[NumericPrelude] GCD as monoid

[Henning Thielemann]

On Sun, 4 Jul 2010, Paul McJones wrote:

> Henning,
>
> I don't quite see where you're headed with this proposal. If the problem
> of units is complicating things, would it be useful to define a
> semigroup rather than a monoid?

I encountered that problem when writing some pointer arithmetic in a 
Writer monad/applicative functor. I used the Writer monad to maintain the 
required alignment, which is the GCD of the alignments of all atomic 
pointer accesses. A Writer monad uses the Monoid class for "writing to 
something", where in my case "writing" means updating the global 
alignment. In practice pointer alignments are always powers of two, but 
using GCD we could handle any strange alignment. Then I wanted to define a 
GCD Monoid generally, and encountered that Prelude's GCD does not work, 
since:

Prelude> gcd 0 (-1)
1