Combining predicate transformer semantics for effects: a case study in parsing regular languages

Abstract: This paper describes how to verify a parser for regular expressions in a functional programming language using predicate transformer semantics for a variety of effects. Where our previous work in this area focused on the semantics for a single effect, parsing requires a combination of effects: non-determinism, general recursion and mutable state. Reasoning about such combinations of effects is notoriously difficult, yet our approach using predicate transformers enables the careful separation of program syntax, correctness proofs and termination proofs.