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A New and Formalized Proof of Abstract Completion

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Interactive Theorem Proving (ITP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8558))

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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.

Supported by JSPS KAKENHI Grant Number 25730004 and the Austrian Science Fund (FWF) projects I963 and J3202.

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Author information

Authors and Affiliations

  1. JAIST, Japan

    Nao Hirokawa

  2. University of Innsbruck, Austria

    Aart Middeldorp & Christian Sternagel

Authors
  1. Nao Hirokawa
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  2. Aart Middeldorp
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  3. Christian Sternagel
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Editor information

Editors and Affiliations

  1. NICTA, Sydney, NSW, Australia

    Gerwin Klein

  2. University of Wyoming, Laramie, WY, USA

    Ruben Gamboa

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Hirokawa, N., Middeldorp, A., Sternagel, C. (2014). A New and Formalized Proof of Abstract Completion. In: Klein, G., Gamboa, R. (eds) Interactive Theorem Proving. ITP 2014. Lecture Notes in Computer Science, vol 8558. Springer, Cham. https://doi.org/10.1007/978-3-319-08970-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-08970-6_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08969-0

  • Online ISBN: 978-3-319-08970-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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