Mine has a formally proven borrow checker built on linear types, along with algebraic effects, with an LLVM compiler written in lean -- the type checker uses exactly the proven calculus.
If you are going to build a language with claude, I highly, highly recommend writing it in Lean or Coq and starting by formalizing a pre-existing paper or system that has the properties you want.
Claude gets confused and takes shortcuts constantly, and if you don't have a proven base, you are really going ot struggle. I had to throw away months of work as i got bogged down trying to resolve special cases and bugs that just evaporated when i switched to a proven calculus.