for equational laws to be sensible requires a sensible notion of equality, the Eq for Floating point numbers is meant for handling corner cases (eg: am i about to divide by zero), not "semantic/denotational equivalence" Exact equality is fundamentally incorrect for finite precision mathematical computation. You typically want to have something like nearlyEq tolerance a b = if distance a b <= tolerance then True else False Floating point is geometry, not exact things https://hackage.haskell.org/package/ieee754-0.7.3/docs/Data-AEq.html is a package that provides an approx equality notion. Basically, floating points work the way they do because its a compromise that works decently for those who really need it. If you dont need to use floating point, dont! :) On Fri, Sep 26, 2014 at 9:28 AM, Jason Choy <jjwchoy@gmail.com> wrote:
subject to certain caveats. It's not unfair to say that
floating point multiplication is (nearly) associative "within a few ulp".
I'm not disputing this.
However, you can't deny that this monoid law is broken for the floating point operations:
mappend x (mappend y z) = mappend (mappend x y) z
Perhaps I'm being pedantic, but this law should hold for all x, y, z, and it clearly doesn't.