A divertimento on MonadPlus and nondeterminism

In the Haskell community, there is a controversy about what the laws of the MonadPlus type constructor class ought to be. We suggest that there is no single universal correct answer, however there is a universal method. Important classes of notions of finitary nondeterminism are captured by what we call monads of semigroups and monads of monoids, but also by monads of different specializations of semigroups and monoids. Some of these specializations of monads are exotic and amusing too.