Improving Context-Sensitive Dependency Pairs

Alarcón, Beatriz; Emmes, Fabian; Fuhs, Carsten; Giesl, Jürgen; Gutiérrez, Raúl; Lucas, Salvador; Schneider–Kamp, Peter; Thiemann, René

doi:10.1007/978-3-540-89439-1_44

Cited by 16 publications

(44 citation statements)

References 30 publications

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“…Finally, in Section 6 we summarize our approach and its application in the examples, discuss its relationship to previous approaches and briefly touch the important perspective and open problem of (at least partially) automating the generation of suitable forbidden patterns in practice. 1 …”

Section: This Trs Is Non-terminating and Not Even Weakly Normalizingmentioning

confidence: 99%

Extending Context-Sensitivity in Term Rewriting

Gramlich

Schernhammer

2010

Electron. Proc. Theor. Comput. Sci.

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We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears in a certain context. This shape and context is expressed through forbidden patterns. In particular we analyze the relationships among this novel approach and the commonly used notion of context-sensitivity in term rewriting, as well as the feasibility of rewriting with forbidden patterns from a computational point of view. The latter feasibility is characterized by demanding that restricting a rewrite relation yields an improved termination behaviour while still being powerful enough to compute meaningful results. Sufficient criteria for both kinds of properties in certain classes of rewrite systems with forbidden patterns are presented.

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Section: This Trs Is Non-terminating and Not Even Weakly Normalizingmentioning

confidence: 99%

Extending Context-Sensitivity in Term Rewriting

Gramlich

Schernhammer

2010

Electron. Proc. Theor. Comput. Sci.

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“…Proof of item (2) follows the results in [GM02b] and more precisely, the ones in [Emm08] that adapt them to the CSDP framework of [AEF+08]. For details about some statements in the following, we recall the reader to the corresponding lemmas in these papers to simplify the proof.…”

Section: Part IIImentioning

confidence: 82%

“…The proof of the previous lemma differs from the one in [AEF+08] in the refinement done in the notion of hiding context mentioned in [GL10] and it is slightly different from the one in [GL10] since we are dealing with innermost rewriting and all µ-replacing variables of the instantiated left-hand sides of the rules applied in a innermost µ-rewrite sequence are in µ-normal form: no matter if they are in a nonactive position on the right-hand side, they cannot start any reduction. In [GL10] it is not necessary either since in a µ-rewrite sequence, these variables could start a reduction but due to minimality, these reductions would be finite.…”

Section: Publications (Full Text)mentioning

confidence: 91%

“…First notion of hiding context was found in [AEF+08] but it has been recently slightly redefined in [GL10]. We follow the last definition since it present some advantages.…”

Section: Definition 2 (Hidden Term [Agl10])mentioning

confidence: 99%

“…P Note that the processor is only sound because we refine the result to be applied only to the set of usable rules instead of over the whole set of rules as in standard rewriting [GTSF06] or even for context-sensitive in [AEF+08]. In this way, (i.e.…”

Section: Proofmentioning

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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mu-term: Verify Termination Properties Automatically (System Description)

Gutiérrez

Lucas

2020

Automated Reasoning

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We report on the new version of mu-term, a tool for proving termination properties of variants of rewrite systems, including conditional, context-sensitive, equational, and order-sorted rewrite systems. We follow a unified, logic-based approach to describe rewriting computations. The automatic generation of logical models for suitable firstorder theories and formulas provides a common basis to implement the proofs.Supported by EU (FEDER), and projects RTI2018-094403-B-C32,PROMETEO/ 2019/098, and SP20180225. Also by INCIBE program "Ayudas para la excelencia de los equipos de investigación avanzada en ciberseguridad" (Raúl Gutiérrez).

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Improving Context-Sensitive Dependency Pairs

Cited by 16 publications

References 30 publications

Extending Context-Sensitivity in Term Rewriting

Extending Context-Sensitivity in Term Rewriting

Towards a Framework for Proving Termination of Maude Programs

mu-term: Verify Termination Properties Automatically (System Description)

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