Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

  • Julian NageleEmail author
  • Aart Middeldorp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9807)


This paper presents the first formalization of three classic confluence criteria for first-order term rewrite systems by Huet and Toyama. We have formalized proofs, showing that (1) linear strongly closed systems, (2) left-linear parallel closed systems, and (3) left-linear almost parallel closed systems are confluent. The third result is extended to commutation. The proofs were carried out in the proof assistant Isabelle/HOL as part of the library IsaFoR and integrated into the certifier CeTA, significantly increasing the number of certifiable proofs produced by automatic confluence tools.


Critical Pair Proof Assistant Tree Automaton Parallel Step Interactive Theorem Prover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Nao Hirokawa for suggesting Lemma 6 and Bertram Felgenhauer and Christian Sternagel for insightful discussion.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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