[Haskell-cafe] Alternative versus Monoid

[Brent Yorgey]

On Thu, Dec 15, 2011 at 09:05:13PM +0000, Conor McBride wrote:
> 
> On 15 Dec 2011, at 15:19, Brent Yorgey wrote:
> 
> >On Thu, Dec 15, 2011 at 06:49:13PM +1000, Gregory Crosswhite wrote:
> >>
> >>So at the end of the day... what is the point of even making
> >>Maybe and [] instances of Alternative?
> >
> >The Alternative and Monoid instances for [] are equivalent.  However,
> >the Alternative and Monoid instances for Maybe are not. To wit:
> >
> >>(Just (Sum  4)) <|> (Just (Sum 3))
> > Just (Sum {getSum = 4})
> >
> >>(Just (Sum 4)) `mappend` (Just (Sum 3))
> > Just (Sum {getSum = 7})
> 
> The current monoid instance for Maybe is, in my view, unfortunate.
> 
> Types are about semantic purpose, not just data representation.
> Many purposes can be represented in the same way. We should identify
> the purpose of a type (or type constructor), then define instances
> consistent with that purpose. And better, we acquire by instance
> inference compound instances consistent with that purpose! (A similar
> view is often articulated well by Conal Elliott. But perhaps it's
> just a "Con" thing.)
> 
> The purpose of Maybe, it seems to me, is to model failure and
> prioritized choice, after the manner of exceptions. It's clear
> what the failure-and-prioritized-choice monoid is.
> 
> It so happens that the same data representation can be used to make
> a semigroup into a monoid by attaching an identity element. That's
> a different semantic purpose, which deserves a different type.

I agree.  Moreover, the current Monoid instance for (Maybe a) does not
even achieve this, since it requires a *Monoid* instance on a, rather
than a semigroup.  

Note that the 'semigroups' package defines an 'Option' type which does
lift Semigroup instances to Monoid instances.  I, for one, would be
quite in favor of changing the current Monoid (Maybe a) instance to
correspond to the failure-and-prioritized-choice semantics (i.e. the
semantics currently given to the 'First' wrapper).

-Brent