Copyright	(C) 2011 Edward Kmett,
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Data.Functor.Apply

Contents

Functors
Apply - a strong lax semimonoidal endofunctor
Wrappers

Description

Synopsis

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 ZipList
Functor Handler
Functor STM
Functor ReadPrec
Functor ReadP
Functor Maybe
Functor Put
Functor Identity
Functor Digit
Functor Node
Functor Elem
Functor Id
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)
Functor (ST s)
Functor (StateL s)
Functor (StateR s)
Functor (Const m)
Monad m => Functor (WrappedMonad m)
Functor (ST s)
Arrow a => Functor (ArrowMonad a)
Functor (Proxy *)
Functor m => Functor (IdentityT m)
Functor (State s)
Functor (Map k)
Functor m => Functor (MaybeT m)
Functor m => Functor (ListT m)
Functor (HashMap k)
Functor f => Functor (MaybeApply f)
Functor f => Functor (WrappedApplicative f)
Arrow a => Functor (WrappedArrow a b)
(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 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 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.

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

Replace the contents of a functor uniformly with a constant value.

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:

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

Minimal complete definition

(<.>)

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

Instances

Apply []
Apply IO
Apply ZipList
Apply Maybe
Apply Identity
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)
Apply w => Apply (IdentityT w)
Ord k => Apply (Map k)	A Map is not `Applicative`, but it is an instance of `Apply`
(Functor m, Monad m) => Apply (MaybeT m)
Apply m => Apply (ListT m)
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 Source

A variant of <.> with the arguments reversed.

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

Lift a binary function into a comonad with zipping

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

Wrappers

newtype WrappedApplicative f a Source

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative
Fields unwrapApplicative :: f a

Instances

Alternative f => Alternative (WrappedApplicative f)
Functor f => Functor (WrappedApplicative f)
Applicative f => Applicative (WrappedApplicative f)
Applicative f => Apply (WrappedApplicative f)
Alternative f => Alt (WrappedApplicative f)
Alternative f => Plus (WrappedApplicative f)

newtype MaybeApply f a Source

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)