MonadLib.Compose

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.

Documentation

mid :: ReaderM m s => m s

Alias for ask. Compare with Control.Category.id.

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

Composable monads. Compare with Control.Category.Category. Note that there are two different monad types involved in each instance.

Methods

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

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 a

Apply a constant value to a composable monad.

Instances

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 a

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 a

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 a

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