interface Closed : (Type -> Type -> Type) -> Type Closed profunctors preserve the closed structure of a category.
Laws:
* `lmap (. f) . closed = rmap (. f) . closed`
* `closed . closed = dimap uncurry curry . closed`
* `dimap const ($ ()) . closed = id`
Parameters: p
Constraints: Profunctor p
Methods:
closed : p a b -> p (x -> a) (x -> b) The action of a closed profunctor.
Implementations:
Closed Morphism Functor f => Closed (Costar f) Profunctor p => Closed (Closure p) Closed (Environment p)
closed : Closed p => p a b -> p (x -> a) (x -> b) The action of a closed profunctor.
Totality: total
Visibility: public exportcurry' : Closed p => p (a, b) c -> p a (b -> c)- Totality: total
Visibility: public export record Closure : (Type -> Type -> Type) -> Type -> Type -> Type The comonad generated by the reflective subcategory of profunctors that
implement `Closed`.
Totality: total
Visibility: public export
Constructor: MkClosure : p (x -> a) (x -> b) -> Closure p a b
Projection: .runClosure : Closure p a b -> p (x -> a) (x -> b)
Hints:
Profunctor p => Closed (Closure p) Profunctor p => Functor (Closure p a) Strong p => GenStrong Pair (Closure p) Profunctor p => Profunctor (Closure p) ProfunctorAdjunction Environment Closure ProfunctorComonad Closure ProfunctorFunctor Closure
.runClosure : Closure p a b -> p (x -> a) (x -> b)- Totality: total
Visibility: public export runClosure : Closure p a b -> p (x -> a) (x -> b)- Totality: total
Visibility: public export close : Closed p => p :-> q -> p :-> Closure q- Totality: total
Visibility: public export unclose : Profunctor q => p :-> Closure q -> p :-> q- Totality: total
Visibility: public export data Environment : (Type -> Type -> Type) -> Type -> Type -> Type The monad generated by the reflective subcategory of profunctors that
implement `Closed`.
Totality: total
Visibility: public export
Constructor: MkEnv : ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
Hints:
Closed (Environment p) Profunctor p => Functor (Environment p a) Profunctor (Environment p) ProfunctorAdjunction Environment Closure ProfunctorFunctor Environment ProfunctorMonad Environment
environment : Closed q => p :-> q -> Environment p :-> q- Totality: total
Visibility: public export unenvironment : Environment p :-> q -> p :-> q- Totality: total
Visibility: public export