On Fri, Jun 08, 2007 at 07:24:09AM -0700, Alex Jacobson wrote:
> Dan Piponi wrote:
> >On 6/7/07, Alex Jacobson <[EMAIL PROTECTED]> 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
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