I’ve never used ATS to do what the GP is suggesting of incrementally wrapping C with proofs, but I can’t imagine this being simpler than just rewriting the C in Rust. You wouldn’t get the same proofs, but you would get memory and thread safety, which for many apps would be an incremental improvement.
I haven’t taught ATS, but I found it harder to learn than Idris, and I can’t imagine C programmers which have a hard time with Rust learning it quicker than they would learn Idris or Rust.
sometimes it's impossible without falling back to unsafe Rust, which kind of undermines the initial incentive. C codebases heavily utilise pointer arithmetic programming.
Simplicity is a good trait though, and there are a few promising initiatives in that regard in ATS3 - https://github.com/githwxi/ATS-Xanadu#project-description
In reality most Rust code hardly ever needs to be unsafe and the existence of unsafe code in libraries you use hardly ever has any impact on the security and stability of what you ship, because there just isn't very much of it compared to the safe code. The "trophy cases" for Rust fuzzing bear witness to this.
> C codebases heavily utilise pointer arithmetic programming.
You don't write unsafe Rust code everywhere C code would use pointer arithmetic. You use safe Rust idioms and APIs instead.
If it turns out that writing Linux drivers in Rust requires writing a lot of unsafe Rust code in each driver, then that would certainly be a failure. I don't see any reason to believe that will be the case.
I haven't tried F*, but from quick googling of "aliasing", it seems that a similar kind of checks can be achieved with view-changes in ATS (but please correct me if I'm missing the point) - http://ats-lang.sourceforge.net/DOCUMENT/INT2PROGINATS/HTML/...