Data.Functor.Apply

Functors

class Functor f where

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

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

(<$) :: 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 []

Functor IO

Functor Id

Functor Identity

Functor ZipList

Functor Handler

Functor First

Functor Last

Functor Maybe

Functor Id

Functor Put

Functor Digit

Functor Node

Functor Elem

Functor FingerTree

Functor IntMap

Functor Tree

Functor Seq

Functor ViewL

Functor ViewR

Functor Min

Functor Max

Functor First

Functor Last

Functor Option

Functor NonEmpty

Functor ((->) r)

Functor (Either a)

Functor ((,) a)

Ix i => Functor (Array i)

Functor (StateL s)

Functor (StateR s)

Functor (Const m)

Monad m => Functor (WrappedMonad m)

Arrow a => Functor (ArrowMonad a)

Functor (Proxy *)

Functor (StateL s)

Functor (StateR s)

Bifunctor p => Functor (Join p)

Functor m => Functor (IdentityT m)

Functor (State s)

Functor (Map k)

Functor (Arg a)

Functor f => Functor (Reverse f)

Derived instance.

Functor f => Functor (Backwards f)

Derived instance.

Functor m => Functor (MaybeT m)

Functor m => Functor (ListT m)

Functor f => Functor (Lift f)

Functor (Constant a)

Functor (HashMap k)

Functor f => Functor (MaybeApply f)

Functor f => Functor (WrappedApplicative f)

Arrow a => Functor (WrappedArrow a b)

Functor f => Functor (Alt * f)

Bifunctor p => Functor (WrappedBifunctor p a)

Functor g => Functor (Joker g a)

Bifunctor p => Functor (Flip p a)

Functor (Clown f a)

(Functor f, Functor g) => Functor (Coproduct f g)

Functor w => Functor (TracedT m w)

Functor w => Functor (StoreT s w)

Functor w => Functor (EnvT e w)

Functor (Cokleisli w a)

Functor (Tagged k s)

(Functor f, Functor g) => Functor (Sum f g)

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

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

Functor m => Functor (WriterT w m)

Functor m => Functor (WriterT w m)

Functor m => Functor (ErrorT e m)

Functor m => Functor (ExceptT e m)

Functor m => Functor (StateT s m)

Functor m => Functor (StateT s m)

Functor m => Functor (ReaderT r m)

Functor (ContT r m)

Functor f => Functor (Static f a)

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

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

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

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

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

An infix synonym for fmap.

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: 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:

associative composition: (.) <$> u <.> v <.> w = u <.> (v <.> w)

Minimal complete definition

(<.>)

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

Instances

Apply []

Apply IO

Apply Identity

Apply ZipList

Apply Maybe

Apply IntMap

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

Apply Tree

Apply Seq

Apply Option

Apply NonEmpty

Apply ((->) m)

Apply (Either a)

Semigroup m => Apply ((,) m)

Semigroup m => Apply (Const m)

Monad m => Apply (WrappedMonad m)

Biapply p => Apply (Join p)

Apply w => Apply (IdentityT w)

Ord k => Apply (Map k)

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

Apply f => Apply (Reverse f)

Apply f => Apply (Backwards f)

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

Apply m => Apply (ListT m)

Apply f => Apply (Lift f)

Semigroup f => Apply (Constant f)

Apply f => Apply (MaybeApply f)

Applicative f => Apply (WrappedApplicative f)

Arrow a => Apply (WrappedArrow a b)

Apply w => Apply (TracedT m w)

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

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

Apply (Cokleisli w a)

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

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

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

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

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

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

Bind m => Apply (StateT s m)

Bind m => Apply (StateT s m)

Apply m => Apply (ReaderT e m)

Apply (ContT r m)

Apply f => Apply (Static f a)

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

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

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

A variant of <.> with the arguments reversed.

liftF2 :: Apply w => (a -> b -> c) -> w a -> w b -> w c

Lift a binary function into a comonad with zipping

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

Lift a ternary function into a comonad with zipping

Wrappers

newtype WrappedApplicative f a

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative

Fields

unwrapApplicative :: f a

Instances

Functor f => Functor (WrappedApplicative f)

Applicative f => Applicative (WrappedApplicative f)

Alternative f => Alternative (WrappedApplicative f)

Applicative f => Apply (WrappedApplicative f)

Alternative f => Alt (WrappedApplicative f)

Alternative f => Plus (WrappedApplicative f)

newtype MaybeApply f a

Transform a Apply into an Applicative by adding a unit.

Constructors

MaybeApply

Fields

runMaybeApply :: Either (f a) a

Instances

Functor f => Functor (MaybeApply f)

Apply f => Applicative (MaybeApply f)

Comonad f => Comonad (MaybeApply f)

Extend f => Extend (MaybeApply f)

Apply f => Apply (MaybeApply f)