a0 -> Either a b -> Either a a0 # Functor (V1 :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> V1 a -> V1 b #(<$) :: a -> V1 b -> V1 a # Functor (U1 :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> U1 a -> U1 b #(<$) :: a -> U1 b -> U1 a # Functor ((,) a) # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) #(<$) :: a0 -> (a, b) -> (a, a0) # Functor (ST s) # Since: base-2.1 Instance detailsDefined in GHC.ST Methodsfmap :: (a -> b) -> ST s a -> ST s b #(<$) :: a -> ST s b -> ST s a # Functor (Array i) # Since: base-2.1 Instance detailsDefined in GHC.Arr Methodsfmap :: (a -> b) -> Array i a -> Array i b #(<$) :: a -> Array i b -> Array i a # Functor (Proxy :: Type -> Type) # Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodsfmap :: (a -> b) -> Proxy a -> Proxy b #(<$) :: a -> Proxy b -> Proxy a # Arrow a => Functor (ArrowMonad a) # Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # Monad m => Functor (WrappedMonad m) # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a # Functor (ST s) # Since: base-2.1 Instance detailsDefined in Control.Monad.ST.Lazy.Imp Methodsfmap :: (a -> b) -> ST s a -> ST s b #(<$) :: a -> ST s b -> ST s a # Functor (Arg a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a0 -> b) -> Arg a a0 -> Arg a b #(<$) :: a0 -> Arg a b -> Arg a a0 # Functor f => Functor (Rec1 f) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b #(<$) :: a -> Rec1 f b -> Rec1 f a # Functor (URec Char :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Char a -> URec Char b #(<$) :: a -> URec Char b -> URec Char a # # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Double a -> URec Double b #(<$) :: a -> URec Double b -> URec Double a # Functor (URec Float :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Float a -> URec Float b #(<$) :: a -> URec Float b -> URec Float a # Functor (URec Int :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Int a -> URec Int b #(<$) :: a -> URec Int b -> URec Int a # Functor (URec Word :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Word a -> URec Word b #(<$) :: a -> URec Word b -> URec Word a # Functor (URec (Ptr ()) :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a # Functor f => Functor (Alt f) # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Alt f a -> Alt f b #(<$) :: a -> Alt f b -> Alt f a # Functor f => Functor (Ap f) # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Ap f a -> Ap f b #(<$) :: a -> Ap f b -> Ap f a # Functor (Const m :: Type -> Type) # Since: base-2.1 Instance detailsDefined in Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b #(<$) :: a -> Const m b -> Const m a # Arrow a => Functor (WrappedArrow a b) # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 #(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # Functor ((->) r :: Type -> Type) # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b #(<$) :: a -> (r -> b) -> r -> a # Functor (K1 i c :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b #(<$) :: a -> K1 i c b -> K1 i c a # (Functor f, Functor g) => Functor (f :+: g) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #(<$) :: a -> (f :+: g) b -> (f :+: g) a # (Functor f, Functor g) => Functor (f :*: g) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #(<$) :: a -> (f :*: g) b -> (f :*: g) a # (Functor f, Functor g) => Functor (Sum f g) # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Sum Methodsfmap :: (a -> b) -> Sum f g a -> Sum f g b #(<$) :: a -> Sum f g b -> Sum f g a # (Functor f, Functor g) => Functor (Product f g) # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodsfmap :: (a -> b) -> Product f g a -> Product f g b #(<$) :: a -> Product f g b -> Product f g a # Functor f => Functor (M1 i c f) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b #(<$) :: a -> M1 i c f b -> M1 i c f a # (Functor f, Functor g) => Functor (f :.: g) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #(<$) :: a -> (f :.: g) b -> (f :.: g) a # (Functor f, Functor g) => Functor (Compose f g) # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Compose Methodsfmap :: (a -> b) -> Compose f g a -> Compose f g b #(<$) :: a -> Compose f g b -> Compose f g a #

(<$) :: Functor f => a -> f b -> f a infixl 4 # Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version. ($>) :: 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) $> "foo" (1,"foo")  Since: base-4.7.0.0 (<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:  ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b Whereas $ is function application, <$> is function application lifted over a Functor. #### Examples Expand Convert from a Maybe Int to a Maybe String using show: >>> show <$> Nothing
Nothing
>>> show <$> Just 3 Just "3"  Convert from an Either Int Int to an Either Int String using show: >>> show <$> Left 17
Left 17
>>> show <$> Right 17 Right "17"  Double each element of a list: >>> (*2) <$> [1,2,3]
[2,4,6]


Apply even to the second element of a pair:

>>> even <$> (2,2) (2,True)  (<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 # Flipped version of <$>.

(<&>) = 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

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