A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
A computational logic handbook
A computational logic handbook
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TYPES '93 Proceedings of the international workshop on Types for proofs and programs
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Annals of Mathematics and Artificial Intelligence
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Journal of Automated Reasoning
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TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
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TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
Development Closed Critical Pairs
HOA '95 Selected Papers from the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
More Church-Rosser Proofs (in Isabelle/HOL)
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A Proof of the Church-Rosser Theorem and its Representation in a Logical Framework
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Normalization by Evaluation for Typed Lambda Calculus with Coproducts
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
ACM Transactions on Design Automation of Electronic Systems (TODAES)
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SBCCI '06 Proceedings of the 19th annual symposium on Integrated circuits and systems design
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
A PVS Theory for Term Rewriting Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Verification of the completeness of unification algorithms à la Robinson
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
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A mechanical proof of the Knuth---Bendix Critical Pair Theorem in the higher-order language of the theorem prover PVS is described. This well-known theorem states that a Term Rewriting System is locally confluent if and only if all its critical pairs are joinable. The formalization of this theorem follows Huet's well-known structure of proof in which the restriction on strong normalization or Noetherian was dropped and the result presented as a lemma. In order to formalize the Knuth---Bendix Critical Pair Theorem we rely on previously developed PVS theories for abstract reduction systems, named ars, and term rewriting systems, named trs, which were built upon the PVS libraries for finite sequences and sets. On the one hand, the theory trs is composed of subtheories for dealing with the structure of terms, for replacements of subterms and substitutions and jointly with the theory ars it allows for adequate specifications of elaborate notions of term rewriting systems such as the one of critical pairs. On the other hand, ars specifies basic definitions and notions of abstract reduction systems such as reduction, termination, normal forms, and confluence as well as non basic concepts such as strong normalization.