ZipLex: Verified Invertible Lexing with Memoized Derivatives and Zippers

We present ZipLex, a verified framework for invertible lexical analysis. Unlike past verified lexers that focus only on satisfying the semantics of regular expressions and the maximal munch property, ZipLex also guarantees that lexing and printing are mutual inverses. Our design relies on two sets of ideas: (1) a new abstraction of token sequences that captures the separability of tokens in a sequence while supporting their efficient manipulation, and (2) a combination of verified data structures and optimizations, including Huet's zippers and memoized derivatives, to achieve practical performance. We implemented ZipLex in Scala and verified its correctness, including invertibility, using the Stainless verifier. Our evaluation demonstrates that ZipLex supports realistic applications such as JSON processing and lexers of programming languages. In comparison to other verified lexers (which do not enforce invertibility), ZipLex is 4x slower than Coqlex and two orders of magnitude faster than Verbatim++, showing that verified invertibility can be achieved without prohibitive cost.