Re: Laws for Monads with zero and plus

[Philip Wadler]

For sets and bags we have

        zero >>= k              =  zero
        m >>= \x -> zero        =  zero
        (m ++ n) >>= k          =  m >>= k ++ n >>= k
        m >>= \x -> k x ++ h x  =  m >>= k ++ n >>= k.

But the fourth law does not hold for lists, and the second law does
not hold if we consider the case where m is bottom.  I would usually
insist on at least the first and third laws for monad zero and plus,
and in addition that they form a monoid.  -- P