Abstract

Standardization theorem is one of the most important theory for foundation of computation. Since it was firstly referred to by Curry and Feys, much effort have been made by several researchers. One of the most important work was done by Klop, who brought a nice idea to treat standardization in elegant way. It is called the transformational approach. In this paper we follow his method but introduce a new labelling method which is suitable for analysis of standardization for term rewriting systems. We show proof of standardization theorem for left-linear term rewriting systems with this labelling method. Furthermore, we also consider a standardization theorem for conditional term rewriting systems. Standardization is possible even for conditional system with extra variables in the right-hand side of rewrite rules. This work is the first result towards standardization of conditional rewrite systems.

Citations