Safe Haskell	Safe
Language	Haskell2010

Control.Invertible.MonadArrow

Description

A symmetric version of the Kleisli monad transformer arrow. BiKleisli provides this Kleisli-like arrow over bijections.

The Alimarine paper just calls it "MoT" for Monad Transformer.

Synopsis

Documentation

newtype MonadArrow a m b c Source #

Bidirectional Kleisli-like monad arrow transformer.

Constructors

MonadArrow
Fields runMonadArrow :: a (m b) (m c)

Instances

Category * a => Category * (MonadArrow a m) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
Groupoid * a => Groupoid * (MonadArrow a m) Source #
Methods inv :: k1 a b -> k1 b a #
Semigroupoid * a => Semigroupoid * (MonadArrow a m) Source #
Methods o :: c j k1 -> c i j -> c i k1 #
Monad m => Arrow (MonadArrow (->) m) Source #
Methods arr :: (b -> c) -> MonadArrow (->) m b c # first :: MonadArrow (->) m b c -> MonadArrow (->) m (b, d) (c, d) # second :: MonadArrow (->) m b c -> MonadArrow (->) m (d, b) (d, c) # (***) :: MonadArrow (->) m b c -> MonadArrow (->) m b' c' -> MonadArrow (->) m (b, b') (c, c') # (&&&) :: MonadArrow (->) m b c -> MonadArrow (->) m b c' -> MonadArrow (->) m b (c, c') #
Monad m => Arrow (MonadArrow (<->) m) Source #
Methods arr :: (b -> c) -> MonadArrow (<->) m b c # first :: MonadArrow (<->) m b c -> MonadArrow (<->) m (b, d) (c, d) # second :: MonadArrow (<->) m b c -> MonadArrow (<->) m (d, b) (d, c) # (***) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b' c' -> MonadArrow (<->) m (b, b') (c, c') # (&&&) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b c' -> MonadArrow (<->) m b (c, c') #
Monad m => ArrowChoice (MonadArrow (->) m) Source #
Methods left :: MonadArrow (->) m b c -> MonadArrow (->) m (Either b d) (Either c d) # right :: MonadArrow (->) m b c -> MonadArrow (->) m (Either d b) (Either d c) # (+++) :: MonadArrow (->) m b c -> MonadArrow (->) m b' c' -> MonadArrow (->) m (Either b b') (Either c c') # (\|\|\|) :: MonadArrow (->) m b d -> MonadArrow (->) m c d -> MonadArrow (->) m (Either b c) d #
Monad m => ArrowChoice (MonadArrow (<->) m) Source #
Methods left :: MonadArrow (<->) m b c -> MonadArrow (<->) m (Either b d) (Either c d) # right :: MonadArrow (<->) m b c -> MonadArrow (<->) m (Either d b) (Either d c) # (+++) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b' c' -> MonadArrow (<->) m (Either b b') (Either c c') # (\|\|\|) :: MonadArrow (<->) m b d -> MonadArrow (<->) m c d -> MonadArrow (<->) m (Either b c) d #
MonadPlus m => ArrowZero (MonadArrow (->) m) Source #
Methods zeroArrow :: MonadArrow (->) m b c #
MonadPlus m => ArrowZero (MonadArrow (<->) m) Source #
Methods zeroArrow :: MonadArrow (<->) m b c #
MonadPlus m => ArrowPlus (MonadArrow (->) m) Source #
Methods (<+>) :: MonadArrow (->) m b c -> MonadArrow (->) m b c -> MonadArrow (->) m b c #
MonadPlus m => ArrowPlus (MonadArrow (<->) m) Source #
Methods (<+>) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b c -> MonadArrow (<->) m b c #
Monad m => BiArrow' (MonadArrow (<->) m) Source #

(BiArrow a, Monad m) => BiArrow (MonadArrow a m) Source #
Methods (<->) :: (b -> c) -> (c -> b) -> MonadArrow a m b c Source # invert :: MonadArrow a m b c -> MonadArrow a m c b Source #

type BiKleisli m a b = MonadArrow (<->) m a b Source #

A MonadArrow over bijections.