Algebra.Arrow

Documentation

module Algebra.Monad

class (Split k, Choice k) => Arrow k where

Methods

arr :: (a -> b) -> k a b

Instances

Arrow (->)

Monad m => Arrow (Kleisli m)

Monad m => Arrow (StateA m)

Arrow k => Arrow (ListA k)

(>>^) :: Functor f => f a -> (a -> b) -> f b infixr 4

(^>>) :: Cofunctor (Flip f c) => (a -> b) -> f b c -> f a c infixr 4

class Arrow k => Apply k where

Methods

apply :: k (k a b, a) b

Instances

Apply (->)

Monad m => Apply (Kleisli m)

comapA :: Arrow arr => (a -> b) -> Flip arr c b -> Flip arr c a

app :: Apply k => k a b -> k a b

dup :: Arrow arr => arr a (a, a)

newtype Kleisli m a b

Constructors

Kleisli

Fields

runKleisli :: a -> m b

Instances

Monad m => Split (Kleisli m)

Monad m => Choice (Kleisli m)

Monad m => Category (Kleisli m)

Monad m => Deductive (Kleisli m)

Monad m => Apply (Kleisli m)

Monad m => Arrow (Kleisli m)

Functor f => Functor (Kleisli f a)

Contravariant f => Contravariant (Kleisli f a)

Isomorphic (a -> m b) (c -> m' d) (Kleisli m a b) (Kleisli m' c d)

newtype ListA k a b

Constructors

ListA

Fields

runListA :: k [a] [b]

Instances

Arrow k => Split (ListA k)

Arrow k => Choice (ListA k)

Category k => Category (ListA k)

Deductive k => Deductive (ListA k)

Arrow k => Arrow (ListA k)