Diagrammatic Confluence and Completion

Authors:
Jean-Pierre Jouannaud;Vincent Oostrom
Affiliations:
INRIA-Rocquencourt, France and Tsinghua University, Beijing, China;University of Utrecht, The Netherlands
Venue:
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Year:
2009

Citing 7
Cited 4

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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.