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The idea with notations isn't to make custom symbology impossible, just clearly signaled, much in the same way Rust macros can do whatever they want but have to be underneath some macro_name!esque indicator. Check out my rough design thoughts for more if you're interested :) https://github.com/blainehansen/magma/blob/main/posts/design-of-magma.md
Prusti too.
Taken by https://github.com/tectonic-typesetting/tectonic. Cool project too.
I have verified some theory in Coq https://github.com/joonazan/line-combination-proofs/tree/master/proofs and would like to verify a Rust implementation, too.
In my opinion the best way of going about it is translating the Rust to Coq that has the same semantics (but different performance) as pioneered in https://github.com/Kha/electrolysis. Unfortunately that project isn't usable today as it requires an ancient version of Rust and Lean.
Yeah once this project is actually real it could be used for that ha :) Your description kinda reminds me fiat: https://github.com/mit-plv/fiat which generates code from just a correctness specification.