profunctors-5.6.2: Profunctors

Copyright | (C) 2014-2018 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | experimental
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Profunctor.Closed

Description

Synopsis

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

#### Instances

Instances details

(Distributive f, Monad f) => Closed (Kleisli f) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Kleisli f a b -> Kleisli f (x -> a) (x -> b) #
Profunctor p => Closed (Closure p) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Closure p a b -> Closure p (x -> a) (x -> b) #
Closed (Environment p) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Environment p a b -> Environment p (x -> a) (x -> b) #
Profunctor p => Closed (CofreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods closed :: CofreeMapping p a b -> CofreeMapping p (x -> a) (x -> b) #
Closed (FreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods closed :: FreeMapping p a b -> FreeMapping p (x -> a) (x -> b) #
Closed p => Closed (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods closed :: Coyoneda p a b -> Coyoneda p (x -> a) (x -> b) #
Closed p => Closed (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods closed :: Yoneda p a b -> Yoneda p (x -> a) (x -> b) #
Closed (Tagged :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Tagged a b -> Tagged (x -> a) (x -> b) #
Functor f => Closed (Cokleisli f) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Cokleisli f a b -> Cokleisli f (x -> a) (x -> b) #
Functor f => Closed (Costar f) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Costar f a b -> Costar f (x -> a) (x -> b) #
Distributive f => Closed (Star f) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Star f a b -> Star f (x -> a) (x -> b) #
Closed (->) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: (a -> b) -> (x -> a) -> (x -> b) #
(Closed p, Closed q) => Closed (Product p q) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Product p q a b -> Product p q (x -> a) (x -> b) #
(Closed p, Closed q) => Closed (Sum p q) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Sum p q a b -> Sum p q (x -> a) (x -> b) #
(Functor f, Closed p) => Closed (Tannen f p) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Tannen f p a b -> Tannen f p (x -> a) (x -> b) #
(Functor f, Closed p) => Closed (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods closed :: Cayley f p a b -> Cayley f p (x -> a) (x -> b) #
(Closed p, Closed q) => Closed (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods closed :: Procompose p q a b -> Procompose p q (x -> a) (x -> b) #

newtype Closure (p :: Type -> Type -> Type) 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

Instances details

ProfunctorComonad Closure # |
Instance details Defined in Data.Profunctor.Closed Methods proextract :: forall (p :: Type -> Type -> Type). Profunctor p => Closure p :-> p # produplicate :: forall (p :: Type -> Type -> Type). Profunctor p => Closure p :-> Closure (Closure p) #
ProfunctorAdjunction Environment Closure # |
Instance details Defined in Data.Profunctor.Closed Methods unit :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> Closure (Environment p) # counit :: forall (p :: Type -> Type -> Type). Profunctor p => Environment (Closure p) :-> p #
ProfunctorFunctor Closure # |
Instance details Defined in Data.Profunctor.Closed Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> Closure p :-> Closure q #
Category p => Category (Closure p :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Closed Methods id :: Closure p a a # (.) :: Closure p b c -> Closure p a b -> Closure p a c #
Arrow p => Arrow (Closure p) # |
Instance details Defined in Data.Profunctor.Closed 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') #
ArrowLoop p => ArrowLoop (Closure p) # |
Instance details Defined in Data.Profunctor.Closed Methods loop :: Closure p (b, d) (c, d) -> Closure p b c #
ArrowPlus p => ArrowPlus (Closure p) # |
Instance details Defined in Data.Profunctor.Closed Methods (<+>) :: Closure p b c -> Closure p b c -> Closure p b c #
ArrowZero p => ArrowZero (Closure p) # |
Instance details Defined in Data.Profunctor.Closed Methods zeroArrow :: Closure p b c #
Profunctor p => Closed (Closure p) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Closure p a b -> Closure p (x -> a) (x -> b) #
Strong p => Strong (Closure p) # |
Instance details Defined in Data.Profunctor.Closed 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 => Profunctor (Closure p) # |
Instance details Defined in Data.Profunctor.Closed 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 # (#.) :: forall a b c q. Coercible c b => q b c -> Closure p a b -> Closure p a c # (.#) :: forall a b c q. Coercible b a => Closure p b c -> q a b -> Closure p a c #
(Profunctor p, ArrowPlus p) => Alternative (Closure p a) # |
Instance details Defined in Data.Profunctor.Closed 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) => Applicative (Closure p a) # |
Instance details Defined in Data.Profunctor.Closed 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 => Functor (Closure p a) # |
Instance details Defined in Data.Profunctor.Closed 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, Semigroup b, Monoid b) => Monoid (Closure p a b) # |
Instance details Defined in Data.Profunctor.Closed 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 #
(Profunctor p, Arrow p, Semigroup b) => Semigroup (Closure p a b) # |
Instance details Defined in Data.Profunctor.Closed 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 #

close :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Closed p => (p :-> q) -> p :-> Closure q #

    close . unclose ≡ id
    unclose . close ≡ id

unclose :: forall (q :: Type -> Type -> Type) (p :: Type -> Type -> Type). Profunctor q => (p :-> Closure q) -> p :-> q #

    close . unclose ≡ id
    unclose . close ≡ id

data Environment (p :: Type -> Type -> Type) a b where #

Constructors

Environment :: forall z y b (p :: Type -> Type -> Type) x a. ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b |

#### Instances

Instances details

ProfunctorMonad Environment # |
Instance details Defined in Data.Profunctor.Closed Methods proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> Environment p # projoin :: forall (p :: Type -> Type -> Type). Profunctor p => Environment (Environment p) :-> Environment p #
ProfunctorAdjunction Environment Closure # |
Instance details Defined in Data.Profunctor.Closed Methods unit :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> Closure (Environment p) # counit :: forall (p :: Type -> Type -> Type). Profunctor p => Environment (Closure p) :-> p #
ProfunctorFunctor Environment # |
Instance details Defined in Data.Profunctor.Closed Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> Environment p :-> Environment q #
Closed (Environment p) # |
Instance details Defined in Data.Profunctor.Closed Methods closed :: Environment p a b -> Environment p (x -> a) (x -> b) #
Profunctor (Environment p) # |

Instance details

Defined in Data.Profunctor.Closed

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 #

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

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

Functor (Environment p a) # |
Instance details Defined in Data.Profunctor.Closed Methods fmap :: (a0 -> b) -> Environment p a a0 -> Environment p a b # (<$) :: a0 -> Environment p a b -> Environment p a a0 #

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