Inductive-data-type Systems

In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed lambda-calculus enriched by pattern-matching definitions following a certain format, called the "General Schema", which generalizes the usual recursor definitions for natural numbers and similar "basic inductive types". This combined language was shown to be strongly normalizing. The purpose of this paper is to reformulate and extend the General Schema in order to make it easily extensible, to capture a more general class of inductive types, called "strictly positive", and to ease the strong normalization proof of the resulting system. This result provides a computation model for the combination of an algebraic specification language based on abstract data types and of a strongly typed functional language with strictly positive inductive types.Comment: Theoretical Computer Science (2002

Basic completion strategies as another application of the Maude strategy language

The two levels of data and actions on those data provided by the separation between equations and rules in rewriting logic are completed by a third level of strategies to control the application of those actions. This level is implemented on top of Maude as a strategy language, which has been successfully used in a wide range of applications. First we summarize the Maude strategy language design and review some of its applications; then, we describe a new case study, namely the description of completion procedures as transition rules + control, as proposed by Lescanne.Comment: In Proceedings WRS 2011, arXiv:1204.531

On Unfolding Completeness for Rewriting Logic Theories

Many transformation systems for program optimization, program synthesis, and program specialization are based on fold/unfold transformations. In this paper, we investigate the semantic properties of a narrowing-based unfolding transformation that is useful to transform rewriting logic theories. We also present a transformation methodology that is able to determine whether an unfolding transformation step would cause incompleteness and avoid this problem by completing the transformed rewrite theory with suitable extra rules. More precisely, our methodology identifies the sources of incompleteness and derives a set of rules that are added to the transformed rewrite theory in order to preserve the semantics of the original theory.Alpuente Frasnedo, M.; Baggi, M.; Ballis, D.; Falaschi, M. (2010). On Unfolding Completeness for Rewriting Logic Theories. http://hdl.handle.net/10251/863

Analysis of the Runtime Resource Provisioning of BPMN Processes using Maude

International audienceCompanies are continuously adjusting their resources to their needs following different strategies. However, the dynamic provisioning strategies are hard to compare. This paper proposes an automatic analysis technique to evaluate and compare the execution time and resource occupancy of a business process relative to a workload and a provisioning strategy. Such analysis is performed on models conforming to an extension of BPMN with quantitative information, including resource availability and constraints. Within this framework, the approach is fully mechanized using a formal and executable specification in the rewriting logic framework, which relies on existing techniques and tools for simulating probabilistic and real-time specifications

Order-sorted Homeomorphic Embedding modulo Combinations of Associativity and/or Commutativity Axioms

[EN] The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context of order-sorted rewrite theories that support symbolic execution methods modulo equational axioms. This paper generalizes the symbolic homeomorphic embedding relation to order-sorted rewrite theories that may contain various combinations of associativity and/or commutativity axioms for different binary operators. We systematically measure the performance of different, increasingly efficient formulations of the homeomorphic embedding relation modulo axioms that we implement in Maude. Our experimental results show that the most efficient version indeed pays off in practice.M. Alpuente and S. Escobar have been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETEO/2019/098, and by the European Union's Horizon 2020 research and innovation programme under grant agreement No. 952215 (TAILOR). J. Meseguer has been supported by NRL under contract number N00173-17-1-G002. A. Cuenca-Ortega has been supported by the SENESCYT, Ecuador (scholarship program 2013).Alpuente Frasnedo, M.; Cuenca-Ortega, A.; Escobar Román, S.; Meseguer, J. (2020). Order-sorted Homeomorphic Embedding modulo Combinations of Associativity and/or Commutativity Axioms. Fundamenta Informaticae. 177(3-4):297-329. https://doi.org/10.3233/FI-2020-1991S2973291773-

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. 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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). 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