Two Decades of Maude

This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Applications and extensions of context-sensitive rewriting

[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312

Programming and symbolic computation in Maude

[EN] Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite theories. Maude has also a formal environment of verification tools. Symbolic computation is a powerful technique for reasoning about the correctness of concurrent systems and for increasing the power of formal tools. We present several new symbolic features of Maude that enhance formal reasoning about Maude programs and the effectiveness of formal tools. They include: (i) very general unification modulo user-definable equational theories, and (ii) symbolic reachability analysis of concurrent systems using narrowing. The paper does not focus just on symbolic features: it also describes several other new Maude features, including: (iii) Maude's strategy language for controlling rewriting, and (iv) external objects that allow flexible interaction of Maude object-based concurrent systems with the external world. In particular, meta-interpreters are external objects encapsulating Maude interpreters that can interact with many other objects. To make the paper self-contained and give a reasonably complete language overview, we also review the basic Maude features for equational rewriting and rewriting with rules, Maude programming of concurrent object systems, and reflection. Furthermore, we include many examples illustrating all the Maude notions and features described in the paper.Duran has been partially supported by MINECO/FEDER project TIN2014-52034-R. Escobar has been partially supported by the EU (FEDER) and the MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETE0/2019/098, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. MartiOliet and Rubio have been partially supported by MCIU Spanish project TRACES (TIN2015-67522-C3-3-R). Rubio has also been partially supported by a MCIU grant FPU17/02319. Meseguer and Talcott have been partially supported by NRL Grant N00173 -17-1-G002. Talcott has also been partially supported by ONR Grant N00014-15-1-2202.Durán, F.; Eker, S.; Escobar Román, S.; NARCISO MARTÍ OLIET; José Meseguer; Rubén Rubio; Talcott, C. (2020). Programming and symbolic computation in Maude. Journal of Logical and Algebraic Methods in Programming. 110:1-58. https://doi.org/10.1016/j.jlamp.2019.100497S158110Alpuente, M., Escobar, S., Espert, J., & Meseguer, J. (2014). A modular order-sorted equational generalization algorithm. Information and Computation, 235, 98-136. doi:10.1016/j.ic.2014.01.006K. Bae, J. Meseguer, Predicate abstraction of rewrite theories, in: [36], 2014, pp. 61–76.Bae, K., & Meseguer, J. (2015). Model checking linear temporal logic of rewriting formulas under localized fairness. Science of Computer Programming, 99, 193-234. doi:10.1016/j.scico.2014.02.006Bae, K., Meseguer, J., & Ölveczky, P. C. (2014). Formal patterns for multirate distributed real-time systems. Science of Computer Programming, 91, 3-44. doi:10.1016/j.scico.2013.09.010P. Borovanský, C. Kirchner, H. Kirchner, P.E. Moreau, C. Ringeissen, An overview of ELAN, in: [77], 1998, pp. 55–70.Bouhoula, A., Jouannaud, J.-P., & Meseguer, J. (2000). Specification and proof in membership equational logic. Theoretical Computer Science, 236(1-2), 35-132. doi:10.1016/s0304-3975(99)00206-6Bravenboer, M., Kalleberg, K. T., Vermaas, R., & Visser, E. (2008). Stratego/XT 0.17. A language and toolset for program transformation. Science of Computer Programming, 72(1-2), 52-70. doi:10.1016/j.scico.2007.11.003Bruni, R., & Meseguer, J. (2006). Semantic foundations for generalized rewrite theories. Theoretical Computer Science, 360(1-3), 386-414. doi:10.1016/j.tcs.2006.04.012M. Clavel, F. Durán, S. Eker, S. Escobar, P. Lincoln, N. Martí-Oliet, C.L. Talcott, Two decades of Maude, in: [86], 2015, pp. 232–254.Clavel, M., Durán, F., Eker, S., Lincoln, P., Martı́-Oliet, N., Meseguer, J., & Quesada, J. F. (2002). Maude: specification and programming in rewriting logic. Theoretical Computer Science, 285(2), 187-243. doi:10.1016/s0304-3975(01)00359-0Clavel, M., & Meseguer, J. (2002). Reflection in conditional rewriting logic. Theoretical Computer Science, 285(2), 245-288. doi:10.1016/s0304-3975(01)00360-7F. Durán, S. Eker, S. Escobar, N. Martí-Oliet, J. Meseguer, C.L. Talcott, Associative unification and symbolic reasoning modulo associativity in Maude, in: [121], 2018, pp. 98–114.Durán, F., Lucas, S., Marché, C., Meseguer, J., & Urbain, X. (2008). Proving operational termination of membership equational programs. Higher-Order and Symbolic Computation, 21(1-2), 59-88. doi:10.1007/s10990-008-9028-2F. Durán, J. Meseguer, An extensible module algebra for Maude, in: [77], 1998, pp. 174–195.Durán, F., & Meseguer, J. (2003). Structured theories and institutions. Theoretical Computer Science, 309(1-3), 357-380. doi:10.1016/s0304-3975(03)00312-8Durán, F., & Meseguer, J. (2007). Maude’s module algebra. Science of Computer Programming, 66(2), 125-153. doi:10.1016/j.scico.2006.07.002Durán, F., & Meseguer, J. (2012). On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories. The Journal of Logic and Algebraic Programming, 81(7-8), 816-850. doi:10.1016/j.jlap.2011.12.004F. Durán, P.C. Ölveczky, A guide to extending Full Maude illustrated with the implementation of Real-Time Maude, in: [116], 2009, pp. 83–102.S. Escobar, Multi-paradigm programming in Maude, in: [121], 2018, pp. 26–44.Escobar, S., Meadows, C., Meseguer, J., & Santiago, S. (2014). State space reduction in the Maude-NRL Protocol Analyzer. Information and Computation, 238, 157-186. doi:10.1016/j.ic.2014.07.007Escobar, S., Sasse, R., & Meseguer, J. (2012). Folding variant narrowing and optimal variant termination. The Journal of Logic and Algebraic Programming, 81(7-8), 898-928. doi:10.1016/j.jlap.2012.01.002H. Garavel, M. Tabikh, I. Arrada, Benchmarking implementations of term rewriting and pattern matching in algebraic, functional, and object-oriented languages – the 4th rewrite engines competition, in: [121], 2018, pp. 1–25.Goguen, J. A., & Burstall, R. M. (1992). Institutions: abstract model theory for specification and programming. Journal of the ACM, 39(1), 95-146. doi:10.1145/147508.147524Goguen, J. A., & Meseguer, J. (1984). Equality, types, modules, and (why not?) generics for logic programming. The Journal of Logic Programming, 1(2), 179-210. doi:10.1016/0743-1066(84)90004-9Goguen, J. A., & Meseguer, J. (1992). Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science, 105(2), 217-273. doi:10.1016/0304-3975(92)90302-vR. Gutiérrez, J. Meseguer, Variant-based decidable satisfiability in initial algebras with predicates, in: [61], 2018, pp. 306–322.Gutiérrez, R., Meseguer, J., & Rocha, C. (2015). Order-sorted equality enrichments modulo axioms. Science of Computer Programming, 99, 235-261. doi:10.1016/j.scico.2014.07.003Horn, A. (1951). On sentences which are true of direct unions of algebras. Journal of Symbolic Logic, 16(1), 14-21. doi:10.2307/2268661Katelman, M., Keller, S., & Meseguer, J. (2012). Rewriting semantics of production rule sets. The Journal of Logic and Algebraic Programming, 81(7-8), 929-956. doi:10.1016/j.jlap.2012.06.002Kowalski, R. (1979). Algorithm = logic + control. Communications of the ACM, 22(7), 424-436. doi:10.1145/359131.359136Lucanu, D., Rusu, V., & Arusoaie, A. (2017). A generic framework for symbolic execution: A coinductive approach. Journal of Symbolic Computation, 80, 125-163. doi:10.1016/j.jsc.2016.07.012D. Lucanu, V. Rusu, A. Arusoaie, D. Nowak, Verifying reachability-logic properties on rewriting-logic specifications, in: [86], 2015, pp. 451–474.Lucas, S., & Meseguer, J. (2016). Normal forms and normal theories in conditional rewriting. Journal of Logical and Algebraic Methods in Programming, 85(1), 67-97. doi:10.1016/j.jlamp.2015.06.001N. Martí-Oliet, J. Meseguer, A. Verdejo, A rewriting semantics for Maude strategies, in: [116], 2009, pp. 227–247.Martí-Oliet, N., Palomino, M., & Verdejo, A. (2007). Strategies and simulations in a semantic framework. Journal of Algorithms, 62(3-4), 95-116. doi:10.1016/j.jalgor.2007.04.002Meseguer, J. (1992). Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science, 96(1), 73-155. doi:10.1016/0304-3975(92)90182-fMeseguer, J. (2012). Twenty years of rewriting logic. The Journal of Logic and Algebraic Programming, 81(7-8), 721-781. doi:10.1016/j.jlap.2012.06.003Meseguer, J. (2017). Strict coherence of conditional rewriting modulo axioms. Theoretical Computer Science, 672, 1-35. doi:10.1016/j.tcs.2016.12.026J. Meseguer, Generalized rewrite theories and coherence completion, in: [121], 2018, pp. 164–183.Meseguer, J. (2018). Variant-based satisfiability in initial algebras. Science of Computer Programming, 154, 3-41. doi:10.1016/j.scico.2017.09.001Meseguer, J., Goguen, J. A., & Smolka, G. (1989). Order-sorted unification. Journal of Symbolic Computation, 8(4), 383-413. doi:10.1016/s0747-7171(89)80036-7Meseguer, J., & Ölveczky, P. C. (2012). Formalization and correctness of the PALS architectural pattern for distributed real-time systems. Theoretical Computer Science, 451, 1-37. doi:10.1016/j.tcs.2012.05.040Meseguer, J., Palomino, M., & Martí-Oliet, N. (2008). Equational abstractions. Theoretical Computer Science, 403(2-3), 239-264. doi:10.1016/j.tcs.2008.04.040Meseguer, J., & Roşu, G. (2007). The rewriting logic semantics project. Theoretical Computer Science, 373(3), 213-237. doi:10.1016/j.tcs.2006.12.018Meseguer, J., & Roşu, G. (2013). The rewriting logic semantics project: A progress report. Information and Computation, 231, 38-69. doi:10.1016/j.ic.2013.08.004Meseguer, J., & Skeirik, S. (2017). Equational formulas and pattern operations in initial order-sorted algebras. Formal Aspects of Computing, 29(3), 423-452. doi:10.1007/s00165-017-0415-5Meseguer, J., & Thati, P. (2007). Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. Higher-Order and Symbolic Computation, 20(1-2), 123-160. doi:10.1007/s10990-007-9000-6C. Olarte, E. Pimentel, C. Rocha, Proving structural properties of sequent systems in rewriting logic, in: [121], 2018, pp. 115–135.Ölveczky, P. C., & Meseguer, J. (2007). Semantics and pragmatics of Real-Time Maude. Higher-Order and Symbolic Computation, 20(1-2), 161-196. doi:10.1007/s10990-007-9001-5Ölveczky, P. C., & Thorvaldsen, S. (2009). Formal modeling, performance estimation, and model checking of wireless sensor network algorithms in Real-Time Maude. Theoretical Computer Science, 410(2-3), 254-280. doi:10.1016/j.tcs.2008.09.022Rocha, C., Meseguer, J., & Muñoz, C. (2017). Rewriting modulo SMT and open system analysis. Journal of Logical and Algebraic Methods in Programming, 86(1), 269-297. doi:10.1016/j.jlamp.2016.10.001Şerbănuţă, T. F., Roşu, G., & Meseguer, J. (2009). A rewriting logic approach to operational semantics. Information and Computation, 207(2), 305-340. doi:10.1016/j.ic.2008.03.026Skeirik, S., & Meseguer, J. (2018). Metalevel algorithms for variant satisfiability. Journal of Logical and Algebraic Methods in Programming, 96, 81-110. doi:10.1016/j.jlamp.2017.12.006S. Skeirik, A. Ştefănescu, J. Meseguer, A constructor-based reachability logic for rewrite theories, in: [61], 2018, pp. 201–217.Strachey, C. (2000). Higher-Order and Symbolic Computation, 13(1/2), 11-49. doi:10.1023/a:1010000313106A. Ştefănescu, S. Ciobâcă, R. Mereuta, B.M. Moore, T. Serbanuta, G. Roşu, All-path reachability logic, in: [36], 2014, pp. 425–440.Tushkanova, E., Giorgetti, A., Ringeissen, C., & Kouchnarenko, O. (2015). A rule-based system for automatic decidability and combinability. Science of Computer Programming, 99, 3-23. doi:10.1016/j.scico.2014.02.00

Model checking strategy-controlled rewriting systems (extended version)

Strategies are widespread in Computer Science. In the domain of reduction and rewriting systems, strategies are studied as recipes to restrict and control reduction steps and rule applications, which are intimately local, in a derivation-global sense. This idea has been exploited by various tools and rewriting-based specification languages, where strategies are an additional specification layer. Systems so described need to be analyzed too. This article discusses model checking of systems controlled by strategies and presents a working strategy-aware LTL model checker for the Maude specification language, based on rewriting logic, and its strategy language. This extended version includes the proofs of the propositions in the conference paper, and a complete description of the small-step operational semantics used to define model checking for the Maude strategy language

Rewriting Strategies and Strategic Rewrite Programs (Updated version)

This survey aims at providing unified definitions of strategies , strategic rewriting and strategic programs. It gives examples of main constructs and languages used to write strategies. It also explores some properties of strategic rewriting and operational semantics of strategic programs. Current research topics are identified

Rewriting Strategies and Strategic Rewrite Programs

International audienceThis survey aims at providing unified definitions of strategies, strategic rewriting and strategic programs. It gives examples of main constructs and languages used to write strategies. It also explores some properties of strategic rewriting and operational semantics of strategic programs. Current research topics are identified

Dependency pairs for proving termination properties of conditional term rewriting systems

[EN] The notion of operational termination provides a logic-based definition of termination of computational systems as the absence of infinite inferences in the computational logic describing the operational semantics of the system. For Conditional Term Rewriting Systems we show that operational termination is characterized as the conjunction of two termination properties. One of them is traditionally called termination and corresponds to the absence of infinite sequences of rewriting steps (a horizontal dimension). The other property, that we call V-termination, concerns the absence of infinitely many attempts to launch the subsidiary processes that are required to perform a single rewriting step (a vertical dimension). We introduce appropriate notions of dependency pairs to characterize termination, V-termination, and operational termination of Conditional Term Rewriting Systems. This can be used to obtain a powerful and more expressive framework for proving termination properties of Conditional Term Rewriting Systems.Partially supported by the EU (FEDER), Spanish MINECO projects TIN 2013-45732-C4-1-P and TIN2015-69175-C4-1-R, GV project PROMETEOII/2015/013, and NSF grant CNS 13-19109. Salvador Lucas' research was partly developed during a sabbatical year at UIUCLucas Alba, S.; Meseguer, J. (2017). Dependency pairs for proving termination properties of conditional term rewriting systems. Journal of Logical and Algebraic Methods in Programming. 86(1):236-268. https://doi.org/10.1016/j.jlamp.2016.03.003S23626886

Equational logic and rewriting

International audienceIn this survey, we do not address higher order logics nor type theory, but rather restrict to first-order concepts. We focus on equational logic and its relation to rewriting logic and we consider their impact on automated deduction and programming languages

Session-based concurrency in Maude:Executable semantics and type checking

Session types are a well-established approach to communication correctness in message-passing processes. Widely studied from a process calculi perspective, here we pursue an unexplored strand and investigate the use of the Maude system for implementing session-typed process languages and reasoning about session-typed process specifications. We present four technical contributions. First, we develop and implement in Maude an executable specification of the operational semantics of a session-typed π-calculus by Vasconcelos. Second, we also develop an executable specification of its associated algorithmic type checking, and describe how both specifications can be integrated. Third, we show that our executable specification can be coupled with reachability and model checking tools in Maude to detect well-typed but deadlocked processes. Finally, we demonstrate the robustness of our approach by adapting it to a higher-order session π-calculus, in which exchanged values include names but also abstractions (functions from names to processes). All in all, our contributions define a promising new approach to the (semi)automated analysis of communication correctness in message-passing concurrency