Why `sort()` need `T` to be `Ord`?

[steffahn]

@jbe

So do I understand right that if the missing axiom was added, then PartialOrd is partial preorder?

No, the missing axioms “a < b and b == c implies a < c” and “a == b and b < c implies a < c” are necessary in order to ensure that <= is transitive. The partial preorder would furthermore require this

@steffahn

additional constraint that a <= b implies a <= a and b <= b . (Called "partial reflexivity", or "reflexivity where the relation is defined" in the German Wikipedia article.)

Note that, if you assume that PartialOrd only defines <= and all other comparisons are defined in terms of <= as I explained above

@steffahn

You can define the rest:
a == b iff a <= b && b <= a
a != b iff !(a == b)
a < b iff a <= b && a != b
a > b iff b < a
a >= b iff b <= a

Then the

@jbe

four different values

for partial_cmp are nothing more than the four different results of testing both a <= b and b <= a.

a <= b	b <= a	PartialOrd::partial_cmp(&a, &b)
true	true	Some(Equal)
true	false	Some(Less)
false	true	Some(Greater)
false	false	None

---

@jbe

I.e. PartialOrd isn't a partial order then, just like I suspected in my previous post?

No, indeed not a partial order. The main point is that PartialOrd doesn't require reflexivity for <= (since it doesn't even require reflexivity for ==).