[Haskell] MonadPlus

[Jan-Willem Maessen]

On Apr 30, 2005, at 9:51 AM, Jacques Carette wrote:

> Ashley Yakeley <ashley at semantic.org> wrote:
>> I've added a bit more to <http://haskell.org/hawiki/MonadPlus>.
>> I highly recommend people read it before they start claiming in 
>> papers that such-and-such a type "may thus be an instance of 
>> MonadPlus".
>
> Very nice.
>
> One of the problems I have encountered with MonadPlus is that too many 
> people try to force it to be a Monoid, when it doesn't always want to 
> be.  Your suggestion of separating out the identity operation from the 
> binary operation makes it much clearer that these various Monads are 
> actually instances of Magma(s)
> http://en.wikipedia.org/wiki/Magma_%28algebra%29
> than necessarily a Monoid.

And the binary operation in a Magma has *no* properties.  My feeling is 
that there MonadPlus must have *some* set of properties in order to be 
useful---otherwise it's just an ad-hoc mechanism to call a pile of 
different binary operations "mplus".  I think most people would agree 
that's undesiriable, and the only confusion is which properties must 
hold.

I claim "monoid" is a point of agreement, at least.

>  On the above Wikipedia article, there is a useful ontology of 
> identities that can be useful to describe various Magmas.

And points up the sheer complexity of the hierarchy that would result 
if we tried to slice it into minimal orthogonal pieces (even if we 
immediately reject, say, division as uninteresting).

The focus must be on identifying the properties that really matter, 
encoding those, and rejecting those which merely add unnecessary 
complexity.

>
> Jacques
>
> PS: your discussion of the laws of MonadPlus reinforces to me the real 
> need for being able to declare the laws that a typeclass should 
> satisfy, not just the signature.

On this I cannot but agree.  But we don't usually count on being able 
to prove these by construction.

-Jan-Willem Maessen