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  1. module Data.Profunctor

    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/

  2. class Profunctor (p :: Type -> Type -> Type)

    profunctors Data.Profunctor

    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

  3. class (ProfunctorFunctor f, ProfunctorFunctor u) => ProfunctorAdjunction (f :: Type -> Type -> Type -> Type -> Type -> Type) (u :: Type -> Type -> Type -> Type -> Type -> Type) | f -> u, u -> f

    profunctors Data.Profunctor.Adjunction

    Laws: 

    unit . counit ≡ id
counit . unit ≡ id

  4. data PastroSum (p :: Type -> Type -> Type) a b

    profunctors Data.Profunctor.Choice

    PastroSum -| TambaraSum PastroSum freely constructs strength with respect to Either.

  5. PastroSum :: forall y z b (p :: Type -> Type -> Type) x a . (Either y z -> b) -> p x y -> (a -> Either x z) -> PastroSum p a b

    profunctors Data.Profunctor.Choice

    No documentation available.

  6. data Procompose (p :: k -> k1 -> Type) (q :: k2 -> k -> Type) (d :: k2) (c :: k1)

    profunctors Data.Profunctor.Composition

    Procompose p q is the Profunctor composition of the Profunctors p and q. For a good explanation of Profunctor composition in Haskell see Dan Piponi's article: http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html Procompose has a polymorphic kind since 5.6.

  7. class ProfunctorFunctor t => ProfunctorComonad (t :: Type -> Type -> Type -> Type -> Type -> Type)

    profunctors Data.Profunctor.Monad

    Laws: 

    proextract . promap f ≡ f . proextract
proextract . produplicate ≡ id
promap proextract . produplicate ≡ id
produplicate . produplicate ≡ promap produplicate . produplicate

  8. class ProfunctorFunctor (t :: Type -> Type -> Type -> k -> k1 -> Type)

    profunctors Data.Profunctor.Monad

    ProfunctorFunctor has a polymorphic kind since 5.6.

  9. class ProfunctorFunctor t => ProfunctorMonad (t :: Type -> Type -> Type -> Type -> Type -> Type)

    profunctors Data.Profunctor.Monad

    Laws: 

    promap f . proreturn ≡ proreturn . f
projoin . proreturn ≡ id
projoin . promap proreturn ≡ id
projoin . projoin ≡ projoin . promap projoin

  10. data Prep (p :: Type -> k -> Type) (a :: k)

    profunctors Data.Profunctor.Rep 

    Prep -| Star :: [Hask, Hask] -> Prof
    This gives rise to a monad in Prof, (Star.Prep), and a comonad in [Hask,Hask] (Prep.Star) Prep has a polymorphic kind since 5.6.

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