Why MonadPlus and not Monad + Monoid?

Question

I\'m trying to understand the motivation behind the MonadPlus. Why is it necessary if there are already the typeclasses Monad and Monoid

Answer 1

Your guard' does not match your Monoid m a type.

If you mean Monoid (m a), then you need to define what mempty is for m (). Once you've done that, you've defined a MonadPlus.

In other words, MonadPlus defines two opeartions: mzero and mplus satisfying two rules: mzero is neutral with respect to mplus, and mplus is associative. This satisfies the definition of a Monoid so that mzero is mempty and mplus is mappend.

The difference is that MonadPlus m is a monoid m a for any a, but Monoid m defines a monoid only for m. Your guard' works because you only needed m to be a Monoid only for (). But MonadPlus is stronger, it claims m a to be a monoid for any a.