Bringing back Monad Comprehensions (in style)

[Max Bolingbroke]

On 5 October 2010 15:41, George Giorgidze <giorgidze at gmail.com> wrote:
> One can also look at how recently introduced 'order by' and 'group by'
> constructs generalise to monad comprehensions. If that works, one could
> implement even more "stylish" monad comprehension notation.

They do: see the comments by MichaelAdams at
http://haskell.org/haskellwiki/Simonpj/Talk:ListComp. Last I checked,
the code there was slightly buggy but correct in spirit.

What *doesn't* generalise is the zip comprehensions extension:

[(x, y) | x <- xs | y <- ys] == zip xs ys

The required operator :: m a -> m b -> m (a, b) is that of the ZipList
applicative functor, not that of the standard applicative functor for
lists. Probably to generalise this you need a new typeclass like this
one (copied from my own library):

class Functor z => Zippable z where
    -- Naturality:
    --  fmap (first f)  (zip_ as bs) == zip_ (fmap f as) bs
    --  fmap (second f) (zip_ as bs) == zip_ as (fmap f bs)
    --
    -- Information preservation:
    --  fmap fst (zip_ as bs) == as
    --  fmap snd (zip_ as bs) == bs

    zip_ :: z a -> z b -> z (a, b)
    zip_ = zipWith_ (,)

    zipWith_ :: (a -> b -> c) -> z a -> z b -> z c
    zipWith_ f as bs = fmap (uncurry f) (zip_ as bs)

It probably needs some extra laws to say how it interacts with the
Monad operators.

>  * Do you think that it would be hard to integrate this extension into
>    current GHC codebase?

Pretty easy IMHO. The list comprehensions are already half-set up for
this job, and you should be able to reuse lots of the code that
handles the monad notation desugaring.

>  * Have you already thought about how to generalise 'order by' and 'group
>    by' to monad comprehensions?

See above.

>  * Have you already thought about how to address the original objections to
>    the monad comprehension notation?

I thought it was rejected because it caused newbies to get confusing
type error messages: they expected *list* error messages but got
errors mentioning a scary *Monad* thing. Personally I'm not sure how
to solve that, but if it's only available as an extension this won't
cause a problem.

Cheers,
Max