This paper proposes some simple methods, based on the Church-Rosser property, for testing the equivalence in a restricted domain of two reduction systems. Using the Church-Rosser property, sufficient conditions for the equivalence of abstract reduction systems are proved. These conditions can be effectively applied to test the equivalence in a restricted domain of term rewriting systems. In add...

The Rewriting-calculus (Rho-calculus), is a minimal framework embedding Lambdacalculus and Term Rewriting Systems, by allowing abstraction on variables and patterns. The Rho-calculus features higher-order functions (from Lambda-calculus) and pattern-matching (from Term Rewriting Systems). In this paper, we study extensively a second-order Rho-calculus à la Church (RhoF) that enjoys subject redu...

Innnitary rewriting allows innnitely large terms and innnitely long reduction sequences. There are two computational motivations for studying these: the innnite data structures implicit in lazy functional programming, and the use of rewriting of possibly cyclic graphs as an implementation technique for functional languages. We survey the fundamental properties of innnitary rewriting in orthogon...

We give a relatively simple coinductive proof of confluence, modulo equivalence of root-active terms, of nearly orthogonal infinitary term rewriting systems. Nearly orthogonal systems allow certain root overlaps, but no non-root overlaps. Using a slightly more complicated method we also show confluence modulo equivalence of hypercollapsing terms. The condition we impose on root overlaps is simi...

Term Rewriting Systems are now commonly used as a modeling language for programs or systems. On those rewriting based models, reachability analysis, i.e. proving or disproving that a given term is reachable from a set of input terms, provides an efficient verification technique. For disproving reachability (i.e. proving non reachability of a term) on non terminating and non confluent rewriting ...

Rewriting systems are used in various areas of computer science, and especially in lambda-calculus, higherorder logics and functional programming. We show that the unsupervised learning networks can implement parallel rewriting. We show how this general correspondence can be refined in order to perform parallel term rewriting in neural networks, for any given first-order term. We simulate these...

This paper introduces the notion of abstract domains for constructor-based conditional term rewriting systems and deenes 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 abs...

Essentially, in a reversible programming language, for each forward computation step from state S to state S′, there exists a constructive and deterministic method to go backwards from state S′ to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or qu...

We introduce a new technique for proving termination of term rewriting systems. The technique, a specialization of Zantema’s semantic labelling technique, is especially useful for establishing the correctness of transformation methods that attempt to prove termination by transforming term rewriting systems into systems whose termination is easier to prove. We apply the technique to modularity, ...

First, using a recent modularity result Ohl94b] for unconditional term rewriting systems (TRSs), it is shown that semi-completeness is a modular property of constructor-sharing join conditional term rewriting systems (CTRSs). Second, we do not only extend results of Middeldorp Mid93] on the modularity of termination for disjoint CTRSs to constructor-sharing systems but also simplify the proofs ...