| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
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
>>>fmap show (Just 1) -- (a -> b) -> f a -> f bJust "1" -- (Int -> String) -> Maybe Int -> Maybe String
>>>fmap show Nothing -- (a -> b) -> f a -> f bNothing -- (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 <$>:
>>>fmap show (Just 1) -- (Int -> String) -> Maybe Int -> Maybe StringJust "1">>>show <$> (Just 1) -- (Int -> String) -> Maybe Int -> Maybe StringJust "1"
Documentation
class Functor f 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:
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.
Instances
| Functor [] # | Since: base-2.1 |
| Functor Maybe # | Since: base-2.1 |
| Functor IO # | Since: base-2.1 |
| Functor Par1 # | Since: base-4.9.0.0 |
| Functor NonEmpty # | Since: base-4.9.0.0 |
| Functor NoIO # | Since: base-4.8.0.0 |
| Functor ReadP # | Since: base-2.1 |
| Functor ReadPrec # | Since: base-2.1 |
| Functor Down # | Since: base-4.11.0.0 |
| Functor Product # | Since: base-4.8.0.0 |
| Functor Sum # | Since: base-4.8.0.0 |
| Functor Dual # | Since: base-4.8.0.0 |
| Functor Last # | Since: base-4.8.0.0 |
| Functor First # | Since: base-4.8.0.0 |
| Functor STM # | Since: base-4.3.0.0 |
| Functor Handler # | Since: base-4.6.0.0 |
| Functor Identity # | Since: base-4.8.0.0 |
| Functor ZipList # | Since: base-2.1 |
| Functor ArgDescr # | Since: base-4.6.0.0 |
| Functor OptDescr # | Since: base-4.6.0.0 |
| Functor ArgOrder # | Since: base-4.6.0.0 |
| Functor Option # | Since: base-4.9.0.0 |
| Functor Last # | Since: base-4.9.0.0 |
| Functor First # | Since: base-4.9.0.0 |
| Functor Max # | Since: base-4.9.0.0 |
| Functor Min # | Since: base-4.9.0.0 |
| Functor Complex # | Since: base-4.9.0.0 |
| Functor (Either a) # | Since: base-3.0 |
| Functor (V1 :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor ((,) a) # | Since: base-2.1 |
| Functor (ST s) # | Since: base-2.1 |
| Functor (Array i) # | Since: base-2.1 |
| Functor (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
| 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 Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Monad m => Functor (WrappedMonad m) # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Functor (ST s) # | Since: base-2.1 |
| Functor (Arg a) # | Since: base-4.9.0.0 |
| Functor f => Functor (Rec1 f) # | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
| Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
| Functor (Const m :: Type -> Type) # | Since: base-2.1 |
| 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 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor ((->) r :: Type -> Type) # | Since: base-2.1 |
| Functor (K1 i c :: Type -> Type) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Product f g) # | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Compose f g) # | Since: base-4.9.0.0 |
($>) :: Functor f => f a -> b -> f b infixl 4 Source #
Flipped version of <$.
Examples
Replace the contents of a Maybe IntString:
>>>Nothing $> "foo"Nothing>>>Just 90210 $> "foo"Just "foo"
Replace the contents of an Either Int IntString, 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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
void :: Functor f => f a -> f () Source #
void valueIO action.
Examples
Replace the contents of a Maybe Int
>>>void NothingNothing>>>void (Just 3)Just ()
Replace the contents of an Either Int IntEither 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