If you want to compare if two pointers point to the same place, you use https://doc.rust-lang.org/stable/std/ptr/fn.eq.html
Rust just defaults to value equality over reference equality. This is true for everything, not just ZSTs.
(I find the post's framing of "it's stored in the borrow checker" to be a bit odd, but I can't put my finger on exactly what it is. The borrow checker doesn't determine these sorts of semantics, it checks for liveliness and aliasing, so "do these pointers alias" isn't inherently not the borrow checker's job, it just strikes me as an odd way to put it. Maybe it's because you don't "ask the borrow checker for that information" really.)
> I find the post's framing of "it's stored in the borrow checker" to be a bit odd
That's exactly what I wanted to say as well.
I feel like it would have been better to just skip the borrow checker mention and just go "in rust this can not be done reliably ..(section about pointers being the same)"
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If you somehow need this property in your programs, I think you can just add a 1-byte member and use pointer equality. (I'm not a Rust expert.)
(About zero sized objects being the same)
But why does that mean the programmer never has to check? (or if they want that information from the borrow checker how would they get it?) It's not motivated as the intro above for c++ was just "In C++, we might do this to check if two pointers refer to the same object".
So the borrow checker knows already, why does that stop the programmer from wanting to know or separate these cases?