On Fri, Jun 08, 2007 at 07:24:09AM -0700, Alex Jacobson wrote:

Dan Piponi wrote:

...

On 6/7/07, Alex Jacobson wrote:

...

Is there a standard class that looks something like this:

class (Monoid m) => MonoidBreak m where mbreak::a->m a->(m a,m a)

I think you have some kind of kind issue going on here. If m is a Monoid I'm not sure what m a means. Looks like you're trying to factor elements of monoids in some way. Maybe you mean

class (Monoid m) => MonoidBreak m where mbreak::a->m->(m,m)

Though I'm not sure what the relationship between m and a is intended to be.

Ok how about this class:

class (Monoid m) => MonoidBreak m where mbreak::m->m->m

And the condition is

mappend (mbreak y z) y == z

Consider baz x = mbreak x mempty now: baz x `mappend` x = mappend (mbreak x mempty) x = mempty Thus, baz is a left-inverse operator, and (m, mappend, mempty, baz) forms a group. Going the other way using a hypothetical Group class: instance Group m => MonoidBreak m where mbreak n p = p `mappend` negate n satisfies your law. Stefan