A new compilation technique for left-linear term rewriting systems is presented, where rewrite rules are transformed into so-called minimal rewrite rules. These minimal rules have such a simple form that they can be viewed as instructions for an abstract rewriting machine (ARM). Keywords and Phrases: minimal term rewriting systems, abstract machines, program transformations Note: Part of this w...

Using higher-order functions is standard practice in functional programming, but most functional logic programming languages that have been described in the literature lack this feature. The natural way to deal with higher-order functions in the framework of ( rst-order) term rewriting is through so-called applicative term rewriting systems. In this paper we argue that existing calculi for lazy...

The last open problem regarding the modularity of the fundamental properties of Term Rewriting Systems concerns the property of uniqueness of normal forms w.r.t. reduction (UN !). In this article we solve this open problem,showing that UN ! is modular for left-linear Term Rewriting Systems. The noveìpile and delete' technique here introduced allows for quite a short proof, and is of independent...

Given a constructor term rewriting system defining injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a confluent conditional term rewriting system, and unravels the conditional system into an unconditional term rewriting system. In general, the unconditional system is not confluent and thus not computationally equivalent to the conditional system. In th...

In this paper, we propose methods for proving termination of constrained term rewriting systems, where constraints are interpreted by built-in semantics given by users, and rewrite rules are assumed to be sound for the interpretation. To this end, we extend the dependency pair framework for proving termination of unconstrained term rewriting systems to constrained term rewriting systems. Moreov...

In a previous paper we have established the theory of transsnite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of innnitary rewriting, the BB ohm model of the lambda calculus can be seen as an innnitary term model. In contrast to term rewriting, there are several diierent possible notions of innnite term, whic...

We show that non-collapsing orthogonal term rewriting systems do not have the transfinite Church-Rosser property in the setting of Cauchy convergence. In addition, we show that for (a transfinite version of) the Parallel Moves Lemma to hold, any definition of residual for Cauchy convergent rewriting must either part with a number of fundamental properties enjoyed by rewriting systems in the fin...

Term rewriting systems play an important role in various areas, e.g. in abstract data type speciications, for automated theorem proving and as a basic computation model for functional programming languages. In theory and practice, one of the most important properties of term rewriting systems is the strong normalization or ((nite or uniform) termination property which is undecidable in general....