Kunčar, O. and Popescu, A. orcid.org/0000-0001-8747-0619 (2016) From types to sets by local type definitions in higher-order logic. In: Blanchette, J.C. and Merz, S., (eds.) Interactive Theorem Proving: 7th International Conference, ITP 2016, Nancy, France, August 22-25, 2016, Proceedings. 7th International Conference, ITP 2016, 22-25 Aug 2016, Nancy, France. Lecture Notes in Computer Science, LNTCS,volume 9807 . Springer International Publishing , pp. 200-218. ISBN 9783319431437
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 soundness. 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
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Springer International Publishing Switzerland. 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. |
Keywords: | Type Class; Dependent Type; Type Definition; Type Constructor; Transfer Rule |
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 16:15 |
Last Modified: | 21 Oct 2022 12:58 |
Status: | Published |
Publisher: | Springer International Publishing |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-319-43144-4_13 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191514 |