Abstract We present ZipLex , a verified framework for invertible linear-time lexical analysis following the longest match (maximal munch) semantics. Unlike past verified lexers that focus only on satisfying the semantics of regular expressions and the longest match property, ZipLex also guarantees that lexing and printing are mutual inverses. Thanks to verified memoization, it also ensures that the lexical analysis of a string is linear in the size of the string. Our design and implementation rely 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 memoization with a standalone verified imperative hash table. Our hash table offers competitive performance as shown by our evaluation. We implemented and verified ZipLex using the Stainless deductive verifier for Scala. Our evaluation demonstrates that ZipLex supports realistic applications such as JSON processing and lexers of programming languages, and behaves linearly even in cases that make flex-style approaches quadratic. ZipLex is two orders of magnitude faster than Verbatim, showing that verified invertibility and linear-time algorithms can be developed without prohibitive cost. Compared to Coqlex, ZipLex also offers linear (instead of quadratic) time lexing, and is the first lexer that comes with invertibility proofs for printing token sequences.

Abstract We report our experience in enhancing automated grading in an undergraduate programming course using formal verification. In our experiment, we deploy a program verifier to check the equivalence between student submissions and our reference solutions, alongside the existing testing-based grading infrastructure. We were able to use program equivalence to differentiate student submissions according to their high-level program structure, in particular their recursion pattern, even when their input-output behaviour is identical. Consequently, we achieve (1) higher confidence in correctness of idiomatic solutions but also (2) more thorough assessment of solution landscape that reveals solutions beyond those envisioned by instructors.

Abstract In this work, we verify, using the Stainless program verifier, the mutable from the Scala standard library, a hash table using open addressing within a single array. As an executable specification, we write an immutable map based on a list of tuples and verify it against the mathematical definition of a map. We then show that ’s operations correspond to operations of this association list. To express the resizing of the hash table array, we introduce a new reference-swapping construct in Stainless. This allows us to apply the decorator design pattern without introducing aliasing. Our verification effort led us to find and fix a bug in the original implementation that manifests for large hash tables. Our performance analysis shows the verified version to be within a 1.5 factor of the original data structure.