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Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number-theoretic finiteness results for class groups, in the Lean prover as part of the mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and ’s decentralized collaboration processes involved in this project.

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.

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