On 13/01/06, Brian Hulley
Cale Gibbard wrote:
<Snip> So long as we're going to have a defaulting mechanism, it seems a bit odd to restrict it to Num, and to classes in the Prelude.
Instead of having literals such as 1 that could be Int, Integer, or Float etc, why not just have one Number type declared as something like:
data Number = NInt Int | NInteger Integer | NFloat Float | NDouble Double | NRational Integer Integer | NComplex Number Number
etc so that all numeric literals would just be translated by the compiler into a Number. Arithmetic ops would then not be overloaded but the compiler could hopefully optimize out the extra indirection caused by using Number instead of plain Int, Integer, etc.
Regards, Brian.
This is not very extensible though. You can't extend that type later with numeric types of your own (e.g. polynomials, power series, an arbitrary precision computable real type, or some finite field). Having a Num typeclass allows for users to add their own numeric types at will. Also, implicit coercions would be required to implement the operations on your type, which I'm not sure is such a good idea. The real problem is that the syntax is overloaded. Somehow I don't fancy the requirement to type NInteger 5 (respectively 5 :: Integer) whenever I want to refer to 5 in an arithmetic expression, and determining which constructor to apply automatically is the same problem as the defaulting mechanism solves. (Only, with the algebraic union, it must be solved at each and every numeric literal, rather than the comparatively fewer times it would need to be solved in general to make the system of type constraints determined.) Ambiguity is actually seldom a real problem in practice. Usually something comes along and fixes the type -- it's only really at the GHCi/Hugs prompt that this is usually a major issue. This is another reason perhaps why it hasn't been generalised. Probably the real reason that it's restricted to Num is that instances of Num are the only types with such overloaded syntax in the language. (I can write 5, and have it mean an Integer, Complex Double, a Rational, or a constant power series of some type I cooked up.) There are other situations where ambiguities can arise, but to be honest, I've never been too annoyed by them. Still, it sort of looks odd to have a feature which looks like it could be vastly more general, but which only applies to this one Prelude class Num, and only in contexts involving other Prelude classes. Thinking about it more is making it clearer why it is restricted to Num, though it's not obvious that it should remain that way forever. The original question posed by Daniel is whether we should lift the restriction that all of the classes involved are in a standard library when doing defaulting. That's such a subtle and odd point that there almost certainly is a reason for it. Does anyone know it? - Cale