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)


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.


Inference Rule Reduction Order Critical Pair Correctness Proof Peak Decreasingness 
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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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