Safe Haskell	Safe
Language	Haskell2010

Protolude.Functor

Synopsis

class Functor (f :: Type -> Type ) where
- fmap :: (a -> b) -> f a -> f b
($>) :: Functor f => f a -> b -> f b
(<$) :: Functor f => a -> f b -> f a
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<<$>>) :: ( Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)
(<&>) :: Functor f => f a -> (a -> b) -> f b
void :: Functor f => f a -> f ()
foreach :: Functor f => f a -> (a -> b) -> f b

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.

Methods

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

Using ApplicativeDo : ' fmap f as ' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

Instances

Instances details

Functor []	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] Source # (<$) :: a -> [b] -> [a] Source #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source # (<$) :: a -> Maybe b -> Maybe a Source #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source # (<$) :: a -> IO b -> IO a Source #
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b Source # (<$) :: a -> Par1 b -> Par1 a Source #
Functor Async
Instance details Defined in Control.Concurrent.Async Methods fmap :: (a -> b) -> Async a -> Async b Source # (<$) :: a -> Async b -> Async a Source #
Functor Concurrently
Instance details Defined in Control.Concurrent.Async Methods fmap :: (a -> b) -> Concurrently a -> Concurrently b Source # (<$) :: a -> Concurrently b -> Concurrently a Source #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b Source # (<$) :: a -> Complex b -> Complex a Source #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b Source # (<$) :: a -> Min b -> Min a Source #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b Source # (<$) :: a -> Max b -> Max a Source #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Functor Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Option a -> Option b Source # (<$) :: a -> Option b -> Option a Source #
Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source # (<$) :: a -> ZipList b -> ZipList a Source #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b Source # (<$) :: a -> Identity b -> Identity a Source #
Functor Handler	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b Source # (<$) :: a -> Handler b -> Handler a Source #
Functor STM	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b Source # (<$) :: a -> STM b -> STM a Source #
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b Source # (<$) :: a -> Down b -> Down a Source #
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source # (<$) :: a -> ReadP b -> ReadP a Source #
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
Functor IntMap
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> IntMap a -> IntMap b Source # (<$) :: a -> IntMap b -> IntMap a Source #
Functor Seq
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b Source # (<$) :: a -> Seq b -> Seq a Source #
Functor FingerTree
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b Source # (<$) :: a -> FingerTree b -> FingerTree a Source #
Functor Digit
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Digit a -> Digit b Source # (<$) :: a -> Digit b -> Digit a Source #
Functor Node
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Node a -> Node b Source # (<$) :: a -> Node b -> Node a Source #
Functor Elem
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Elem a -> Elem b Source # (<$) :: a -> Elem b -> Elem a Source #
Functor ViewL
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewL a -> ViewL b Source # (<$) :: a -> ViewL b -> ViewL a Source #
Functor ViewR
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewR a -> ViewR b Source # (<$) :: a -> ViewR b -> ViewR a Source #
Functor P	Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b Source # (<$) :: a -> P b -> P a Source #
Functor ( Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source # (<$) :: a0 -> Either a b -> Either a a0 Source #
Functor ( V1 :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b Source # (<$) :: a -> V1 b -> V1 a Source #
Functor ( U1 :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b Source # (<$) :: a -> U1 b -> U1 a Source #
Functor ( (,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source # (<$) :: a0 -> (a, b) -> (a, a0) Source #
Functor ( ST s)	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b Source # (<$) :: a -> ST s b -> ST s a Source #
Functor ( Array i)	Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b Source # (<$) :: a -> Array i b -> Array i a Source #
Functor ( Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source # (<$) :: a0 -> Arg a b -> Arg a a0 Source #
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 Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source #
Arrow a => Functor ( ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #
Functor ( Proxy :: Type -> Type )	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b Source # (<$) :: a -> Proxy b -> Proxy a Source #
Functor ( Map k)
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b Source # (<$) :: a -> Map k b -> Map k a Source #
Functor m => Functor ( ListT m)
Instance details Defined in Control.Monad.Trans.List Methods fmap :: (a -> b) -> ListT m a -> ListT m b Source # (<$) :: a -> ListT m b -> ListT m a Source #
Functor m => Functor ( MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods fmap :: (a -> b) -> MaybeT m a -> MaybeT m b Source # (<$) :: a -> MaybeT m b -> MaybeT m a Source #
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 Source # (<$) :: a -> Rec1 f b -> Rec1 f a Source #
Functor ( URec Char :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b Source # (<$) :: a -> URec Char b -> URec Char a Source #
Functor ( URec Double :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source # (<$) :: a -> URec Double b -> URec Double a Source #
Functor ( URec Float :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source # (<$) :: a -> URec Float b -> URec Float a Source #
Functor ( URec Int :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b Source # (<$) :: a -> URec Int b -> URec Int a Source #
Functor ( URec Word :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b Source # (<$) :: a -> URec Word b -> URec Word a Source #
Functor ( URec ( Ptr ()) :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec ( Ptr ()) a -> URec ( Ptr ()) b Source # (<$) :: a -> URec ( Ptr ()) b -> URec ( Ptr ()) a Source #
Functor ( (,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source # (<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source #
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 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Functor m => Functor ( Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # (<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source #
Functor ( Const m :: Type -> Type )	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b Source # (<$) :: a -> Const m b -> Const m a Source #
Functor f => Functor ( Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source # (<$) :: a -> Ap f b -> Ap f a Source #
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 Source # (<$) :: a -> Alt f b -> Alt f a Source #
( Applicative f, Monad f) => Functor ( WhenMissing f x)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a Source #
Functor m => Functor ( IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods fmap :: (a -> b) -> IdentityT m a -> IdentityT m b Source # (<$) :: a -> IdentityT m b -> IdentityT m a Source #
Functor m => Functor ( ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b Source # (<$) :: a -> ErrorT e m b -> ErrorT e m a Source #
Functor m => Functor ( ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b Source # (<$) :: a -> ExceptT e m b -> ExceptT e m a Source #
Functor m => Functor ( ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b Source # (<$) :: a -> ReaderT r m b -> ReaderT r m a Source #
Functor m => Functor ( StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b Source # (<$) :: a -> StateT s m b -> StateT s m a Source #
Functor m => Functor ( StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b Source # (<$) :: a -> StateT s m b -> StateT s m a Source #
Functor m => Functor ( WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b Source # (<$) :: a -> WriterT w m b -> WriterT w m a Source #
Functor m => Functor ( WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b Source # (<$) :: a -> WriterT w m b -> WriterT w m a Source #
Functor ((->) r :: Type -> Type )	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b Source # (<$) :: a -> (r -> b) -> r -> a Source #
Functor ( K1 i c :: Type -> Type )	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b Source # (<$) :: a -> K1 i c b -> K1 i c a Source #
( 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 Source # (<$) :: a -> (f :+: g) b -> (f :+: g) a Source #
( Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b Source # (<$) :: a -> (f :: g) b -> (f :: g) a Source #
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) Source # (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source #
( Functor f, Functor g) => Functor ( Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b Source # (<$) :: a -> Product f g b -> Product f g a Source #
( 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 Source # (<$) :: a -> Sum f g b -> Sum f g a Source #
Functor f => Functor ( WhenMatched f x y)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a Source #
( Applicative f, Monad f) => Functor ( WhenMissing f k x)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a Source #
Functor f => Functor ( M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source # (<$) :: a -> M1 i c f b -> M1 i c f a Source #
( 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 Source # (<$) :: a -> (f :.: g) b -> (f :.: g) a Source #
( Functor f, Functor g) => Functor ( Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b Source # (<$) :: a -> Compose f g b -> Compose f g a Source #
Functor f => Functor ( WhenMatched f k x y)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a Source #
Functor m => Functor ( RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b Source # (<$) :: a -> RWST r w s m b -> RWST r w s m a Source #
Functor m => Functor ( RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b Source # (<$) :: a -> RWST r w s m b -> RWST r w s m a Source #

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

Flipped version of <$ .

Using ApplicativeDo : ' as $> b ' can be understood as the do expression

do as
   pure b

with an inferred Functor constraint.

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 -> 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.

Using ApplicativeDo : ' a <$ bs ' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

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

(<&>) :: 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

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.

Using ApplicativeDo : ' void as ' can be understood as the do expression

do as
   pure ()

with an inferred Functor constraint.

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

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