MonadPlus

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

1 Which satisfies what?

2 Which rules?

3 What should be done?