Completeness of Combinations of Constructor Systems

8 years 6 months ago
Completeness of Combinations of Constructor Systems
A term rewriting system is called complete if it is both confluent and strongly norrealizing. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear TRS's. In this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to systems which are composed of disjoint parts. The importance of our method is that we may decompose a given constructor system into parts which possibly share function symbols and rewrite rules in order to infer completeness. We obtain a similar technique for semi-completeness, i.e. the combination of ...
Aart Middeldorp, Yoshihito Toyama
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Where RTA
Authors Aart Middeldorp, Yoshihito Toyama
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