functor-apply-0.9.0: Strong lax semimonoidal endofunctors (Applicative sans pure)

MaintainerEdward Kmett <>







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, Data.Maybe.Maybe and System.IO.IO satisfy these laws.


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.

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

An infix synonym for fmap.

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

TODO: move into Data.Functor

Apply - a strong lax semimonoidal endofunctor

class Functor f => Apply f whereSource

A strong lax semi-monoidal endofunctor


(<.>) :: 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


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

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

Apply Option 
Apply Identity 
Apply ((->) m) 
Apply (Either a) 
Semigroup m => Apply ((,) m) 
Semigroup m => Apply (Const m) 
Monad m => Apply (WrappedMonad m) 
Ord k => Apply (Map k)

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

Apply w => Apply (IdentityT w) 
Apply f => Apply (MaybeApply f) 
Applicative f => Apply (WrappedApplicative f) 
Arrow a => Apply (WrappedArrow a b) 
Apply (Cokleisli w a) 

(<..>) :: 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


newtype MaybeApply f a Source

Transform a Apply into an Applicative by adding a unit.




runMaybeApply :: Either (f a) a