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Published in:
2014 | OriginalPaper | Chapter
A New and Formalized Proof of Abstract Completion
Authors : Nao Hirokawa, Aart Middeldorp, Christian Sternagel
Published in: Interactive Theorem Proving
Publisher: Springer International Publishing
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Completion is one of the most studied techniques in term rewriting. We present a new proof of the correctness of abstract completion that is based on peak decreasingness, a special case of decreasing diagrams. Peak decreasingness replaces Newman’s Lemma and allows us to avoid proof orders in the correctness proof of completion. As a result, our proof is simpler than the one presented in textbooks, which is confirmed by our Isabelle/HOL formalization. Furthermore, we show that critical pair criteria are easily incorporated in our setting.