FunctorM

[Ashley Yakeley]

In article <20040528001157.GA1924 at momenergy.repetae.net>,
 John Meacham <john at repetae.net> wrote:

> class FunctorM f where
>     fmapM :: Monad m => (a -> m b) -> f a -> m (f b)

I have an equivalent (I think) class in HBase in its big library of 
Functor classes:

    class (Functor f) =>
     ExtractableFunctor f where
    {
        fextract :: forall g a. (FunctorApplyReturn g) =>
            f (g a) -> g (f a);
    };

    for :: (ExtractableFunctor f,FunctorApplyReturn m) =>
     (a -> m b) -> (f a -> m (f b));
    for foo fa = fextract (fmap foo fa);

The important thing here is that a FunctorApplyReturn is more general 
than Monad, it has only return and "fapply :: f (a -> b) -> f a -> f b".

Given this, it's also possible to write this function (by using a state 
monad):

    ftolist :: (ExtractableFunctor f) => f a -> [a]

The main Functor classes in HBase are arranged like this:

    Functor <= FunctorApply <= FunctorApplyReturn <= Monad

Doubtless if I knew a little more category theory, I'd have better names 
for them. It would be nice if the standard libraries adopted a 
superclass arrangement like this...

-- 
Ashley Yakeley, Seattle WA