semigroupoids-4.0: Semigroupoids: Category sans id

Portabilityportable
Stabilityprovisional
MaintainerEdward Kmett <ekmett@gmail.com>
Safe HaskellSafe

Data.Functor.Apply

Contents

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.

Methods

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

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

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 Identity 
Functor Digit 
Functor Node 
Functor Elem 
Functor Id 
Functor FingerTree 
Functor Tree 
Functor Seq 
Functor ViewL 
Functor ViewR 
Functor IntMap 
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 m => Functor (IdentityT m) 
Functor (State s) 
Functor (Map k) 
Functor (HashMap k) 
Functor m => Functor (MaybeT m) 
Functor m => Functor (ListT m) 
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 (ContT r m) 
Functor m => Functor (ErrorT e m) 
Functor m => Functor (ReaderT r m) 
Functor m => Functor (StateT s m) 
Functor m => Functor (WriterT w m) 
Functor m => Functor (StateT s m) 
Functor m => Functor (WriterT w m) 
(Functor f, Functor g) => Functor (Compose f g) 
(Functor f, Functor g) => Functor (Product f g) 
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

An infix synonym for fmap.

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

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

Apply - a strong lax semimonoidal endofunctor

class Functor f => Apply f whereSource

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

Laws: 

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

Methods

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

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

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

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

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

Instances

Apply [] 
Apply IO 
Apply ZipList 
Apply Maybe 
Apply Identity 
Apply Tree 
Apply Seq 
Apply IntMap

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

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

(Bind 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 (ContT r m) 
(Bind m, Monad m) => Apply (ErrorT e m) 
Apply m => Apply (ReaderT e m) 
Bind m => Apply (StateT s m) 
(Apply m, Semigroup w) => Apply (WriterT w m) 
Bind m => Apply (StateT s m) 
(Apply m, Semigroup w) => Apply (WriterT w m) 
(Apply f, Apply g) => Apply (Compose f g) 
(Apply f, Apply g) => Apply (Product f g) 
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 bSource

A variant of <.> with the arguments reversed.

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

Lift a binary function into a comonad with zipping

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

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

newtype MaybeApply f a Source

Transform a Apply into an Applicative by adding a unit.

Constructors

MaybeApply 

Fields

runMaybeApply :: Either (f a) a
 

Instances