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.

Minimal complete definition

closed

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

Instances

Closed (->)

Methods

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

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

Methods

closed :: Kleisli f a b -> Kleisli f (x -> a) (x -> b)

Functor f => Closed (Cokleisli f)

Methods

closed :: Cokleisli f a b -> Cokleisli f (x -> a) (x -> b)

Closed (Tagged *)

Methods

closed :: Tagged * a b -> Tagged * (x -> a) (x -> b)

Functor f => Closed (Costar f)

Methods

closed :: Costar f a b -> Costar f (x -> a) (x -> b)

Distributive f => Closed (Star f)

Methods

closed :: Star f a b -> Star f (x -> a) (x -> b)

Closed (Environment p)

Methods

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

Profunctor p => Closed (Closure p)

Methods

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

Closed (FreeMapping p)

Methods

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

Profunctor p => Closed (CofreeMapping p)

Methods

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

Closed p => Closed (Coyoneda p)

Methods

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

Closed p => Closed (Yoneda p)

Methods

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

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

Methods

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

(Closed p, Closed q) => Closed (Product * * p q)

Methods

closed :: Product * * p q a b -> Product * * p q (x -> a) (x -> b)

(Functor f, Closed p) => Closed (Tannen * * * f p)

Methods

closed :: Tannen * * * f p a b -> Tannen * * * f p (x -> a) (x -> b)

newtype Closure p a b

Closure adjoins a Closed structure to any Profunctor.

Analogous to Tambara for Strong.

Constructors

Closure

Fields

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

Instances

ProfunctorComonad Closure

Methods

proextract :: Profunctor p => Closure p :-> p

produplicate :: Profunctor p => Closure p :-> Closure (Closure p)

ProfunctorFunctor Closure

Methods

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

ProfunctorAdjunction Environment Closure

Methods

unit :: Profunctor p => p :-> Closure (Environment p)

counit :: Profunctor p => Environment (Closure p) :-> p

Arrow p => Arrow (Closure p)

Methods

arr :: (b -> c) -> Closure p b c

first :: Closure p b c -> Closure p (b, d) (c, d)

second :: Closure p b c -> Closure p (d, b) (d, c)

(***) :: Closure p b c -> Closure p b' c' -> Closure p (b, b') (c, c')

(&&&) :: Closure p b c -> Closure p b c' -> Closure p b (c, c')

ArrowZero p => ArrowZero (Closure p)

Methods

zeroArrow :: Closure p b c

ArrowPlus p => ArrowPlus (Closure p)

Methods

(<+>) :: Closure p b c -> Closure p b c -> Closure p b c

ArrowLoop p => ArrowLoop (Closure p)

Methods

loop :: Closure p (b, d) (c, d) -> Closure p b c

Profunctor p => Profunctor (Closure p)

Methods

dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d

lmap :: (a -> b) -> Closure p b c -> Closure p a c

rmap :: (b -> c) -> Closure p a b -> Closure p a c

(#.) :: Coercible * c b => (b -> c) -> Closure p a b -> Closure p a c

(.#) :: Coercible * b a => Closure p b c -> (a -> b) -> Closure p a c

Strong p => Strong (Closure p)

Methods

first' :: Closure p a b -> Closure p (a, c) (b, c)

second' :: Closure p a b -> Closure p (c, a) (c, b)

Profunctor p => Closed (Closure p)

Methods

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

Category * p => Category * (Closure p)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

Profunctor p => Functor (Closure p a)

Methods

fmap :: (a -> b) -> Closure p a a -> Closure p a b

(<$) :: a -> Closure p a b -> Closure p a a

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

Methods

pure :: a -> Closure p a a

(<*>) :: Closure p a (a -> b) -> Closure p a a -> Closure p a b

(*>) :: Closure p a a -> Closure p a b -> Closure p a b

(<*) :: Closure p a a -> Closure p a b -> Closure p a a

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

Methods

empty :: Closure p a a

(<|>) :: Closure p a a -> Closure p a a -> Closure p a a

some :: Closure p a a -> Closure p a [a]

many :: Closure p a a -> Closure p a [a]

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

Methods

mempty :: Closure p a b

mappend :: Closure p a b -> Closure p a b -> Closure p a b

mconcat :: [Closure p a b] -> 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

Methods

proreturn :: Profunctor p => p :-> Environment p

projoin :: Profunctor p => Environment (Environment p) :-> Environment p

ProfunctorFunctor Environment

Methods

promap :: Profunctor p => (p :-> q) -> Environment p :-> Environment q

ProfunctorAdjunction Environment Closure

Methods

unit :: Profunctor p => p :-> Closure (Environment p)

counit :: Profunctor p => Environment (Closure p) :-> p

Profunctor (Environment p)

Methods

dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d

lmap :: (a -> b) -> Environment p b c -> Environment p a c

rmap :: (b -> c) -> Environment p a b -> Environment p a c

(#.) :: Coercible * c b => (b -> c) -> Environment p a b -> Environment p a c

(.#) :: Coercible * b a => Environment p b c -> (a -> b) -> Environment p a c

Closed (Environment p)

Methods

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

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