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A New and Formalized Proof of Abstract Completion

  • Nao Hirokawa
  • Aart Middeldorp
  • Christian Sternagel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8558)

Abstract

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.

Keywords

Inference Rule Reduction Order Critical Pair Correctness Proof Peak Decreasingness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nao Hirokawa
    • 1
  • Aart Middeldorp
    • 2
  • Christian Sternagel
    • 2
  1. 1.JAISTJapan
  2. 2.University of InnsbruckAustria

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