Operational Termination of Membership Equational Programs: the Order-Sorted Way

Lucas, Salvador; Meseguer, José

doi:10.1016/j.entcs.2009.05.021

Cited by 18 publications

(24 citation statements)

References 23 publications

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“…Regarding tool support for the method we have presented, our current experimental prototype should be extended and integrated within the MTT tool [6]. In this way, our termination technique modulo combinations of axioms will become applicable to an even wider range of rewrite theories, that can be transformed into order-sorted ones by non-termination-preserving transformations [8,21].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Termination Modulo Combinations of Equational Theories

Durán

Lucas

Meseguer

2009

Lecture Notes in Computer Science

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Abstract. Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics-and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left-and right-identity axioms for various function symbols.

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Section: Related Work and Conclusionmentioning

confidence: 99%

Termination Modulo Combinations of Equational Theories

Durán

Lucas

Meseguer

2009

Lecture Notes in Computer Science

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“…The rewrite system − → E is sort decreasing modulo B if and only if for each (t → u if γ) ∈ − → E and substitution θ, ls(tθ) ≥ ls(uθ) if (Σ, B, − → E ) γθ. The system − → E is operationally terminating modulo B [25] if and only if there is no infinite well-formed proof tree in (Σ, B, − → E ) (see [45] for terminology and details). Furthermore, − → E is confluent modulo B if and only if for all t, t 1 , t 2 ∈ T Σ (X), if t → * E/B t 1 and t → * E/B t 2 , then there is u ∈ T Σ (X) such that t 1 → * E/B u and t 2 → * E/B u.…”

Section: Preliminariesmentioning

confidence: 99%

Rewriting modulo SMT and open system analysis

Rocha

Meseguer

Muñoz

2017

Journal of Logical and Algebraic Methods in Programming

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Abstract. This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.

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“…• Transformation B : from CS-OS-CTRSs to CS-OS-TRSs [LM09]. This transformation plays a similar role than B for the order-sorted case.…”

Section: A Conditional Trs (Ctrs) Is a Triple R = (σ A R)mentioning

confidence: 99%

“…• TransformationÖ-L : from CS-OS-TRSs to CS-TRSs [LM09]. It generalizes, to the context-sensitive level, a well-known transformation bÿ Olveczky and Lysne [ÖL96].…”

Section: A Conditional Trs (Ctrs) Is a Triple R = (σ A R)mentioning

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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Operational Termination of Membership Equational Programs: the Order-Sorted Way

Cited by 18 publications

References 23 publications

Termination Modulo Combinations of Equational Theories

Termination Modulo Combinations of Equational Theories

Rewriting modulo SMT and open system analysis

Towards a Framework for Proving Termination of Maude Programs

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