On confluence and residuals in Cauchy convergent transfinite rewriting

Authors:
Jakob Grue Simonsen
Affiliations:
Department of Computer Science, University of Copenhagen (DIKU), Universitetsparken 1, 2100 Copenhagen Ø, Denmark
Venue:
Information Processing Letters
Year:
2004

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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.