On Wed, Feb 14, 2001 at 08:10:39AM -0800, Andrew Kennedy wrote:
To be frank, the poster that you cite doesn't know what he's talking about. He makes two elementary mistakes:
Quite right, I didn't know what I was talking about. I still don't. But I do hope to learn.
(a) attempting to encode dimension/unit checking in an existing type system;
We're probably thinking about different contexts, but please see the attached file (below) for a partial solution. I used Hugs' dependent types to get type inference. This makes me uneasy, because I know that Hugs' instance checking is, in general, not decidable; I don't know if the fragment I use is decidable. You can remove the dependent types, but then you need to type all the results, etc., explicitly. This version doesn't handle negative exponents; perhaps what you say here:
As others have pointed out, (a) doesn't work because the algebra of units of measure is not free - units form an Abelian group (if integer exponents are used) or a vector space over the rationals (if rational exponents are used) and so it's not possible to do unit-checking by equality-on-syntax or unit-inference by ordinary syntactic unification. ...
is that I won't be able to do it? Note that I didn't write it out, but this version can accomodate multiple units of measure.
(b) not appreciating the need for parametric polymorphism over dimensions/units. ... Furthermore, parametric polymorphism is essential for code reuse - one can't even write a generic squaring function (say) without it.
I'm not sure what you're getting at here; I can easily write a squaring function in the version I wrote. It uses ad-hoc polymorphism rather than parametric polymorphism. It also gives much uglier types; e.g., the example from your paper f (x,y,z) = x*x + y*y*y + z*z*z*z*z gets some horribly ugly context: f :: (Additive a, Mul b c d, Mul c c e, Mul e c b, Mul d c a, Mul f f a, Mul g h a, Mul h h g) => (f,h,c) -> a Not that I recommend this solution, mind you. I think language support would be much better. But specific language support for units rubs me the wrong way: I'd much rather see a general notion of types with integer parameters, which you're allowed to add. This would be useful in any number of places. Is this what you're suggesting below?
To turn to the original question, I did once give a moment's thought to the combination of type classes and types for units-of-measure. I don't think there's any particular problem: units (or dimensions) are a new "sort" or "kind", just as "row" is in various proposals for record polymorphism in Haskell. As long as this is tracked through the type system, everything should work out fine. Of course, I may have missed something, in which case I'd be very interested to know about it.
Incidentally, I went and read your paper just now. Very interesting. You mentioned one problem came up that sounds interesting: to give a nice member of the equivalence class of the principal type. This boils down to picking a nice basis for a free Abelian group with a few distinguished elements. Has any progress been made on that? Best, Dylan Thurston