The MonadPlus class is defined like this:
class (Monad m) => MonadPlus m where mzero :: m a mplus :: m a -> m a -> m a
The precise set of rules that MonadPlus should obey is not agreed upon.
- Monoid — mplus and mzero form a monoid:
mplus mzero a = a mplus a mzero = a mplus (mplus a b) c = mplus a (mplus b c)
- Left Zero — mzero is a left zero for >>=:
mzero >>= k = mzero
- Left Distribution:
mplus a b >>= k = mplus (a >>= k) (b >>= k)
- Left Catch — this is rarely advocated, but Maybe and IO satisfy this as an alternative to Left Distribution.
mplus (return a) b = return a
Martin & Gibbons choose Monoid, Left Zero, and Left Distribution. This makes  a MonadPlus, but not Maybe or IO.