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

Verificación de aplicaciones web dinámicas con Web-TLR

Web-TLR is a software tool designed for model-checking Web applications that is based on rewriting logic. Web applications are expressed as rewrite theories that can be formally verified by using the Maude built-in LTLR model-checker. Whenever a property is refuted, it produces a counterexample trace that underlies the failing model checking computation. However, the analysis (or even the simple inspection) of large counterexamples may prove to be unfeasible due to the size and complexity of the traces under examination. This work aims to improve the understandability of the counterexamples generated by Web-TLR by developing an integrated framework for debugging Web applications that integrates a trace-slicing technique for rewriting logic theories that is particularly tailored to Web-TLR. The verification environment is also provided with a user-friendly, graphical Web interface that shields the user from unnecessary information. Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. Our trace slicing technique allows us to systematically trace back rewrite sequences modulo equational axioms (such as associativity and commutativity) by means of an algorithm that dynamically simpli es the traces by detecting control and data dependencies, and dropping useless data that do not infuence the final result. Our methodology is particularly suitable for analyzing complex, textually-large system computations such as those delivered as counter-example traces by Maude model-checkers. The slicing facility implemented in Web-TLR allows the user to select the pieces of information that she is interested into by means of a suitable pattern-matching language supported by wildcards. The selected information is then traced back through inverse rewrite sequences. The slicing process drastically simpli es the computation trace by dropping useless data that do not influence the nal result. By using this facility, the Web engineer can focus on the relevant fragments of the failing application, which greatly reduces the manual debugging e ort and also decreases the number of iterative verfications.Espert Real, J. (2011). Verificación de aplicaciones web dinámicas con Web-TLR. http://hdl.handle.net/10251/11219.Archivo delegad

Slicing-based debugging of web applications in rewriting logic

The pervasiveness of computing on the Internet has led to an explosive growth of Web applications that, together with their ever-increasing complexity, have turned their design and development in a major challenge. Unfortunately, the huge expansion of development and utilization of Web computation has not been paired by the development of methods, models and debugging tools to help the developer diagnose, quickly and easily, potential problems in a Web application. There is an urgent demand of analysis and verification facilities capable to prevent insecure software that could cause unavailability of systems or services, or provide access to private data or internal resources of a given organization. The main goal of this MSc thesis is to improve the debugging of Web applications by embedding novel analysis and verification techniques that rely on the program semantics. As a practical realization of the ideas, we use Web-TLR that is a verification engine for dynamic Web applications based on Rewrite Logic. We extend Web-TLR with a novel functionality that supports effective Web debugging for realistic Web applications involving complex execution traces. This functionality is based on a backward trace slicing technique that is based on dynamic labeling. In order to extend the class of programs covered by the debugging methodology we formalize a generalization of the slicer to Conditional Rewriting Logic theories, greatly simplifying the debugging task by providing a novel and sophisticated form of pattern matching.Frechina Navarro, F. (2011). Slicing-based debugging of web applications in rewriting logic. http://hdl.handle.net/10251/15637Archivo delegad

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

Variant-Based Satisfiability

Although different satisfiability decision procedures can be combined by algorithms such as those of Nelson-Oppen or Shostak, current tools typically can only support a finite number of theories to use in such combinations. To make SMT solving more widely applicable, generic satisfiability algorithms that can allow a potentially infinite number of decidable theories to be user-definable, instead of needing to be built in by the implementers, are highly desirable. This work studies how folding variant narrowing, a generic unification algorithm that offers good extensibility in unification theory, can be extended to a generic variant-based satisfiability algorithm for the initial algebras of its user-specified input theories when such theories satisfy Comon-Delaune's finite variant property (FVP) and some extra conditions. Several, increasingly larger infinite classes of theories whose initial algebras enjoy decidable variant-based satisfiability are identified, and a method based on descent maps to bring other theories into these classes and to improve the generic algorithm's efficiency is proposed and illustrated with examples.Partially supported by NSF Grant CNS 13-19109.Ope

Rewriting-based Verification and Debugging of Web Systems

The increasing complexity of Web system has led to the development of sophisticated formal methodologies for verifying and correcting Web data and Web programs. In general, establishing whether a Web system behaves correctly with respect to the original intention of the programmer or checking its internal consistency are non-trivial tasks as witnessed by many studies in the literature. In this dissertation, we face two challenging problems related to the verification of Web systems. Firstly, we extend a previous Web verification framework based on partial rewriting by providing a semi-automatic technique for repairing Web systems. We propose a basic repairing methodology that is endowed with several strategies for optimizing the number of repair actions that must be executed in order to fix a given Web site. Also, we develop an improvement of the Web verification framework that is based on abstract interpretation and greatly enhances both efficiency and scalability of the original technique. Secondly, we formalize a framework for the specification and model-checking of dynamic Web applications that is based on Rewriting Logic. Our framework allows one to simulate the user navigation and the evaluation of Web scripts within a Web application, and also check important related properties such us reachability and consistency. When a property is refuted, a counter-example with the erroneous trace is delivered. Such information can be analyzed in order to debug the Web application under examination by means of a novel backward trace slicing technique that we formulated for this purpose. This technique consists in tracing back, along an execution trace, all the relevant symbols of the term (or state) that we are interested to observe.Romero ., DO. (2011). Rewriting-based Verification and Debugging of Web Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12496Palanci

Synchronous products of rewrite systems (extended version)

We present and formalize a concept of synchronous product for rewrite systems, and also a corresponding concept for general transition systems, used as semantics for the former. A series of examples shows their practical usefulness: for the strategic control of systems, and for modular specification and verification

Constrained narrowing for conditional equational theories modulo axioms

For an unconditional equational theory (Sigma, E) whose oriented equations (E) over arrow are confluent and terminating, narrowing provides an E-unification algorithm. This has been generalized by various authors in two directions: (i) by considering unconditional equational theories (Sigma, E boolean OR B) where the (E) over arrow are confluent, terminating and coherent modulo axioms B, and (ii) by considering conditional equational theories. Narrowing for a conditional theory (Sigma, E boolean OR B) has also been studied, but much less and with various restrictions. In this paper we extend these prior results by allowing conditional equations with extra variables in their conditions, provided the corresponding rewrite rules (E) over arrow are confluent, strictly coherent, operationally terminating modulo B and satisfy a natural determinism condition allowing incremental computation of matching substitutions for their extra variables. We also generalize the type structure of the types and operations in Sigma to be order-sorted. The narrowing method we propose, called constrained narrowing, treats conditions as constraints whose solution is postponed. This can greatly reduce the search space of narrowing and allows notions such as constrained variant and constrained unifier that can cover symbolically possibly infinite sets of actual variants and unifiers. It also supports a hierarchical method of solving constraints. We give an inference system for hierarchical constrained narrowing modulo B and prove its soundness and completeness. (C) 2015 Elsevier B.V. All rights reserved.We thank the anonymous referees for their constructive criticism and their very detailed and helpful suggestions for improving an earlier version of this work. We also thank Luis Aguirre for kindly giving us additional suggestions to improve the text. This work has been partially supported by NSF Grant CNS 13-19109 and by the EU (FEDER) and the Spanish MINECO under grant TIN 2013-45732-C4-1-P, and by Generalitat Valenciana PROMETEOII/2015/013.Cholewa, A.; Escobar Román, S.; Meseguer, J. (2015). Constrained narrowing for conditional equational theories modulo axioms. Science of Computer Programming. 112:24-57. https://doi.org/10.1016/j.scico.2015.06.001S245711

Generalized Rewrite Theories, Coherence Completion and Symbolic Methods

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those for standard rewrite theories, including a generalized notion of coherence, are given. Symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations. Using these foundations, several symbolic reasoning methods using generalized rewrite theories are studied, including: (i) symbolic description of sets of terms by pattern predicates; (ii) reasoning about universal reachability properties by generalized rewriting; (iii) reasoning about existential reachability properties by constrained narrowing; and (iv) symbolic verification of safety properties such as invariants and stability properties.This work has been partially supported by NRL under contract number N00173-17-1-G002.Ope

Formal Design of Cloud Computing Systems in Maude

Cloud computing systems are complex distributed systems whose design is challenging for two main reasons: (1) since they are distributed systems, a correct design is very hard to achieve by testing alone; and (2) cloud computing applications have high availability and performance requirements; but these are hard to measure before implementation and hard to compare between different implementations. This paper summarizes our experience in using formal specification in Maude and model checking analysis to quickly explore the design space of a cloud computing system to achieve a high quality design that: (1) has verified correctness guarantees; (2) has better performance properties than other design alternatives so explored; (3) can be achieved before an actual implementation; and (4) can be used for both rapid prototyping and for automatic code generation.Ope