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

Conference paper

Kunčar, O. and Popescu, A. 2016. From types to sets by local type definitions in higher-order logic. ITP 2016: 7th International Conference on Interactive Theorem Proving. Nancy, France 22 - 25 Aug 2016 Springer. https://doi.org/10.1007/978-3-319-43144-4_13
TypeConference paper
TitleFrom types to sets by local type definitions in higher-order logic
AuthorsKunčar, O. and Popescu, A.
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.

Research GroupFoundations of Computing group
ConferenceITP 2016: 7th International Conference on Interactive Theorem Proving
ISSN0302-9743
ISBN
Hardcover9783319431437
PublisherSpringer
Publication dates
Print22 Aug 2016
Online07 Aug 2016
Publication process dates
Deposited19 Jun 2017
Accepted01 May 2016
Output statusPublished
Accepted author manuscript
Copyright Statement

The final publication is available at Springer
via http://dx.doi.org/10.1007/978-3-319-43144-4_13

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

Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-319-43144-4_13
LanguageEnglish
Book titleInteractive Theorem Proving. ITP 2016. Lecture Notes in Computer Science, vol 9807
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