Proving Termination of Context-Sensitive Rewriting with MU-TERM

Alarcón, Beatriz; Gutiérrez, Raúl; Iborra, José L.; Lucas, Salvador

doi:10.1016/j.entcs.2007.05.041

Cited by 17 publications

(29 citation statements)

References 25 publications

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“…The corresponding implementation in the tool mu-term [3] outperformed all previous tools for termination of CS rewriting.…”

Section: Example 1 Consider This Context-sensitive Term Rewrite Systmentioning

confidence: 99%

“…We implemented our new non-collapsing CS-DPs and all DP processors from this paper in the termination prover AProVE [15]. 20 In contrast, the prover mu-term [3] uses the collapsing CS-DPs. Moreover, the processors for these CS-DPs are not formulated within the DP framework and thus, they cannot be applied in the same flexible and modular way.…”

Section: Experiments and Conclusionmentioning

confidence: 99%

See 1 more Smart Citation

Improving Context-Sensitive Dependency Pairs

Alarcón

Emmes

Fuhs

et al. 2008

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. Context-sensitive dependency pairs (CS-DPs) are currently the most powerful method for automated termination analysis of contextsensitive rewriting. However, compared to DPs for ordinary rewriting, CS-DPs suffer from two main drawbacks: (a) CS-DPs can be collapsing. This complicates the handling of CS-DPs and makes them less powerful in practice. (b) There does not exist a "DP framework " for CS-DPs which would allow one to apply them in a flexible and modular way. This paper solves drawback (a) by introducing a new definition of CS-DPs. With our definition, CS-DPs are always non-collapsing and thus, they can be handled like ordinary DPs. This allows us to solve drawback (b) as well, i.e., we extend the existing DP framework for ordinary DPs to contextsensitive rewriting. We implemented our results in the tool AProVE and successfully evaluated them on a large collection of examples.

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“…The corresponding implementation in the tool mu-term [3] outperformed all previous tools for termination of CS rewriting.…”

Section: Example 1 Consider This Context-sensitive Term Rewrite Systmentioning

confidence: 99%

Section: Experiments and Conclusionmentioning

confidence: 99%

Improving Context-Sensitive Dependency Pairs

Alarcón

Emmes

Fuhs

et al. 2008

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, also a user-defined strategy may be supplied in the strategy language of T T T 2 . Alternatively, termination checks can be performed externally with AProVE or MuTerm [1]. For the retrieval of encompassments and variants, one of the implemented term indexing techniques can be selected (path indexing, discrimination trees, code trees or naive search in the node set).…”

Section: Web Interfacementioning

confidence: 99%

“…In the context of completion, we often consider a pair (E, R) of equations E and rewrite rules R. An equational proof step s ↔ p e t in (E, R) is an equality step if e is an equation ≈ r in E or a rewrite step if e is a rule → r in R, and either s = u [ (1) of equational proof steps. Note that (E, R) admits an equational proof of s ≈ t if and only if s ↔ * E∪R t holds.…”

Section: Preliminariesmentioning

confidence: 99%

Multi-Completion with Termination Tools

et al. 2012

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Knuth-Bendix completion is a classical calculus in automated deduction for transforming a set of equations into a confluent and terminating set of directed equations which can be used to decide the induced equational theory. Multicompletion with termination tools constitutes an approach that differs from the classical method in two respects: (1) external termination tools replace the reduction order-a typically critical parameter-as proposed by , and (2) multi-completion as introduced by Kurihara and Kondo (1999) is used to keep track of multiple orientations in parallel while exploiting sharing to boost efficiency. In this paper we describe the inference system, give the full proof of its correctness and comment on completeness issues. Critical pair criteria and isomorphisms are presented as refinements together with all proofs. We furthermore describe the implementation of our approach in the tool mkbTT, present extensive experimental results and report on new completions.

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“…The former is trivially finite by the Dependency Graph processor of Theorem 4.41. The latter can be solved by any modern termination tool implementing the DP method, such as Aprove [Giesl et al, 2004], Mu-Term [Alarcón et al, 2007], or the small, RPO based reduction pair solver in our tool [Narradar].…”

Section: The Argument Filtering Processormentioning

confidence: 99%

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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Proving Termination of Context-Sensitive Rewriting with MU-TERM

Cited by 17 publications

References 25 publications

Improving Context-Sensitive Dependency Pairs

Improving Context-Sensitive Dependency Pairs

Multi-Completion with Termination Tools

Termination of Narrowing: Automated Proofs and Modularity Properties

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