Safe Haskell	Safe-Inferred
Language	Haskell2010

Control.Invertible.MonadArrow

Description

A symmetric version of the Kleisli monad transformer arrow. This admits three isomorphic MonadBijection types:

```
MonadArrow (<->) m a b
```
```
Bijection (MonadFunction m) a b
```
```
m a <-> m b
```

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

Synopsis

newtype MonadArrow (a :: Type -> Type -> Type) (m :: Type -> Type) b c = MonadArrow {
- runMonadArrow :: a (m b) (m c)
}
type MonadFunction = MonadArrow (->)
type MonadBijection (m :: Type -> Type) = MonadArrow (<->) m
type MonadBijection' (m :: Type -> Type) = Bijection (MonadFunction m)
type MonadBijection'' (m :: Type -> Type) a b = m a <-> m b
monadBijection :: forall (m :: Type -> Type) a b. MonadBijection' m a b <-> MonadBijection m a b
monadBijection' :: MonadBijection'' m a b <-> MonadBijection' m a b

Documentation

newtype MonadArrow (a :: Type -> Type -> Type) (m :: Type -> Type) b c Source #

Bidirectional Kleisli-like monad arrow transformer.

Constructors

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

Instances

Instances details

Category a => Category (MonadArrow a m :: Type -> Type -> Type) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods id :: MonadArrow a m a0 a0 # (.) :: MonadArrow a m b c -> MonadArrow a m a0 b -> MonadArrow a m a0 c #
Groupoid a => Groupoid (MonadArrow a m :: Type -> Type -> Type) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods inv :: MonadArrow a m a0 b -> MonadArrow a m b a0 Source #
Semigroupoid a => Semigroupoid (MonadArrow a m :: Type -> Type -> Type) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods o :: MonadArrow a m j k1 -> MonadArrow a m i j -> MonadArrow a m i k1 Source #
Monad m => Arrow (MonadArrow (<->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow 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 #
Instance details Defined in Control.Invertible.MonadArrow 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 #
Instance details Defined in Control.Invertible.MonadArrow 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 #
Instance details Defined in Control.Invertible.MonadArrow 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 => ArrowPlus (MonadArrow (<->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods (<+>) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b c -> MonadArrow (<->) m b c #
MonadPlus m => ArrowPlus (MonadArrow (->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods (<+>) :: MonadArrow (->) m b c -> MonadArrow (->) m b c -> MonadArrow (->) m b c #
MonadPlus m => ArrowZero (MonadArrow (<->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods zeroArrow :: MonadArrow (<->) m b c #
MonadPlus m => ArrowZero (MonadArrow (->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods zeroArrow :: MonadArrow (->) m b c #
(BiArrow a, Monad m) => BiArrow (MonadArrow a m) Source #
Instance details Defined in Control.Invertible.MonadArrow Methods (<->) :: (b -> c) -> (c -> b) -> MonadArrow a m b c Source # invert :: MonadArrow a m b c -> MonadArrow a m c b Source #
Monad m => BiArrow' (MonadArrow (<->) m) Source #
Instance details Defined in Control.Invertible.MonadArrow

type MonadFunction = MonadArrow (->) Source #

Specialization of MonadArrow to function arrows.

type MonadBijection (m :: Type -> Type) = MonadArrow (<->) m Source #

type MonadBijection' (m :: Type -> Type) = Bijection (MonadFunction m) Source #

type MonadBijection'' (m :: Type -> Type) a b = m a <-> m b Source #

monadBijection :: forall (m :: Type -> Type) a b. MonadBijection' m a b <-> MonadBijection m a b Source #

Convert between isomorphic representations of MonadBijections.

monadBijection' :: MonadBijection'' m a b <-> MonadBijection' m a b Source #

Convert between isomorphic representations of MonadBijections.