Traits in `std::cmp` and mathematical terminology

[jbe]

From the previous thread:

@jdahlstrom

@tczajka

Maybe you could argue that f32 doesn't really have a partial order (I would say it's close enough), but even if so, doesn't mean the trait is not a partial order trait, it's just that impl PartialOrder for f32 doesn't do the right thing.

Which is funny, of course, given that AFAIK the whole reason PartialOrd exists is the IEEE 754 floating-point semantics. Is there even precedence for objects that behave like IEEE floats in mathematics? Are they weird enough to not match any more-or-less commonly used terminology?

NULL in SQL has similar semantics but seems more sane in that it embraces true three-valued logic: its "PartialEq" actually returns "Option" in Rust terms. So NULL == NULL is neither true nor false, it is itself NULL, as in unknown, just like NULL < NULL.

I would say f32 and f64 have a (strict) partial order. Numbers compare as expected, −∞ < 0 < ∞, NaN ≮ NaN. But the <= and >= operators can't behave like a non-strict partial order because NaN != NaN.

I would say the IEEE floats in mathematical terms have

• a strict partial order

in combination with

• an (independent) partial equivalence relation.

And yeah, it is kinda funny that PartialOrd was likely introduced because of IEEE 754. Or were there other reasons?

I'm not sure what SQL's comparison regarding NULL is in mathematical terms. I guess it'd require some exotic three-valued logic.

Edit: Sorry to have pulled this over to the new thread. I wasn't sure what to do. @steffahn gave a nice(er) answer in the other thread.