What would happen if this was the definition?
instance MonadPlus [] where mzero = [] mplus a b
| a == [] = b | otherwise = a
Isn't the above a monoid as well?
Yes.
Is there only on correct definition of a monad/monoid on lists - or does anything that satisfies the monad laws count? I got the impression you could define anthing you liked for mzero and mplus - providing the laws are upheld?
I'm not arguing that definition would be "wrong". It is a monoid. This is the instance for (): instance MonadPlus() where mzero = () mplus a b = () And this would be "correct" too: instance MonadPlus Maybe where mzero = Nothing mplus a b = Nothing instance MonadPlus [] where mzero = [] mplus a b = [] Which are not really useful. I'm claiming that the fact that Maybe is a trivial Monoid doesn't mean we should "dumb" down other instances, like the one on lists. The usual definition of Monoid on lists is [] as identity and ++ as the monoid operation. That is how it's defined in class monoid, and I expect this relation to hold: instance MonadPlus m => Monoid (m a) where mempty = mzero mappend = mplus
Then, I'd say you're not thinking of monadic sums, but of catching errors, and the appropriate place for that is the class MonadError.
I am thinking about how some monads are summed - like Maybe and the Parser monad.
But, this is not how monadic parsers are summed. Just look into the instace of MonadError for Text.ParserCombinators.ReadP.P. Again it would be the case for parsers that would return just one possible parsing, but not for parsers that return [(a,String)]. J.A.