My intention wasn't to add these laws, but to replace the existing
MonadPlus ones. (Adding new laws wouldn't help with the original ones being
invalid.) But you're right, the laws I proposed follow from Monad laws and
from
mzero >>= f = mzero
This single law is enough to ensure that any chain of operations containing
`mzero` "ends" at this point.
So the best solution seems to just remove the problematic
v >> mzero = mzero
2014-02-04 Dan Burton
I'm not sure what should be the proper solution. Perhaps to change the
laws to: return x >> mzero = mzero (v >> mzero) >>= f = (v >> mzero)` That is, if an expression ends with `mzero`, it behaves like `mzero`.
These laws are redundant with existing laws. The first:
return x >> z = z
Is true forall x and z, and can be proven by just the monad laws. The second:
(v >> mzero) >>= f = (v >> mzero)
Can be proven by the associativity of monadic operations:
(v >> mzero) >>= f = v >> (mzero >>= f)
And the other MonadPlus law already states that (mzero >>= f) = mzero. So I don't think any new laws are needed. I just think the (v >> mzero = mzero) law should be removed, or else a *lot* of instances of MonadPlus need to come with a disclaimer that they are not law-abiding.
-- Dan Burton