Abstraction of Conditional Term Rewriting Systems

This paper introduces the notion of abstract domains for constructor-based conditional term rewriting systems and defines the notion of abstract term rewriting systems (abstract TRS) over these domains. These new term rewriting systems are mainly used to determine or to approximate the normal forms of ground instances of concrete terms (with variables). We propose a method to compute such an abstract TRS as the least fixed point of a transformation over abstract TRS's. The computed abstract TRS allows to determine efficiently an approximation of any concrete term. Among the possible applications of the introduced concepts, we quote: improvement of the implementation of functional-logic programming languages, E-unification, satisfiability, proofs by induction, etc