[Haskell-cafe] haskell gsoc proposal for richer numerical type classes and supporting algorithms

[Gregory Crosswhite]

On Apr 8, 2010, at 5:30 PM, Casey McCann wrote:

> On Thu, Apr 8, 2010 at 7:58 PM, wren ng thornton <wren at freegeek.org> wrote:
> 
> Exactly. NaN /= NaN
[...]
> Indeed. NaN means that equality is not reflexive for floats in
> general, only a subset of them.

First of all, it isn't clear to me that NaN /= NaN, since in ghci the expression "1.0/0.0 == 1.0/0.0" evaluates to True.  But even if that were the case, I would call that more of a technicality then meaning that equality is not reflexive for floats, since NaN is roughly the floating-point equivalent of _|_, and using the same argument one could also say that reflexivity does not hold in general for equating values of *any* Haskell type since (_|_ == _|_) does not return true but rather _|_.

(Don't get me wrong, I agree with your point that multiplication and addition are neither associative nor distributive and other such nasty things occur when dealing with floating point numbers,  it's just that I think that saying they are so messed up that even equality is not reflexive is a little harsher than they actually deserve.  ;-) )

Cheers,
Greg