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Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting

Authors Frédéric Blanqui, Guillaume Genestier, Olivier Hermant



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Author Details

Frédéric Blanqui
  • INRIA, France
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France
Guillaume Genestier
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France
  • MINES ParisTech, PSL University, Paris, France
Olivier Hermant
  • MINES ParisTech, PSL University, Paris, France

Acknowledgements

The authors thank the anonymous referees for their comments, which have improved the quality of this article.

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Frédéric Blanqui, Guillaume Genestier, and Olivier Hermant. Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 9:1-9:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSCD.2019.9

Abstract

Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order rewriting systems. This extends previous results by Wahlstedt on the one hand and the first author on the other hand to strong normalization and non-orthogonal rewriting systems. This new criterion is implemented in the type-checker Dedukti.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Type theory
Keywords
  • termination
  • higher-order rewriting
  • dependent types
  • dependency pairs

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