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Abstract: We show that non-collapsing orthogonal term rewriting systems do not have the transfinite Church-Rosser property in the setting of Cauchy convergence. In addition, we show that for (a transfinite version of) the Parallel Moves Lemma to hold, any definition of residual for Cauchy convergent rewriting must either part with a number of fundamental properties enjoyed by rewriting systems in the finitary and strongly convergent settings, or fail to hold for very simple rewriting systems. (Update)
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BibTeX entry: (Update)
@misc{ simonsen-confluence,
author = "Jakob Grue Simonsen",
title = "On Confluence and Residuals in Cauchy Convergent Transfinite Rewriting",
url = "citeseer.ist.psu.edu/simonsen04confluence.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
474 Term Rewriting Systems - Klop - 1992
353 Term Rewriting and All That (context) - Baader, Nipkow - 1998
200 Introduction to Mathematical Logic (context) - Mendelson - 1997
53 Theoretical Computer Science (context) - Dershowitz, Kaplan et al. - 1991
23 Meaningless Terms in Rewriting - Kennaway, van Oostrom et al. - 1999
6 volume 55 of Cambridge Tracts in Theoretical Computer Scienc.. (context) - Rewriting - 2003
5 Trans nite Reductions in Orthogonal Term Rewriting (context) - Kennaway, Klop et al. - 1995
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