Kunčar, O. and Popescu, A. orcid.org/0000-0001-8747-0619 (2019) From types to sets by local type definition in higher-order logic. Journal of Automated Reasoning, 62 (2). pp. 237-260. ISSN 0168-7433
Abstract
Types in higher-order logic (HOL) are naturally interpreted as nonempty sets. This intuition is reflected in the type definition rule for the HOL-based systems (including Isabelle/HOL), where a new type can be defined whenever a nonempty set is exhibited. However, in HOL this definition mechanism cannot be applied inside proof contexts. We propose a more expressive type definition rule that addresses the limitation and we prove its consistency. This higher expressive power opens the opportunity for a HOL tool that relativizes type-based statements to more flexible set-based variants in a principled way. We also address particularities of Isabelle/HOL and show how to perform the relativization in the presence of type classes.
Metadata
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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: | HOL; Isabelle; Local typedef; Type definition; Relativization; Type classes; Overloading; Dependent types; Model; Consistency; Transfer; Type-based theorems; Set-based theorems | ||||
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: |
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 30 Sep 2022 13:27 | ||||
Last Modified: | 30 Sep 2022 13:28 | ||||
Status: | Published | ||||
Publisher: | Springer Science and Business Media LLC | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.1007/s10817-018-9464-6 |