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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
- Subject
- Computer Science; Mathematical Logic and Formal Languages; Artificial Intelligence; Mathematical Logic and Foundations; Symbolic and Algebraic Manipulation
- ISSN
- 0168-7433
- eISSN
- 1573-0670
- DOI
- 10.1007/s10817-018-9464-6
- Publisher site
- See Article on Publisher Site
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.
Journal
Journal of Automated Reasoning – Springer Journals
Published: Jun 4, 2018