Proposal: Add concatMapM function (#2042)

[Yitzchak Gale]

I wrote:
>>>> perhaps nowadays the type ought to be:
>>>> concatMapM :: (Monad m, Traversable t) => (a -> m (t b)) -> t a -> m (t b)

apfelmus wrote:
>>> I don't think that works in such generality since that would imply...
> that every Traversable  would have to be a monad.

Ah, of course. Sorry, I wrote that in the wee hours of the morning.

Now I also understand Ross Patterson's answer - that a Monoid
structure could also be substituted for the Monad structure,
because concat generalizes both to join and to mappend.

> Since this is not always the case (really?)

Right. Given a tree of trees, there are many ways to paste
them together into a single tree, but all of those ways use
the actual tree structure, not just the fact that I can traverse
over trees.

You can't paste them together - but you can traverse them.
So I guess the corresponding concept for traversables is
that are composable over monads:

mapMapM :: (Traversable t, Traversable t', Monad m) =>
  (b -> m c) -> (a -> m (t b)) -> t' a -> m (t' (t c))
mapMapM f g = (>>= mapM (mapM f)) . mapM g

I don't immediately see any composability over
applicatives. Am I missing something obvious?

Thanks,
Yitz