Here's one paper covering the derivation of a typed functional LALR(1) parser in which derivations are given explicitly in symbolic language, while proofs are just prose claims that an inductive proof is similar to the derivation:

    https://scholar.google.com/scholar?&q=Hinze%2C%20R.%2C%20Paterson%2C%20R.%3A%20Derivation%20of%20a%20typed%20functional%20LR%20parser%20%282003%29

Here's one for the semantics of the Cedille functional language core in which proofs are given as key components in symbolic language with prose to to tie them together; all theorems, lemmas, etc are given symbolically.

    https://arxiv.org/abs/1806.04709

And here's one introducing dependent intersection types (as used in Cedille) which references formal machine-checked proofs and only provides a sketch of the proof result in prose:

   https://doi.org/10.1109/LICS.2003.1210048

(For the latter, actually finding the machine checked proof might be tricky: I didn't see it overtly cited and I didn't go looking).