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I don't think the Julia implementation makes much use of typing. A related Haskell codebase for Hamiltonian (not Lagrangian) mechanics that I found really helpful to scan was https://blog.jle.im/entry/hamiltonian-dynamics-in-haskell.ht... -

Awesome, thanks for that. Haskell really seems like the language for this.

Or maybe porting it to typed racket could be a worthwhile project.

If you wanna start it, I'd be happy to contribute!