Data.Functor.Apply

Functors

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.

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.

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 Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

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

(<$) :: a -> Down b -> Down 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 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 Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 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 IntMap

Defined in Data.IntMap.Internal

Methods

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

(<$) :: a -> IntMap b -> IntMap a

Functor Digit

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> Digit b -> Digit a

Functor Elem

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> Elem b -> Elem a

Functor FingerTree

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> FingerTree b -> FingerTree a

Functor Node

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> Node b -> Node a

Functor Seq

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> Seq b -> Seq a

Functor ViewL

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> ViewL b -> ViewL a

Functor ViewR

Defined in Data.Sequence.Internal

Methods

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

(<$) :: a -> ViewR b -> ViewR a

Functor Tree

Defined in Data.Tree

Methods

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

(<$) :: a -> Tree b -> Tree 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 AnnotDetails

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

(<$) :: a -> AnnotDetails b -> AnnotDetails a

Functor Doc

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

(<$) :: a -> Doc b -> Doc a

Functor Span

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

(<$) :: a -> Span b -> Span a

Functor Q

Defined in Language.Haskell.TH.Syntax

Methods

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

(<$) :: a -> Q b -> Q a

Functor TyVarBndr

Defined in Language.Haskell.TH.Syntax

Methods

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

(<$) :: a -> TyVarBndr b -> TyVarBndr 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 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 []

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

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

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0

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 (Array i)

Since: base-2.1

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b

(<$) :: a -> Array i b -> Array i a

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b

(<$) :: a -> U1 b -> U1 a

Functor (V1 :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Functor (Map k)

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> Map k a -> Map k b

(<$) :: a -> Map k b -> Map k a

Functor f => Functor (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

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

(<$) :: a -> MaybeApply f b -> MaybeApply f a

Functor f => Functor (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

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

(<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a

Functor f => Functor (Lift f)

Defined in Control.Applicative.Lift

Methods

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

(<$) :: a -> Lift f b -> Lift f a

Functor m => Functor (ListT m)

Defined in Control.Monad.Trans.List

Methods

fmap :: (a -> b) -> ListT m a -> ListT m b

(<$) :: a -> ListT m b -> ListT m a

Functor m => Functor (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

fmap :: (a -> b) -> MaybeT m a -> MaybeT m b

(<$) :: a -> MaybeT m b -> MaybeT m a

Functor (HashMap k)

Defined in Data.HashMap.Internal

Methods

fmap :: (a -> b) -> HashMap k a -> HashMap k b

(<$) :: a -> HashMap k b -> HashMap k 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 m => Functor (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b

(<$) :: a0 -> Kleisli m a b -> Kleisli m a 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 f => Functor (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b

(<$) :: a -> Rec1 f b -> Rec1 f a

Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a

Functor (URec Char :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b

(<$) :: a -> URec Char b -> URec Char a

Functor (URec Double :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b

(<$) :: a -> URec Double b -> URec Double a

Functor (URec Float :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b

(<$) :: a -> URec Float b -> URec Float a

Functor (URec Int :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b

(<$) :: a -> URec Int b -> URec Int a

Functor (URec Word :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b

(<$) :: a -> URec Word b -> URec Word a

Functor (Mag a b)

Defined in Data.Biapplicative

Methods

fmap :: (a0 -> b0) -> Mag a b a0 -> Mag a b b0

(<$) :: a0 -> Mag a b b0 -> Mag a b a0

Bifunctor p => Functor (Join p)

Defined in Data.Bifunctor.Join

Methods

fmap :: (a -> b) -> Join p a -> Join p b

(<$) :: a -> Join p b -> Join p a

Functor w => Functor (EnvT e w)

Defined in Control.Comonad.Trans.Env

Methods

fmap :: (a -> b) -> EnvT e w a -> EnvT e w b

(<$) :: a -> EnvT e w b -> EnvT e w a

Functor w => Functor (StoreT s w)

Defined in Control.Comonad.Trans.Store

Methods

fmap :: (a -> b) -> StoreT s w a -> StoreT s w b

(<$) :: a -> StoreT s w b -> StoreT s w a

Functor w => Functor (TracedT m w)

Defined in Control.Comonad.Trans.Traced

Methods

fmap :: (a -> b) -> TracedT m w a -> TracedT m w b

(<$) :: a -> TracedT m w b -> TracedT m w a

(Applicative f, Monad f) => Functor (WhenMissing f x)

Since: containers-0.5.9

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b

(<$) :: a -> WhenMissing f x b -> WhenMissing f x a

Functor f => Functor (Static f a)

Defined in Data.Semigroupoid.Static

Methods

fmap :: (a0 -> b) -> Static f a a0 -> Static f a b

(<$) :: a0 -> Static f a b -> Static f a a0

Functor (Tagged s)

Defined in Data.Tagged

Methods

fmap :: (a -> b) -> Tagged s a -> Tagged s b

(<$) :: a -> Tagged s b -> Tagged s a

Functor f => Functor (Backwards f)

Derived instance.

Defined in Control.Applicative.Backwards

Methods

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

(<$) :: a -> Backwards f b -> Backwards f a

Functor m => Functor (AccumT w m)

Defined in Control.Monad.Trans.Accum

Methods

fmap :: (a -> b) -> AccumT w m a -> AccumT w m b

(<$) :: a -> AccumT w m b -> AccumT w m a

Functor m => Functor (ErrorT e m)

Defined in Control.Monad.Trans.Error

Methods

fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b

(<$) :: a -> ErrorT e m b -> ErrorT e m a

Functor m => Functor (ExceptT e m)

Defined in Control.Monad.Trans.Except

Methods

fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b

(<$) :: a -> ExceptT e m b -> ExceptT e m a

Functor m => Functor (IdentityT m)

Defined in Control.Monad.Trans.Identity

Methods

fmap :: (a -> b) -> IdentityT m a -> IdentityT m b

(<$) :: a -> IdentityT m b -> IdentityT m a

Functor m => Functor (ReaderT r m)

Defined in Control.Monad.Trans.Reader

Methods

fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b

(<$) :: a -> ReaderT r m b -> ReaderT r m a

Functor m => Functor (SelectT r m)

Defined in Control.Monad.Trans.Select

Methods

fmap :: (a -> b) -> SelectT r m a -> SelectT r m b

(<$) :: a -> SelectT r m b -> SelectT r m a

Functor m => Functor (StateT s m)

Defined in Control.Monad.Trans.State.Lazy

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b

(<$) :: a -> StateT s m b -> StateT s m a

Functor m => Functor (StateT s m)

Defined in Control.Monad.Trans.State.Strict

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b

(<$) :: a -> StateT s m b -> StateT s m a

Functor m => Functor (WriterT w m)

Defined in Control.Monad.Trans.Writer.CPS

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b

(<$) :: a -> WriterT w m b -> WriterT w m a

Functor m => Functor (WriterT w m)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b

(<$) :: a -> WriterT w m b -> WriterT w m a

Functor m => Functor (WriterT w m)

Defined in Control.Monad.Trans.Writer.Strict

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b

(<$) :: a -> WriterT w m b -> WriterT w m a

Functor (Constant a :: Type -> Type)

Defined in Data.Functor.Constant

Methods

fmap :: (a0 -> b) -> Constant a a0 -> Constant a b

(<$) :: a0 -> Constant a b -> Constant a a0

Functor f => Functor (Reverse f)

Derived instance.

Defined in Data.Functor.Reverse

Methods

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

(<$) :: a -> Reverse f b -> Reverse 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 f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (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

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b

(<$) :: a -> (f :+: g) b -> (f :+: g) a

Functor (K1 i c :: TYPE LiftedRep -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b

(<$) :: a -> K1 i c b -> K1 i c a

Functor (Cokleisli w a)

Defined in Control.Comonad

Methods

fmap :: (a0 -> b) -> Cokleisli w a a0 -> Cokleisli w a b

(<$) :: a0 -> Cokleisli w a b -> Cokleisli w a a0

Functor f => Functor (WhenMatched f x y)

Since: containers-0.5.9

Defined in Data.IntMap.Internal

Methods

fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b

(<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a

(Applicative f, Monad f) => Functor (WhenMissing f k x)

Since: containers-0.5.9

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b

(<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a

Functor (ContT r m)

Defined in Control.Monad.Trans.Cont

Methods

fmap :: (a -> b) -> ContT r m a -> ContT r m b

(<$) :: a -> ContT r m b -> ContT r m 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 f, Functor g) => Functor (f :.: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b

(<$) :: a -> (f :.: g) b -> (f :.: g) a

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b

(<$) :: a -> M1 i c f b -> M1 i c f a

Functor (Clown f a :: Type -> Type)

Defined in Data.Bifunctor.Clown

Methods

fmap :: (a0 -> b) -> Clown f a a0 -> Clown f a b

(<$) :: a0 -> Clown f a b -> Clown f a a0

Bifunctor p => Functor (Flip p a)

Defined in Data.Bifunctor.Flip

Methods

fmap :: (a0 -> b) -> Flip p a a0 -> Flip p a b

(<$) :: a0 -> Flip p a b -> Flip p a a0

Functor g => Functor (Joker g a)

Defined in Data.Bifunctor.Joker

Methods

fmap :: (a0 -> b) -> Joker g a a0 -> Joker g a b

(<$) :: a0 -> Joker g a b -> Joker g a a0

Bifunctor p => Functor (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

fmap :: (a0 -> b) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b

(<$) :: a0 -> WrappedBifunctor p a b -> WrappedBifunctor p a a0

Functor f => Functor (WhenMatched f k x y)

Since: containers-0.5.9

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b

(<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a

Functor m => Functor (RWST r w s m)

Defined in Control.Monad.Trans.RWS.CPS

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b

(<$) :: a -> RWST r w s m b -> RWST r w s m a

Functor m => Functor (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Lazy

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b

(<$) :: a -> RWST r w s m b -> RWST r w s m a

Functor m => Functor (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Strict

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b

(<$) :: a -> RWST r w s m b -> RWST r w s m a

(Functor (f a), Functor (g a)) => Functor (Product f g a)

Defined in Data.Bifunctor.Product

Methods

fmap :: (a0 -> b) -> Product f g a a0 -> Product f g a b

(<$) :: a0 -> Product f g a b -> Product f g a a0

(Functor f, Bifunctor p) => Functor (Tannen f p a)

Defined in Data.Bifunctor.Tannen

Methods

fmap :: (a0 -> b) -> Tannen f p a a0 -> Tannen f p a b

(<$) :: a0 -> Tannen f p a b -> Tannen f p a a0

(Bifunctor p, Functor g) => Functor (Biff p f g a)

Defined in Data.Bifunctor.Biff

Methods

fmap :: (a0 -> b) -> Biff p f g a a0 -> Biff p f g a b

(<$) :: a0 -> Biff p f g a b -> Biff p f g a a0

(<$>) :: 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

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 -> 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

Apply - a strong lax semimonoidal endofunctor

class Functor f => Apply f where

A strong lax semi-monoidal endofunctor. This is equivalent to an Applicative without pure.

Laws:

(.) <$> u <.> v <.> w = u <.> (v <.> w)
x <.> (f <$> y) = (. f) <$> x <.> y
f <$> (x <.> y) = (f .) <$> x <.> y

The laws imply that .> and <. really ignore their left and right results, respectively, and really return their right and left results, respectively. Specifically,

(mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
(mf <$> m) <. (nf <$> n) = mf <$> (m <. n)

Minimal complete definition

(<.>) | liftF2

Methods

(<.>) :: f (a -> b) -> f a -> f b infixl 4

(.>) :: f a -> f b -> f b infixl 4

 a .> b = const id <$> a <.> b

(<.) :: f a -> f b -> f a infixl 4

 a <. b = const <$> a <.> b

liftF2 :: (a -> b -> c) -> f a -> f b -> f c

Lift a binary function into a comonad with zipping

Instances

Apply ZipList

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ZipList (a -> b) -> ZipList a -> ZipList b

(.>) :: ZipList a -> ZipList b -> ZipList b

(<.) :: ZipList a -> ZipList b -> ZipList a

liftF2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

Apply Complex

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Complex (a -> b) -> Complex a -> Complex b

(.>) :: Complex a -> Complex b -> Complex b

(<.) :: Complex a -> Complex b -> Complex a

liftF2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c

Apply Identity

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Identity (a -> b) -> Identity a -> Identity b

(.>) :: Identity a -> Identity b -> Identity b

(<.) :: Identity a -> Identity b -> Identity a

liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c

Apply First

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: First (a -> b) -> First a -> First b

(.>) :: First a -> First b -> First b

(<.) :: First a -> First b -> First a

liftF2 :: (a -> b -> c) -> First a -> First b -> First c

Apply Last

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Last (a -> b) -> Last a -> Last b

(.>) :: Last a -> Last b -> Last b

(<.) :: Last a -> Last b -> Last a

liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c

Apply Down

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Down (a -> b) -> Down a -> Down b

(.>) :: Down a -> Down b -> Down b

(<.) :: Down a -> Down b -> Down a

liftF2 :: (a -> b -> c) -> Down a -> Down b -> Down c

Apply First

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: First (a -> b) -> First a -> First b

(.>) :: First a -> First b -> First b

(<.) :: First a -> First b -> First a

liftF2 :: (a -> b -> c) -> First a -> First b -> First c

Apply Last

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Last (a -> b) -> Last a -> Last b

(.>) :: Last a -> Last b -> Last b

(<.) :: Last a -> Last b -> Last a

liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c

Apply Max

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Max (a -> b) -> Max a -> Max b

(.>) :: Max a -> Max b -> Max b

(<.) :: Max a -> Max b -> Max a

liftF2 :: (a -> b -> c) -> Max a -> Max b -> Max c

Apply Min

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Min (a -> b) -> Min a -> Min b

(.>) :: Min a -> Min b -> Min b

(<.) :: Min a -> Min b -> Min a

liftF2 :: (a -> b -> c) -> Min a -> Min b -> Min c

Apply Dual

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Dual (a -> b) -> Dual a -> Dual b

(.>) :: Dual a -> Dual b -> Dual b

(<.) :: Dual a -> Dual b -> Dual a

liftF2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

Apply Product

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Product (a -> b) -> Product a -> Product b

(.>) :: Product a -> Product b -> Product b

(<.) :: Product a -> Product b -> Product a

liftF2 :: (a -> b -> c) -> Product a -> Product b -> Product c

Apply Sum

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Sum (a -> b) -> Sum a -> Sum b

(.>) :: Sum a -> Sum b -> Sum b

(<.) :: Sum a -> Sum b -> Sum a

liftF2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

Apply Par1

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Par1 (a -> b) -> Par1 a -> Par1 b

(.>) :: Par1 a -> Par1 b -> Par1 b

(<.) :: Par1 a -> Par1 b -> Par1 a

liftF2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c

Apply IntMap

An IntMap is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b

(.>) :: IntMap a -> IntMap b -> IntMap b

(<.) :: IntMap a -> IntMap b -> IntMap a

liftF2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c

Apply Seq

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Seq (a -> b) -> Seq a -> Seq b

(.>) :: Seq a -> Seq b -> Seq b

(<.) :: Seq a -> Seq b -> Seq a

liftF2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c

Apply Tree

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Tree (a -> b) -> Tree a -> Tree b

(.>) :: Tree a -> Tree b -> Tree b

(<.) :: Tree a -> Tree b -> Tree a

liftF2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c

Apply IO

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IO (a -> b) -> IO a -> IO b

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

(<.) :: IO a -> IO b -> IO a

liftF2 :: (a -> b -> c) -> IO a -> IO b -> IO c

Apply Q

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Q (a -> b) -> Q a -> Q b

(.>) :: Q a -> Q b -> Q b

(<.) :: Q a -> Q b -> Q a

liftF2 :: (a -> b -> c) -> Q a -> Q b -> Q c

Apply NonEmpty

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

(.>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

(<.) :: NonEmpty a -> NonEmpty b -> NonEmpty a

liftF2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

Apply Maybe

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b

(.>) :: Maybe a -> Maybe b -> Maybe b

(<.) :: Maybe a -> Maybe b -> Maybe a

liftF2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

Apply []

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: [a -> b] -> [a] -> [b]

(.>) :: [a] -> [b] -> [b]

(<.) :: [a] -> [b] -> [a]

liftF2 :: (a -> b -> c) -> [a] -> [b] -> [c]

Monad m => Apply (WrappedMonad m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(.>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b

(<.) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a

liftF2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c

Apply (Either a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Either a (a0 -> b) -> Either a a0 -> Either a b

(.>) :: Either a a0 -> Either a b -> Either a b

(<.) :: Either a a0 -> Either a b -> Either a a0

liftF2 :: (a0 -> b -> c) -> Either a a0 -> Either a b -> Either a c

Apply (Proxy :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Proxy (a -> b) -> Proxy a -> Proxy b

(.>) :: Proxy a -> Proxy b -> Proxy b

(<.) :: Proxy a -> Proxy b -> Proxy a

liftF2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c

Apply (U1 :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: U1 (a -> b) -> U1 a -> U1 b

(.>) :: U1 a -> U1 b -> U1 b

(<.) :: U1 a -> U1 b -> U1 a

liftF2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c

Apply (V1 :: Type -> Type)

A V1 is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: V1 (a -> b) -> V1 a -> V1 b

(.>) :: V1 a -> V1 b -> V1 b

(<.) :: V1 a -> V1 b -> V1 a

liftF2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c

Ord k => Apply (Map k)

A 'Map k' is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Map k (a -> b) -> Map k a -> Map k b

(.>) :: Map k a -> Map k b -> Map k b

(<.) :: Map k a -> Map k b -> Map k a

liftF2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c

Apply f => Apply (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

Applicative f => Apply (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

Apply f => Apply (Lift f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Lift f (a -> b) -> Lift f a -> Lift f b

(.>) :: Lift f a -> Lift f b -> Lift f b

(<.) :: Lift f a -> Lift f b -> Lift f a

liftF2 :: (a -> b -> c) -> Lift f a -> Lift f b -> Lift f c

Apply m => Apply (ListT m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ListT m (a -> b) -> ListT m a -> ListT m b

(.>) :: ListT m a -> ListT m b -> ListT m b

(<.) :: ListT m a -> ListT m b -> ListT m a

liftF2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c

(Functor m, Monad m) => Apply (MaybeT m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b

(.>) :: MaybeT m a -> MaybeT m b -> MaybeT m b

(<.) :: MaybeT m a -> MaybeT m b -> MaybeT m a

liftF2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c

(Hashable k, Eq k) => Apply (HashMap k)

A 'HashMap k' is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: HashMap k (a -> b) -> HashMap k a -> HashMap k b

(.>) :: HashMap k a -> HashMap k b -> HashMap k b

(<.) :: HashMap k a -> HashMap k b -> HashMap k a

liftF2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c

Semigroup m => Apply ((,) m)

A (,) m is not Applicative unless its m is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (m, a -> b) -> (m, a) -> (m, b)

(.>) :: (m, a) -> (m, b) -> (m, b)

(<.) :: (m, a) -> (m, b) -> (m, a)

liftF2 :: (a -> b -> c) -> (m, a) -> (m, b) -> (m, c)

Arrow a => Apply (WrappedArrow a b)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0

(.>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0

(<.) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0

liftF2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c

Semigroup m => Apply (Const m :: Type -> Type)

A Const m is not Applicative unless its m is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Const m (a -> b) -> Const m a -> Const m b

(.>) :: Const m a -> Const m b -> Const m b

(<.) :: Const m a -> Const m b -> Const m a

liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c

Apply f => Apply (Alt f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Alt f (a -> b) -> Alt f a -> Alt f b

(.>) :: Alt f a -> Alt f b -> Alt f b

(<.) :: Alt f a -> Alt f b -> Alt f a

liftF2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c

Apply f => Apply (Rec1 f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b

(.>) :: Rec1 f a -> Rec1 f b -> Rec1 f b

(<.) :: Rec1 f a -> Rec1 f b -> Rec1 f a

liftF2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c

Biapply p => Apply (Join p)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Join p (a -> b) -> Join p a -> Join p b

(.>) :: Join p a -> Join p b -> Join p b

(<.) :: Join p a -> Join p b -> Join p a

liftF2 :: (a -> b -> c) -> Join p a -> Join p b -> Join p c

(Semigroup e, Apply w) => Apply (EnvT e w)

An EnvT e w is not Applicative unless its e is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: EnvT e w (a -> b) -> EnvT e w a -> EnvT e w b

(.>) :: EnvT e w a -> EnvT e w b -> EnvT e w b

(<.) :: EnvT e w a -> EnvT e w b -> EnvT e w a

liftF2 :: (a -> b -> c) -> EnvT e w a -> EnvT e w b -> EnvT e w c

(Apply w, Semigroup s) => Apply (StoreT s w)

A StoreT s w is not Applicative unless its s is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b

(.>) :: StoreT s w a -> StoreT s w b -> StoreT s w b

(<.) :: StoreT s w a -> StoreT s w b -> StoreT s w a

liftF2 :: (a -> b -> c) -> StoreT s w a -> StoreT s w b -> StoreT s w c

Apply w => Apply (TracedT m w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b

(.>) :: TracedT m w a -> TracedT m w b -> TracedT m w b

(<.) :: TracedT m w a -> TracedT m w b -> TracedT m w a

liftF2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c

Apply f => Apply (Static f a)

Defined in Data.Semigroupoid.Static

Methods

(<.>) :: Static f a (a0 -> b) -> Static f a a0 -> Static f a b

(.>) :: Static f a a0 -> Static f a b -> Static f a b

(<.) :: Static f a a0 -> Static f a b -> Static f a a0

liftF2 :: (a0 -> b -> c) -> Static f a a0 -> Static f a b -> Static f a c

Apply (Tagged a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Tagged a (a0 -> b) -> Tagged a a0 -> Tagged a b

(.>) :: Tagged a a0 -> Tagged a b -> Tagged a b

(<.) :: Tagged a a0 -> Tagged a b -> Tagged a a0

liftF2 :: (a0 -> b -> c) -> Tagged a a0 -> Tagged a b -> Tagged a c

Apply f => Apply (Backwards f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b

(.>) :: Backwards f a -> Backwards f b -> Backwards f b

(<.) :: Backwards f a -> Backwards f b -> Backwards f a

liftF2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c

(Functor m, Monad m) => Apply (ErrorT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b

(.>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b

(<.) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a

liftF2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c

(Functor m, Monad m) => Apply (ExceptT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b

(.>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b

(<.) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a

liftF2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c

Apply w => Apply (IdentityT w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IdentityT w (a -> b) -> IdentityT w a -> IdentityT w b

(.>) :: IdentityT w a -> IdentityT w b -> IdentityT w b

(<.) :: IdentityT w a -> IdentityT w b -> IdentityT w a

liftF2 :: (a -> b -> c) -> IdentityT w a -> IdentityT w b -> IdentityT w c

Apply m => Apply (ReaderT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ReaderT e m (a -> b) -> ReaderT e m a -> ReaderT e m b

(.>) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m b

(<.) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m a

liftF2 :: (a -> b -> c) -> ReaderT e m a -> ReaderT e m b -> ReaderT e m c

Bind m => Apply (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(.>) :: StateT s m a -> StateT s m b -> StateT s m b

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

Bind m => Apply (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(.>) :: StateT s m a -> StateT s m b -> StateT s m b

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

Bind m => Apply (WriterT w m)

Since: 5.3.6

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(Apply m, Semigroup w) => Apply (WriterT w m)

A WriterT w m is not Applicative unless its w is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(Apply m, Semigroup w) => Apply (WriterT w m)

A WriterT w m is not Applicative unless its w is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

Semigroup f => Apply (Constant f :: Type -> Type)

A Constant f is not Applicative unless its f is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Constant f (a -> b) -> Constant f a -> Constant f b

(.>) :: Constant f a -> Constant f b -> Constant f b

(<.) :: Constant f a -> Constant f b -> Constant f a

liftF2 :: (a -> b -> c) -> Constant f a -> Constant f b -> Constant f c

Apply f => Apply (Reverse f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Reverse f (a -> b) -> Reverse f a -> Reverse f b

(.>) :: Reverse f a -> Reverse f b -> Reverse f b

(<.) :: Reverse f a -> Reverse f b -> Reverse f a

liftF2 :: (a -> b -> c) -> Reverse f a -> Reverse f b -> Reverse f c

(Apply f, Apply g) => Apply (Product f g)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Product f g (a -> b) -> Product f g a -> Product f g b

(.>) :: Product f g a -> Product f g b -> Product f g b

(<.) :: Product f g a -> Product f g b -> Product f g a

liftF2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c

(Apply f, Apply g) => Apply (f :*: g)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b

(.>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b

(<.) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a

liftF2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c

Semigroup c => Apply (K1 i c :: Type -> Type)

A K1 i c is not Applicative unless its c is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b

(.>) :: K1 i c a -> K1 i c b -> K1 i c b

(<.) :: K1 i c a -> K1 i c b -> K1 i c a

liftF2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0

Apply (Cokleisli w a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Cokleisli w a (a0 -> b) -> Cokleisli w a a0 -> Cokleisli w a b

(.>) :: Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a b

(<.) :: Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a a0

liftF2 :: (a0 -> b -> c) -> Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a c

Apply (ContT r m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b

(.>) :: ContT r m a -> ContT r m b -> ContT r m b

(<.) :: ContT r m a -> ContT r m b -> ContT r m a

liftF2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c

Apply ((->) m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (m -> (a -> b)) -> (m -> a) -> m -> b

(.>) :: (m -> a) -> (m -> b) -> m -> b

(<.) :: (m -> a) -> (m -> b) -> m -> a

liftF2 :: (a -> b -> c) -> (m -> a) -> (m -> b) -> m -> c

(Apply f, Apply g) => Apply (Compose f g)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b

(.>) :: Compose f g a -> Compose f g b -> Compose f g b

(<.) :: Compose f g a -> Compose f g b -> Compose f g a

liftF2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c

(Apply f, Apply g) => Apply (f :.: g)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b

(.>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b

(<.) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a

liftF2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c

Apply f => Apply (M1 i t f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: M1 i t f (a -> b) -> M1 i t f a -> M1 i t f b

(.>) :: M1 i t f a -> M1 i t f b -> M1 i t f b

(<.) :: M1 i t f a -> M1 i t f b -> M1 i t f a

liftF2 :: (a -> b -> c) -> M1 i t f a -> M1 i t f b -> M1 i t f c

Bind m => Apply (RWST r w s m)

Since: 5.3.6

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(Bind m, Semigroup w) => Apply (RWST r w s m)

An RWST r w s m is not Applicative unless its w is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(Bind m, Semigroup w) => Apply (RWST r w s m)

An RWST r w s m is not Applicative unless its w is a Monoid, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(<..>) :: Apply w => w a -> w (a -> b) -> w b infixl 4

A variant of <.> with the arguments reversed.

liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d

Lift a ternary function into a comonad with zipping

gliftF2 :: (Generic1 w, Apply (Rep1 w)) => (a -> b -> c) -> w a -> w b -> w c

Generic liftF2. Caveats:

1. Will not compile if w is a sum type.
2. Types in w that do not mention the type variable must be instances of Semigroup.

Since: 5.3.8

gliftF3 :: (Generic1 w, Apply (Rep1 w)) => (a -> b -> c -> d) -> w a -> w b -> w c -> w d

Generic liftF3. Caveats are the same as for gliftF2.

Since: 5.3.8

Wrappers

newtype WrappedApplicative f a

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative

Fields

• unwrapApplicative :: f a

Instances

Alternative f => Alternative (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

empty :: WrappedApplicative f a

(<|>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: WrappedApplicative f a -> WrappedApplicative f [a]

many :: WrappedApplicative f a -> WrappedApplicative f [a]

Applicative f => Applicative (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

pure :: a -> WrappedApplicative f a

(<*>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

liftA2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

(*>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Functor f => Functor (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

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

(<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a

Alternative f => Alt (WrappedApplicative f)

Defined in Data.Functor.Alt

Methods

(<!>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

many :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

Applicative f => Apply (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

Alternative f => Plus (WrappedApplicative f)

Defined in Data.Functor.Plus

Methods

zero :: WrappedApplicative f a

newtype MaybeApply f a

Transform an Apply into an Applicative by adding a unit.

Constructors

MaybeApply

Fields

• runMaybeApply :: Either (f a) a

Instances

Apply f => Applicative (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

pure :: a -> MaybeApply f a

(<*>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

liftA2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

(*>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

Functor f => Functor (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

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

(<$) :: a -> MaybeApply f b -> MaybeApply f a

Comonad f => Comonad (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

extract :: MaybeApply f a -> a

duplicate :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extend :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

Apply f => Apply (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

Extend f => Extend (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

(<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b infixl 4

Apply a non-empty container of functions to a possibly-empty-with-unit container of values.

(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b infixl 4

Apply a possibly-empty-with-unit container of functions to a non-empty container of values.