We consider a generalized form of inductive definitions as first suggested by Guttag. Partial functions may be defined by introducing error values in the right hand sides. For such definitions the intuitive semantics is not consistent with that of unrestricted rewriting. In general, the addition of rewrite rules capturing the intuitively motivated error propagation will destroy confluence of th...

A rewrite sequence is said to be outermost-fair if every outer-most redex occurrence is eventually eliminated. Outermost-fair rewriting is known to be (head-)normalising for almost orthogonal rewrite systems. In this paper we study (head-)normalisation for the larger class of weakly orthogonal rewrite systems. Normalisation is established and a counterexample against head-normalisation is provi...

We propose the notion of a correct transformation of one rewrite system into another If such a transformation is correct then the normal forms of a term in the original rewrite system can be obtained by computing the normal forms of the interpretation of this term in the transformed rewrite system We show for several transformations from the literature that they are correct most notably for the...

ROC! is a deterministic rewrite strategy language which includes the rewrite rulesas basic operators, and the deterministic choice and the repetition as high-level strategyoperators. In this paper we present a method which, for a given term rewriting system(TRS) R, constructs a new TRS R such that R-rewriting is equivalent (sound and com-plete) with R-rewriting constrained by RO...

The purpose of this study was to apply an effective learning model in increasing the ability appreciate literature while at same time interest and students SMP Negeri 14 Binjai towards literary works. research conducted Classroom Action Research (CAR) with subject 25 grade IX 2020/2021 academic year. object is rewrite contents story (rewrite), retell (retell), conclude moral message as well rel...

This paper describes an extension of head-needed rewriting on term rewriting systems to higher-order rewrite systems. The main di culty of this extension is caused by the -reductions induced from the higher-order reductions. In order to overcome this di culty, we de ne a new descendant of higher-order rewrite systems. This paper shows the new de nition of descendant, its properties and head nor...

We show that termination is decidable for rewrite systems that contain shallow and right-linear rules, collapsing rules, and rightground rules. This class of rewrite systems is expressive enough to include interesting rules. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving and hence the reachability and joinability problems are decidable. Decidabil...

The Knuth-Bendix completion procedure generates a confluent set of rewrite rules by repeatedly superposing left hand sides of rewrite rules and adding any generated critical pairs as new rewrite rules. The process may terminate in two ways; with success: there are no more (nontrivial) critical pairs, or with failure: a critical pair is generated which cannot be oriented by the ordering. The pro...

We introduce an abstract general notion of system of equations and rewrites between terms, called Term Equational Rewrite System (TERS), and develop a sound logical deduction system, called Term Equational Rewrite Logic (TERL), to reason about equality and rewriting. Further, we give an analysis of algebraic free constructions which together with an internal completeness result may be used to s...

Rewriting is a computational process in which one term is derived from another by replacing a subterm with another subterm in accordance with a set of rules. If such a set of rules rewrite system has the property that no derivation can continue indeenitely, it is said to be terminating. Showing termination is an important component of theorem proving and of great interest in programming languag...