Copyright	(C) 2014-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Closed

Description

Synopsis

class Profunctor p => Closed p where
newtype Closure p a b = Closure {
- runClosure :: forall x. p (x -> a) (x -> b)
}
close :: Closed p => (p :-> q) -> p :-> Closure q
unclose :: Profunctor q => (p :-> Closure q) -> p :-> q
data Environment p a b where
- Environment :: ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
curry' :: Closed p => p (a, b) c -> p a (b -> c)

Documentation

class Profunctor p => Closed p where Source #

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) Source #

Laws:

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

Instances

(Distributive f, Monad f) => Closed (Kleisli f) Source #
Instance details Methods closed :: Kleisli f a b -> Kleisli f (x -> a) (x -> b) Source #
Functor f => Closed (Cokleisli f) Source #
Instance details Methods closed :: Cokleisli f a b -> Cokleisli f (x -> a) (x -> b) Source #
Closed (Tagged :: * -> * -> *) Source #
Instance details Methods closed :: Tagged a b -> Tagged (x -> a) (x -> b) Source #
Functor f => Closed (Costar f) Source #
Instance details Methods closed :: Costar f a b -> Costar f (x -> a) (x -> b) Source #
Distributive f => Closed (Star f) Source #
Instance details Methods closed :: Star f a b -> Star f (x -> a) (x -> b) Source #
Closed (Environment p) Source #
Instance details Methods closed :: Environment p a b -> Environment p (x -> a) (x -> b) Source #
Profunctor p => Closed (Closure p) Source #
Instance details Methods closed :: Closure p a b -> Closure p (x -> a) (x -> b) Source #
Closed (FreeMapping p) Source #
Instance details Methods closed :: FreeMapping p a b -> FreeMapping p (x -> a) (x -> b) Source #
Profunctor p => Closed (CofreeMapping p) Source #
Instance details Methods closed :: CofreeMapping p a b -> CofreeMapping p (x -> a) (x -> b) Source #
Closed p => Closed (Coyoneda p) Source #
Instance details Methods closed :: Coyoneda p a b -> Coyoneda p (x -> a) (x -> b) Source #
Closed p => Closed (Yoneda p) Source #
Instance details Methods closed :: Yoneda p a b -> Yoneda p (x -> a) (x -> b) Source #
Closed ((->) :: * -> * -> *) Source #
Instance details Methods closed :: (a -> b) -> (x -> a) -> x -> b Source #
(Closed p, Closed q) => Closed (Procompose p q) Source #
Instance details Methods closed :: Procompose p q a b -> Procompose p q (x -> a) (x -> b) Source #
(Closed p, Closed q) => Closed (Product p q) Source #
Instance details Methods closed :: Product p q a b -> Product p q (x -> a) (x -> b) Source #
(Functor f, Closed p) => Closed (Tannen f p) Source #
Instance details Methods closed :: Tannen f p a b -> Tannen f p (x -> a) (x -> b) Source #

newtype Closure p a b Source #

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 Source #
Instance details Methods proextract :: Profunctor p => Closure p :-> p Source # produplicate :: Profunctor p => Closure p :-> Closure (Closure p) Source #
ProfunctorFunctor Closure Source #
Instance details Methods promap :: Profunctor p => (p :-> q) -> Closure p :-> Closure q Source #
ProfunctorAdjunction Environment Closure Source #
Instance details Methods unit :: Profunctor p => p :-> Closure (Environment p) Source # counit :: Profunctor p => Environment (Closure p) :-> p Source #
Arrow p => Arrow (Closure p) Source #
Instance details 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) Source #
Instance details Methods zeroArrow :: Closure p b c #
ArrowPlus p => ArrowPlus (Closure p) Source #
Instance details Methods (<+>) :: Closure p b c -> Closure p b c -> Closure p b c #
ArrowLoop p => ArrowLoop (Closure p) Source #
Instance details Methods loop :: Closure p (b, d) (c, d) -> Closure p b c #
Profunctor p => Profunctor (Closure p) Source #
Instance details Methods dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d Source # lmap :: (a -> b) -> Closure p b c -> Closure p a c Source # rmap :: (b -> c) -> Closure p a b -> Closure p a c Source # (#.) :: Coercible c b => (b -> c) -> Closure p a b -> Closure p a c Source # (.#) :: Coercible b a => Closure p b c -> (a -> b) -> Closure p a c Source #
Strong p => Strong (Closure p) Source #
Instance details Methods first' :: Closure p a b -> Closure p (a, c) (b, c) Source # second' :: Closure p a b -> Closure p (c, a) (c, b) Source #
Profunctor p => Closed (Closure p) Source #
Instance details Methods closed :: Closure p a b -> Closure p (x -> a) (x -> b) Source #
Category p => Category (Closure p :: * -> * -> *) Source #
Instance details Methods id :: Closure p a a # (.) :: Closure p b c -> Closure p a b -> Closure p a c #
Profunctor p => Functor (Closure p a) Source #
Instance details Methods fmap :: (a0 -> b) -> Closure p a a0 -> Closure p a b # (<$) :: a0 -> Closure p a b -> Closure p a a0 #
(Profunctor p, Arrow p) => Applicative (Closure p a) Source #
Instance details Methods pure :: a0 -> Closure p a a0 # (<>) :: Closure p a (a0 -> b) -> Closure p a a0 -> Closure p a b # liftA2 :: (a0 -> b -> c) -> Closure p a a0 -> Closure p a b -> Closure p a c # (>) :: Closure p a a0 -> Closure p a b -> Closure p a b # (<*) :: Closure p a a0 -> Closure p a b -> Closure p a a0 #
(Profunctor p, ArrowPlus p) => Alternative (Closure p a) Source #
Instance details Methods empty :: Closure p a a0 # (<\|>) :: Closure p a a0 -> Closure p a a0 -> Closure p a a0 # some :: Closure p a a0 -> Closure p a [a0] # many :: Closure p a a0 -> Closure p a [a0] #
(Profunctor p, Arrow p, Semigroup b) => Semigroup (Closure p a b) Source #
Instance details Methods (<>) :: Closure p a b -> Closure p a b -> Closure p a b # sconcat :: NonEmpty (Closure p a b) -> Closure p a b # stimes :: Integral b0 => b0 -> Closure p a b -> Closure p a b #
(Profunctor p, Arrow p, Semigroup b, Monoid b) => Monoid (Closure p a b) Source #
Instance details 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 Source #

close . unclose ≡ id
unclose . close ≡ id

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

close . unclose ≡ id
unclose . close ≡ id

data Environment p a b where Source #

Constructors

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

Instances

ProfunctorMonad Environment Source #
Instance details Methods proreturn :: Profunctor p => p :-> Environment p Source # projoin :: Profunctor p => Environment (Environment p) :-> Environment p Source #
ProfunctorFunctor Environment Source #
Instance details Methods promap :: Profunctor p => (p :-> q) -> Environment p :-> Environment q Source #
ProfunctorAdjunction Environment Closure Source #
Instance details Methods unit :: Profunctor p => p :-> Closure (Environment p) Source # counit :: Profunctor p => Environment (Closure p) :-> p Source #
Profunctor (Environment p) Source #
Instance details Methods dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d Source # lmap :: (a -> b) -> Environment p b c -> Environment p a c Source # rmap :: (b -> c) -> Environment p a b -> Environment p a c Source # (#.) :: Coercible c b => (b -> c) -> Environment p a b -> Environment p a c Source # (.#) :: Coercible b a => Environment p b c -> (a -> b) -> Environment p a c Source #
Closed (Environment p) Source #
Instance details Methods closed :: Environment p a b -> Environment p (x -> a) (x -> b) Source #

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