Improving the Context-sensitive Dependency Graph

Alarcón, Beatriz; Gutiérrez, Raúl; Lucas, Salvador

doi:10.1016/j.entcs.2007.05.040

Cited by 9 publications

(13 citation statements)

References 14 publications

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“…Since a TRS is a 1-sorted MS-TRS, and a MS-TRS is an OS-TRS with discrete poset of sorts, our method includes the standard DP method, and a MS-DP method for proving termination of MS-TRSs as special cases. 2 See Section 10 for a brief discussion of parametric polymorphism.…”

Section: Is-even(y) -> Is-even(opposite(y))mentioning

confidence: 99%

Order-sorted dependency pairs

Lucas

Meseguer

2008

Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming

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Types (or sorts) are pervasive in computer science and in rewritingbased programming languages, which often support subtypes (subsorts) and subtype polymorphism. Programs in these languages can be modeled as order-sorted term rewriting systems (OS-TRSs). Often, termination of such programs heavily depends on sort information. But few techniques are currently available for proving termination of OS-TRSs; and they often fail for interesting OS-TRSs. In this paper we generalize the dependency pairs approach to prove termination of OS-TRSs. Preliminary experiments suggest that this technique can succeed where existing ones fail, yielding easier and simpler termination proofs.

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Section: Is-even(y) -> Is-even(opposite(y))mentioning

confidence: 99%

Order-sorted dependency pairs

Lucas

Meseguer

2008

Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming

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“…As noticed in [1], the need for collapsing dependency pairs causes severe disadvantages since it becomes quite hard to extend methods for proving termination from ordinary rewriting to context-sensitive rewriting. While progress has been made to some extent [2,3,18], the resulting methods are weak in practice.…”

Section: Example 23 Consider the Following Ordinary Trs [2]mentioning

confidence: 99%

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Falke

Kapur

2010

Functional and Constraint Logic Programming

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Abstract. Context-sensitive rewriting is a restriction of rewriting that can be used to elegantly model declarative specification and programming languages such as Maude. Furthermore, it can be used to model lazy evaluation in functional languages such as Haskell. Building upon our previous work on an expressive and elegant class of rewrite systems (called CERSs) that contains built-in numbers and supports the use of collection data structures such as sets or multisets, we consider contextsensitive rewriting with CERSs in this paper. This integration results in a natural way for specifying algorithms in the rewriting framework. In order to prove termination of this kind of rewriting automatically, we develop a dependency pair framework for context-sensitive rewriting with CERSs, resulting in a flexible termination method that can be automated effectively. Several powerful termination techniques are developed within this framework. An implementation in the termination prover AProVE has been successfully evaluated on a large collection of examples.

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“…The dependency pairs method [AG00, GAO02,GTS04,GTSF06,HM04,HM05], one of the most powerful techniques for proving termination of rewriting, had not been investigated in connection with proofs of termination of CSR until [AGL06]. As shown in [AGL07], proofs of termination using context-sensitive dependency pairs (CSDPs) are much more powerful and faster than any other technique for proving termination of CSR. As we show here, dealing with innermost CSR, we have a similar situation.…”

Section: Innermost Termination Of Context-sensitive Rewritingmentioning

confidence: 99%

“…So this is the first proposal of a direct method for proving termination of innermost CSR. We have extended the DP framework [ GTS04,GTSF06] to prove innermost termination of TRSs to innermost CSR (thus also extending [AGL07]). Our benchmarks show that the use of ICSDPs dramatically improves the performance of existing (transformational) methods for proving termination of innermost CSR.…”

Section: Applications and Practical Impactmentioning

confidence: 99%

“…In recent years, we have worked to extend the DP framework to verify a number of termination properties of (variants of) TRSs: termination of context-sensitive rewriting [AGL06, AGL07,AGL10], termination of innermost context-sensitive rewriting [ AL07,AL09], termination of order-sorted rewriting [LM08], and termination of rewriting modulo specific axioms [ ALM10,AGLM11]. The main reason is because many systems can be nonterminating if those features are not taken into account when proving termination like strategy annotations or sorts.…”

Section: Introductionmentioning

confidence: 99%

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Towards a Framework for Proving Termination of Maude Programs

Jiménez¹

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Españato Bienve, responsible for my happiness. AcknowledgmentsI would like to thank Salvador Lucas, my scientific father, for being a good advisor, not only for this thesis but also about life. He was often very strict, but just did what any good father would do. He has helped me appreciate the satisfaction of doing things well.I would also like to thank María Alpuente for giving me the first opportunity to join the elp family. It has been a pleasure to share these five years with all of them and the mist group: Toni, Tama, Raúl, Rafa, Josep, Gustavo, Mauricio, Diego, Alexei, Sonia, Marco, Dani, Pepe, Nando, Alicia, Germán, Cesar, Santi, Jose, María José, . . . and those that came only for a few months and gained a place in my heart: Vesna, Michele and Patricia.Special mention goes to those that were not just workmates but also friends: Cesar (little bird) is the most incredible person I have met here, only he knows how much I owe him. Toni is the best lab mate ever. We have walked together from the beginning and we have shared many good moments. Tama, my spoiled child, I can only wish him all the best in the life, he certainly deserves it.Many thanks to my coauthors, especially to Raúl, for all his help and support. I am proud of the great work that we have done together. It has been a pleasure having such a good companion along this difficult path. Thanks to Rafa for always having a nice word to say and making me laugh.I would also like to thank all the people that I met around the world and allowed me to learn from them. These include Jürgen Giesl and the group at the RWTH Aachen: Carsten, Peter, Stephan, Ivan, René,. . . ; and José Meseguer and the group at UIUC that made me feel at home: Camilo, Ralf, Edgar,. . . and specially Mike.Special thanks go to my parents and brothers. I know you will never understand a word of this thesis, but you have always supported me in any decision I have made. AbstractMaude is a declarative programming language based on rewriting logic that incorporates many features that in order to prove certain computational properties lead to difficulties. The task of proving termination of rewrite systems in indeed quite hard but applied to real programming languages, becomes more complicated due to these inherent features. Therefore, methods for proving termination of such programs require specific techniques and a careful analysis. Several papers have studied how to prove termination of (a subset of) Maude programs. However, all of them follow a transformational approach where the original program is transformed until it reaches a rewrite system that can be managed with existing techniques and termination tools. In practice, the fact of transforming the original systems used to complicate the proof of termination since it introduces new symbols and rules in the system. In this thesis, we tackle the problem of proving termination of (a subset of) Maude programs by means of direct methods.On the one hand, we pay attention to the strategy of Maude. Maude is an eager language where the a...

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Improving the Context-sensitive Dependency Graph

Cited by 9 publications

References 14 publications

Order-sorted dependency pairs

Order-sorted dependency pairs

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Towards a Framework for Proving Termination of Maude Programs

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