Data.Profunctor.Closed

Documentation

class Profunctor p => Closed p where

A strong profunctor allows the monoidal structure to pass through.

A closed profunctor allows the closed structure to pass through.

Methods

closed :: p a b -> p (x -> a) (x -> b)

Instances

Closed (->)

(Distributive f, Monad f) => Closed (Kleisli f)

Functor f => Closed (Cokleisli f)

Closed (Tagged *)

Monoid r => Closed (Forget r)

Functor f => Closed (DownStar f)

Distributive f => Closed (UpStar f)

Profunctor p => Closed (Closure p)

(Closed p, Closed q) => Closed (Procompose p q)

newtype Closure p a b

Closure adjoins a Closed structure to any Profunctor.

Analogous to Tambara for Closed.

Constructors

Closure

Fields

runClosure :: forall x. p (x -> a) (x -> b)

Instances

ProfunctorComonad Closure

ProfunctorFunctor Closure

ProfunctorAdjunction Environment Closure

Arrow p => Arrow (Closure p)

ArrowZero p => ArrowZero (Closure p)

ArrowPlus p => ArrowPlus (Closure p)

ArrowLoop p => ArrowLoop (Closure p)

Category p => Category (Closure p)

Profunctor p => Profunctor (Closure p)

Strong p => Strong (Closure p)

Profunctor p => Closed (Closure p)

Profunctor p => Functor (Closure p a)

(Profunctor p, Arrow p) => Applicative (Closure p a)

(Profunctor p, ArrowPlus p) => Alternative (Closure p a)

(Profunctor p, Arrow p, Monoid b) => Monoid (Closure p a b)

close :: Closed p => (p :-> q) -> p :-> Closure q

 close . unclose ≡ id
 unclose . close ≡ id

unclose :: Profunctor q => (p :-> Closure q) -> p :-> q

 close . unclose ≡ id
 unclose . close ≡ id

data Environment p a b where

Constructors

Environment :: ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b

Instances

ProfunctorMonad Environment

ProfunctorFunctor Environment

ProfunctorAdjunction Environment Closure

Profunctor p => Profunctor (Environment p)