Kunčar, O. and Popescu, A. orcid.org/0000-0001-8747-0619 (2019) A consistent foundation for Isabelle/HOL. Journal of Automated Reasoning, 62 (4). pp. 531-555. ISSN 0168-7433
Abstract
The interactive theorem prover Isabelle/HOL is based on the well understood higher-order logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). However, Isabelle/HOL brings its own personal touch to HOL: overloaded constant definitions, used to provide the users with Haskell-like type classes. These features are a delight for the users, but unfortunately are not easy to get right as an extension of HOL—they have a history of inconsistent behavior. It has been an open question under which criteria overloaded constant definitions and type definitions can be combined together while still guaranteeing consistency. This paper presents a solution to this problem: non-overlapping definitions and termination of the definition-dependency relation (tracked not only through constants but also through types) ensures relative consistency of Isabelle/HOL.
Metadata
Authors/Creators: |
|
||||
---|---|---|---|---|---|
Copyright, Publisher and Additional Information: | © 2018 Springer Science+Business Media B.V., part of Springer Nature. This is an author-produced version of a paper subsequently published in Journal of Automated Reasoning. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | Higher-order logic; Theorem proving; Isabelle/HOL; Consistency; Model-theoretic semantics; Ad hoc overloading | ||||
Dates: |
|
||||
Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) | ||||
Funding Information: |
|
||||
Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 30 Sep 2022 13:39 | ||||
Last Modified: | 30 Sep 2022 13:47 | ||||
Status: | Published | ||||
Publisher: | Springer Science and Business Media LLC | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.1007/s10817-018-9454-8 |