category-extras-0.52.1: Various modules and constructs inspired by category theory Source code Contents Index

Control.Functor.Composition Portability non-portable (class-associated types) Stability experimental Maintainer Edward Kmett <ekmett@gmail.com>

Description

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.

Synopsis

newtype CompF f g a = CompF { runCompF :: f (g a) } class Composition o where decompose :: (f `o` g) x -> f (g x) compose :: f (g x) -> (f `o` g) x associateComposition :: (Functor f, Composition c) => c (c f g) h a -> c f (c g h) a coassociateComposition :: (Functor f, Composition c) => c f (c g h) a -> c (c f g) h a type :.: = CompF data Comp p f g a b type :++: = Comp Either type :**: = Comp (,) 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

Documentation

newtype CompF f g a Source

Basic functor composition Constructors CompF 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)

class Composition o where Source

Methods decompose :: (f `o` g) x -> f (g x) Source compose :: f (g x) -> (f `o` g) x Source 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 Source

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 Source

type :.: = CompF Source

An infix alias for functor composition

data Comp p f g a b Source

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 Source

Bifunctor coproduct

type :**: = Comp (,) Source

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 Source

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