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Confluence of Conditional Rewriting Modulo

Author Salvador Lucas

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Author Details

Salvador Lucas
  • DSIC & VRAIN, Universitat Politècnica de València, Spain

Funding

  • Lucas, Salvador: Supported by project PID2021-122830OB-C42 funded by MCIN/AEI/ 10.13039/501100011033 and by "ERDF A way of making Europe" and by the grant CIPROM/2022/6 funded by Generalitat Valenciana.

Acknowledgements

I thank the anonymous referees for their helpful remarks.

Cite AsGet BibTex

Salvador Lucas. Confluence of Conditional Rewriting Modulo. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CSL.2024.37

Abstract

We investigate confluence of rewriting with Equational Generalized Term Rewriting Systems R, consisting of Horn clauses, some of them defining conditional equations s = t ⇐ c and rewriting rules 𝓁 → r ⇐ c. In both cases, c is a sequence of atoms, possibly defined by using additional Horn clauses. Such systems include Equational Term Rewriting Systems and (join, oriented, and semi-equational) Conditional Term Rewriting Systems. A set of equations E defines an equivalence =_E and quotient set T(F,X)/=_E of terms, where reductions s →_{R/E}t using rules in R occur. For such systems, we obtain a finite set of conditional pairs π, which can be viewed as logical sentences, to prove and disprove confluence of →_{R/E} by (dis)proving joinability of such conditional pairs π.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
  • Theory of computation → Logic and verification
  • Theory of computation → Equational logic and rewriting
Keywords
  • Conditional rewriting
  • Confluence
  • Program analysis

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