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Skew and ω-Skew Confluence and Abstract Böhm Semantics

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Processes, Terms and Cycles: Steps on the Road to Infinity

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3838))

Abstract

Skew confluence was introduced as a characterization of non-confluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec. We present a new notion called ω-skew confluence which constitutes a sufficient and necessary condition for uniqueness. We also present a theory that can lift uniqueness results from term rewriting systems to rewriting systems on terms with letrec. We present our results in the setting of Abstract Böhm Semantics, which is a generalization of Böhm like trees to abstract reduction systems.

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Author information

Authors and Affiliations

  1. University of Oregon,  

    Zena M. Ariola

  2. University of Innsbruck,  

    Stefan Blom

Authors
  1. Zena M. Ariola
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  2. Stefan Blom
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Aart Middeldorp

  2. Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS, Utrecht, The Netherlands

    Vincent van Oostrom

  3. Department of Theoretical Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Femke van Raamsdonk

  4. VU Vrije Universiteit Amsterdam,  

    Roel de Vrijer

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Ariola, Z.M., Blom, S. (2005). Skew and ω-Skew Confluence and Abstract Böhm Semantics. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_19

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  • DOI: https://doi.org/10.1007/11601548_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30911-6

  • Online ISBN: 978-3-540-32425-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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