Control.Functor.Composition

Generalized functor composition. Since we have many reasons for which you might want to compose a functor, and many expected results. i.e. monads via adjunctions, monads via composition with a pointed endofunctor, etc. we have to make multiple composition operators.

Documentation

newtype CompF f g a

Basic functor composition

Constructors

CompF

Fields

runCompF :: f (g a)

Instances

Composition CompF

Functor f => HFunctor (CompF f)

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

(Full f, Full g) => Full (CompF f g)

(ExpFunctor f, ExpFunctor g) => ExpFunctor (CompF f g)

(Adjunction f1 g1, Adjunction f2 g2) => Adjunction (CompF f2 f1) (CompF g1 g2)

(Adjunction f1 g1, Adjunction f2 g2) => Representable (CompF g1 g2) (CompF f2 f1 ())

class Composition o where

Methods

decompose :: (f `o` g) x -> f (g x)

compose :: f (g x) -> (f `o` g) x

Instances

Composition CompF

Composition ACompF

Composition DistCompF

Composition PreCompF

Composition PostCompF

Composition PointedCompF

associateComposition :: (Functor f, Composition c) => c (c f g) h a -> c f (c g h) a

The only reason the compositions are all the same is for type inference. This can be liberalized.

coassociateComposition :: (Functor f, Composition c) => c f (c g h) a -> c (c f g) h a

type :.: = CompF

An infix alias for functor composition

data Comp p f g a b

Bifunctor composition

Instances

(Bifunctor p Hask Hask Hask, Symmetric Hask f, Symmetric Hask g) => Symmetric Hask (Comp p f g)

(Bifunctor p Hask Hask Hask, Braided Hask f, Braided Hask g) => Braided Hask (Comp p f g)

(Bifunctor p c d Hask, QFunctor f b c, QFunctor g b d) => QFunctor (Comp p f g) b Hask

(Bifunctor p c d Hask, PFunctor f a c, PFunctor g a d) => PFunctor (Comp p f g) a Hask

(Bifunctor p c d Hask, Bifunctor f a b c, Bifunctor g a b d) => Bifunctor (Comp p f g) a b Hask

(Bifunctor p Hask Hask Hask, Bifunctor f Hask Hask Hask, Bifunctor g Hask Hask Hask) => Functor (Comp p f g a)

type :++: = Comp Either

Bifunctor coproduct

type :**: = Comp (,)

Bifunctor product

liftComp :: Bifunctor p r s Hask => r (f a b) (f c d) -> s (g a b) (g c d) -> Comp p f g a b -> Comp p f g c d