2009 | OriginalPaper | Chapter
Diagrammatic Confluence and Completion
Authors : Jean-Pierre Jouannaud, Vincent van Oostrom
Published in: Automata, Languages and Programming
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.