On Thu, 2010-06-03 at 12:44 +1200, Richard O'Keefe wrote:
On Jun 3, 2010, at 1:13 AM, 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 think you just made my point: Commutativity is NOT one of the standard properties that * is EXPECTED to possess.
I don't think that many people expect * to be not commutative (I'm not speaking about people who deal with Mathematics - I mean 'average person' and 'average programmer').
If you look at the Int and Double instance of Random in the Random.hs that comes with Hugs, you'll see they use different code. It's not because of any problem with / per se but because they need genuinely different algorithms.
Point taken. Regards