profunctors-5.6.2: Profunctors

Copyright | (C) 2011-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | portable
Safe Haskell | Safe
Language | Haskell2010

Data.Profunctor

Contents

- Profunctors
  - Profunctorial Strength
  - Closed
  - Profunctorial Costrength
  - Common Profunctors

Description

For a good explanation of profunctors in Haskell see Dan Piponi's article:

http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html

For more information on strength and costrength, see:

http://comonad.com/reader/2008/deriving-strength-from-laziness/

Synopsis

- class Profunctor p where
  - dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
  - lmap :: (a -> b) -> p b c -> p a c
  - rmap :: (b -> c) -> p a b -> p a c
- class Profunctor p => Strong p where
  - first' :: p a b -> p (a, c) (b, c)
  - second' :: p a b -> p (c, a) (c, b)
- uncurry' :: Strong p => p a (b -> c) -> p (a, b) c
- class Profunctor p => Choice p where
  - left' :: p a b -> p (Either a c) (Either b c)
  - right' :: p a b -> p (Either c a) (Either c b)
- class Profunctor p => Closed p where
  - closed :: p a b -> p (x -> a) (x -> b)
- curry' :: Closed p => p (a, b) c -> p a (b -> c)
- class (Traversing p, Closed p) => Mapping p where
  - map' :: Functor f => p a b -> p (f a) (f b)
  - roam :: ((a -> b) -> s -> t) -> p a b -> p s t
- class Profunctor p => Costrong p where
  - unfirst :: p (a, d) (b, d) -> p a b
  - unsecond :: p (d, a) (d, b) -> p a b
- class Profunctor p => Cochoice p where
  - unleft :: p (Either a d) (Either b d) -> p a b
  - unright :: p (Either d a) (Either d b) -> p a b
- newtype Star f d c = Star {
  - runStar :: d -> f c
  }
- newtype Costar f d c = Costar {
  - runCostar :: f d -> c
  }
- newtype WrappedArrow p a b = WrapArrow {
  - unwrapArrow :: p a b
  }
- newtype Forget r a b = Forget {
  - runForget :: a -> r
  }
- type (:->) p q = forall a b. p a b -> q a b

# Profunctors

class Profunctor p where #

Formally, the class `Profunctor` represents a profunctor from `Hask` -> `Hask`.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a `Profunctor` by either defining `dimap` or by defining both `lmap` and `rmap`.

If you supply `dimap`, you should ensure that:

    dimap id id ≡ id

If you supply `lmap` and `rmap`, ensure:

    lmap id ≡ id
    rmap id ≡ id

If you supply both, you should also ensure:

    dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

    dimap (f . g) (h . i) ≡ dimap g h . dimap f i
    lmap (f . g) ≡ lmap g . lmap f
    rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

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

Map over both arguments at the same time.

    dimap f g ≡ lmap f . rmap g

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

Map the first argument contravariantly.

    lmap f ≡ dimap f id

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

Map the second argument covariantly.

    rmap ≡ dimap id

#### Instances

Instances details

Monad m => Profunctor (Kleisli m) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: forall a b c q. Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: forall a b c q. Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #
Profunctor (CopastroSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: forall a b c q. Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #
Profunctor (CotambaraSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: forall a b c q. Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #
Profunctor (PastroSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: forall a b c q. Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #
Profunctor p => Profunctor (TambaraSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: forall a b c q. Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: forall a b c q. Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #
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 (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 #
Profunctor p => Profunctor (CofreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> CofreeMapping p b c -> CofreeMapping p a d # lmap :: (a -> b) -> CofreeMapping p b c -> CofreeMapping p a c # rmap :: (b -> c) -> CofreeMapping p a b -> CofreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeMapping p a b -> CofreeMapping p a c # (.#) :: forall a b c q. Coercible b a => CofreeMapping p b c -> q a b -> CofreeMapping p a c #
Profunctor (FreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d # lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c # rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c # (.#) :: forall a b c q. Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c #
Profunctor (Copastro p) # |
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: forall a b c q. Coercible b a => Copastro p b c -> q a b -> Copastro p a c #
Profunctor (Cotambara p) # |
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: forall a b c q. Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #
Profunctor (Pastro p) # |
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Pastro p a b -> Pastro p a c # (.#) :: forall a b c q. Coercible b a => Pastro p b c -> q a b -> Pastro p a c #
Profunctor p => Profunctor (Tambara p) # |
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: forall a b c q. Coercible b a => Tambara p b c -> q a b -> Tambara p a c #
Profunctor p => Profunctor (CofreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d # lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c # rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c #
Profunctor (FreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d # lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c # rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c # (#.) :: forall a b c q. Coercible c b => q b c -> FreeTraversing p a b -> FreeTraversing p a c # (.#) :: forall a b c q. Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c #
Profunctor (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods dimap :: (a -> b) -> (c -> d) -> Coyoneda p b c -> Coyoneda p a d # lmap :: (a -> b) -> Coyoneda p b c -> Coyoneda p a c # rmap :: (b -> c) -> Coyoneda p a b -> Coyoneda p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Coyoneda p a b -> Coyoneda p a c # (.#) :: forall a b c q. Coercible b a => Coyoneda p b c -> q a b -> Coyoneda p a c #
Profunctor (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods dimap :: (a -> b) -> (c -> d) -> Yoneda p b c -> Yoneda p a d # lmap :: (a -> b) -> Yoneda p b c -> Yoneda p a c # rmap :: (b -> c) -> Yoneda p a b -> Yoneda p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Yoneda p a b -> Yoneda p a c # (.#) :: forall a b c q. Coercible b a => Yoneda p b c -> q a b -> Yoneda p a c #
Profunctor (Tagged :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d # lmap :: (a -> b) -> Tagged b c -> Tagged a c # rmap :: (b -> c) -> Tagged a b -> Tagged a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tagged a b -> Tagged a c # (.#) :: forall a b c q. Coercible b a => Tagged b c -> q a b -> Tagged a c #
Functor w => Profunctor (Cokleisli w) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: forall a b c q. Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #
Functor f => Profunctor (Costar f) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #
Profunctor (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #
Functor f => Profunctor (Star f) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #
Profunctor (->) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d # lmap :: (a -> b) -> (b -> c) -> a -> c # rmap :: (b -> c) -> (a -> b) -> a -> c # (#.) :: forall a b c q. Coercible c b => q b c -> (a -> b) -> a -> c # (.#) :: forall a b c q. Coercible b a => (b -> c) -> q a b -> a -> c #
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d # lmap :: (a -> b) -> Clown f b c -> Clown f a c # rmap :: (b -> c) -> Clown f a b -> Clown f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Clown f a b -> Clown f a c # (.#) :: forall a b c q. Coercible b a => Clown f b c -> q a b -> Clown f a c #
Functor f => Profunctor (Joker f :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d # lmap :: (a -> b) -> Joker f b c -> Joker f a c # rmap :: (b -> c) -> Joker f a b -> Joker f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Joker f a b -> Joker f a c # (.#) :: forall a b c q. Coercible b a => Joker f b c -> q a b -> Joker f a c #
Profunctor p => Profunctor (Codensity p) # |
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Codensity p b c -> Codensity p a d # lmap :: (a -> b) -> Codensity p b c -> Codensity p a c # rmap :: (b -> c) -> Codensity p a b -> Codensity p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Codensity p a b -> Codensity p a c # (.#) :: forall a b c q. Coercible b a => Codensity p b c -> q a b -> Codensity p a c #
Arrow p => Profunctor (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
(Profunctor p, Profunctor q) => Profunctor (Product p q) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: forall a b c q0. Coercible b a => Product p q b c -> q0 a b -> Product p q a c #
(Profunctor p, Profunctor q) => Profunctor (Sum p q) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d # lmap :: (a -> b) -> Sum p q b c -> Sum p q a c # rmap :: (b -> c) -> Sum p q a b -> Sum p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c # (.#) :: forall a b c q0. Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #
(Functor f, Profunctor p) => Profunctor (Tannen f p) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: forall a b c q. Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #
(Functor f, Profunctor p) => Profunctor (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d # lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c # rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c # (#.) :: forall a b c q. Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c # (.#) :: forall a b c q. Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c #
(Profunctor p, Profunctor q) => Profunctor (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d # lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c # rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c # (.#) :: forall a b c q0. Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #
(Profunctor p, Profunctor q) => Profunctor (Rift p q) # |
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d # lmap :: (a -> b) -> Rift p q b c -> Rift p q a c # rmap :: (b -> c) -> Rift p q a b -> Rift p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c # (.#) :: forall a b c q0. Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #
(Profunctor p, Profunctor q) => Profunctor (Ran p q) # |
Instance details Defined in Data.Profunctor.Ran Methods dimap :: (a -> b) -> (c -> d) -> Ran p q b c -> Ran p q a d # lmap :: (a -> b) -> Ran p q b c -> Ran p q a c # rmap :: (b -> c) -> Ran p q a b -> Ran p q a c # (#.) :: forall a b c q0. Coercible c b => q0 b c -> Ran p q a b -> Ran p q a c # (.#) :: forall a b c q0. Coercible b a => Ran p q b c -> q0 a b -> Ran p q a c #
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g) # |
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: forall a b c q. Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: forall a b c q. Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #

## Profunctorial Strength

class Profunctor p => Strong p where #

Generalizing `Star` of a strong `Functor`

Note: Every `Functor` in Haskell is strong with respect to `(,)`.

This describes profunctor strength with respect to the product structure of Hask.

http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf

Minimal complete definition

first' | second'

Methods

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

Laws:

    first' ≡ dimap swap swap . second'
    lmap fst ≡ rmap fst . first'
    lmap (second' f) . first' ≡ rmap (second' f) . first'
    first' . first' ≡ dimap assoc unassoc . first' where
      assoc ((a,b),c) = (a,(b,c))
      unassoc (a,(b,c)) = ((a,b),c)

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

Laws:

    second' ≡ dimap swap swap . first'
    lmap snd ≡ rmap snd . second'
    lmap (first' f) . second' ≡ rmap (first' f) . second'
    second' . second' ≡ dimap unassoc assoc . second' where
      assoc ((a,b),c) = (a,(b,c))
      unassoc (a,(b,c)) = ((a,b),c)

#### Instances

Instances details

Monad m => Strong (Kleisli m) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Kleisli m a b -> Kleisli m (a, c) (b, c) # second' :: Kleisli m a b -> Kleisli m (c, a) (c, 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 => Strong (CofreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods first' :: CofreeMapping p a b -> CofreeMapping p (a, c) (b, c) # second' :: CofreeMapping p a b -> CofreeMapping p (c, a) (c, b) #
Strong (FreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods first' :: FreeMapping p a b -> FreeMapping p (a, c) (b, c) # second' :: FreeMapping p a b -> FreeMapping p (c, a) (c, b) #
Strong (Pastro p) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Pastro p a b -> Pastro p (a, c) (b, c) # second' :: Pastro p a b -> Pastro p (c, a) (c, b) #
Profunctor p => Strong (Tambara p) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Tambara p a b -> Tambara p (a, c) (b, c) # second' :: Tambara p a b -> Tambara p (c, a) (c, b) #
Profunctor p => Strong (CofreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods first' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c) # second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b) #
Strong (FreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods first' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c) # second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b) #
Strong p => Strong (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods first' :: Coyoneda p a b -> Coyoneda p (a, c) (b, c) # second' :: Coyoneda p a b -> Coyoneda p (c, a) (c, b) #
Strong p => Strong (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods first' :: Yoneda p a b -> Yoneda p (a, c) (b, c) # second' :: Yoneda p a b -> Yoneda p (c, a) (c, b) #
Strong (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Forget r a b -> Forget r (a, c) (b, c) # second' :: Forget r a b -> Forget r (c, a) (c, b) #
Functor m => Strong (Star m) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Star m a b -> Star m (a, c) (b, c) # second' :: Star m a b -> Star m (c, a) (c, b) #
Strong (->) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: (a -> b) -> (a, c) -> (b, c) # second' :: (a -> b) -> (c, a) -> (c, b) #
Contravariant f => Strong (Clown f :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Clown f a b -> Clown f (a, c) (b, c) # second' :: Clown f a b -> Clown f (c, a) (c, b) #
Arrow p => Strong (WrappedArrow p) # | `Arrow` is `Strong` `Category`
Instance details Defined in Data.Profunctor.Strong Methods first' :: WrappedArrow p a b -> WrappedArrow p (a, c) (b, c) # second' :: WrappedArrow p a b -> WrappedArrow p (c, a) (c, b) #
(Strong p, Strong q) => Strong (Product p q) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Product p q a b -> Product p q (a, c) (b, c) # second' :: Product p q a b -> Product p q (c, a) (c, b) #
(Strong p, Strong q) => Strong (Sum p q) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Sum p q a b -> Sum p q (a, c) (b, c) # second' :: Sum p q a b -> Sum p q (c, a) (c, b) #
(Functor f, Strong p) => Strong (Tannen f p) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Tannen f p a b -> Tannen f p (a, c) (b, c) # second' :: Tannen f p a b -> Tannen f p (c, a) (c, b) #
(Functor f, Strong p) => Strong (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods first' :: Cayley f p a b -> Cayley f p (a, c) (b, c) # second' :: Cayley f p a b -> Cayley f p (c, a) (c, b) #
(Strong p, Strong q) => Strong (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods first' :: Procompose p q a b -> Procompose p q (a, c) (b, c) # second' :: Procompose p q a b -> Procompose p q (c, a) (c, b) #

uncurry' :: Strong p => p a (b -> c) -> p (a, b) c #

class Profunctor p => Choice p where #

The generalization of `Costar` of `Functor` that is strong with respect to `Either`.

Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.

Minimal complete definition

left' | right'

Methods

left' :: p a b -> p (Either a c) (Either b c) #

Laws:

    left' ≡ dimap swapE swapE . right' where
      swapE :: Either a b -> Either b a
      swapE = either Right Left
    rmap Left ≡ lmap Left . left'
    lmap (right f) . left' ≡ rmap (right f) . left'
    left' . left' ≡ dimap assocE unassocE . left' where
      assocE :: Either (Either a b) c -> Either a (Either b c)
      assocE (Left (Left a)) = Left a
      assocE (Left (Right b)) = Right (Left b)
      assocE (Right c) = Right (Right c)
      unassocE :: Either a (Either b c) -> Either (Either a b) c
      unassocE (Left a) = Left (Left a)
      unassocE (Right (Left b)) = Left (Right b)
      unassocE (Right (Right c)) = Right c

right' :: p a b -> p (Either c a) (Either c b) #

Laws:

    right' ≡ dimap swapE swapE . left' where
      swapE :: Either a b -> Either b a
      swapE = either Right Left
    rmap Right ≡ lmap Right . right'
    lmap (left f) . right' ≡ rmap (left f) . right'
    right' . right' ≡ dimap unassocE assocE . right' where
      assocE :: Either (Either a b) c -> Either a (Either b c)
      assocE (Left (Left a)) = Left a
      assocE (Left (Right b)) = Right (Left b)
      assocE (Right c) = Right (Right c)
      unassocE :: Either a (Either b c) -> Either (Either a b) c
      unassocE (Left a) = Left (Left a)
      unassocE (Right (Left b)) = Left (Right b)
      unassocE (Right (Right c)) = Right c

#### Instances

Instances details

Monad m => Choice (Kleisli m) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) # right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) #
Choice (PastroSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: PastroSum p a b -> PastroSum p (Either a c) (Either b c) # right' :: PastroSum p a b -> PastroSum p (Either c a) (Either c b) #
Profunctor p => Choice (TambaraSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: TambaraSum p a b -> TambaraSum p (Either a c) (Either b c) # right' :: TambaraSum p a b -> TambaraSum p (Either c a) (Either c b) #
Profunctor p => Choice (CofreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods left' :: CofreeMapping p a b -> CofreeMapping p (Either a c) (Either b c) # right' :: CofreeMapping p a b -> CofreeMapping p (Either c a) (Either c b) #
Choice (FreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods left' :: FreeMapping p a b -> FreeMapping p (Either a c) (Either b c) # right' :: FreeMapping p a b -> FreeMapping p (Either c a) (Either c b) #
Choice p => Choice (Tambara p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tambara p a b -> Tambara p (Either a c) (Either b c) # right' :: Tambara p a b -> Tambara p (Either c a) (Either c b) #
Profunctor p => Choice (CofreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods left' :: CofreeTraversing p a b -> CofreeTraversing p (Either a c) (Either b c) # right' :: CofreeTraversing p a b -> CofreeTraversing p (Either c a) (Either c b) #
Choice (FreeTraversing p) # |
Instance details Defined in Data.Profunctor.Traversing Methods left' :: FreeTraversing p a b -> FreeTraversing p (Either a c) (Either b c) # right' :: FreeTraversing p a b -> FreeTraversing p (Either c a) (Either c b) #
Choice p => Choice (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods left' :: Coyoneda p a b -> Coyoneda p (Either a c) (Either b c) # right' :: Coyoneda p a b -> Coyoneda p (Either c a) (Either c b) #
Choice p => Choice (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods left' :: Yoneda p a b -> Yoneda p (Either a c) (Either b c) # right' :: Yoneda p a b -> Yoneda p (Either c a) (Either c b) #
Choice (Tagged :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tagged a b -> Tagged (Either a c) (Either b c) # right' :: Tagged a b -> Tagged (Either c a) (Either c b) #
Comonad w => Choice (Cokleisli w) # | `extract` approximates `costrength`
Instance details Defined in Data.Profunctor.Choice Methods left' :: Cokleisli w a b -> Cokleisli w (Either a c) (Either b c) # right' :: Cokleisli w a b -> Cokleisli w (Either c a) (Either c b) #
Monoid r => Choice (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Applicative f => Choice (Star f) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Choice (->) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: (a -> b) -> Either a c -> Either b c # right' :: (a -> b) -> Either c a -> Either c b #
Functor f => Choice (Joker f :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Joker f a b -> Joker f (Either a c) (Either b c) # right' :: Joker f a b -> Joker f (Either c a) (Either c b) #
ArrowChoice p => Choice (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Product p q) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Product p q a b -> Product p q (Either a c) (Either b c) # right' :: Product p q a b -> Product p q (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Sum p q) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Sum p q a b -> Sum p q (Either a c) (Either b c) # right' :: Sum p q a b -> Sum p q (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Tannen f p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tannen f p a b -> Tannen f p (Either a c) (Either b c) # right' :: Tannen f p a b -> Tannen f p (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods left' :: Cayley f p a b -> Cayley f p (Either a c) (Either b c) # right' :: Cayley f p a b -> Cayley f p (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods left' :: Procompose p q a b -> Procompose p q (Either a c) (Either b c) # right' :: Procompose p q a b -> Procompose p q (Either c a) (Either c b) #

## Closed

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.

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) #

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

class (Traversing p, Closed p) => Mapping p where #

Minimal complete definition

Nothing

Methods

map' :: Functor f => p a b -> p (f a) (f b) #

Laws:

    map' . rmap f ≡ rmap (fmap f) . map'
    map' . map' ≡ dimap Compose getCompose . map'
    dimap Identity runIdentity . map' ≡ id

roam :: ((a -> b) -> s -> t) -> p a b -> p s t #

#### Instances

Instances details

(Monad m, Distributive m) => Mapping (Kleisli m) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Kleisli m a b -> Kleisli m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Kleisli m a b -> Kleisli m s t #
Profunctor p => Mapping (CofreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => CofreeMapping p a b -> CofreeMapping p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> CofreeMapping p a b -> CofreeMapping p s t #
Mapping (FreeMapping p) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => FreeMapping p a b -> FreeMapping p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> FreeMapping p a b -> FreeMapping p s t #
Mapping p => Mapping (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Coyoneda p a b -> Coyoneda p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Coyoneda p a b -> Coyoneda p s t #
Mapping p => Mapping (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods map' :: Functor f => Yoneda p a b -> Yoneda p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Yoneda p a b -> Yoneda p s t #
(Applicative m, Distributive m) => Mapping (Star m) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Star m a b -> Star m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Star m a b -> Star m s t #
Mapping (->) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => (a -> b) -> f a -> f b # roam :: ((a -> b) -> s -> t) -> (a -> b) -> s -> t #
(Functor f, Mapping p) => Mapping (Tannen f p) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f0 => Tannen f p a b -> Tannen f p (f0 a) (f0 b) # roam :: ((a -> b) -> s -> t) -> Tannen f p a b -> Tannen f p s t #
(Functor f, Mapping p) => Mapping (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods map' :: Functor f0 => Cayley f p a b -> Cayley f p (f0 a) (f0 b) # roam :: ((a -> b) -> s -> t) -> Cayley f p a b -> Cayley f p s t #
(Mapping p, Mapping q) => Mapping (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods map' :: Functor f => Procompose p q a b -> Procompose p q (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Procompose p q a b -> Procompose p q s t #

## Profunctorial Costrength

class Profunctor p => Costrong p where #

Analogous to `ArrowLoop`, `loop` = `unfirst`

Minimal complete definition

unfirst | unsecond

Methods

unfirst :: p (a, d) (b, d) -> p a b #

Laws:

    unfirst ≡ unsecond . dimap swap swap
    lmap (,()) ≡ unfirst . rmap (,())
    unfirst . lmap (second f) ≡ unfirst . rmap (second f)
    unfirst . unfirst = unfirst . dimap assoc unassoc where
      assoc ((a,b),c) = (a,(b,c))
      unassoc (a,(b,c)) = ((a,b),c)

unsecond :: p (d, a) (d, b) -> p a b #

Laws:

    unsecond ≡ unfirst . dimap swap swap
    lmap ((),) ≡ unsecond . rmap ((),)
    unsecond . lmap (first f) ≡ unsecond . rmap (first f)
    unsecond . unsecond = unsecond . dimap unassoc assoc where
      assoc ((a,b),c) = (a,(b,c))
      unassoc (a,(b,c)) = ((a,b),c)

#### Instances

Instances details

MonadFix m => Costrong (Kleisli m) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Kleisli m (a, d) (b, d) -> Kleisli m a b # unsecond :: Kleisli m (d, a) (d, b) -> Kleisli m a b #
Costrong (Copastro p) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Copastro p (a, d) (b, d) -> Copastro p a b # unsecond :: Copastro p (d, a) (d, b) -> Copastro p a b #
Costrong (Cotambara p) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Cotambara p (a, d) (b, d) -> Cotambara p a b # unsecond :: Cotambara p (d, a) (d, b) -> Cotambara p a b #
Costrong p => Costrong (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods unfirst :: Coyoneda p (a, d) (b, d) -> Coyoneda p a b # unsecond :: Coyoneda p (d, a) (d, b) -> Coyoneda p a b #
Costrong p => Costrong (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods unfirst :: Yoneda p (a, d) (b, d) -> Yoneda p a b # unsecond :: Yoneda p (d, a) (d, b) -> Yoneda p a b #
Costrong (Tagged :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Tagged (a, d) (b, d) -> Tagged a b # unsecond :: Tagged (d, a) (d, b) -> Tagged a b #
Functor f => Costrong (Cokleisli f) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Cokleisli f (a, d) (b, d) -> Cokleisli f a b # unsecond :: Cokleisli f (d, a) (d, b) -> Cokleisli f a b #
Functor f => Costrong (Costar f) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Costar f (a, d) (b, d) -> Costar f a b # unsecond :: Costar f (d, a) (d, b) -> Costar f a b #
Costrong (->) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: ((a, d) -> (b, d)) -> a -> b # unsecond :: ((d, a) -> (d, b)) -> a -> b #
ArrowLoop p => Costrong (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: WrappedArrow p (a, d) (b, d) -> WrappedArrow p a b # unsecond :: WrappedArrow p (d, a) (d, b) -> WrappedArrow p a b #
(Costrong p, Costrong q) => Costrong (Product p q) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Product p q (a, d) (b, d) -> Product p q a b # unsecond :: Product p q (d, a) (d, b) -> Product p q a b #
(Costrong p, Costrong q) => Costrong (Sum p q) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Sum p q (a, d) (b, d) -> Sum p q a b # unsecond :: Sum p q (d, a) (d, b) -> Sum p q a b #
(Functor f, Costrong p) => Costrong (Tannen f p) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Tannen f p (a, d) (b, d) -> Tannen f p a b # unsecond :: Tannen f p (d, a) (d, b) -> Tannen f p a b #
(Functor f, Costrong p) => Costrong (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods unfirst :: Cayley f p (a, d) (b, d) -> Cayley f p a b # unsecond :: Cayley f p (d, a) (d, b) -> Cayley f p a b #
(Corepresentable p, Corepresentable q) => Costrong (Procompose p q) # |
Instance details Defined in Data.Profunctor.Composition Methods unfirst :: Procompose p q (a, d) (b, d) -> Procompose p q a b # unsecond :: Procompose p q (d, a) (d, b) -> Procompose p q a b #

class Profunctor p => Cochoice p where #

Minimal complete definition

unleft | unright

Methods

unleft :: p (Either a d) (Either b d) -> p a b #

Laws:

    unleft ≡ unright . dimap swapE swapE where
      swapE :: Either a b -> Either b a
      swapE = either Right Left
    rmap (either id absurd) ≡ unleft . lmap (either id absurd)
    unfirst . rmap (second f) ≡ unfirst . lmap (second f)
    unleft . unleft ≡ unleft . dimap assocE unassocE where
      assocE :: Either (Either a b) c -> Either a (Either b c)
      assocE (Left (Left a)) = Left a
      assocE (Left (Right b)) = Right (Left b)
      assocE (Right c) = Right (Right c)
      unassocE :: Either a (Either b c) -> Either (Either a b) c
      unassocE (Left a) = Left (Left a)
      unassocE (Right (Left b)) = Left (Right b)
      unassocE (Right (Right c)) = Right c

unright :: p (Either d a) (Either d b) -> p a b #

Laws:

    unright ≡ unleft . dimap swapE swapE where
      swapE :: Either a b -> Either b a
      swapE = either Right Left
    rmap (either absurd id) ≡ unright . lmap (either absurd id)
    unsecond . rmap (first f) ≡ unsecond . lmap (first f)
    unright . unright ≡ unright . dimap unassocE assocE where
      assocE :: Either (Either a b) c -> Either a (Either b c)
      assocE (Left (Left a)) = Left a
      assocE (Left (Right b)) = Right (Left b)
      assocE (Right c) = Right (Right c)
      unassocE :: Either a (Either b c) -> Either (Either a b) c
      unassocE (Left a) = Left (Left a)
      unassocE (Right (Left b)) = Left (Right b)
      unassocE (Right (Right c)) = Right c

#### Instances

Instances details

Cochoice (CopastroSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: CopastroSum p (Either a d) (Either b d) -> CopastroSum p a b # unright :: CopastroSum p (Either d a) (Either d b) -> CopastroSum p a b #
Cochoice (CotambaraSum p) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: CotambaraSum p (Either a d) (Either b d) -> CotambaraSum p a b # unright :: CotambaraSum p (Either d a) (Either d b) -> CotambaraSum p a b #
Cochoice p => Cochoice (Coyoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods unleft :: Coyoneda p (Either a d) (Either b d) -> Coyoneda p a b # unright :: Coyoneda p (Either d a) (Either d b) -> Coyoneda p a b #
Cochoice p => Cochoice (Yoneda p) # |
Instance details Defined in Data.Profunctor.Yoneda Methods unleft :: Yoneda p (Either a d) (Either b d) -> Yoneda p a b # unright :: Yoneda p (Either d a) (Either d b) -> Yoneda p a b #
Applicative f => Cochoice (Costar f) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Costar f (Either a d) (Either b d) -> Costar f a b # unright :: Costar f (Either d a) (Either d b) -> Costar f a b #
Cochoice (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Forget r (Either a d) (Either b d) -> Forget r a b # unright :: Forget r (Either d a) (Either d b) -> Forget r a b #
Traversable f => Cochoice (Star f) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Star f (Either a d) (Either b d) -> Star f a b # unright :: Star f (Either d a) (Either d b) -> Star f a b #
Cochoice (->) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: (Either a d -> Either b d) -> a -> b # unright :: (Either d a -> Either d b) -> a -> b #
(Cochoice p, Cochoice q) => Cochoice (Product p q) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Product p q (Either a d) (Either b d) -> Product p q a b # unright :: Product p q (Either d a) (Either d b) -> Product p q a b #
(Cochoice p, Cochoice q) => Cochoice (Sum p q) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Sum p q (Either a d) (Either b d) -> Sum p q a b # unright :: Sum p q (Either d a) (Either d b) -> Sum p q a b #
(Functor f, Cochoice p) => Cochoice (Tannen f p) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Tannen f p (Either a d) (Either b d) -> Tannen f p a b # unright :: Tannen f p (Either d a) (Either d b) -> Tannen f p a b #
(Functor f, Cochoice p) => Cochoice (Cayley f p) # |
Instance details Defined in Data.Profunctor.Cayley Methods unleft :: Cayley f p (Either a d) (Either b d) -> Cayley f p a b # unright :: Cayley f p (Either d a) (Either d b) -> Cayley f p a b #

## Common Profunctors

newtype Star f d c #

Lift a `Functor` into a `Profunctor` (forwards).

`Star` has a polymorphic kind since `5.6`.

Constructors

Star |
Fields runStar :: d -> f c

#### Instances

Instances details

Monad f => Category (Star f :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k). Star f a a (.) :: forall (b :: k) (c :: k) (a :: k). Star f b c -> Star f a b -> Star f a c
Applicative f => Choice (Star f) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Traversable f => Cochoice (Star f) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Star f (Either a d) (Either b d) -> Star f a b # unright :: Star f (Either d a) (Either d b) -> Star f a 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) #
(Applicative m, Distributive m) => Mapping (Star m) # |
Instance details Defined in Data.Profunctor.Mapping Methods map' :: Functor f => Star m a b -> Star m (f a) (f b) # roam :: ((a -> b) -> s -> t) -> Star m a b -> Star m s t #
Functor f => Representable (Star f) # |
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (Star f) :: Type -> Type # Methods tabulate :: (d -> Rep (Star f) c) -> Star f d c #
Functor m => Strong (Star m) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Star m a b -> Star m (a, c) (b, c) # second' :: Star m a b -> Star m (c, a) (c, b) #
Applicative m => Traversing (Star m) # |
Instance details Defined in Data.Profunctor.Traversing Methods traverse' :: Traversable f => Star m a b -> Star m (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Star m a b -> Star m s t #
Functor f => Profunctor (Star f) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #
Functor f => Sieve (Star f) f # |
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: Star f a b -> a -> f b #
Contravariant f => Contravariant (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a' -> a0) -> Star f a a0 -> Star f a a' (>$) :: b -> Star f a b -> Star f a a0
Alternative f => Alternative (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods empty :: Star f a a0 (<|>) :: Star f a a0 -> Star f a a0 -> Star f a a0 some :: Star f a a0 -> Star f a [a0] many :: Star f a a0 -> Star f a [a0]
Applicative f => Applicative (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Star f a a0 (<*>) :: Star f a (a0 -> b) -> Star f a a0 -> Star f a b liftA2 :: (a0 -> b -> c) -> Star f a a0 -> Star f a b -> Star f a c (*>) :: Star f a a0 -> Star f a b -> Star f a b (<*) :: Star f a a0 -> Star f a b -> Star f a a0
Functor f => Functor (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Star f a a0 -> Star f a b # (<$) :: a0 -> Star f a b -> Star f a a0 #
Monad f => Monad (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Star f a a0 -> (a0 -> Star f a b) -> Star f a b (>>) :: Star f a a0 -> Star f a b -> Star f a b return :: a0 -> Star f a a0
MonadPlus f => MonadPlus (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods mzero :: Star f a a0 mplus :: Star f a a0 -> Star f a a0 -> Star f a a0
Distributive f => Distributive (Star f a) # |
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Star f a a0) -> Star f a (f0 a0) # collect :: Functor f0 => (a0 -> Star f a b) -> f0 a0 -> Star f a (f0 b) # distributeM :: Monad m => m (Star f a a0) -> Star f a (m a0) # collectM :: Monad m => (a0 -> Star f a b) -> m a0 -> Star f a (m b) #
type Rep (Star f) # |
Instance details Defined in Data.Profunctor.Rep type Rep (Star f) = f

newtype Costar f d c #

Lift a `Functor` into a `Profunctor` (backwards).

`Costar` has a polymorphic kind since `5.6`.

Constructors

Costar |
Fields runCostar :: f d -> c

#### Instances

Instances details

Applicative f => Cochoice (Costar f) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Costar f (Either a d) (Either b d) -> Costar f a b # unright :: Costar f (Either d a) (Either d b) -> Costar f a 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) #
Functor f => Corepresentable (Costar f) # |
Instance details Defined in Data.Profunctor.Rep Associated Types type Corep (Costar f) :: Type -> Type # Methods cotabulate :: (Corep (Costar f) d -> c) -> Costar f d c #
Functor f => Costrong (Costar f) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Costar f (a, d) (b, d) -> Costar f a b # unsecond :: Costar f (d, a) (d, b) -> Costar f a b #
Functor f => Profunctor (Costar f) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #
Functor f => Cosieve (Costar f) f # |
Instance details Defined in Data.Profunctor.Sieve Methods cosieve :: Costar f a b -> f a -> b #
Applicative (Costar f a) # |
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Costar f a a0 (<*>) :: Costar f a (a0 -> b) -> Costar f a a0 -> Costar f a b liftA2 :: (a0 -> b -> c) -> Costar f a a0 -> Costar f a b -> Costar f a c (*>) :: Costar f a a0 -> Costar f a b -> Costar f a b (<*) :: Costar f a a0 -> Costar f a b -> Costar f a a0
Functor (Costar f a) # |
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Costar f a a0 -> Costar f a b # (<$) :: a0 -> Costar f a b -> Costar f a a0 #
Monad (Costar f a) # |
Instance details Defined in Data.Profunctor.Types Methods (>>=) :: Costar f a a0 -> (a0 -> Costar f a b) -> Costar f a b (>>) :: Costar f a a0 -> Costar f a b -> Costar f a b return :: a0 -> Costar f a a0
Distributive (Costar f d) # |
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Costar f d a) -> Costar f d (f0 a) # collect :: Functor f0 => (a -> Costar f d b) -> f0 a -> Costar f d (f0 b) # distributeM :: Monad m => m (Costar f d a) -> Costar f d (m a) # collectM :: Monad m => (a -> Costar f d b) -> m a -> Costar f d (m b) #
type Corep (Costar f) # |
Instance details Defined in Data.Profunctor.Rep type Corep (Costar f) = f

newtype WrappedArrow p a b #

Wrap an arrow for use as a `Profunctor`.

`WrappedArrow` has a polymorphic kind since `5.6`.

Constructors

WrapArrow |
Fields unwrapArrow :: p a b

#### Instances

Instances details

Category p => Category (WrappedArrow p :: k -> k -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods id :: forall (a :: k0). WrappedArrow p a a (.) :: forall (b :: k0) (c :: k0) (a :: k0). WrappedArrow p b c -> WrappedArrow p a b -> WrappedArrow p a c
Arrow p => Arrow (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods arr :: (b -> c) -> WrappedArrow p b c first :: WrappedArrow p b c -> WrappedArrow p (b, d) (c, d) second :: WrappedArrow p b c -> WrappedArrow p (d, b) (d, c) (***) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (b, b') (c, c') (&&&) :: WrappedArrow p b c -> WrappedArrow p b c' -> WrappedArrow p b (c, c')
ArrowApply p => ArrowApply (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods app :: WrappedArrow p (WrappedArrow p b c, b) c
ArrowChoice p => ArrowChoice (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods left :: WrappedArrow p b c -> WrappedArrow p (Either b d) (Either c d) right :: WrappedArrow p b c -> WrappedArrow p (Either d b) (Either d c) (+++) :: WrappedArrow p b c -> WrappedArrow p b' c' -> WrappedArrow p (Either b b') (Either c c') (|||) :: WrappedArrow p b d -> WrappedArrow p c d -> WrappedArrow p (Either b c) d
ArrowLoop p => ArrowLoop (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods loop :: WrappedArrow p (b, d) (c, d) -> WrappedArrow p b c
ArrowZero p => ArrowZero (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods zeroArrow :: WrappedArrow p b c
ArrowChoice p => Choice (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #
ArrowLoop p => Costrong (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: WrappedArrow p (a, d) (b, d) -> WrappedArrow p a b # unsecond :: WrappedArrow p (d, a) (d, b) -> WrappedArrow p a b #
Arrow p => Strong (WrappedArrow p) # | `Arrow` is `Strong` `Category`
Instance details Defined in Data.Profunctor.Strong Methods first' :: WrappedArrow p a b -> WrappedArrow p (a, c) (b, c) # second' :: WrappedArrow p a b -> WrappedArrow p (c, a) (c, b) #
Arrow p => Profunctor (WrappedArrow p) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #

newtype Forget r a b #

`Forget` has a polymorphic kind since `5.6`.

Constructors

Forget |
Fields runForget :: a -> r

#### Instances

Instances details

Monoid r => Choice (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Cochoice (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Choice Methods unleft :: Forget r (Either a d) (Either b d) -> Forget r a b # unright :: Forget r (Either d a) (Either d b) -> Forget r a b #
Representable (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Rep Associated Types type Rep (Forget r) :: Type -> Type # Methods tabulate :: (d -> Rep (Forget r) c) -> Forget r d c #
Strong (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Strong Methods first' :: Forget r a b -> Forget r (a, c) (b, c) # second' :: Forget r a b -> Forget r (c, a) (c, b) #
Monoid m => Traversing (Forget m :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Traversing Methods traverse' :: Traversable f => Forget m a b -> Forget m (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> Forget m a b -> Forget m s t #
Profunctor (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #
Sieve (Forget r :: Type -> Type -> Type) (Const r :: Type -> Type) # |
Instance details Defined in Data.Profunctor.Sieve Methods sieve :: Forget r a b -> a -> Const r b #
Foldable (Forget r a :: Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods fold :: Monoid m => Forget r a m -> m foldMap :: Monoid m => (a0 -> m) -> Forget r a a0 -> m foldMap' :: Monoid m => (a0 -> m) -> Forget r a a0 -> m foldr :: (a0 -> b -> b) -> b -> Forget r a a0 -> b foldr' :: (a0 -> b -> b) -> b -> Forget r a a0 -> b foldl :: (b -> a0 -> b) -> b -> Forget r a a0 -> b foldl' :: (b -> a0 -> b) -> b -> Forget r a a0 -> b foldr1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 foldl1 :: (a0 -> a0 -> a0) -> Forget r a a0 -> a0 toList :: Forget r a a0 -> [a0] null :: Forget r a a0 -> Bool length :: Forget r a a0 -> Int elem :: Eq a0 => a0 -> Forget r a a0 -> Bool maximum :: Ord a0 => Forget r a a0 -> a0 minimum :: Ord a0 => Forget r a a0 -> a0 sum :: Num a0 => Forget r a a0 -> a0 product :: Num a0 => Forget r a a0 -> a0
Contravariant (Forget r a :: Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods contramap :: (a' -> a0) -> Forget r a a0 -> Forget r a a' (>$) :: b -> Forget r a b -> Forget r a a0
Traversable (Forget r a :: Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0)
Functor (Forget r a :: Type -> Type) # |
Instance details Defined in Data.Profunctor.Types Methods fmap :: (a0 -> b) -> Forget r a a0 -> Forget r a b # (<$) :: a0 -> Forget r a b -> Forget r a a0 #
Monoid r => Monoid (Forget r a b) # | Via `Monoid r => (a -> r)` Since: 5.6.2
Instance details Defined in Data.Profunctor.Types Methods mempty :: Forget r a b mappend :: Forget r a b -> Forget r a b -> Forget r a b mconcat :: [Forget r a b] -> Forget r a b
Semigroup r => Semigroup (Forget r a b) # | Via `Semigroup r => (a -> r)` Since: 5.6.2
Instance details Defined in Data.Profunctor.Types Methods (<>) :: Forget r a b -> Forget r a b -> Forget r a b sconcat :: NonEmpty (Forget r a b) -> Forget r a b stimes :: Integral b0 => b0 -> Forget r a b -> Forget r a b
type Rep (Forget r :: Type -> Type -> Type) # |
Instance details Defined in Data.Profunctor.Rep type Rep (Forget r :: Type -> Type -> Type) = Const r :: Type -> Type

type (:->) p q = forall a b. p a b -> q a b infixr 0 #

(`:->`) has a polymorphic kind since `5.6`.