Termination of narrowing via termination of rewriting

Nishida, Naoki; Vidal, Germán

doi:10.1007/s00200-010-0122-4

Cited by 21 publications

(37 citation statements)

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“…A significant body of work has been done on termination of logic programs under top-down evaluation (De Schreye and Decorte 1994;Voets and De Schreye 2011;Marchiori 1996;Ohlebusch 2001;Codish et al 2005;Serebrenik and De Schreye 2005;Nishida and Vidal 2010;Schneider-Kamp et al 2009;Schneider-Kamp et al 2010;Nguyen et al 2007;Bruynooghe et al 2007;Bonatti 2004;Baselice et al 2009) and in the area of term rewriting (Zantema 1995;Sternagel and Middeldorp 2008;Arts and Giesl 2000;Endrullis et al 2008;Ferreira and Zantema 1996). Termination properties of query evaluation for normal programs under tabling have been studied in (Riguzzi and Swift 2013;Riguzzi and Swift 2014;Verbaeten et al 2001).…”

Section: Related Workmentioning

confidence: 99%

Using linear constraints for logic program termination analysis

Greco¹,

Molinaro²,

Trubitsyna³

2016

Theory and Practice of Logic Programming

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It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their introduction is that the evaluation of a program might not terminate and checking whether it terminates or not is undecidable. To cope with this problem, several classes of logic programs have been proposed where the use of function symbols is restricted but the program evaluation termination is guaranteed. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel classes of rule-bounded and cycle-bounded programs, which overcome different limitations of current approaches by performing a more global analysis of how terms are propagated from the body to the head of rules. Results on the correctness, the complexity, and the expressivity of the proposed approach are provided. Under consideration in Theory and Practice of Logic Programming (TPLP).

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Section: Related Workmentioning

confidence: 99%

Using linear constraints for logic program termination analysis

Greco¹,

Molinaro²,

Trubitsyna³

2016

Theory and Practice of Logic Programming

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“…A significant body of work has been done on termination of logic programs under top-down evaluation [9,36,22,25,8,30,24,28,29,23,5,4,3] and in the area of term rewriting [37,32,2,11,12]. Termination properties of query evaluation for normal programs under tabling have been studied in [26,27,34].…”

Section: Related Workmentioning

confidence: 99%

Checking Termination of Logic Programs with Function Symbols through Linear Constraints

Greco

Molinaro

Trubitsyna

2014

Rules on the Web. From Theory to Applications

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Abstract. Enriching answer set programming with function symbols makes modeling easier, increases the expressive power, and allows us to deal with infinite domains. However, this comes at a cost: common inference tasks become undecidable. To cope with this issue, recent research has focused on finding trade-offs between expressivity and decidability by identifying classes of logic programs that impose limitations on the use of function symbols but guarantee decidability of common inference tasks. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel class of rulebounded programs. While current techniques perform a limited analysis of how terms are propagated from an individual argument to another, our technique is able to perform a more global analysis, thereby overcoming several limitations of current approaches. We also present a further class of cycle-bounded programs where groups of rules are analyzed together. We show different results on the correctness and the expressivity of the proposed techniques.

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“…In [Nishida and Miura, 2006;Nishida et al, 2003], the approach of [Arts and Giesl , 2000] is adapted to the termination of narrowing, whereas [Vidal , 2008;Nishida and Vidal , 2010] proves termination of narrowing w.r.t. a given set of initial queries, relying on a restricted form of termination of rewriting based on relative termination.…”

Section: Automatic Terminationmentioning

confidence: 99%

“…However, both [Nishida and Miura, 2006;Nishida et al, 2003] and [Vidal , 2008;Nishida and Vidal , 2010] apply only to restricted classes of TRSs, namely rightlinear TRSs (i.e., no repeated variables occur in the right-hand sides of the rules), or constructor systems (the arguments of the lhs's of the rules are constructor terms). These two classes are overly restrictive for many of the applications of narrowing mentioned in Section 1.…”

Section: Automatic Terminationmentioning

confidence: 99%

“…The only possible derivation for this term (or any other) is finite, whereas the TRS does not fit in any of the syntactic characterizations for trat 2 , and cannot be proven terminating by any of the existing automated approaches ( [Nishida and Miura, 2006;Vidal, 2008;Nishida and Vidal, 2010]), nor does it fit in any of the terminating classes introduced in Chapter 3. However as we will prove in the following, the system is terminating for narrowing.…”

Section: Termination Of Narrowing With Dependency Pairsmentioning

confidence: 99%

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Termination of Narrowing: Automated Proofs and Modularity Properties

López¹

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In 1936, Alan Turing proved that the halting problem, that is, deciding whether a program terminates, is an undecidable problem for most practical programming languages. Even so, termination is so relevant that a vast number of techniques for proving the termination of programs have been researched in the recent decades. Term rewriting systems provide an abstract theoretical framework ideally suited for the study of termination. In term rewriting systems, evaluation of a term corresponds to the left-to-right, non-deterministic application of rewriting rules.Narrowing is a generalization of term rewriting that provides a mechanism for automated reasoning. For instance, given a set of rules defining addition and multiplication with natural numbers, rewriting allows to perform evaluation of arithmetic expressions, whereas narrowing allows to solve equations with variables over arithmetic expressions. This thesis constitutes an in-depth study of the termination properties of narrowing. The contributions are as follows.First, we identify classes of systems where narrowing behaves well, in the sense that it always terminates for any system belonging to these classes. Many methods of analysis, such as the semantics-based analysis of program properties by means of narrowing, benefit from this characterization.Second, we develop an automatic method to prove termination of narrowing for a given system, based on the abstract framework of dependency pairs. For the first time, such an automatic method is not restricted to specific classes of TRSs and hence is universally applicable.Third, we propose another automatic method to prove termination of narrowing from a given term, also on top of the framework of dependency pairs. Termination from a given term is relevant for many applications, including the termination analysis of programming languages. Our method generalizes the current state-of-the-art, enabling the study of termination of logic programs in terms of the termination of narrowing, something which was not possible previously.Fourth and last, the modularity properties of the termination of narrowing are considered in detail. That is, given two systems A and B where narrowing is terminating, determine whether it is still terminating in the union system. This notion of modularity has implications in many of the applications of narrowing. We develop the case of combining systems for equational unification.Furthermore, the automated approaches of the second and third contributions above have been implemented in Narradar, our tool for automatic proofs of termination of narrowing. ResumenEn 1936 Alan Turing demostró que el halting problem, esto es, el problema de decidir si un programa termina o no, es un problema indecidible para la inmensa mayoría de los lenguajes de programación. A pesar de ello, la terminación es un problema tan relevante que en lasúltimas décadas un gran número de técnicas han sido desarrolladas para demostrar la terminación de forma automática de la máxima cantidad posible de programas. Los...

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Termination of narrowing via termination of rewriting

Cited by 21 publications

References 58 publications

Using linear constraints for logic program termination analysis

Using linear constraints for logic program termination analysis

Checking Termination of Logic Programs with Function Symbols through Linear Constraints

Termination of Narrowing: Automated Proofs and Modularity Properties

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