max is not stable for preorders

[jech]

In a preorder, min of two equivalent elements should return the first parameter, and max should return the second. This makes the following properties true:

• (min(x,y), max(x,y)) is either (x,y) or (y,x);
• (x,y)->(min(x,y), max(x,y)) is a stable sort.

The definition of max at operators.jl:56 is wrong — it returns the first argument for equivalent arguments:

import Base: isless

type Twain
    a :: Int
    b :: Int
end

isless(x :: Twain, y :: Twain) = x.a < y.a

# max(Twain(2,3), Twain(2,4))

You'll find a more detailed discussion in Chapter 7 of https://www.stepanovpapers.com/notes.pdf .

[jiahao]

"Wrong" is too strong a statement: max is not wrong to the extent that it provides no guarantee of stability.

I changed the title of this issue to reflect your primary concern.

[StefanKarpinski]

These seem like good identities to respect, but I agree, calling this wrong is too strong.

[jech]

Agreed.