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A Verified Cyclicity Checker For Theories with Overloaded Constants
KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.ORCID iD: 0000-0001-7708-348X
2022 (English)In: 13th International Conference on Interactive Theorem Proving (ITP 2022), Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2022, Vol. 237, article id 15Conference paper, Published paper (Refereed)
Abstract [en]

Non-terminating (dependencies of) definitions can lead to logical contradictions, for example when defining a boolean constant as its own negation. Some proof assistants thus detect and disallow non-terminating definitions. Termination is generally undecidable when constants may have different definitions at different type instances, which is called (ad-hoc) overloading. The Isabelle/HOL proof assistant supports overloading of constant definitions, but relies on an unclear foundation for this critical termination check. With this paper we aim to close this gap: we present a mechanised proof that, for restricted overloading, non-terminating definitions are of a detectable cyclic shape, and we describe a mechanised algorithm with its correctness proof. In addition we demonstrate this cyclicity checker on parts of the Isabelle/HOL main library. Furthermore, we introduce the first-ever formally verified kernel of a proof assistant for higher-order logic with overloaded definitions. All our results are formalised in the HOL4 theorem prover.

Place, publisher, year, edition, pages
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2022. Vol. 237, article id 15
Series
Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969 ; 237
Keywords [en]
ad-hoc overloading, cyclicity, definitions, Isabelle/HOL, non-termination
National Category
Language Technology (Computational Linguistics)
Identifiers
URN: urn:nbn:se:kth:diva-317525DOI: 10.4230/LIPIcs.ITP.2022.15Scopus ID: 2-s2.0-85136278762OAI: oai:DiVA.org:kth-317525DiVA, id: diva2:1695285
Conference
13th International Conference on Interactive Theorem Proving, ITP 2022, 7 August 2022 through 10 August 2022, Haifa, Israel
Note

QC 20220913

Part of proceedings: ISBN 978-395977252-5

Available from: 2022-09-13 Created: 2022-09-13 Last updated: 2022-09-13Bibliographically approved

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Gengelbach, Arve

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  • apa
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