# Laws for Monad and MonadPlus.

**Dylan Thurston
**
dpt@math.harvard.edu

*Tue, 13 Mar 2001 15:13:26 -0500*

On Tue, Mar 13, 2001 at 04:15:31PM -0330, Theodore Norvell wrote:
>* What about MonadPlus? By analogy with semirings, I came up with:
*>*
*>* Zero: mzero >>= k = mzero = p >>= (\x -> mzero)
*>* Identity: p `mplus` mzero = p = mzero `mplus` p
*>* Commutativity: p `mplus` q = q `mplus` p
*>* Right distributivity: (p `mplus` q) >>= k = (p >>= k) `mplus` (q >>= k)
*>* Left distributivity: p >>= (\x->j x `mplus` k x) = (p >>= j) `mplus` (p >== k)
*>* [provided x is not free in j or k]
*>*
*>* But commutativity does not hold for Maybe or [], left distributivity
*>* does not hold for Maybe and right distributivity does not hold for [],
*>* so these can't be right.
*
Incidentally, a Set monad seems to do better: it would satisfy all
these laws.
Best,
Dylan