Hidden Type Variables and Conditional Extension for More Expressive Generic Programs

Generic object-oriented programming languages combine parametric polymorphism and nominal subtype polymorphism, thereby providing better data abstraction, greater code reuse, and fewer run-time errors. However, most generic object-oriented languages provide a straightforward combination of the two kinds of polymorphism, which prevents the expression of advanced type relationships. Furthermore, most generic object-oriented languages have a type-erasure semantics: instantiations of type parameters are not available at run time, and thus may not be used by type-dependent operations. This dissertation shows that two features, which allow the expression of many advanced type relationships, can be added to a generic object-oriented programming language without type erasure: 1. type variables that are not parameters of the class that declares them, and 2. extension that is dependent on the satisfiability of one or more constraints. We refer to the first feature as hidden type variables and the second feature as conditional extension. Hidden type variables allow: covariance and contravariance without variance annotations or special type arguments such as wildcards; a single type to extend, and inherit methods from, infinitely many instantiations of another type; a limited capacity to augment the set of superclasses after that class is defined; and the omission of redundant type arguments. Conditional extension allows the properties of a collection type to be dependent on the properties of its element type. This dissertation describes the semantics and implementation of hidden type variables and conditional extension. A sound type system is presented. In addition, a sound and terminating type checking algorithm is presented. Although designed for the Fortress programming language, hidden type variables and conditional extension can be incorporated into other generic object-oriented languages. Many of the same problems would arise, and solutions analogous to those we present would apply

Evaluation of Datalog queries and its application to the static analysis of Java code

Two approaches for evaluating Datalog programs are presented: one based on boolean equation systems, and the other based on rewriting logic. The work is presented in the context of the static analysis of Java programs specified in Datalog.Feliú Gabaldón, MA. (2010). Evaluation of Datalog queries and its application to the static analysis of Java code. http://hdl.handle.net/10251/14016Archivo delegad

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Relational extensions to feature logic: applications to constraint based grammars

This thesis investigates the logical and computational foundations of unification-based or more appropriately constraint based grammars. The thesis explores extensions to feature logics (which provide the basic knowledge representation services to constraint based grammars) with multi-valued or relational features. These extensions are useful for knowledge representation tasks that cannot be expressed within current feature logics.The approach bridges the gap between concept languages (such as KL-ONE), which are the mainstay of knowledge representation languages in AI, and feature logics. Va¬ rious constraints on relational attributes are considered such as existential membership, universal membership, set descriptions, transitive relations and linear precedence con¬ straints.The specific contributions of this thesis can be summarised as follows: 1. Development of an integrated feature/concept logic 2. Development of a constraint logic for so called partial set descriptions 3. Development of a constraint logic for expressing linear precedence constraints 4. The design of a constraint language CL-ONE that incorporates the central ideas provided by the above study 5. A study of the application of CL-ONE for constraint based grammarsThe thesis takes into account current insights in the areas of constraint logic programming, object-oriented languages, computational linguistics and knowledge representation

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

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

Set based failure diagnosis for concurrent constraint programming

Oz is a recent high-level programming language, based on an extension of the concurrent constraint model by higher-order procedures and state. Oz is a dynamically typed language like Prolog, Scheme, or Smalltalk. We investigate two approaches of making static type analysis available for Oz: Set-based failure diagnosis and strong typing. We define a new system of set constraints over feature trees that is appropriate for the analysis of record structures, and we investigate its satisfiability, emptiness, and entailment problem. We present a set-based diagnosis for constraint logic programming and concurrent constraint programming as first-order fragments of Oz, and we prove that it correctly detects inevitable run-time errors. We also propose an analysis for a larger sublanguage of Oz. Complementarily, we define an Oz-style language called Plain that allows an expressive strong type system. We present such a type system and prove its soundness.Oz ist eine anwendungsnahe Programmiersprache, deren Grundlage eine Erweiterung des Modells nebenläufiger Constraintprogrammierung um Prozeduren höherer Stufe und Zustand ist. Oz ist eine Sprache mit dynamischer Typüberprüfung wie Prolog, Scheme oder Smalltalk. Wir untersuchen zwei Ansätze, statische Typüberprüfung für Oz zu ermöglichen: Mengenbasierte Fehlerdiagnose und Starke Typisierung. Wir definieren ein neues System von Mengenconstraints über Featurebäumen, das für die Analyse von Recordstrukturen geeignet ist, und wir untersuchen das Erfüllbarkeits-, das Leerheits- und das Subsumtionsproblem für dieses Constraintsystem. Wir präsentieren eine mengenbasierte Diagnose für Constraint-Logikprogrammierung und für nebenläufige Constraintprogrammierung als Teilsprachen von Oz, und wir beweisen, daß diese unvermeidliche Laufzeitfehler erkennt. Wir schlagen auch eine mengenbasierte Analyse für eine grössere Teilsprache von Oz vor. Komplementär dazu definieren wir eine Oz-artige Sprache genannt Plain, die ein expressives starkes Typsystem erlaubt. Wir stellen ein solches Typsystem vor und beweisen seine Korrektheit

Logic-based techniques for program analysis and specification synthesis

La Tesis investiga técnicas ágiles dentro del paradigma declarativo para dar solución a dos problemas: el análisis de programas y la inferencia de especificaciones a partir de programas escritos en lenguajes multiparadigma y en lenguajes imperativos con tipos, objetos, estructuras y punteros. Respecto al estado actual de la tesis, la parte de análisis de programas ya está consolidada, mientras que la parte de inferencia de especificaciones sigue en fase de desarrollo activo. La primera parte da soluciones para la ejecución de análisis de punteros especificados en Datalog. En esta parte se han desarrollado dos técnicas de ejecución de especificaciones en dicho lenguaje Datalog: una de ellas utiliza resolutores de sistemas de ecuaciones booleanas, y la otra utiliza la lógica de reescritura implementada eficientemente en el lenguaje Maude. La segunda parte desarrolla técnicas de inferencia de especificaciones a partir de programas. En esta parte se han desarrollado dos métodos de inferencia de especificaciones. El primer método se desarrolló para el lenguaje lógico-funcional Curry y permite inferir especificaciones ecuacionales mediante interpretación abstracta de los programas. El segundo método está siendo desarrollado para lenguajes imperativos realistas, y se ha aplicado a un subconjunto del lenguaje de programación C. Este método permite inferir especificaciones en forma de reglas que representan las distintas relaciones entre las propiedades que el estado de un programa satisface antes y después de su ejecución. Además, estas propiedades son expresables en términos de las abstracciones funcionales del propio programa, resultando en una especificación de muy alto nivel y, por lo tanto, de más fácil comprensión.Feliú Gabaldón, MA. (2013). Logic-based techniques for program analysis and specification synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33747TESI

Polynomial Path Orders

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts. On the one hand POP* induces polynomial innermost runtime complexity and hence may serve as a syntactic, and fully automatable, method to analyse the innermost runtime complexity of term rewrite systems. On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*.Comment: LMCS version. This article supersedes arXiv:1209.379

Set based failure diagnosis for concurrent constraint programming

Oz is a recent high-level programming language, based on an extension of the concurrent constraint model by higher-order procedures and state. Oz is a dynamically typed language like Prolog, Scheme, or Smalltalk. We investigate two approaches of making static type analysis available for Oz: Set-based failure diagnosis and strong typing. We define a new system of set constraints over feature trees that is appropriate for the analysis of record structures, and we investigate its satisfiability, emptiness, and entailment problem. We present a set-based diagnosis for constraint logic programming and concurrent constraint programming as first-order fragments of Oz, and we prove that it correctly detects inevitable run-time errors. We also propose an analysis for a larger sublanguage of Oz. Complementarily, we define an Oz-style language called Plain that allows an expressive strong type system. We present such a type system and prove its soundness.Oz ist eine anwendungsnahe Programmiersprache, deren Grundlage eine Erweiterung des Modells nebenläufiger Constraintprogrammierung um Prozeduren höherer Stufe und Zustand ist. Oz ist eine Sprache mit dynamischer Typüberprüfung wie Prolog, Scheme oder Smalltalk. Wir untersuchen zwei Ansätze, statische Typüberprüfung für Oz zu ermöglichen: Mengenbasierte Fehlerdiagnose und Starke Typisierung. Wir definieren ein neues System von Mengenconstraints über Featurebäumen, das für die Analyse von Recordstrukturen geeignet ist, und wir untersuchen das Erfüllbarkeits-, das Leerheits- und das Subsumtionsproblem für dieses Constraintsystem. Wir präsentieren eine mengenbasierte Diagnose für Constraint-Logikprogrammierung und für nebenläufige Constraintprogrammierung als Teilsprachen von Oz, und wir beweisen, daß diese unvermeidliche Laufzeitfehler erkennt. Wir schlagen auch eine mengenbasierte Analyse für eine grössere Teilsprache von Oz vor. Komplementär dazu definieren wir eine Oz-artige Sprache genannt Plain, die ein expressives starkes Typsystem erlaubt. Wir stellen ein solches Typsystem vor und beweisen seine Korrektheit