Fawzi Mohamed
Vectors don't act like numbers, a vector space is not a field, even if they have some common operations.
That's a long-standing flaw in the design of numeric classes. It's not a problem with typeclasses per se.
I find it misleading to define something a number when it does not satisfy all the properties of numbers.
Justifiably so. But if you had a class Additive, would you be unhappy about defining (+) on non-numbers?
The numerical prelude might fix this, but still I think that class and overloading should be distinct concepts.
I think the problem here is that you are using the word class to mean something different from Haskell classes. Haskell typeclasses /are/ overloading, and that's what I understand them as. They were originally introduced as a solution to the question of how to handle equality so that one didn't have to use different names for the same concept on different types. -- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2006-09-13)