From: "Barak A. Pearlmutter"

...

... An invalid comparison evaluating to _|_ is arguably more correct, but I personally find the idea of introducing more bottoms rather distasteful.

Too late!  NaN is pretty much the _|_ of IEEE Floating Point.

That was certainly the intent of the IEEE standard, and is why NaN is so contagious.  But they wanted to relax the usual strictness of their languages (FORTRAN, C) when this particular _|_ is around.  So NaN is contagious through strict arithmetic (+, *, etc) like _|_.  But it has strange behaviour with respect to comparison.  In the context of Haskell, which does not have the issue of needing to relax strictness just for NaN, I think the "right thing" would be to have compare give _|_, and maybe also <, >, ==.  After all, NaN is outside the carefully defined total ordering of all other IEEE floating point values including +/- Infinity.

+1 John