[Haskell-cafe] Type arithmetic with ATs/TFs

[Andrew Coppin]

Robert Greayer wrote:
> What Ryan said, and here's an example of addition with ATs,
> specifically (not thoroughly tested, but tested a little).  The
> translation to TFs sans ATs is straightforward.
>
> class Add a b where
>     type SumType a b
>
> instance Add Zero Zero where
>     type SumType Zero Zero = Zero
>
> instance Add (Succ a) Zero where
>     type SumType (Succ a) Zero = Succ a
>
> instance Add Zero (Succ a) where
>     type SumType Zero (Succ a) = Succ a
>
> instance Add (Succ a) (Succ b) where
>     type SumType (Succ a) (Succ b) = Succ (Succ (SumType a b))
>   

I'm pretty sure this is almost exactly what I wrote in the first place, 
and it didn't work. I'll try again and see if I get anywhere...