Conor McBride
I've always been a little bothered by the MonadPlus class: zero and plus are associated (no pun intended) in my mind with monoidal structure. Is there more to MonadPlus than a clumsy workaround for the lack of quantified constraints?
Yes. For every functor m with a MonadPlus instance, m () has /two/ monoids, (mzero, mplus) and (return (), (>>)). MonadPlus is thus no more a workaround than the category Field; MonadPlus is simply a way to specify that a functor has two monoid-like structures, one more exact than the other, together with the expectation that the two monoids are related in a manner similar to the relationship of the two (more-or-less-) groups that make up a field.
If we could have quantified constraints, e.g.
(Monad m, forall x. Monoid (m x))
wouldn't that be better than having Monad-specific monoids?
No. Consider the monad Writer (IO ()). The Writer monad wants a Monoid instance, and the most natural such instance is often (return (), (>>)). OTOH, this monad is always wrong in the cases where, currently, you would use mplus. So you can't just replace MonadPlus with Monoid; you need to be more specific about your choice of monoid than can be accounted for by a single class. <snip> Jon Cast