Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Closed

2 types
1 class
3 values

Packageprofunctors-5.6.3
Exports6
LanguageHaskell2010
LicenceBSD-3-Clause
SourceClosed.hs

classclass Profunctor p => Closed (p :: Type -> Type -> Type) 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)

Laws:

lmap (. f) . closed ≡ rmap (. f) . closed
closed . closed ≡ dimap uncurry curry . closed
dimap const ($()) . closed ≡ id

Instances17Closed, …

Closed TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (Environment p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Closed p => Closed (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Closed p => Closed (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Closed (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Closed (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
(Distributive f, Monad f) => Closed (Kleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Distributive f => Closed (Star f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor f => Closed (Cokleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor f => Closed (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (->)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Closed p, Closed q) => Closed (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Closed p, Closed q) => Closed (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Functor f, Closed p) => Closed (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Functor f, Closed p) => Closed (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Closed p, Closed q) => Closed (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

newtypenewtype Closure (p :: Type -> Type -> Type) a b

Closure adjoins a Closed structure to any Profunctor.

Analogous to Data.Profunctor.Tambara.Tambara for Strong.

Constructors

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

Instances16ProfunctorComonad, ProfunctorAdjunction, ProfunctorFunctor, Category, Arrow, ArrowLoop, …

ProfunctorComonad ClosureDefined in profunctors-5.6.3 · Data.Profunctor.Closed
ProfunctorAdjunction Environment ClosureDefined in profunctors-5.6.3 · Data.Profunctor.Closed
ProfunctorFunctor ClosureDefined in profunctors-5.6.3 · Data.Profunctor.Closed
Category p => Category (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Arrow p => Arrow (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
ArrowLoop p => ArrowLoop (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
ArrowPlus p => ArrowPlus (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
ArrowZero p => ArrowZero (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Closed (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Strong p => Strong (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Profunctor (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor p => Functor (Closure p a)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Profunctor p, Arrow p) => Applicative (Closure p a)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Profunctor p, ArrowPlus p) => Alternative (Closure p a)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Profunctor p, Arrow p, Semigroup b) => Semigroup (Closure p a b)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
(Profunctor p, Arrow p, Semigroup b, Monoid b) => Monoid (Closure p a b)Defined in profunctors-5.6.3 · Data.Profunctor.Closed

valueclose :: Closed p => p :-> q -> p :-> Closure q

close . unclose ≡ id
unclose . close ≡ id

valueunclose :: Profunctor q => p :-> Closure q -> p :-> q

close . unclose ≡ id
unclose . close ≡ id

datadata Environment (p :: Type -> Type -> Type) a b where

Constructors

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

Instances6ProfunctorMonad, ProfunctorAdjunction, ProfunctorFunctor, Closed, Profunctor, Functor

ProfunctorMonad EnvironmentDefined in profunctors-5.6.3 · Data.Profunctor.Closed
ProfunctorAdjunction Environment ClosureDefined in profunctors-5.6.3 · Data.Profunctor.Closed
ProfunctorFunctor EnvironmentDefined in profunctors-5.6.3 · Data.Profunctor.Closed
Closed (Environment p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Profunctor (Environment p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Functor (Environment p a)Defined in profunctors-5.6.3 · Data.Profunctor.Closed

valuecurry' :: Closed p => p (a, b) c -> p a (b -> c)