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Diagrammatic Confluence and Completion

Jean-Pierre Jouannaud 1 Vincent van Oostrom 2
1 FORMES - Formal Methods for Embedded Systems
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : We give a new elegant proof that decreasing diagrams imply confluence based on a proof reduction technique, which is then the basis of a novel completion method which proof-reduction relation transforms arbitrary proofs into rewrite proofs even in presence of non-terminating reductions. Unlike previous methods, no ordering of the set of terms is required, but can be used if available. Unlike ordered completion, rewrite proofs are closed under instantiation. Examples are presented, including Kleene's and Huet's classical examples showing that non-terminating local-confluent relations may not be confluent.
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https://hal.inria.fr/inria-00436070
Contributor : Jean-Pierre Jouannaud <>
Submitted on : Thursday, November 26, 2009 - 8:30:52 AM
Last modification on : Tuesday, March 17, 2020 - 3:00:48 AM

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Jean-Pierre Jouannaud, Vincent van Oostrom. Diagrammatic Confluence and Completion. International Conference in Automata, Languages and Programming, Paul Spirakis, Jul 2009, Rhodes, Greece. ⟨10.1007/978-3-642-02930-1_18⟩. ⟨inria-00436070⟩

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