Popescu, A. orcid.org/0000-0001-8747-0619 and Traytel, D. orcid.org/0000-0001-7982-2768 (2023) Admissible types-to-PERs relativization in higher-order logic. Proceedings of the ACM on Programming Languages, 7 (POPL). pp. 1214-1245. ISSN 2475-1421
Abstract
Relativizing statements in Higher-Order Logic (HOL) from types to sets is useful for improving productivity when working with HOL-based interactive theorem provers such as HOL4, HOL Light and Isabelle/HOL. This paper provides the first comprehensive definition and study of types-to-sets relativization in HOL, done in the more general form of types-to-PERs (partial equivalence relations). We prove that, for a large practical fragment of HOL which includes container types such as datatypes and codatatypes, types-to-PERs relativization is admissible, in that the provability of the original, type-based statement implies the provability of its relativized, PER-based counterpart. Our results also imply the admissibility of a previously proposed axiomatic extension of HOL with local type definitions. We have implemented types-to-PERs relativization as an Isabelle tool that performs relativization of HOL theorems on demand.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | higher-order logic (HOL); proof theory; interactive theorem proving; type; definition; relativization; Isabelle/HOL; partial equivalence relation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Mar 2023 10:55 |
Last Modified: | 17 Mar 2023 10:55 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.1145/3571235 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:197460 |