The fully formalized correctness proof of the ISO standard parser is 13000 lines long. The parser together with its specification has 635 lines. Its correctness proof has been created in three weeks. If the prefix, infix and postfix operators satisfy the conditions stated in the ISO Prolog standard, then a token list can be parsed into a parse tree in at most one way. LPTP is able to find short derivations automatically.
Larger proofs have to be created interactively.
In S. Adian and A. Nerode, editors, Logical Foundations of Computer Science LFCS '97 - Logic at Yaroslavl, Russia. In R. Dyckhoff, et.