Re: [Haskell-cafe] Re: Numeric type classes

The sum function really only needs the argument list to be a monoid. And the same is true for the product function, but with 1 and * as the monoid operators. Sum and product are really the same function. :) I don't think Haskell really has the mechanisms for setting up an algebraic class hierarchy the right way. Consider some classes we might want to build: SemiGroup Monoid AbelianMonoid Group AbelianGroup SemiRing Ring ... The problem is that going from, say, AbelianMonoid to SemiRing you want to add a new Monoid (the multiplicative) to the class. So SemiRing is a subclass of Monoid in two different way, both for + and for *. I don't know of any nice way to express this is Haskell. -- Lennart On Sep 13, 2006, at 03:26 , ajb@spamcop.net wrote:

G'day all.

Quoting Jason Dagit :

...

I was making an embedded domain specific language for excel spreadsheet formulas recently and found that making my formula datatype an instance of Num had huge pay offs.

Just so you know, what we're talking about here is a way to make that even _more_ useful by dicing up Num.

...

I can even use things like Prelude.sum to add up cells.

Ah, but the sum function only needs 0 and (+), so it doesn't need the full power of Num. It'd be even _more_ useful if it worked on all data types which supported 0 and (+), but not necessarily (*):

sum :: (AdditiveAbelianMonoid a) => [a] -> a

product :: (MultiplicativeAbelianMonoid a) => [a] -> a

Those are bad typeclass names, but you get the idea.

Right now, to reuse sum, people have to come up with fake implementations for Num operations that simply don't make sense on their data type, like signum on Complex numbers.

...

All I really needed was to define Show and Num correctly, neither of which took much mental effort or coding tricks.

You also needed to derive Eq, which gives you, in your case, structural equality rather than semantic equality (which is probably undecidable for your DSL).

Cheers, Andrew Bromage _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe