This paper presents a formalization of decreasing diagrams in the theorem prover Isabelle. It discusses mechanical proofs showing that any locally decreasing abstract rewrite system is confluent. The valley and the conversion version of decreasing diagrams are considered.
@InProceedings{zankl:LIPIcs.RTA.2013.352, author = {Zankl, Harald}, title = {{Confluence by Decreasing Diagrams – Formalized}}, booktitle = {24th International Conference on Rewriting Techniques and Applications (RTA 2013)}, pages = {352--367}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-53-8}, ISSN = {1868-8969}, year = {2013}, volume = {21}, editor = {van Raamsdonk, Femke}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2013.352}, URN = {urn:nbn:de:0030-drops-40723}, doi = {10.4230/LIPIcs.RTA.2013.352}, annote = {Keywords: term rewriting, confluence, decreasing diagrams, formalization} }
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