On Wed, 2 Jun 2010, Maciej Piechotka wrote:
On Wed, 2010-06-02 at 14:01 +1200, Richard O'Keefe wrote:
For what applications is it "useful" to use the same symbol for operations obeying (or in the case of floating point operations, *approximating* operations obeying) distinct laws?
If the given operations do share something in common. For example * is usually commutative. However you do use it with quaternions (Hamilton product). You even write ij = k despite the fact that ji = -k.
I do not like to see the type class mechanism as a way to use common identifiers and symbols in as many as possible applications. Instead for me type classes are a way to write algorithms in a way that they can be used for many particular types. So far I had no algorithm that works equally well on integral 'div' and fractional '/'. Can you give me an example of an algorithm, where in one case instantiation to Integer and 'div' is sensible and in another case instantation to Rational and '/' is sensible?