On Sat, Jun 25, 2011 at 2:02 PM, Brent Yorgey
Actually, there are (at least) four: there's also the one where mappend = liftA2 mappend, i.e. introduce potential failure into a monoid operation defined on the values. I wrote about it here:
Just out of curiosity, what was the problem that wanted this kind of monoid for the solution? I always find concrete examples useful in addition to the abstract explorations and toy examples. It's Map not Maybe, but in my case, I have "damage", which is user-modified data that will have to be recomputed. Given a Map from IDs to damage ranges, mappending two bits of damage means the ranges (themselves monoids of course) also have to be mappended. The case for not lifting is that elsewhere, during said recomputation, I accumulate some intermediate results for display. It's actually a bug if two results share the same ID, but in any case it wouldn't make sense to merge them, and the value type isn't in monoid.