Kunčar, O. and Popescu, A. (2017) Comprehending Isabelle/HOL’s Consistency. In: Programming Languages and Systems: 26th European Symposium on Programming, ESOP 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22–29, 2017, Proceedings. 26th European Symposium on Programming, ESOP 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, 22-29 Apr 2017, Uppsala, Sweden. Lecture Notes in Computer Science, LNTCS,volume 10201 . Springer Berlin Heidelberg , pp. 724-749. ISBN 9783662544334
Abstract
The proof assistant Isabelle/HOL is based on an extension of Higher-Order Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means—following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Springer-Verlag GmbH Germany. This is an author-produced version of a paper subsequently published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
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) |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/N019547/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 20 Oct 2022 15:55 |
Last Modified: | 20 Oct 2022 16:26 |
Status: | Published |
Publisher: | Springer Berlin Heidelberg |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-662-54434-1_27 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191512 |