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Compositional Confluence Criteria

Authors Kiraku Shintani , Nao Hirokawa

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Author Details

Kiraku Shintani
  • Japan Advanced Institute of Science and Technology, Ishikawa, Japan
Nao Hirokawa
  • Japan Advanced Institute of Science and Technology, Ishikawa, Japan

Funding

  • Hirokawa, Nao: JSPS KAKENHI Grant Numbers 22K11900.

Acknowledgements

We are grateful to Jean-Pierre Jouannaud, Vincent van Oostrom, and Yoshihito Toyama for their valuable comments on preliminary results of this work. We thank the reviewers for their thorough reading and suggestions, which helped us to improve the presentation.

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Kiraku Shintani and Nao Hirokawa. Compositional Confluence Criteria. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FSCD.2022.28

Abstract

We show how confluence criteria based on decreasing diagrams are generalized to ones composable with other criteria. For demonstration of the method, the confluence criteria of orthogonality, rule labeling, and critical pair systems for term rewriting are recast into composable forms. In addition to them, we prove that Toyama’s parallel closedness result based on parallel critical pairs subsumes his almost parallel closedness theorem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
Keywords
  • term rewriting
  • confluence
  • decreasing diagrams

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