From types to sets by local type definitions in higher-order logic

Kunčar, Ondřej and Popescu, Andrei (2016) From types to sets by local type definitions in higher-order logic. Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science, vol 9807. In: ITP 2016: 7th International Conference on Interactive Theorem Proving, 22-25 Aug 2016, Nancy, France. ISBN 9783319431437. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-319-43144-4_13)

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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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published as: Kunčar O., Popescu A. (2016) From Types to Sets by Local Type Definitions in Higher-Order Logic. In: Blanchette J., Merz S. (eds) Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science, vol 9807. Springer, Cham
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 22095
Notes on copyright: The final publication is available at Springer
via http://dx.doi.org/10.1007/978-3-319-43144-4_13
Useful Links:
Depositing User: Andrei Popescu
Date Deposited: 19 Jun 2017 15:50
Last Modified: 15 Jun 2021 05:46
URI: https://eprints.mdx.ac.uk/id/eprint/22095

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