Am Freitag, 11. Januar 2008 13:21 schrieb jerzy.karczmarczuk@info.unicaen.fr:
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 -
I was arguing from a software technology point of view: if (==) yields false when comparing a value with itself, this can break code (like a set implementation) which relies on certain guarantees. The fact that Haskell allows to define (==) rather arbitrarily doesn’t mean that the use of arbitrary definitions of (==) is what we want. It’s just that the language is to weak to express axioms. My impression is that staying close to math is good from a software technology point of view. And it has the advantage of less confusion for the user.
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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.
Even if I don’t use numerics, I do care about the Haskell language as a whole.
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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...
I don’t see what’s so extreme about suggesting that IEEE floating point comparison should maybe be a seperate operator. And I think, it is really inappropriate to compare this to horrible sects and doctrines. Do you really want to argue that someone who insists on a rather clean language is dangerous? Than more or less everyone on this list would be dangerous—from a C programmer’s point of view.
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.
Please don’t suggest that “illegalizing” some Ord instance is similar to killing people out of religious motives.
Jerzy Karczmarczuk
Best wishes, Wolfgang