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

Minimal complete definition

bifmap

Methods

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

Instances

BifunctorFunctor k1 k k k1 (Flip k k1)

Methods

bifmap :: (k :-> k) p q -> (Flip k k1 :-> k) (t p) (t q)

BifunctorFunctor k k1 k k1 (Sum k k1 p)

Methods

bifmap :: (k :-> k) p q -> (Sum k k1 p :-> k) (t p) (t q)

BifunctorFunctor k k1 k k1 (Product k k1 p)

Methods

bifmap :: (k :-> k) p q -> (Product k k1 p :-> k) (t p) (t q)

Functor f => BifunctorFunctor k k1 k k1 (Tannen k k1 * f)

Methods

bifmap :: (k :-> k) p q -> (Tannen k k1 * f :-> k) (t p) (t 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 k k1 (Sum k k1 p)

Methods

bireturn :: p a b -> t p a b

bibind :: (Sum k k1 p :-> k) p (t q) -> (Sum k k1 p :-> k) (t p) (t q)

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

(Functor f, Monad f) => BifunctorMonad k k1 (Tannen k k1 * f)

Methods

bireturn :: p a b -> t p a b

bibind :: (Tannen k k1 * f :-> k) p (t q) -> (Tannen k k1 * f :-> k) (t p) (t q)

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

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 k k1 (Product k k1 p)

Methods

biextract :: t p a b -> p a b

biextend :: (Product k k1 p :-> k) (t p) q -> (Product k k1 p :-> k) (t p) (t q)

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

Comonad f => BifunctorComonad k k1 (Tannen k k1 * f)

Methods

biextract :: t p a b -> p a b

biextend :: (Tannen k k1 * f :-> k) (t p) q -> (Tannen k k1 * f :-> k) (t p) (t q)

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

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