Partial Order Infinitary Term Rewriting and Böhm Trees

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    Abstract

    We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding Böhm extensions. The Böhm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the Böhm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.
    Original languageUndefined/Unknown
    Title of host publicationProceedings of the 21st International Conference on Rewriting Techniques and Applications
    EditorsChristopher Lynch
    Number of pages18
    Volume6
    Place of PublicationDagstuhl, Germany
    PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH
    Publication date2010
    Pages67-84
    ISBN (Print)978-3-939897-18-7
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Infinitary Term Rewriting
    • Partial Order Convergence
    • Metric Convergence
    • Orthogonal Term Rewriting Systems
    • Böhm Extensions

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