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

[jbe]

@louy2

If there are partial orders and those are PartialOrd, and there are weak orders but those are not Ord, then what is Ord ?

According to the documentation, Ord is a total order. That also makes sense to me, because it will always compare an element to another element as either being smaller or greater, unless it is equal.

@steffahn

IMO, Ord is definitely a trait for weak orders. It's just incorrectly documented (it should say "total pre-order", yet it does say "total order" im the docs).

Isn't a weak order the same as a total order if we simply put all non-comparable items in the same equivalence class? Maybe these two are actually the same and it's just a semantic difference?

Now I'm confused

But I just noticed that a "total order" indeed depends on how equality is defined (or a used equivalence relation). And the Ord trait does require that equality (or a certain equivalence relation defined through Eq) does behave in a certain way.

@steffahn

Look at Eq which is correctly documented as a trait for equivalence relations, not for equality.

Yes, Eq could be any equivalence relation.

@steffahn

(The use of "total order" in the docs makes some sense if the equivalence by the Eq implementation is (mis-)interpreted as equality. After all, a total preorder is the same as an actual total order on the equivalence classes.)

Now the question is… Is the equality / non-equality operator here an arbitrary equivalence relation? I would say yes, because we're not operating with numbers or any particular objects here in the mathematical definition. If yes, then I'd say Ord can be seen as "total order".

My point is: Ord interacts with Eq, and thus I'd say it's correct to describe it as total order.