Proving termination via measure transfer in equivalence checking

Milovančević, D. and Fuhs, Carsten and Bucev, M. and Kunčak, V. (2024) Proving termination via measure transfer in equivalence checking. In: Kosmatov, N. and Kovács, L. (eds.) Integrated Formal Methods. Lecture Notes in Computer Science 15234. Springer, pp. 75-84. ISBN 9783031765537.

Abstract

Program verification can benefit from proofs with varied induction schemas. A natural class of induction schemas, functional induction, consists of those derived from definitions of functions. For such inductive proofs to be sound, it is necessary to establish that the functions terminate, which is a challenging problem on its own. In this paper, we consider termination in the context of equivalence checking of a candidate program against a provably terminating reference program annotated with termination measures. Using equivalence checking, our approach automatically matches function calls in the reference and candidate programs and proves termination by transferring measures from a measure-annotated program to one without annotations. We evaluate this approach on existing and newly written termination benchmarks, as well as on exercises in programming courses. Our evaluation corpus comprises around 10K lines of code. We show empirically that the termination measures of reference programs often successfully prove the termination of equivalent candidate programs, ensuring the soundness of inductive reasoning in a fully automated manner.

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