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

Narrowing and Unification in the Maude Programming Language

[ES] Los protocolos de seguridad en las comunicaciones evolucionan cada día buscando mejoras y corrección de errores, muchos de los cuales pueden llevar a vulnerabilidades con consecuencias fatales. Por ello, se vuelve de vital importancia el encontrar algoritmos y herramientas capaces de encontrar esas vulnerabilidades para poder solucio-narlas cuanto antes. Uno de estos algoritmos es el narrowing, implementado en Maude, un lenguaje utilizado por varias herramientas de análisis de protocolos, que, a pesar de ser potente y eficiente en muchos casos, tiene algunas limitaciones, que pueden ser resueltas mediante la utilización de variantes del algoritmo. Una posible variante es el canonical narrowing, que se basa en restricciones de irreductibilidad para descartar aquellas secuencias del narrowing estándar que pueden obviarse porque no representan secuencias de reescritura reales.[EN] Communications security protocols evolve every day seeking improvements and bug fixes, many of which can lead to vulnerabilities with fatal consequences. For this reason, it becomes vitally important to find algorithms and tools capable of finding these vulnerabilities in order to fix them as soon as possible. One of these algorithms is narrowing, implemented in Maude, a language used by various protocol analysis tools, which, despite being powerful and efficient in many cases, has some limitations, which can be resolved by using variants of the algorithm. A possible variant is canonical narrowing, which relies on irreducibility constraints to discard those sequences of the standard narrowing that can be ignored because they do not represent actual rewrite sequences.López Rueda, R. (2021). Narrowing and Unification in the Maude Programming Language. Universitat Politècnica de València. http://hdl.handle.net/10251/173970TFG

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

Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA

The area of formal analysis of cryptographic protocols has been an active one since the mid 80’s. The idea is to verify communication protocols that use encryption to guarantee secrecy and that use authentication of data to ensure security. Formal methods are used in protocol analysis to provide formal proofs of security, and to uncover bugs and security flaws that in some cases had remained unknown long after the original protocol publication, such as the case of the well known Needham-Schroeder Public Key (NSPK) protocol. In this thesis we tackle problems regarding the three main pillars of protocol verification: modelling capabilities, verifiable properties, and efficiency. This thesis is devoted to investigate advanced features in the analysis of cryptographic protocols tailored to the Maude-NPA tool. This tool is a model-checker for cryptographic protocol analysis that allows for the incorporation of different equational theories and operates in the unbounded session model without the use of data or control abstraction. An important contribution of this thesis is relative to theoretical aspects of protocol verification in Maude-NPA. First, we define a forwards operational semantics, using rewriting logic as the theoretical framework and the Maude programming language as tool support. This is the first time that a forwards rewriting-based semantics is given for Maude-NPA. Second, we also study the problem that arises in cryptographic protocol analysis when it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the protocol equational theory. We also study techniques to extend Maude-NPA capabilities to support the verification of a wider class of protocols and security properties. First, we present a framework to specify and verify sequential protocol compositions in which one or more child protocols make use of information obtained from running a parent protocol. Second, we present a theoretical framework to specify and verify protocol indistinguishability in Maude-NPA. This kind of properties aim to verify that an attacker cannot distinguish between two versions of a protocol: for example, one using one secret and one using another, as it happens in electronic voting protocols. Finally, this thesis contributes to improve the efficiency of protocol verification in Maude-NPA. We define several techniques which drastically reduce the state space, and can often yield a finite state space, so that whether the desired security property holds or not can in fact be decided automatically, in spite of the general undecidability of such problems.Santiago Pinazo, S. (2015). Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/4852

Abstract Logical Model Checking of Infinite-State Systems Using Narrowing

A concurrent system can be naturally specified as a rewrite theory R = (Sigma, E, R) where states are elements of the initial algebra of terms modulo E and concurrent transitions are axiomatized by the rewrite rules R. Under simple conditions, narrowing with rules R modulo equations E can be used to symbolically represent the system\u27s state space by means of terms with logical variables. We call this symbolic representation a "logical state space" and it can also be used for model checking verification of LTL properties. Since in general such a logical state space can be infinite, we propose several abstraction techniques for obtaining either an over-approximation or an under-approximation of the logical state space: (i) a folding abstraction that collapses patterns into more general ones, (ii) an easy-to-check method to define (bisimilar) equational abstractions, and (iii) an iterated bounded model checking method that can detect if a logical state space within a given bound is complete. We also show that folding abstractions can be faithful for safety LTL properties, so that they do not generate any spurious counterexamples. These abstraction methods can be used in combination and, as we illustrate with examples, can be effective in making the logical state space finite. We have implemented these techniques in the Maude system, providing the first narrowing-based LTL model checker we are aware of

Matching Logic

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, at the same time admitting its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning with equality remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages that have an operational semantics, but it is not limited to this

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

Modelling and analyzing adaptive self-assembling strategies with Maude

Building adaptive systems with predictable emergent behavior is a challenging task and it is becoming a critical need. The research community has accepted the challenge by introducing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. We recently proposed a conceptual framework for adaptation centered around the role of control data. In this paper we show that it can be naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model. Moreover, we exploit this model to specify and analyse a prominent example of adaptive system: robot swarms equipped with obstacle-avoidance self-assembly strategies. The analysis exploits the statistical model checker PVesta