Nothing if unsafe Rust is considered, though Zig does not require you to fight the language nearly as much. This is especially obvious with embedded. Zig's philosophy of no hidden control flow or allocation makes things simple. Simplicity is power.
For certain problems you would want a TLA+ specification for safety and especially liveness either way. It's not like Rust absolutely guarantees correctness in all cases.
Rust sits in a sweet spot between C/Zig and languages like Java, but it's not an appropriate replacement for either of them.
Certainly Rust sits where C++ is. Zig and Rust are definitely best used for different things, but I think sweating rust off as in between C and Java is inaccurate.
This is kind of a trick question because they are all Turing Complete, but so is Assembly. The best way to interpret your question, then, is not “what is possible” but rather “what is simple to express correctly” and “what is simple to get correct eventually”. Those are questions about how tricky it is to get something to compile in the language and which tools exist to help determine whether a compiled program does what’s expected and does not do what’s not expected.
It wasn't a trick question. I'm not asking it in the same tone as someone would ask 'What can C do that Java can't?'.
I believe that Rust can be as low level as you want. If you have to fight the language to accomplish something, it's because you're probably trying to do something unsafe, and Rust will let you do that if you pay the price.
I was looking for examples of real cases where Zig is a better option than Rust. And while Zig is a lovely language, its main points against Rust are that it lets you do unsafe things more easily, and it's easier to learn.
