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Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory

Authors Gabriel Hondet, Frédéric Blanqui

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Author Details

Gabriel Hondet
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, Inria, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France
Frédéric Blanqui
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, Inria, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France

Acknowledgements

The authors thank Gilles Dowek and the anonymous referees very much for their remarks.

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Gabriel Hondet and Frédéric Blanqui. Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.TYPES.2020.6

Abstract

The λΠ-calculus modulo theory is a logical framework in which various logics and type systems can be encoded, thus helping the cross-verification and interoperability of proof systems based on those logics and type systems. In this paper, we show how to encode predicate subtyping and proof irrelevance, two important features of the PVS proof assistant. We prove that this encoding is correct and that encoded proofs can be mechanically checked by Dedukti, a type checker for the λΠ-calculus modulo theory using rewriting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Higher order logic
  • Theory of computation → Equational logic and rewriting
Keywords
  • Predicate Subtyping
  • Logical Framework
  • PVS
  • Dedukti
  • Proof Irrelevance

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