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Infinite Runs in Abstract Completion

Authors Nao Hirokawa, Aart Middeldorp, Christian Sternagel, Sarah Winkler

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Nao Hirokawa
Aart Middeldorp
Christian Sternagel
Sarah Winkler

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Nao Hirokawa, Aart Middeldorp, Christian Sternagel, and Sarah Winkler. Infinite Runs in Abstract Completion. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.FSCD.2017.19

Abstract

Completion is one of the first and most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In an earlier paper we presented a new and formalized correctness proof of abstract completion for finite runs. In this paper we extend our analysis and our formalization to infinite runs, resulting in a new proof that fair infinite runs produce complete presentations of the initial equations. We further consider ordered completion - an important extension of completion that aims to produce ground-complete presentations of the initial equations. Moreover, we revisit and extend results of Métivier concerning canonicity of rewrite systems. All proofs presented in the paper have been formalized in Isabelle/HOL.
Keywords
  • term rewriting
  • abstract completion
  • ordered completion
  • canonicity
  • Isabelle/HOL

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