A Rust-based Dependently-Typed Lambda Calculus

I follow the CS 2520R write-up very closely; see Expr in lib.rs for more details on the language syntax and implementation. In summary, I use names for all variables, a hash-map of arrays for fast Environment look-ups, and compare expressions after full $\beta$-reduction and up to $\alpha$-equivalence. Unfortunately, my type-checker is undecidable, but for the purposes of demonstration, I cap normalization to 1000 steps before failure.

In main.rs, I include an incomplete proof of the commutativity of addition:

cargo run -- release

The final three theorems (plus_right_zero, plus_right_suc, and plus_comm) are difficult to translate, and I was unable to produce a valid type. Compared to traditional FP, Rust is unique in allowing us to micro-manage the heap, and I avoid copying and re-allocating where possible. However, this also increased code complexity, and my implementation is quite hard to debug. This was also my first time using Rust, but I definitely learned a lot.