Arts, T. and Zantema, H. 1993. Termination of logic programs via labelled term rewrite systems. In Proceedings of CSN'95, Utrecht, The Netherlands, November. 22-34.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....1994] Brodsky and Sagiv 1989] Franchez et al. 1985] In [Rao et al. 1998] this discussion is nicely summarized, extended with valuable additional issues and brought up to date, especially on the level of the transformational techniques (including a.o. Aguzzi and Modigliani 1994] [Arts and Zantema 1993], Ganzinger and Waldmann 1993] and [Marchiori 1994] We do not repeat these general comparative arguments here, but refer to [De Schreye and Decorte 1994] and [Rao et al. 1998] instead. In this section, we discuss the relation between our technique and some other more recent contributions to the ....

Arts, T. and Zantema, H. 1993. Termination of logic programs via labelled term rewrite systems. In Proceedings of CSN'95, Utrecht, The Netherlands, November. 22-34.

.... in studying termination of logic programs by transforming them into TRSs [14] and implementation of functional logic programming languages [7] A logic program terminates for a class of queries if the derived TRS innermost terminates (not necessarily terminate under all reduction strategies) [2]. In the functional logic programming, innermost reduction strategy is used for both narrowing as well as rewrite steps. In this paper, we study about the strong innermost normalization property of TRSs. If a rewrite system terminates, every subsystem of it terminates as well. This nice property ....

T. Arts, H. Zantema, Termination of logic programs via labelled term rewrite systems, Tech. Rep. RUU-CS-95-32, Utrecht University, 1995.

....for which the above transformation derives terminating TRSs is same as that of [21] 42 Aguzzi and Modigliani [1] identified a class of programs, called input driven programs for which the derived TRS terminates if and only if the logic program terminates for well moded queries. Arts and Zantema [5] worked on this issue further and investigated the classes of programs for which the derived TRS (their transformation is essentially same as that of [1, 9] can be proved terminating using recursive path ordering and semantic labelling. Using the results of Zantema [40] they show that their ....

T. Arts and H. Zantema. Termination of logic programs via labelled term rewrite systems. TR UU-CS-1994-20, Utrecht University, 1994.

....for non overlapping syntactically deterministic composable CTRSs. Secondly, Ganzinger and Waldmann [GW93] proved that a translation of a well moded logic program P into a quasi reductive deterministic CTRS RP yields a termination proof for P . Using an imperative procedure, Arts and Zantema [AZ95,AZ96] transformed a logic program P directly into an unconditional TRS (which in essence coincides with U(RP ) and showed that innermost termination of this system ensures termination of P . Consequently, it is remarked in [AZ95] that the suggested method is applicable to a wider class of logic ....

....proof for P . Using an imperative procedure, Arts and Zantema [AZ95,AZ96] transformed a logic program P directly into an unconditional TRS (which in essence coincides with U(RP ) and showed that innermost termination of this system ensures termination of P . Consequently, it is remarked in [AZ95] that the suggested method is applicable to a wider class of logic programs and hence it is stronger than the other results . Although U(RP ) is not necessarily non overlapping, it can be shown that in this particular case innermost termination and termination are equivalent. A consequence is ....

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T. Arts and H. Zantema. Termination of logic programs via labelled term rewrite systems. In Proceedings of Computing Science in the Netherlands, pages 22--34, 1995.

....the righthand sides of the rules. There is another important application of our main result. It has already been mentioned that a well moded logic program P is terminating whenever it can be transformed into a quasi reductive deterministic CTRS RP . Using an imperative procedure, Arts and Zantema [AZ95,AZ96] transformed a logic program P directly into an unconditional TRS which in essence coincides with U(RP ) They proved that single redex termination of U(RP ) implies termination of P. Although U(RP ) is not necessarily non overlapping, it can be shown that in this particular case single redex ....

....and the joinability of all conditional critical pairs; see Theorem 32. Theorem 50. If P is an LR well moded logic program such that RP is quasi reductive, then P is terminating. If moreover every conditional critical pair in RP is joinable, then P is uniquely terminating. Arts and Zantema [AZ95,AZ96] stated an imperative procedure 5 which directly transforms a logic program P into an unconditional TRS. This TRS 6 is essentially the same as U(RP ) They showed that single redex termination of U(RP ) suffices to prove termination of P; see [AZ95, Thm. 4.8] and [Art97, Thm. 8.2.9] ....

T. Arts and H. Zantema. Termination of Logic Programs via Labelled Term Rewrite Systems. In Proceedings of Computing Science in the Netherlands, pages 22--34, 1995.

....rule : loop avoidance and answers synthesis. Unfortunately, Linear Completion is not completely satisfying since divergence may persist for certain kinds of logic programs. We just take some simple examples to illustrate the problem. Let us consider the following specification extracted from [3] : geq(x; x) geq(s(x) y) geq(x; y) This program is translated into the rewrite program : geq(x; x) true (1) geq(s(x) y) geq(x; y) 2) This transformation is, not only semantics preserving (see [8] but also termination preserving in that sense that if a Prolog interpreter ....

....redundant computation. In [16] it is shown that this technique is terminating and complete for all programs which have a finite model. However, this mechanism needs a concurrent implementation and, when the set of answers is infinite, memoing has no synthesis capacity. There are other works ([3], 13] 15] issued from rewriting field to deal with logic programming. Their aim is not to define a new execution mechanism, as in linear completion, but rather to analyse the termination properties of logic programs evaluated with SLD resolution. In these approaches, the idea is to relate the ....

T. Arts, H. Zantema "Termination of logic programs via labelled term rewrite systems." Utrecht University, Technical Report UU-CS-1994-20 May 1994.

....termination of some TRSs exist, we propose the following approach for automatically proving left termination of well moded logic programs: transform the logic program into a TRS and prove termination of the TRS by existing techniques like RPO and by techniques to be developed. The result in [AZ94] states that this approach indeed covers a great and important class of logic programs called structural recursive logic programs. But it covers far more logic programs. For example, termination of the logic program geq(x; x) p(0) geq(s(x) y) geq(x; y) p(s(x) geq(x; y) p(y) is not ....

....correspond to the predicate symbols and the k symbols introduced in the algorithm. The constructor symbols correspond to the function symbols and constants of the logic program, also denoted by Fun, together with the out symbols introduced in the algorithm, also denoted by Out. For details see [AZ94]. 3.2. Definition. Let t 1 ; t n be terms. We write var(t 1 ; t n ) for the ordered sequence (with respect to some fixed total order on variables) of all variables in t 1 ; t n . For example var(p(z) max(x; x; x) less(0; y) is the sequence x; y; z. program Transform (P ....

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Thomas Arts and Hans Zantema. Termination of logic programs via labelled term rewrite systems. Technical Report UU-CS-1994-20, Utrecht University, May 1994.

....is preserved. More precisely, if the TRS terminates, then the original well moded logic program is left terminating, thus terminates for all well moded goals. Other authors followed this approach and came up with transformations suitable for proving termination of a larger class of logic programs [GW92, CR93, AM93, AZ94, Mar94]. Most transformation algorithms transform the logic programs into constructor systems (CSs) a subclass of the TRSs. This paper describes a technique to prove termination of CSs. The technique is in particular suitable for, but not limited to, those CSs that are obtained from the transformation ....

....algorithm with a second transformation of the resulting conditional rewrite system into a TRS. Our transformation is inspired by this two step transformation. Independently, in [AM93] a transformation was presented to transform a well moded logic program together with a goal into a TRS. We proved [AZ94] that for our transformation single redex normalisation of the TRS is sufficient to conclude termination of the well moded logic programs independent of the given well moded goal, which is stronger than the other results. We also proved that the proposed transformation is complete with respect to ....

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Thomas Arts and Hans Zantema. Termination of logic programs via labelled term rewrite systems. Technical Report UU-CS-1994-20, Utrecht University.

....the logic program into a term rewrite system (TRS) such that the termination property is preserved. More precisely, if the TRS terminates, then the original well moded logic program is leftterminating. Other authors followed this approach and came up with transformations [GW92, CR93, AM93, AZ94, Mar94] suitable for proving termination of more logic programs. Most transformation algorithms transform the logic programs into constructor systems (CSs) a subclass of the TRSs. This paper describes a technique that is able to prove termination of CSs. The technique is in particular suitable ....

....the logic programs into constructor systems (CSs) a subclass of the TRSs. This paper describes a technique that is able to prove termination of CSs. The technique is in particular suitable for, but not limited to, those CSs that are obtained from the transformation algorithm described in [AZ94] Although the technique is mainly developed for logic programs, it is not necessary to know anything about logic programs or the transformations of logic programs into CSs, to understand the technique presented in this paper. As a typical example, let the constructor system R 1 be f(x) ....

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Thomas Arts and Hans Zantema. Termination of logic programs via labelled term rewrite systems. Technical Report UU-CS-1994-20, Utrecht University, PO box 80.089, 3508 TB Utrecht, May 1994.

....any rule has to be equal to the corresponding right hand side; in this extension the left hand side is allowed to be greater than the corresponding right hand side. Recent applications of semantic labelling outside the scope of pure term rewriting are in process algebra ( 8] logic programming ([2]) and in explicit substitution in calculus as described by the system SUBST. Two papers ( 11, 5] were devoted exclusively to termination of SUBST. In [21, 22] we gave a simpler proof even proving simple termination of SUBST, using the technique of distribution elimination. In section 6 we give ....

Arts, T., and Zantema, H. Termination of logic programs via labelled term rewrite systems. Tech. Rep. UU-CS-1994-20, Utrecht University, May 1994.

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