Data.Functor.Pairing

type Pairing f g = forall c b a. (a -> b -> c) -> f a -> g b -> c

A pairing between functors f and g.

This asserts that any sums in f can annihilate any products in g, and vice versa.

This library provides some useful pairings, and ways of lifting pairings over various constructions on Functors.

Operator alias for Data.Functor.Pairing.Pairing (non-associative / precedence 4)

zap :: forall b a g f. f ⋈ g -> f (a -> b) -> g a -> b

sym :: forall g f. f ⋈ g -> g ⋈ f

Pairing is symmetric

identity :: Identity ⋈ Identity

The identity functor pairs with itself

productCoproduct :: forall g2 f2 g1 f1. f1 ⋈ g1 -> f2 ⋈ g2 -> (Product f1 f2) ⋈ (Coproduct g1 g2)

Functor products pair with functor coproducts

stateStore :: forall s g f. f ⋈ g -> (StateT s f) ⋈ (StoreT s g)

StateT pairs with StoreT.

readerEnv :: forall e g f. f ⋈ g -> (ReaderT e f) ⋈ (EnvT e g)

ReaderT pairs with EnvT.

writerTraced :: forall w g f. f ⋈ g -> (WriterT w f) ⋈ (TracedT w g)

WriterT pairs with TracedT.

freeCofree :: forall g f. Functor f => Functor g => f ⋈ g -> (Free f) ⋈ (Cofree g)

Free pairs with Cofree.