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 k2 k1 k1 k2 (Flip k1 k2)

Methods

bifmap :: (Flip k1 k2 :-> k) p q -> (k :-> k) (t p) (t q)

BifunctorFunctor k1 k2 k1 k2 (Product k1 k2 p)

Methods

bifmap :: (Product k1 k2 p :-> k) p q -> (k :-> k) (t p) (t q)

BifunctorFunctor k1 k2 k1 k2 (Sum k1 k2 p)

Methods

bifmap :: (Sum k1 k2 p :-> k) p q -> (k :-> k) (t p) (t q)

Functor f => BifunctorFunctor k1 k2 k1 k2 (Tannen * k1 k2 f)

Methods

bifmap :: (Tannen * k1 k2 f :-> k) p q -> (k :-> 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 k1 k2 (Sum k1 k2 p)

Methods

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

bibind :: (Sum k1 k2 p :-> k) p (t q) -> (Sum k1 k2 p :-> k) (t p) (t q)

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

(Functor f, Monad f) => BifunctorMonad k1 k2 (Tannen * k1 k2 f)

Methods

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

bibind :: (Tannen * k1 k2 f :-> k) p (t q) -> (Tannen * k1 k2 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 k1 k2 (Product k1 k2 p)

Methods

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

biextend :: (Product k1 k2 p :-> k) (t p) q -> (Product k1 k2 p :-> k) (t p) (t q)

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

Comonad f => BifunctorComonad k1 k2 (Tannen * k1 k2 f)

Methods

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

biextend :: (Tannen * k1 k2 f :-> k) (t p) q -> (Tannen * k1 k2 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