Rule-Based Software Verification and Correction

The increasing complexity of software systems has led to the development of sophisticated formal Methodologies for verifying and correcting data and programs. In general, establishing whether a program behaves correctly w.r.t. the original programmer s intention or checking the consistency and the correctness of a large set of data are not trivial tasks as witnessed by many case studies which occur in the literature. In this dissertation, we face two challenging problems of verification and correction. Specifically, verification and correction of declarative programs, and the verification and correction of Web sites (i.e. large collections of semistructured data). Firstly, we propose a general correction scheme for automatically correcting declarative, rule-based programs which exploits a combination of bottom-up as well as topdown inductive learning techniques. Our hybrid hodology is able to infer program corrections that are hard, or even impossible, to obtain with a simpler,automatic top-down or bottom-up learner. Moreover, the scheme will be also particularized to some well-known declarative programming paradigm: that is, the functional logic and the functional programming paradigm. Secondly, we formalize a framework for the automated verification of Web sites which can be used to specify integrity conditions for a given Web site, and then automatically check whether these conditions are fulfilled. We provide a rule-based, formal specification language which allows us to define syntactic as well as semantic properties of the Web site. Then, we formalize a verification technique which detects both incorrect/forbidden patterns as well as lack of information, that is, incomplete/missing Web pages. Useful information is gathered during the verification process which can be used to repair the Web site. So, after a verification phase, one can also infer semi-automatically some possible corrections in order to fix theWeb site. The methodology is based on a novel rewritBallis, D. (2005). Rule-Based Software Verification and Correction [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/194

Imposing Assertions in Maude via Program Transformation

[EN] Program transformation is widely used for producing correct mutations of a given program so as to satisfy the user's intent that can be expressed by means of some sort of specification (e.g. logical assertions, functional specifications, reference implementations, summaries, examples). This paper describes an automated correction methodology for Maude programs that is based on program transformation and can be used to enforce a safety policy, given by a set A of system assertions, in a Maude program R that might disprove some of the assertions. The outcome of the technique is a safe program refinement R' of R in which every computation is a good run, i.e., it satisfies the assertions in A. Furthermore, the transformation ensures that no good run of R is removed from R'. Advantages of this correction methodology can be summarized as follows. A fully automatic program transformation featuring both program diagnosis and repair that preserves all executability requirements. A simple logical notation to declaratively express invariant properties and other safety constraints through assertions. No dynamic information is required to infer program fixes: the methodology is static and does not need to collect any error symptom at runtime.This work has been partially supported by the EU (FEDER) and the Spanish MINECO under grant RTI2018-094403-B-C32, and by Generalitat Valenciana under grant PROMETEO/2019/098.Alpuente Frasnedo, M.; Ballis, D.; Sapiña-Sanchis, J. (2019). Imposing Assertions in Maude via Program Transformation. MethodsX. 6:2577-2583. https://doi.org/10.1016/j.mex.2019.10.035S25772583

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

Backward Trace Slicing for Rewriting Logic Theories -Technical report -

Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis of Rewriting Logic theories. 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 simplifies the traces by detecting control and data dependencies, and dropping useless data that do not influence 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.Alpuente Frasnedo, M.; Ballis, D.; Espert, J.; Romero, D. (2011). Backward Trace Slicing for Rewriting Logic Theories -Technical report -. http://hdl.handle.net/10251/1077

Inspecting rewriting logic computations (in a parametric and stepwise way)

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-54624-2_12Trace inspection is concerned with techniques that allow the trace content to be searched for specific components. This paper presents a rich and highly dynamic, parameterized technique for the trace inspection of Rewriting Logic theories that allows the non-deterministic execution of a given unconditional rewrite theory to be followed up in different ways. Using this technique, an analyst can browse, slice, filter, or search the traces as they come to life during the program execution. Starting from a selected state in the computation tree, the navigation of the trace is driven by a user-defined, inspection criterion that specifies the required exploration mode. By selecting different inspection criteria, one can automatically derive a family of practical algorithms such as program steppers and more sophisticated dynamic trace slicers that facilitate the dynamic detection of control and data dependencies across the computation tree. Our methodology, which is implemented in the Anima graphical tool, allows users to capture the impact of a given criterion thereby facilitating the detection of improper program behaviors.This work has been partially supported by the EU (FEDER), the Spanish MEC project ref. TIN2010-21062-C02-02, the Spanish MICINN complementary action ref. TIN2009-07495-E, and by Generalitat Valenciana ref. PROMETEO2011/052. This work was carried out during the tenure of D. Ballis’ ERCIM “Alain Bensoussan ”Postdoctoral Fellowship. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n. 246016. F. Frechina was supported by FPU-ME grant AP2010-5681.Alpuente Frasnedo, M.; Ballis, D.; Frechina, F.; Sapiña Sanchis, J. (2014). Inspecting rewriting logic computations (in a parametric and stepwise way). En Specification, algebra, and software: essays dedicated to Kokichi Futatsugi. Springer Verlag (Germany). 229-255. https://doi.org/10.1007/978-3-642-54624-2_12S229255Alpuente, M., Ballis, D., Baggi, M., Falaschi, M.: A Fold/Unfold Transformation Framework for Rewrite Theories extended to CCT. In: Proc. PEPM 2010, pp. 43–52. ACM (2010)Alpuente, M., Ballis, D., Espert, J., Romero, D.: Model-checking Web Applications with Web-TLR. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 341–346. Springer, Heidelberg (2010)Alpuente, M., Ballis, D., Espert, J., Romero, D.: Backward Trace Slicing for Rewriting Logic Theories. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 34–48. Springer, Heidelberg (2011)Alpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Slicing-Based Trace Analysis of Rewriting Logic Specifications with iJulienne. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 121–124. Springer, Heidelberg (2013)Alpuente, M., Ballis, D., Frechina, F., Romero, D.: Using Conditional Trace Slicing for improving Maude programs. Science of Computer Programming (2013) (to appear)Alpuente, M., Ballis, D., Romero, D.: A Rewriting Logic Approach to the Formal Specification and Verification of Web applications. Science of Computer Programming (2013) (to appear)Baggi, M., Ballis, D., Falaschi, M.: Quantitative Pathway Logic for Computational Biology. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 68–82. Springer, Heidelberg (2009)Bruni, R., Meseguer, J.: Semantic Foundations for Generalized Rewrite Theories. Theoretical Computer Science 360(1-3), 386–414 (2006)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Maude Manual (Version 2.6). Technical report, SRI Int’l Computer Science Laboratory (2011), http://maude.cs.uiuc.edu/maude2-manual/Clements, J., Flatt, M., Felleisen, M.: Modeling an Algebraic Stepper. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 320–334. Springer, Heidelberg (2001)Durán, F., Meseguer, J.: A Maude Coherence Checker Tool for Conditional Order-Sorted Rewrite Theories. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 86–103. Springer, Heidelberg (2010)Eker, S.: Associative-Commutative Matching via Bipartite Graph Matching. The Computer Journal 38(5), 381–399 (1995)Eker, S.: Associative-Commutative Rewriting on Large Terms. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 14–29. Springer, Heidelberg (2003)Klop, J.W.: Term Rewriting Systems. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science, vol. I, pp. 1–112. Oxford University Press (1992)Martí-Oliet, N., Meseguer, J.: Rewriting Logic: Roadmap and Bibliography. Theoretical Computer Science 285(2), 121–154 (2002)Meseguer, J.: Conditional Rewriting Logic as a Unified Model of Concurrency. Theoretical Computer Science 96(1), 73–155 (1992)Meseguer, J.: The Temporal Logic of Rewriting: A Gentle Introduction. In: Degano, P., De Nicola, R., Meseguer, J. (eds.) Montanari Festschrift. LNCS, vol. 5065, pp. 354–382. Springer, Heidelberg (2008)Plotkin, G.D.: The Origins of Structural Operational Semantics. The Journal of Logic and Algebraic Programming 60-61(1), 3–15 (2004)Riesco, A., Verdejo, A., Caballero, R., Martí-Oliet, N.: Declarative Debugging of Rewriting Logic Specifications. In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 308–325. Springer, Heidelberg (2009)Riesco, A., Verdejo, A., Martí-Oliet, N.: Declarative Debugging of Missing Answers for Maude. In: Proc. RTA 2010. LIPIcs, vol. 6, pp. 277–294 (2010)TeReSe. Term Rewriting Systems. Cambridge University Press (2003

Debugging Maude programs via runtime assertion checking and trace slicing

[EN] This is the author’s version of a work that was accepted for publication in . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Logical and Algebraic Methods in Programming, [VOL 85, ISSUE 5, (2016)] DOI 10.1016/j.jlamp.2016.03.001.In this paper we propose a dynamic analysis methodology for improving the diagnosis of erroneous Maude programs. The key idea is to combine runtime checking and dynamic trace slicing for automatically catching errors at runtime while reducing the size and complexity of the erroneous traces to be analyzed (i.e., those leading to states failing to satisfy some of the assertions). First, we formalize a technique that is aimed at automatically detecting deviations of the program behavior (symptoms) with respect to two types of user-defined assertions: functional assertions and system assertions. The proposed dynamic checking is provably sound in the sense that all errors flagged are definitely violations of the specifications. Then, upon eventual assertion violations we generate accurate trace slices that help identify the cause of the error. Our methodology is based on (i) a logical notation for specifying assertions that are imposed on execution runs; (ii) a runtime checking technique that dynamically tests the assertions; and (iii) a mechanism based on (equational) least general generalization that automatically derives accurate criteria for slicing from falsified assertions. Finally, we report on an implementation of the proposed technique in the assertion-based, dynamic analyzer ABETS and show how the forward and backward tracking of asserted program properties leads to a thorough trace analysis algorithm that can be used for program diagnosis and debugging. © 2016 Elsevier Inc. All rights reserved.This work has been partially supported by the EU (FEDER) and the Spanish MINECO under grants TIN2015-69175-C4-1-R and TIN2013-45732-C4-1-P, and by Generalitat Valenciana Ref. PROMETEOII/2015/013. F. Frechina was supported by FPU-ME grant AP2010-5681, and J. Sapiña was supported by FPI-UPV grant SP2013-0083 and mobility grant VIIT-3946.Alpuente Frasnedo, M.; Ballis, D.; Frechina, F.; Sapiña-Sanchis, J. (2016). Debugging Maude programs via runtime assertion checking and trace slicing. Journal of Logical and Algebraic Methods in Programming. 85(5):707-736. https://doi.org/10.1016/j.jlamp.2016.03.001S70773685

Symbolic Analysis of Maude Theories with Narval

[EN] Concurrent functional languages that are endowed with symbolic reasoning capabilities such as Maude offer a high-level, elegant, and efficient approach to programming and analyzing complex, highly nondeterministic software systems. Maude's symbolic capabilities are based on equational unification and narrowing in rewrite theories, and provide Maude with advanced logic programming capabilities such as unification modulo user-definable equational theories and symbolic reachability analysis in rewrite theories. Intricate computing problems may be effectively and naturally solved in Maude thanks to the synergy of these recently developed symbolic capabilities and classical Maude features, such as: (i) rich type structures with sorts (types), subsorts, and overloading; (ii) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity; and (iii) classical reachability analysis in rewrite theories. However, the combination of all of these features may hinder the understanding of Maude symbolic computations for non-experienced developers. The purpose of this article is to describe how programming and analysis of Maude rewrite theories can be made easier by providing a sophisticated graphical tool called Narval that supports the fine-grained inspection of Maude symbolic computations.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grants PROMETEO/2019/098 and APOSTD/2019/127, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286.Alpuente Frasnedo, M.; Escobar Román, S.; Sapiña-Sanchis, J.; Ballis, D. (2019). Symbolic Analysis of Maude Theories with Narval. Theory and Practice of Logic Programming. 19(5-6):874-890. https://doi.org/10.1017/S1471068419000243S874890195-

Combining Runtime Checking and Slicing to Improve Maude Error Diagnosis

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23165-5_3This paper introduces the idea of using assertion checking for enhancing the dynamic slicing of Maude computation traces. Since trace slicing can greatly simplify the size and complexity of the analyzed traces, our methodology can be useful for improving the diagnosis of erroneous Maude programs. The proposed methodology is based on (i) a logical notation for specifying two types of user-defined assertions that are imposed on execution runs: functional assertions and system assertions; (ii) a runtime checking technique that dynamically tests the assertions and is provably safe in the sense that all errors flagged are definite violations of the specifications; and (iii) a mechanism based on equational least general generalization that automatically derives accurate criteria for slicing from falsified assertions.This work has been partially supported by the EU (FEDER) and the Spanish MINECO project ref. TIN2013-45732-C4-01 (DAMAS), and by Generalitat Valenciana ref. PROMETEOII/2015/013 (SmartLogic). F. Frechina was supported by FPU-ME grant AP2010-5681, and J. Sapiña was supported by FPI-UPV grant SP2013-0083.Alpuente Frasnedo, M.; Ballis, D.; Frechina Navarro, F.; Sapiña Sanchis, J. (2015). Combining Runtime Checking and Slicing to Improve Maude Error Diagnosis. En Logic, Rewriting, and Concurrency. Essays Dedicated to José Meseguer on the Occasion of His 65th Birthday. 72-96. https://doi.org/10.1007/978-3-319-23165-5_3S7296Alpuente, M., Ballis, D., Espert, J., Romero, D.: Backward trace slicing for rewriting logic theories. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 34–48. Springer, Heidelberg (2011)Alpuente, M., Ballis, D., Frechina, F., Romero, D.: Backward trace slicing for conditional rewrite theories. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 62–76. Springer, Heidelberg (2012)Alpuente, M., Ballis, D., Frechina, F., Romero, D.: Julienne: a trace slicer for conditional rewrite theories. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 28–32. Springer, Heidelberg (2012)Alpuente, M., Ballis, D., Frechina, F., Romero, D.: Using conditional trace slicing for improving Maude programs. Sci. Comput. Program. 80, Part B:385–415 (2014)Alpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Slicing-based trace analysis of rewriting logic specifications with $$I$$ Julienne. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 121–124. Springer, Heidelberg (2013)Alpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Inspecting rewriting logic computations (in a Parametric and Stepwise Way). In: Iida, S., Meseguer, J., Ogata, K. (eds.) Specification, Algebra, and Software. LNCS, vol. 8373, pp. 229–255. Springer, Heidelberg (2014)Alpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Debugging Maude programs via runtime assertion checking and trace slicing. Technical report, Department of Computer Systems and Computation, Universitat Politècnica de València (2015). http://safe-tools.dsic.upv.es/abets/abets-tr.pdfAlpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Exploring conditional rewriting logic computations. J. Symbolic Comput. 69, 3–39 (2015)Alpuente, M., Escobar, S., Espert, J., Meseguer, J.: A modular order-sorted equational generalization algorithm. Inf. Comput. 235, 98–136 (2014)Baader, F., Snyder, W.: Unification Theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 447–533. Elsevier Science (2001)Bruni, R., Meseguer, J.: Semantic foundations for generalized rewrite theories. Theor. Comput. Sci. 360(1–3), 386–414 (2006)Clarke, L.A., Rosenblum, D.S.: A historical perspective on runtime assertion checking in software development. ACM SIGSOFT Softw. Eng. Notes 31(3), 25–37 (2006)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS. Springer, Heidelberg (2007)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Maude Manual (Version 2.6). Technical report, SRI International Computer Science Laboratory (2011). http://maude.cs.uiuc.edu/maude2-manual/Durán, F., Meseguer, J.: A Maude coherence checker tool for conditional order-sorted rewrite theories. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 86–103. Springer, Heidelberg (2010)Durán, F., Roldán, M., Vallecillo, A.: Invariant-driven strategies for Maude. Electron. Notes Theor. Comput. Sci. 124(2), 17–28 (2005)Goguen, J.A., Meseguer, J.: Equality, types, modules, and (why not?) generics for logic programming. J. Logic Program. 1(2), 179–210 (1984)Goguen, J.A., Meseguer, J.: Unifying functional, object-oriented and relational programming with logical semantics. In: Agha, G., Wegner, P., Yonezawa, A. (eds.), Research Directions in Object-Oriented Programming, pp. 417–478. The MIT Press (1987)Klop, J.W.: Term rewriting systems. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.), Handbook of Logic in Computer Science, vol. I, pp. 1–112. Oxford University Press (1992)Korel, B., Laski, J.: Dynamic program slicing. Inf. Process. Lett. 29(3), 155–163 (1988)Lassez, J.L., Maher, M.J., Marriott, K.: Unification Revisited. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 587–625. Morgan Kaufmann, Los Altos, California (1988)Leavens, G.T., Cheon, Y.: Design by Contract with JML (2005). http://www.eecs.ucf.edu/ leavens/JML/jmldbc.pdfMartí-Oliet, N., Palomino, M., Verdejo, A.: Rewriting logic bibliography by topic: 1990–2011. J. Logic Algebraic Program. 81(7–8), 782–815 (2012)Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theoret. Comput. Sci. 96(1), 73–155 (1992)Meseguer, J.: Multiparadigm logic programming. In: Kirchner, H., Levi, G. (eds.) ALP 1992. LNCS, vol. 632, pp. 158–200. Springer, Heidelberg (1992)Rocha, C., Meseguer, J., Muñoz, C.: Rewriting modulo SMT and open system analysis. In: Escobar, S. (ed.) WRLA 2014. LNCS, vol. 8663, pp. 247–262. Springer, Heidelberg (2014)Roşu, G.: From Rewriting Logic, to Programming Language Semantics, to Program Verification. In: Martí-Oliet, N., Ölveczky, P.C., Talcott, C., (eds.) Logic, Rewriting, and Concurrency. LNCS, vol. 9200, pp. 598–616. Springer, Heidelberg (2015)Roldán, M., Durán, F., Vallecillo, A.: Invariant-driven specifications in Maude. Sci. Comput. Program. 74(10), 812–835 (2009)TeReSe. Term Rewriting Systems. Cambridge University Press (2003

Narrowing-based Optimization of Rewrite Theories

Partial evaluation has been never investigated in the context of rewrite theories that allow concurrent systems to be specified by means of rules, with an underlying equational theory being used to model system states as terms of an algebraic data type. In this paper, we develop a symbolic, narrowing-driven partial evaluation framework for rewrite theories that supports sorts, subsort overloading, rules, equations, and algebraic axioms. Our partial evaluation scheme allows a rewrite theory to be optimized by specializing the plugged equational theory with respect to the rewrite rules that define the system dynamics. This can be particularly useful for automatically optimizing rewrite theories that contain overly general equational theories which perform unnecessary computations involving matching modulo axioms, because some of the axioms may be blown away after the transformation. The specialization is done by using appropriate unfolding and abstraction algorithms that achieve significant specialization while ensuring the correctness and termination of the specialization. Our preliminary results demonstrate that our transformation can speed up a number of benchmarks that are difficult to optimize otherwise.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018094403-B-C32,andbyGeneralitatValencianaundergrantPROMETEO/2019/098. JuliaSapiñahasbeensupported by the Generalitat Valenciana APOSTD/2019/127 grantAlpuente Frasnedo, M.; Ballis, D.; Escobar Román, S.; Sapiña Sanchis, J. (2020). Narrowing-based Optimization of Rewrite Theories. Universitat Politècnica de València. http://hdl.handle.net/10251/14557