If you talk to anyone who uses floating point numbers for real they would
find (0/0)==(0/0) perfectly natural.
It disobeys some axioms that Eq instances don't fulfill anyway, but changing
it would make a lot of people surprised too.
In general, the floating point instances break almost all axioms that you
might think exist for numbers.
-- Lennart
On Jan 11, 2008 1:27 AM, Wolfgang Jeltsch
Some people seem to think that == is an equality predicate. This is a big source of confusion for them; until they realize that == is just another function returning Bool they will make claims like [1..]==[1..] having an unnatural result.
The == function is only vaguely related to the equality predicate in
Am Freitag, 11. Januar 2008 08:11 schrieb Lennart Augustsson: that
it is meant to be a computable approximation of semantic equality (but since it's overloaded it can be anything, of course).
-- Lennart
But class methods are expected to fulfill some axioms. I'd suppose that (==) should be an equivalence relation. Of course, this is not implementable because of infininte data structures. But one could relax the axioms such that it's allowed for (==) to return _|_ instead of the expected value. Differentiating between data and codata would of course be the better solution.
However, the fact that (0 / 0) == (0 / 0) yields False is quite shocking. It doesn't adhere to any meaningful axiom set for Eq. So I think that this behavior should be changed. Think of a set implementation which uses (==) to compare set elements for equality. The NaN behavior would break this implementation since it would allow for sets which contain NaN multiple times.
Best wishes, Wolfgang _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe