Portability | portable |
---|---|

Stability | experimental |

This module provides Arrow-like monad composition for monadLib. To be more precise, it is Category-like,
i.e. the parallels are to `Control.Category.Category`

.

`Control.Category.Category`

generalises `.`

and `id`

to arrows and categories. One such arrow is `Kleisli`

,
which represents functions returning monadic values. Incidentally, that's equivalent to `ReaderT`

! So it
turns out that it is possible to generalise `.`

and `id`

to `ReaderT`

(`id`

is just `ask`

), as well as to
many monad transformer stacks that embed a `ReaderT`

inside.

The motivation to create this module was a nagging feeling when reading the documentation for `hxt`

and `HaXml`

:
composing filters is very nice, but the abundance of constant arrows, and the lack of access to the very extensive
set of monad combinators, leads to duplicated effort and unwieldy code (in my humble opinion). I think it is
possible to gain similar functionality with a stack of monad transformers including `ReaderT`

, and `ComposeM`

,
presented here.

- mid :: ReaderM m s => m s
- class (Monad m, Monad n) => ComposeM m n s t | m -> s, n -> t, n s -> m where
- (<<<) :: ComposeM m n s t => m a -> n s -> n a
- (>>>) :: ComposeM m n s t => n s -> m a -> n a
- derive_mcompose :: ComposeM m n s t => Iso m o -> Iso n p -> o a -> p s -> p a
- derive_mapply :: ComposeM m n s t => Iso m o -> Iso n p -> o a -> s -> p a

# Documentation

class (Monad m, Monad n) => ComposeM m n s t | m -> s, n -> t, n s -> m whereSource

Composable monads. Compare with `Control.Category.Category`

.
Note that there are two different monad types involved in each instance.

mcompose :: m a -> n s -> n aSource

Compose two monadic values from right to left. `mcompose f g`

is
comparable to `f . g`

but for monadic values. Compare with `Control.Category..`

.

mapply :: m a -> s -> n aSource

Apply a constant value to a composable monad.

ComposeM ((->) s) ((->) t) s t | |

ComposeM (Reader s) (Reader t) s t | |

ComposeM m n s t => ComposeM (IdT m) (IdT n) s t | |

ComposeM m n s t => ComposeM (ChoiceT m) (ChoiceT n) s t | |

Monad m => ComposeM (ReaderT s m) (ReaderT t m) s t | |

(ComposeM m n s t, Monoid w) => ComposeM (WriterT w m) (WriterT w n) s t | |

ComposeM m n s t => ComposeM (StateT i m) (StateT i n) s t | |

ComposeM m n s t => ComposeM (ExceptionT e m) (ExceptionT e n) s t |

(<<<) :: ComposeM m n s t => m a -> n s -> n aSource

Compose two monadic values from right to left. Compare with `Control.Category.<<<`

.
`f <<< g`

is equivalent to `mcompose f g`

.

(>>>) :: ComposeM m n s t => n s -> m a -> n aSource

Compose two monadic values from left to right. Compare with `Control.Category.>>>`

.
`g >>> f`

is equivalent to `mcompose f g`

.

derive_mcompose :: ComposeM m n s t => Iso m o -> Iso n p -> o a -> p s -> p aSource

derive_mapply :: ComposeM m n s t => Iso m o -> Iso n p -> o a -> s -> p aSource