论文信息 - Diagram Techniques for Confluence

Diagram Techniques for Confluence

We develop diagram techniques for proving confluence in abstract reductions systems. The underlying theory gives a systematic and uniform framework in which a number of known results, widely scattered throughout the literature, can be understood. These results include Newman's Lemma (1942), Lemma 3.1 of Winkler and Buchberger (1985), the Hindley-Rosen Lemma (1964), the Request Lemmas of Staples (1975), the Strong Confluence Lemma of Huet (1980) and the Lemma of De Bruijn (1978).

Vincent van Oostrom | Marc Bezem | Jan Willem Klop

[1] M. Newman. On Theories with a Combinatorial Definition of "Equivalence" , 1942 .

[2] V. van Oostrom,et al. Confluence for Abstract and Higher-Order Rewriting , 1994 .

[3] Wilson A. Sutherland,et al. Introduction to Metric and Topological Spaces , 1975 .

[4] Gerard Huet,et al. Conflunt reductions: Abstract properties and applications to term rewriting systems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[5] Henk Barendregt,et al. The Lambda Calculus: Its Syntax and Semantics , 1985 .

[6] HuetGérard. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980 .

[7] R. Milner. Mathematical Centre Tracts , 1976 .

[8] de Ng Dick Bruijn. A note on weak diamond properties , 1978 .

[9] Bruno Buchberger,et al. A criterion for eliminating unnecessary reductions in the Knuth-Bendix algorithm , 1983, SIGS.

[10] Alfons Geser,et al. Relative Termination , 1990 .

[11] Jan Willem Klop,et al. Combinatory reduction systems , 1980 .

[12] Wiebe van der Hoek,et al. First steps in modal logic , 1997 .

[13] John Staples. Church-Rosser theorems for replacement systems , 1975 .