On Fri, 24 Aug 2001, S.D.Mechveliani wrote:

D. Tweed writes

...

On a purely pragmatic note ( :-) ) these optimisations can't necessarily be safely used in three of the four most common cases, namely Int, Float and Double because of the restricted range of intermediates. Int, Float, Double are not supposed to be provided with the CommutativeRing instance. And most common cases are, to my mind, different: Integer, Rational, (Integer, Rational), Polynomial Integer ...

Ah, I must admit I'd rather missed the point that you were only intending them to apply to things that were of the algebraic class `Commutative Ring'. I was thinking that it'd be something where a particular funciton over a (possibly polymorphic) type could be declared associative, commutative, etc and then those more elementary classes came together in the particular example of the CommutativeRing. For example, the operator ++ on lists is associative, there are useful computational savings to be made utilising this (IIRC Lennart Augustsson had this specal cased in the hbc compiler), but it's difficult to see how you gain anything by trying to pin down any of the other properties of lists that would figure in the mathematically standard classes (there's no inverse as far as I can see so we don't even make it as far as a group). I think from the point of view of lobbying compiler implementors to put in the spade work to make this happen you're more likely to get support if the elegant algebraic classes come as a neat combination of more low-level, `unstructured' features. Don't get me wrong, I like the idea of extending the power of the Haskell compilers, I was just pointing out that the obvious thought that associative- and commutative-rewrite based optimisation `will also be very helpful for programs that are doing "everyday arithmetic" operations (say running a Kalman filter over a sequence of data represented using Doubles)' isn't necessarily true, and it certainly wasn't obvious to me: it was only happening upon the reference in the MetaFont book that made me realise it. ___cheers,_dave________________________________________________________ www.cs.bris.ac.uk/~tweed/pi.htm |tweed's law: however many computers email: tweed@cs.bris.ac.uk | you have, half your time is spent work tel: (0117) 954-5250 | waiting for compilations to finish.