From Types to Sets by Local Type Definition in Higher-Order Logic View Full Text


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Article Info

DATE

2019-02

AUTHORS

Ondřej Kunčar, Andrei Popescu

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. More... »

PAGES

1-24

References to SciGraph publications

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  • 2005. A HOL Theory of Euclidean Space in THEOREM PROVING IN HIGHER ORDER LOGICS
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  • 2013. Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL in CERTIFIED PROGRAMS AND PROOFS
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  • 2009. The HOL-Omega Logic in THEOREM PROVING IN HIGHER ORDER LOGICS
  • 2010. A Mechanized Translation from Higher-Order Logic to Set Theory in INTERACTIVE THEOREM PROVING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10817-018-9464-6

    DOI

    http://dx.doi.org/10.1007/s10817-018-9464-6

    DIMENSIONS

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