Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Functor.Apply

Contents

Functors
Apply - a strong lax semimonoidal endofunctor
Wrappers

Description

Synopsis

class Functor (f :: Type -> Type) where
- fmap :: (a -> b) -> f a -> f b
- (<$) :: a -> f b -> f a
(<$>) :: Functor f => (a -> b) -> f a -> f b
($>) :: Functor f => f a -> b -> f b
class Functor f => Apply f where
- (<.>) :: f (a -> b) -> f a -> f b
- (.>) :: f a -> f b -> f b
- (<.) :: f a -> f b -> f a
- liftF2 :: (a -> b -> c) -> f a -> f b -> f c
(<..>) :: Apply w => w a -> w (a -> b) -> w b
liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
gliftF2 :: (Generic1 w, Apply (Rep1 w)) => (a -> b -> c) -> w a -> w b -> w c
gliftF3 :: (Generic1 w, Apply (Rep1 w)) => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
newtype WrappedApplicative f a = WrapApplicative {
- unwrapApplicative :: f a
}
newtype MaybeApply f a = MaybeApply {
- runMaybeApply :: Either (f a) a
}
(<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b
(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b

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. See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or https://github.com/quchen/articles/blob/master/second_functor_law.md for an explanation.

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

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 #

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

Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b # (<$) :: a -> ZipList b -> ZipList a #
Functor Handler	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b # (<$) :: a -> Handler b -> Handler a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b # (<$) :: a -> Down b -> Down a #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b # (<$) :: a -> Max b -> Max a #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b # (<$) :: a -> Min b -> Min a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Functor NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b # (<$) :: a -> NonEmpty b -> NonEmpty a #
Functor Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b # (<$) :: a -> Par1 b -> Par1 a #
Functor P	Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b # (<$) :: a -> P b -> P a #
Functor ReadP	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b # (<$) :: a -> ReadP b -> ReadP a #
Functor IntMap
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> IntMap a -> IntMap b # (<$) :: a -> IntMap b -> IntMap a #
Functor Digit
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Digit a -> Digit b # (<$) :: a -> Digit b -> Digit a #
Functor Elem
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Elem a -> Elem b # (<$) :: a -> Elem b -> Elem a #
Functor FingerTree
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a #
Functor Node
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Node a -> Node b # (<$) :: a -> Node b -> Node a #
Functor Seq
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> Seq a -> Seq b # (<$) :: a -> Seq b -> Seq a #
Functor ViewL
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewL a -> ViewL b # (<$) :: a -> ViewL b -> ViewL a #
Functor ViewR
Instance details Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> ViewR a -> ViewR b # (<$) :: a -> ViewR b -> ViewR a #
Functor Tree
Instance details Defined in Data.Tree Methods fmap :: (a -> b) -> Tree a -> Tree b # (<$) :: a -> Tree b -> Tree a #
Functor IO	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b # (<$) :: a -> IO b -> IO a #
Functor AnnotDetails
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b # (<$) :: a -> AnnotDetails b -> AnnotDetails a #
Functor Doc
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> Doc a -> Doc b # (<$) :: a -> Doc b -> Doc a #
Functor Span
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> Span a -> Span b # (<$) :: a -> Span b -> Span a #
Functor Q
Instance details Defined in Language.Haskell.TH.Syntax Methods fmap :: (a -> b) -> Q a -> Q b # (<$) :: a -> Q b -> Q a #
Functor TyVarBndr
Instance details Defined in Language.Haskell.TH.Syntax Methods fmap :: (a -> b) -> TyVarBndr a -> TyVarBndr b # (<$) :: a -> TyVarBndr b -> TyVarBndr a #
Functor Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b # (<$) :: a -> Maybe b -> Maybe a #
Functor Solo	Since: base-4.15
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Solo a -> Solo b # (<$) :: a -> Solo b -> Solo a #
Functor List	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] # (<$) :: a -> [b] -> [a] #
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 # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a #
Arrow a => Functor (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 #
Functor (Either a)	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b # (<$) :: a0 -> Either a b -> Either a a0 #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b # (<$) :: a -> U1 b -> U1 a #
Functor (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
Functor (Map k)
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> Map k a -> Map k b # (<$) :: a -> Map k b -> Map k a #
Functor f => Functor (MaybeApply f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> MaybeApply f a -> MaybeApply f b # (<$) :: a -> MaybeApply f b -> MaybeApply f a #
Functor f => Functor (WrappedApplicative f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # (<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a #
Functor f => Functor (Lift f)
Instance details Defined in Control.Applicative.Lift Methods fmap :: (a -> b) -> Lift f a -> Lift f b # (<$) :: a -> Lift f b -> Lift f a #
Functor m => Functor (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods fmap :: (a -> b) -> MaybeT m a -> MaybeT m b # (<$) :: a -> MaybeT m b -> MaybeT m a #
Functor (HashMap k)
Instance details Defined in Data.HashMap.Internal Methods fmap :: (a -> b) -> HashMap k a -> HashMap k b # (<$) :: a -> HashMap k b -> HashMap k a #
Functor ((,) a)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) # (<$) :: a0 -> (a, b) -> (a, a0) #
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Functor m => Functor (Kleisli m a)	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b # (<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Functor f => Functor (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b # (<$) :: a -> Ap f b -> Ap f a #
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b # (<$) :: a -> Alt f b -> Alt f a #
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b # (<$) :: a -> Generically1 f b -> Generically1 f a #
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 # (<$) :: a -> Rec1 f b -> Rec1 f a #
Functor (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b # (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #
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 # (<$) :: a -> URec Char b -> URec Char a #
Functor (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
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 # (<$) :: a -> URec Float b -> URec Float a #
Functor (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
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 # (<$) :: a -> URec Word b -> URec Word a #
Functor (Mag a b)
Instance details Defined in Data.Biapplicative Methods fmap :: (a0 -> b0) -> Mag a b a0 -> Mag a b b0 # (<$) :: a0 -> Mag a b b0 -> Mag a b a0 #
Bifunctor p => Functor (Join p)
Instance details Defined in Data.Bifunctor.Join Methods fmap :: (a -> b) -> Join p a -> Join p b # (<$) :: a -> Join p b -> Join p a #
Functor w => Functor (EnvT e w)
Instance details Defined in Control.Comonad.Trans.Env Methods fmap :: (a -> b) -> EnvT e w a -> EnvT e w b # (<$) :: a -> EnvT e w b -> EnvT e w a #
Functor w => Functor (StoreT s w)
Instance details Defined in Control.Comonad.Trans.Store Methods fmap :: (a -> b) -> StoreT s w a -> StoreT s w b # (<$) :: a -> StoreT s w b -> StoreT s w a #
Functor w => Functor (TracedT m w)
Instance details Defined in Control.Comonad.Trans.Traced Methods fmap :: (a -> b) -> TracedT m w a -> TracedT m w b # (<$) :: a -> TracedT m w b -> TracedT m w a #
(Applicative f, Monad f) => Functor (WhenMissing f x)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a #
Functor f => Functor (Static f a) Source #
Instance details Defined in Data.Semigroupoid.Static Methods fmap :: (a0 -> b) -> Static f a a0 -> Static f a b # (<$) :: a0 -> Static f a b -> Static f a a0 #
Functor (Tagged s)
Instance details Defined in Data.Tagged Methods fmap :: (a -> b) -> Tagged s a -> Tagged s b # (<$) :: a -> Tagged s b -> Tagged s a #
Functor f => Functor (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods fmap :: (a -> b) -> Backwards f a -> Backwards f b # (<$) :: a -> Backwards f b -> Backwards f a #
Functor m => Functor (AccumT w m)
Instance details Defined in Control.Monad.Trans.Accum Methods fmap :: (a -> b) -> AccumT w m a -> AccumT w m b # (<$) :: a -> AccumT w m b -> AccumT w m a #
Functor m => Functor (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b # (<$) :: a -> ExceptT e m b -> ExceptT e m a #
Functor m => Functor (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods fmap :: (a -> b) -> IdentityT m a -> IdentityT m b # (<$) :: a -> IdentityT m b -> IdentityT m a #
Functor m => Functor (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods fmap :: (a -> b) -> ReaderT r m a -> ReaderT r m b # (<$) :: a -> ReaderT r m b -> ReaderT r m a #
Functor m => Functor (SelectT r m)
Instance details Defined in Control.Monad.Trans.Select Methods fmap :: (a -> b) -> SelectT r m a -> SelectT r m b # (<$) :: a -> SelectT r m b -> SelectT r m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods fmap :: (a -> b) -> StateT s m a -> StateT s m b # (<$) :: a -> StateT s m b -> StateT s m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.CPS Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor m => Functor (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods fmap :: (a -> b) -> WriterT w m a -> WriterT w m b # (<$) :: a -> WriterT w m b -> WriterT w m a #
Functor (Constant a :: Type -> Type)
Instance details Defined in Data.Functor.Constant Methods fmap :: (a0 -> b) -> Constant a a0 -> Constant a b # (<$) :: a0 -> Constant a b -> Constant a a0 #
Functor f => Functor (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods fmap :: (a -> b) -> Reverse f a -> Reverse f b # (<$) :: a -> Reverse f b -> Reverse f a #
Functor ((,,) a b)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) # (<$) :: a0 -> (a, b, b0) -> (a, b, a0) #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b # (<$) :: a -> Sum f g b -> Sum f g a #
(Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
Functor (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b # (<$) :: a -> K1 i c b -> K1 i c a #
Functor (Cokleisli w a)
Instance details Defined in Control.Comonad Methods fmap :: (a0 -> b) -> Cokleisli w a a0 -> Cokleisli w a b # (<$) :: a0 -> Cokleisli w a b -> Cokleisli w a a0 #
Functor f => Functor (WhenMatched f x y)	Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (<$) :: 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
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a #
Functor (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods fmap :: (a -> b) -> ContT r m a -> ContT r m b # (<$) :: a -> ContT r m b -> ContT r m a #
Functor ((,,,) a b c)	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) # (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) #
Functor ((->) r)	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b # (<$) :: a -> (r -> b) -> r -> a #
(Functor f, Functor g) => Functor (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b # (<$) :: a -> Compose f g b -> Compose f g a #
(Functor f, Functor g) => Functor (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b # (<$) :: a -> M1 i c f b -> M1 i c f a #
Functor (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods fmap :: (a0 -> b) -> Clown f a a0 -> Clown f a b # (<$) :: a0 -> Clown f a b -> Clown f a a0 #
Bifunctor p => Functor (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods fmap :: (a0 -> b) -> Flip p a a0 -> Flip p a b # (<$) :: a0 -> Flip p a b -> Flip p a a0 #
Functor g => Functor (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods fmap :: (a0 -> b) -> Joker g a a0 -> Joker g a b # (<$) :: a0 -> Joker g a b -> Joker g a a0 #
Bifunctor p => Functor (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods fmap :: (a0 -> b) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b # (<$) :: a0 -> WrappedBifunctor p a b -> WrappedBifunctor p a a0 #
Functor f => Functor (WhenMatched f k x y)	Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.CPS Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
Functor m => Functor (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
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 # (<$) :: a -> RWST r w s m b -> RWST r w s m a #
Functor ((,,,,) a b c d)	Since: base-4.18.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, d, a0) -> (a, b, c, d, b0) # (<$) :: a0 -> (a, b, c, d, b0) -> (a, b, c, d, a0) #
(Functor (f a), Functor (g a)) => Functor (Product f g a)
Instance details Defined in Data.Bifunctor.Product Methods fmap :: (a0 -> b) -> Product f g a a0 -> Product f g a b # (<$) :: a0 -> Product f g a b -> Product f g a a0 #
Functor ((,,,,,) a b c d e)	Since: base-4.18.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, d, e, a0) -> (a, b, c, d, e, b0) # (<$) :: a0 -> (a, b, c, d, e, b0) -> (a, b, c, d, e, a0) #
(Functor f, Bifunctor p) => Functor (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods fmap :: (a0 -> b) -> Tannen f p a a0 -> Tannen f p a b # (<$) :: a0 -> Tannen f p a b -> Tannen f p a a0 #
Functor ((,,,,,,) a b c d e f)	Since: base-4.18.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, d, e, f, a0) -> (a, b, c, d, e, f, b0) # (<$) :: a0 -> (a, b, c, d, e, f, b0) -> (a, b, c, d, e, f, a0) #
(Bifunctor p, Functor g) => Functor (Biff p f g a)
Instance details 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

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 -> 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

Apply - a strong lax semimonoidal endofunctor

class Functor f => Apply f where Source #

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 Source #

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

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

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

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

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

Lift a binary function into a comonad with zipping

Instances

Instances details

Apply ZipList Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source # (.>) :: ZipList a -> ZipList b -> ZipList b Source # (<.) :: ZipList a -> ZipList b -> ZipList a Source # liftF2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source #
Apply Complex Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Complex (a -> b) -> Complex a -> Complex b Source # (.>) :: Complex a -> Complex b -> Complex b Source # (<.) :: Complex a -> Complex b -> Complex a Source # liftF2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source #
Apply Identity Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Identity (a -> b) -> Identity a -> Identity b Source # (.>) :: Identity a -> Identity b -> Identity b Source # (<.) :: Identity a -> Identity b -> Identity a Source # liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source #
Apply First Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: First (a -> b) -> First a -> First b Source # (.>) :: First a -> First b -> First b Source # (<.) :: First a -> First b -> First a Source # liftF2 :: (a -> b -> c) -> First a -> First b -> First c Source #
Apply Last Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Last (a -> b) -> Last a -> Last b Source # (.>) :: Last a -> Last b -> Last b Source # (<.) :: Last a -> Last b -> Last a Source # liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #
Apply Down Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Down (a -> b) -> Down a -> Down b Source # (.>) :: Down a -> Down b -> Down b Source # (<.) :: Down a -> Down b -> Down a Source # liftF2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source #
Apply First Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: First (a -> b) -> First a -> First b Source # (.>) :: First a -> First b -> First b Source # (<.) :: First a -> First b -> First a Source # liftF2 :: (a -> b -> c) -> First a -> First b -> First c Source #
Apply Last Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Last (a -> b) -> Last a -> Last b Source # (.>) :: Last a -> Last b -> Last b Source # (<.) :: Last a -> Last b -> Last a Source # liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #
Apply Max Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Max (a -> b) -> Max a -> Max b Source # (.>) :: Max a -> Max b -> Max b Source # (<.) :: Max a -> Max b -> Max a Source # liftF2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source #
Apply Min Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Min (a -> b) -> Min a -> Min b Source # (.>) :: Min a -> Min b -> Min b Source # (<.) :: Min a -> Min b -> Min a Source # liftF2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source #
Apply Dual Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Dual (a -> b) -> Dual a -> Dual b Source # (.>) :: Dual a -> Dual b -> Dual b Source # (<.) :: Dual a -> Dual b -> Dual a Source # liftF2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #
Apply Product Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Product (a -> b) -> Product a -> Product b Source # (.>) :: Product a -> Product b -> Product b Source # (<.) :: Product a -> Product b -> Product a Source # liftF2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #
Apply Sum Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Sum (a -> b) -> Sum a -> Sum b Source # (.>) :: Sum a -> Sum b -> Sum b Source # (<.) :: Sum a -> Sum b -> Sum a Source # liftF2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #
Apply NonEmpty Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # (.>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<.) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source # liftF2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source #
Apply Par1 Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source # (.>) :: Par1 a -> Par1 b -> Par1 b Source # (<.) :: Par1 a -> Par1 b -> Par1 a Source # liftF2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source #
Apply IntMap Source #	An `IntMap` is not `Applicative`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b Source # (.>) :: IntMap a -> IntMap b -> IntMap b Source # (<.) :: IntMap a -> IntMap b -> IntMap a Source # liftF2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c Source #
Apply Seq Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Seq (a -> b) -> Seq a -> Seq b Source # (.>) :: Seq a -> Seq b -> Seq b Source # (<.) :: Seq a -> Seq b -> Seq a Source # liftF2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c Source #
Apply Tree Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Tree (a -> b) -> Tree a -> Tree b Source # (.>) :: Tree a -> Tree b -> Tree b Source # (<.) :: Tree a -> Tree b -> Tree a Source # liftF2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c Source #
Apply IO Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: IO (a -> b) -> IO a -> IO b Source # (.>) :: IO a -> IO b -> IO b Source # (<.) :: IO a -> IO b -> IO a Source # liftF2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source #
Apply Q Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Q (a -> b) -> Q a -> Q b Source # (.>) :: Q a -> Q b -> Q b Source # (<.) :: Q a -> Q b -> Q a Source # liftF2 :: (a -> b -> c) -> Q a -> Q b -> Q c Source #
Apply Maybe Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source # (.>) :: Maybe a -> Maybe b -> Maybe b Source # (<.) :: Maybe a -> Maybe b -> Maybe a Source # liftF2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #
Apply List Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: [a -> b] -> [a] -> [b] Source # (.>) :: [a] -> [b] -> [b] Source # (<.) :: [a] -> [b] -> [a] Source # liftF2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source #
Monad m => Apply (WrappedMonad m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (.>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<.) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # liftF2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source #
Apply (Either a) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Either a (a0 -> b) -> Either a a0 -> Either a b Source # (.>) :: Either a a0 -> Either a b -> Either a b Source # (<.) :: Either a a0 -> Either a b -> Either a a0 Source # liftF2 :: (a0 -> b -> c) -> Either a a0 -> Either a b -> Either a c Source #
Apply (Proxy :: Type -> Type) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source # (.>) :: Proxy a -> Proxy b -> Proxy b Source # (<.) :: Proxy a -> Proxy b -> Proxy a Source # liftF2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source #
Apply (U1 :: Type -> Type) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: U1 (a -> b) -> U1 a -> U1 b Source # (.>) :: U1 a -> U1 b -> U1 b Source # (<.) :: U1 a -> U1 b -> U1 a Source # liftF2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source #
Apply (V1 :: Type -> Type) Source #	A `V1` is not `Applicative`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: V1 (a -> b) -> V1 a -> V1 b Source # (.>) :: V1 a -> V1 b -> V1 b Source # (<.) :: V1 a -> V1 b -> V1 a Source # liftF2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c Source #
Ord k => Apply (Map k) Source #	A 'Map k' is not `Applicative`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Map k (a -> b) -> Map k a -> Map k b Source # (.>) :: Map k a -> Map k b -> Map k b Source # (<.) :: Map k a -> Map k b -> Map k a Source # liftF2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c Source #
Apply f => Apply (MaybeApply f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b Source # (.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b Source # (<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a Source # liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c Source #
Applicative f => Apply (WrappedApplicative f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b Source # (.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b Source # (<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a Source # liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c Source #
Apply f => Apply (Lift f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Lift f (a -> b) -> Lift f a -> Lift f b Source # (.>) :: Lift f a -> Lift f b -> Lift f b Source # (<.) :: Lift f a -> Lift f b -> Lift f a Source # liftF2 :: (a -> b -> c) -> Lift f a -> Lift f b -> Lift f c Source #
(Functor m, Monad m) => Apply (MaybeT m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b Source # (.>) :: MaybeT m a -> MaybeT m b -> MaybeT m b Source # (<.) :: MaybeT m a -> MaybeT m b -> MaybeT m a Source # liftF2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c Source #
(Hashable k, Eq k) => Apply (HashMap k) Source #	A 'HashMap k' is not `Applicative`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: HashMap k (a -> b) -> HashMap k a -> HashMap k b Source # (.>) :: HashMap k a -> HashMap k b -> HashMap k b Source # (<.) :: HashMap k a -> HashMap k b -> HashMap k a Source # liftF2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c Source #
Semigroup m => Apply ((,) m) Source #	A `(,) m` is not `Applicative` unless its `m` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: (m, a -> b) -> (m, a) -> (m, b) Source # (.>) :: (m, a) -> (m, b) -> (m, b) Source # (<.) :: (m, a) -> (m, b) -> (m, a) Source # liftF2 :: (a -> b -> c) -> (m, a) -> (m, b) -> (m, c) Source #
Arrow a => Apply (WrappedArrow a b) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (.>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<.) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # liftF2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source #
Semigroup m => Apply (Const m :: Type -> Type) Source #	A `Const m` is not `Applicative` unless its `m` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Const m (a -> b) -> Const m a -> Const m b Source # (.>) :: Const m a -> Const m b -> Const m b Source # (<.) :: Const m a -> Const m b -> Const m a Source # liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source #
Apply f => Apply (Alt f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source # (.>) :: Alt f a -> Alt f b -> Alt f b Source # (<.) :: Alt f a -> Alt f b -> Alt f a Source # liftF2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source #
Apply f => Apply (Rec1 f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source # (.>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source # (<.) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source # liftF2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source #
Biapply p => Apply (Join p) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Join p (a -> b) -> Join p a -> Join p b Source # (.>) :: Join p a -> Join p b -> Join p b Source # (<.) :: Join p a -> Join p b -> Join p a Source # liftF2 :: (a -> b -> c) -> Join p a -> Join p b -> Join p c Source #
(Semigroup e, Apply w) => Apply (EnvT e w) Source #	An `EnvT e w` is not `Applicative` unless its `e` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: EnvT e w (a -> b) -> EnvT e w a -> EnvT e w b Source # (.>) :: EnvT e w a -> EnvT e w b -> EnvT e w b Source # (<.) :: EnvT e w a -> EnvT e w b -> EnvT e w a Source # liftF2 :: (a -> b -> c) -> EnvT e w a -> EnvT e w b -> EnvT e w c Source #
(Apply w, Semigroup s) => Apply (StoreT s w) Source #	A `StoreT s w` is not `Applicative` unless its `s` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b Source # (.>) :: StoreT s w a -> StoreT s w b -> StoreT s w b Source # (<.) :: StoreT s w a -> StoreT s w b -> StoreT s w a Source # liftF2 :: (a -> b -> c) -> StoreT s w a -> StoreT s w b -> StoreT s w c Source #
Apply w => Apply (TracedT m w) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b Source # (.>) :: TracedT m w a -> TracedT m w b -> TracedT m w b Source # (<.) :: TracedT m w a -> TracedT m w b -> TracedT m w a Source # liftF2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c Source #
Apply f => Apply (Static f a) Source #
Instance details Defined in Data.Semigroupoid.Static Methods (<.>) :: Static f a (a0 -> b) -> Static f a a0 -> Static f a b Source # (.>) :: Static f a a0 -> Static f a b -> Static f a b Source # (<.) :: Static f a a0 -> Static f a b -> Static f a a0 Source # liftF2 :: (a0 -> b -> c) -> Static f a a0 -> Static f a b -> Static f a c Source #
Apply (Tagged a) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Tagged a (a0 -> b) -> Tagged a a0 -> Tagged a b Source # (.>) :: Tagged a a0 -> Tagged a b -> Tagged a b Source # (<.) :: Tagged a a0 -> Tagged a b -> Tagged a a0 Source # liftF2 :: (a0 -> b -> c) -> Tagged a a0 -> Tagged a b -> Tagged a c Source #
Apply f => Apply (Backwards f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b Source # (.>) :: Backwards f a -> Backwards f b -> Backwards f b Source # (<.) :: Backwards f a -> Backwards f b -> Backwards f a Source # liftF2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c Source #
(Functor m, Monad m) => Apply (ExceptT e m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # (.>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<.) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source # liftF2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c Source #
Apply w => Apply (IdentityT w) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: IdentityT w (a -> b) -> IdentityT w a -> IdentityT w b Source # (.>) :: IdentityT w a -> IdentityT w b -> IdentityT w b Source # (<.) :: IdentityT w a -> IdentityT w b -> IdentityT w a Source # liftF2 :: (a -> b -> c) -> IdentityT w a -> IdentityT w b -> IdentityT w c Source #
Apply m => Apply (ReaderT e m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: ReaderT e m (a -> b) -> ReaderT e m a -> ReaderT e m b Source # (.>) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m b Source # (<.) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m a Source # liftF2 :: (a -> b -> c) -> ReaderT e m a -> ReaderT e m b -> ReaderT e m c Source #
Bind m => Apply (StateT s m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # (.>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<.) :: StateT s m a -> StateT s m b -> StateT s m a Source # liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source #
Bind m => Apply (StateT s m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # (.>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<.) :: StateT s m a -> StateT s m b -> StateT s m a Source # liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source #
Bind m => Apply (WriterT w m) Source #	Since: 5.3.6
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # (.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source #
(Apply m, Semigroup w) => Apply (WriterT w m) Source #	A `WriterT w m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # (.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source #
(Apply m, Semigroup w) => Apply (WriterT w m) Source #	A `WriterT w m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # (.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source #
Semigroup f => Apply (Constant f :: Type -> Type) Source #	A `Constant f` is not `Applicative` unless its `f` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Constant f (a -> b) -> Constant f a -> Constant f b Source # (.>) :: Constant f a -> Constant f b -> Constant f b Source # (<.) :: Constant f a -> Constant f b -> Constant f a Source # liftF2 :: (a -> b -> c) -> Constant f a -> Constant f b -> Constant f c Source #
Apply f => Apply (Reverse f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Reverse f (a -> b) -> Reverse f a -> Reverse f b Source # (.>) :: Reverse f a -> Reverse f b -> Reverse f b Source # (<.) :: Reverse f a -> Reverse f b -> Reverse f a Source # liftF2 :: (a -> b -> c) -> Reverse f a -> Reverse f b -> Reverse f c Source #
(Apply f, Apply g) => Apply (Product f g) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # (.>) :: Product f g a -> Product f g b -> Product f g b Source # (<.) :: Product f g a -> Product f g b -> Product f g a Source # liftF2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source #
(Apply f, Apply g) => Apply (f :*: g) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b Source # (.>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source # (<.) :: (f :: g) a -> (f :: g) b -> (f :: g) a Source # liftF2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c Source #
Semigroup c => Apply (K1 i c :: Type -> Type) Source #	A `K1 i c` is not `Applicative` unless its `c` is a `Monoid`, but it is an instance of `Apply`
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source # (.>) :: K1 i c a -> K1 i c b -> K1 i c b Source # (<.) :: K1 i c a -> K1 i c b -> K1 i c a Source # liftF2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source #
Apply (Cokleisli w a) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Cokleisli w a (a0 -> b) -> Cokleisli w a a0 -> Cokleisli w a b Source # (.>) :: Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a b Source # (<.) :: Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a a0 Source # liftF2 :: (a0 -> b -> c) -> Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a c Source #
Apply (ContT r m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b Source # (.>) :: ContT r m a -> ContT r m b -> ContT r m b Source # (<.) :: ContT r m a -> ContT r m b -> ContT r m a Source # liftF2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c Source #
Apply ((->) m) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: (m -> (a -> b)) -> (m -> a) -> m -> b Source # (.>) :: (m -> a) -> (m -> b) -> m -> b Source # (<.) :: (m -> a) -> (m -> b) -> m -> a Source # liftF2 :: (a -> b -> c) -> (m -> a) -> (m -> b) -> m -> c Source #
(Apply f, Apply g) => Apply (Compose f g) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # (.>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<.) :: Compose f g a -> Compose f g b -> Compose f g a Source # liftF2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source #
(Apply f, Apply g) => Apply (f :.: g) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source # (.>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source # (<.) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source # liftF2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source #
Apply f => Apply (M1 i t f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: M1 i t f (a -> b) -> M1 i t f a -> M1 i t f b Source # (.>) :: M1 i t f a -> M1 i t f b -> M1 i t f b Source # (<.) :: M1 i t f a -> M1 i t f b -> M1 i t f a Source # liftF2 :: (a -> b -> c) -> M1 i t f a -> M1 i t f b -> M1 i t f c Source #
Bind m => Apply (RWST r w s m) Source #	Since: 5.3.6
Instance details 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 Source # (.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source #
(Bind m, Semigroup w) => Apply (RWST r w s m) Source #	An `RWST r w s m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 Source # (.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source #
(Bind m, Semigroup w) => Apply (RWST r w s m) Source #	An `RWST r w s m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 Source # (.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source #

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

A variant of <.> with the arguments reversed.

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

Lift a ternary function into a comonad with zipping

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

Generic liftF2. Caveats:

Will not compile if w is a sum type.
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 Source #

Generic liftF3. Caveats are the same as for gliftF2.

Since: 5.3.8

Wrappers

newtype WrappedApplicative f a Source #

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative
Fields unwrapApplicative :: f a

Instances

Instances details

Alternative f => Alternative (WrappedApplicative f) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Functor.Alt Methods (<!>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a Source # some :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a] Source # many :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a] Source #
Applicative f => Apply (WrappedApplicative f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b Source # (.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b Source # (<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a Source # liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c Source #
Alternative f => Plus (WrappedApplicative f) Source #
Instance details Defined in Data.Functor.Plus Methods zero :: WrappedApplicative f a Source #

newtype MaybeApply f a Source #

Transform an Apply into an Applicative by adding a unit.

Constructors

MaybeApply
Fields runMaybeApply :: Either (f a) a

Instances

Instances details

Apply f => Applicative (MaybeApply f) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Functor.Bind.Class Methods extract :: MaybeApply f a -> a Source # duplicate :: MaybeApply f a -> MaybeApply f (MaybeApply f a) Source # extend :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b Source #
Apply f => Apply (MaybeApply f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b Source # (.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b Source # (<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a Source # liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c Source #
Extend f => Extend (MaybeApply f) Source #
Instance details Defined in Data.Functor.Bind.Class Methods duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a) Source # extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b Source #

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

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 Source #

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