Ketil Malde:
Wolfgang Jeltsch:
However, the fact that (0 / 0) == (0 / 0) yields False is quite shocking. It doesn’t adhere to any meaningful axiom set for Eq.
Tough luck, but that's how floating point works, and what the numericalists know, and possibly even love (although I have my doubts). Sanitizing this behavior would make Haskell less usable for real-world numerical problems.
As a compromise, what about an option to make NaN (and presumably the infinities) cause an immediate exception? (And, cetero censeo, exceptions for Int overflow as well.)
People, you are monsters. First, despite the *common, well known* truth that Haskell is not Mathematics, this illusion seems to be extremely persistent! Haskell is a victim - no, some users are victims of its success as a formal language, not just as a coding tool... They *want* to have Eq as they imagine the equality, including the comparison between incomparable. This is BTW a long standing philosophical problem. For centuries some speculative guys tried to analyse such "assertions" as God == God, or death==death. Or myself==myself. Of course, even if they produced some cute conclusions, they had no whatsoever sense for the others. Now we have the modern variants of it: NaN == NaN, bottom == bottom ... Of course, there are differences, since NaN is, no - ARE well defined *objects*. In IEEE there may be several NaNs, if the exponent is e_max+1, then *any* significand (mantissa for the dinosaurs) is good for a NaN. ++ Then, I see here, and on some other lists some tendency to speculate on the numerics by people who really don't need it, and don't use it. The bombing of NaN *might* be a profound compilation option, but for people who really do numerical work, this is a blessing NOT to have it. - Zero (or minimum, etc.) finders don't explode on your face when the automaton gets out of the range because of the instabilities. - Vectorized computations which produce plenty of good numbers and sometimes diverge, do not invalidate all work. - Ignoring Int overflow is a cheap way of having `mod` (MAXINT+1). Useful for many purposes. - In such vector/matrix packages as Matlab, where arrays may represent geometric objects, NaNs mean: "no coordinates here, empty". Simple and useful. etc. So, don't "sanitize" anything, unless you know what you are really doing! I would suggest to Wolfgang Jeltsch a little more of reserve before making sharp categorical proposals concerning the fl. point computations (and also acknowledge that NaN is not a unique entity). It is easy to propose - in the name of "purity" to massacre existing structures; several religious sects and political doctrines were born in such a way. The result was usually horrible... The Num hierarchy in Haskell is bad, we know it, especially for people who do some more formal mathematics. There are more interesting problems to solve than organising a crusade against IEEE, "illegalizing" the Ord instance for numbers, etc. Jerzy Karczmarczuk