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 k k k k (Flip k k)

Methods

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

BifunctorFunctor k k k k (Sum k k p)

Methods

bifmap :: (k :-> k) a q -> (k :-> k) (Sum k k p a) (Sum k k p q)

BifunctorFunctor k k k k (Product k k p)

Methods

bifmap :: (k :-> k) a q -> (k :-> k) (Product k k p a) (Product k k p q)

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

Methods

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

Methods

bireturn :: a b c -> Sum k k p a b c

bibind :: (k :-> k) a (Sum k k p q) -> (k :-> k) (Sum k k p a) (Sum k k p q)

bijoin :: Sum k k p (Sum k k p a) b c -> Sum k k p a b c

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

Methods

bireturn :: p a b -> Tannen * k k f p a b

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

bijoin :: Tannen * k k f (Tannen * k k f p) a b -> Tannen * k k f 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 k (Product k k p)

Methods

biextract :: Product k k p a b c -> a b c

biextend :: (k :-> k) (Product k k p a) q -> (k :-> k) (Product k k p a) (Product k k p q)

biduplicate :: Product k k p a b c -> Product k k p (Product k k p a) b c

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

Methods

biextract :: Tannen * k k f p a b -> p a b

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

biduplicate :: Tannen * k k f p a b -> Tannen * k k f (Tannen * k k f p) a b

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