Data.Bifunctor.Functor

Documentation

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

Using parametricity as an approximation of a natural transformation in two arguments.

class BifunctorFunctor t where

Methods

bifmap :: (p :-> q) -> t p :-> t q

Instances

BifunctorFunctor (Flip :: (k1 -> k2 -> Type) -> k2 -> k1 -> Type)

Defined in Data.Bifunctor.Flip

Methods

bifmap :: forall (p :: k -> k -> Type) (q :: k -> k -> Type). (p :-> q) -> Flip p :-> Flip q

BifunctorFunctor (Product p :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Product

Methods

bifmap :: forall (p0 :: k -> k -> Type) (q :: k -> k -> Type). (p0 :-> q) -> Product p p0 :-> Product p q

BifunctorFunctor (Sum p :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Sum

Methods

bifmap :: forall (p0 :: k -> k -> Type) (q :: k -> k -> Type). (p0 :-> q) -> Sum p p0 :-> Sum p q

Functor f => BifunctorFunctor (Tannen f :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Tannen

Methods

bifmap :: forall (p :: k -> k -> Type) (q :: k -> k -> Type). (p :-> q) -> Tannen f p :-> Tannen f q

class BifunctorFunctor t => BifunctorMonad t where

Minimal complete definition

bireturn, (bibind | bijoin)

Methods

bireturn :: p :-> t p

bibind :: (p :-> t q) -> t p :-> t q

bijoin :: t (t p) :-> t p

Instances

BifunctorMonad (Sum p :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Sum

Methods

bireturn :: forall (p0 :: k -> k -> Type). p0 :-> Sum p p0

bibind :: forall (p0 :: k -> k -> Type) (q :: k -> k -> Type). (p0 :-> Sum p q) -> Sum p p0 :-> Sum p q

bijoin :: forall (p0 :: k -> k -> Type). Sum p (Sum p p0) :-> Sum p p0

(Functor f, Monad f) => BifunctorMonad (Tannen f :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Tannen

Methods

bireturn :: forall (p :: k -> k -> Type). p :-> Tannen f p

bibind :: forall (p :: k -> k -> Type) (q :: k -> k -> Type). (p :-> Tannen f q) -> Tannen f p :-> Tannen f q

bijoin :: forall (p :: k -> k -> Type). Tannen f (Tannen f p) :-> Tannen f p

biliftM :: BifunctorMonad t => (p :-> q) -> t p :-> t q

class BifunctorFunctor t => BifunctorComonad t where

Minimal complete definition

biextract, (biextend | biduplicate)

Methods

biextract :: t p :-> p

biextend :: (t p :-> q) -> t p :-> t q

biduplicate :: t p :-> t (t p)

Instances

BifunctorComonad (Product p :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Product

Methods

biextract :: forall (p0 :: k -> k -> Type). Product p p0 :-> p0

biextend :: forall (p0 :: k -> k -> Type) (q :: k -> k -> Type). (Product p p0 :-> q) -> Product p p0 :-> Product p q

biduplicate :: forall (p0 :: k -> k -> Type). Product p p0 :-> Product p (Product p p0)

Comonad f => BifunctorComonad (Tannen f :: (k1 -> k2 -> Type) -> k1 -> k2 -> Type)

Defined in Data.Bifunctor.Tannen

Methods

biextract :: forall (p :: k -> k -> Type). Tannen f p :-> p

biextend :: forall (p :: k -> k -> Type) (q :: k -> k -> Type). (Tannen f p :-> q) -> Tannen f p :-> Tannen f q

biduplicate :: forall (p :: k -> k -> Type). Tannen f p :-> Tannen f (Tannen f p)

biliftW :: BifunctorComonad t => (p :-> q) -> t p :-> t q