People are working on the formal specification of rust. It isn't easy. There are at least three projects, maybe more if we include academia https://github.com/

People are working on the formal specification of rust. It isn't easy. There are at least three projects, maybe more if we include academia https://github.com/RalfJung/minirust https://github.com/RalfJung/minirust has a summary of efforts in the end of the readme. the basics of the rust typesystem were proven correct for a restricted rust subset in the rustbelt project.