Kunčar, O. and Popescu, A. orcid.org/0000-0001-8747-0619 (2018) Safety and conservativity of definitions in HOL and Isabelle/HOL. Proceedings of the ACM on Programming Languages, 2 (POPL). 24. ISSN 2475-1421
Abstract
Definitions are traditionally considered to be a safe mechanism for introducing concepts on top of a logic known to be consistent. In contrast to arbitrary axioms, definitions should in principle be treatable as a form of abbreviation, and thus compiled away from the theory without losing provability. In particular, definitions should form a conservative extension of the pure logic. These properties are crucial for modern interactive theorem provers, since they ensure the consistency of the logic, as well as a valid environment for total/certified functional programming.
We prove these properties, namely, safety and conservativity, for Higher-Order Logic (HOL), a logic implemented in several mainstream theorem provers and relied upon by thousands of users. Some unique features of HOL, such as the requirement to give non-emptiness proofs when defining new types and the impossibility to unfold type definitions, make the proof of these properties, and also the very formulation of safety, nontrivial.
Our study also factors in the essential variation of HOL definitions featured by Isabelle/HOL, a popular member of the HOL-based provers family. The current work improves on recent results which showed a weaker property, consistency of Isabelle/HOL's definitions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Association for Computing Machinery. This work is licensed under a Creative Commons Attribution 4.0 International License. (http://creativecommons.org/licenses/by/4.0/) |
Keywords: | higher-order logic (HOL); proof theory; interactive theorem proving; type definitions; conservative extensions; Isabelle/HOL |
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: | 29 May 2020 13:27 |
Last Modified: | 29 May 2020 13:27 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.1145/3158112 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:161207 |