Rust won't solve the ABA problem, no. You'd be in unsafe Rust if you were writing something that could encounter the ABA problem.
You wondered out loud how it was even possible to do that kind of analysis, and that's where my mind went. Evidently people think it's a bad take. That's as deep as it goes.
The ABA problem is a false-positive execution of a CAS speculation on a shared memory location.
It is very easy to create an ABA problem in safe Rust. Data race free sequential consistency, which Rust has, is almost completely orthogonal to the ABA problem.
This is an area of active PLT research, we haven't come anywhere close to addressing the problem in the general case.
I suspect we'll be seeing all kinds of bugs caused by a generation of programmers thinking everything has guard rails in Rust because "safety", so they can turn their brain off and not think. In reality, those promises of safety largely disappear when threads, files, signals, and networks are involved.
At the end of the day, your programs run on computers which exist in the physical world. The abstractions are mostly isomorphic, but it's at the margins where the abstractions aren't isomorphic that all the interesting things happen.
> The ABA problem is a false-positive execution of a CAS speculation on a shared memory location.
In safe Rust, if I have a mutable reference to Foo, and Foo contains a shared reference to Bar, then no other thread has a mutable reference to Foo or Bar. So no other thread will make a CAS on my reference to Bar, or drop Bar and then allocate something at the same memory address, etc.
You could have some higher level ABA problem I suppose, where you acquire a lock, read a value, give up the lock, and then make spurious assumptions about what happens while you've let the lock go. But that's obviously not what we're talking about if we're talking about CAS. (ETA: or if these were application level references, eg indices into a list.)
If we're going to implement a lockfree data structure, we're going to need unsafe Rust to hand-roll interior mutability. Because we're going to be sharing mutable state. Which isn't allowed in safe Rust.