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Processes, Terms and Cycles: Steps on the Road to Infinity pp 554–638Cite as

Axiomatic Rewriting Theory I: A Diagrammatic Standardization Theorem

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

Abstract

By extending nondeterministic transition systems with concurrency and copy mechanisms, Axiomatic Rewriting Theory provides a uniform framework for a variety of rewriting systems, ranging from higher-order systems to Petri nets and process calculi. Despite its generality, the theory is surprisingly simple, based on a mild extension of transition systems with independence: an axiomatic rewriting system is defined as a 1-dimensional transition graph \(\mathcal{G}\) equipped with 2-dimensional transitions describing the redex permutations of the system, and their orientation. In this article, we formulate a series of elementary axioms on axiomatic rewriting systems, and establish a diagrammatic standardization theorem.

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Author information

Authors and Affiliations

  1. Equipe Preuves, Programmes et Systèmes, CNRS, Université Paris 7 Denis Diderot

    Paul-André Melliès

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  1. Paul-André Melliès
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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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Melliès, PA. (2005). Axiomatic Rewriting Theory I: A Diagrammatic Standardization Theorem. 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_23

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  • DOI: https://doi.org/10.1007/11601548_23

  • 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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