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Abstract Models of Transfinite Reductions

Author Patrick Bahr



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Patrick Bahr

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Patrick Bahr. Abstract Models of Transfinite Reductions. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 49-66, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.RTA.2010.49

Abstract

We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.
Keywords
  • Infinitary rewriting
  • metric
  • partial order
  • abstract reduction system
  • axiomatic
  • term rewriting
  • graph rewriting

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