Methods for Proving Termination of Rewriting-based Programming Languages by Transformation

AbstractDespite the remarkable development of the theory of termination of rewriting, its application to high-level (rewriting-based) programming languages is far from being optimal. This is due to the need for features such as conditional equations and rules, types and subtypes, (possibly programmable) strategies for controlling the execution, matching modulo axioms, and so on, that are used in many programs and tend to place such programs outside the scope of current termination tools. The operational meaning of such features is often formalized in a proof theoretic manner by means of an inference system rather than just by a rewriting relation. The corresponding termination notions can also differ from the standard ones. During the last years we have introduced and implemented different notions and transformation techniques which have been proved useful for proving and disproving termination of such programs by using existing tools for proving termination of (variants of) rewriting. In this paper we provide an overview of our main contributions

Datalog-Based program analysis with BES and RWL

This paper describes two techniques for Datalog query evaluation and their application to object-oriented program analysis. The first technique transforms Datalog programs into an implicit Boolean Equation System (Bes) that can then be solved by using linear-time complexity algorithms that are available in existing, general purpose verification toolboxes such as Cadp. In order to improve scalability and to enable analyses involving advanced meta-programming features, we develop a second methodology that transforms Datalog programs into rewriting logic (Rwl) theories. This method takes advantage of the preeminent features and facilities that are available within the high-performance system Maude, which provides a very efficient implementation of Rwl. We provide evidence of the practicality of both approaches by reporting on some experiments with a number of real-world Datalog-based analyses. © 2011 Springer-Verlag.This work has been partially supported by the eu(feder), the Spanish mec/micinn under grants tin2007-68093-C02 and tin2010-21062-C02-02, and the Generalitat Valenciana under grant Emergentes gv/2009/024. M.A.Feliu was partially supported by the Spanish mec fpu grant AP2008-00608.Alpuente Frasnedo, M.; Feliú Gabaldón, MA.; Joubert, C.; Villanueva García, A. (2011). Datalog-Based program analysis with BES and RWL. En Datalog Reloaded. Springer Verlag (Germany). 6702:1-20. https://doi.org/10.1007/978-3-642-24206-9_1S1206702Afrati, F.N., Ullman, J.D.: Optimizing joins in a map-reduce environment. In: Manolescu, I., Spaccapietra, S., Teubner, J., Kitsuregawa, M., Léger, A., Naumann, F., Ailamaki, A., Özcan, F. (eds.) EDBT. ACM International Conference Proceeding Series, vol. 426, pp. 99–110. ACM, New York (2010)Alpuente, M., Feliú, M., Joubert, C., Villanueva, A.: Defining Datalog in Rewriting Logic. Technical Report DSIC-II/07/09, DSIC, Universidad Politécnica de Valencia (2009)Alpuente, M., Feliú, M., Joubert, C., Villanueva, A.: Using Datalog and Boolean Equation Systems for Program Analysis. In: Cofer, D., Fantechi, A. (eds.) FMICS 2008. LNCS, vol. 5596, pp. 215–231. Springer, Heidelberg (2009)Alpuente, M., Feliú, M.A., Joubert, C., Villanueva, A.: Defining datalog in rewriting logic. In: De Schreye, D. (ed.) LOPSTR 2009. LNCS, vol. 6037, pp. 188–204. Springer, Heidelberg (2010)Andersen, H.R.: Model checking and boolean graphs. Theoretical Computer Science 126(1), 3–30 (1994)Bancilhon, F., Maier, D., Sagiv, Y., Ullman, J.D.: Magic Sets and Other Strange Ways to Implement Logic Programs. In: Proc. 5th ACM SIGACT-SIGMOD Symp. on Principles of Database Systems, PODS 1986, pp. 1–15. ACM Press, New York (1986)Ceri, S., Gottlob, G., Tanca, L.: Logic Programming and Databases. Springer, Heidelberg (1990)Chen, T., Ploeger, B., van de Pol, J., Willemse, T.A.C.: Equivalence Checking for Infinite Systems Using Parameterized Boolean Equation Systems. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 120–135. Springer, Heidelberg (2007)Clavel, M., Durán, F., Ejer, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)Dam, A., Ploeger, B., Willemse, T.: Instantiation for Parameterised Boolean Equation Systems. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds.) ICTAC 2008. LNCS, vol. 5160, pp. 440–454. Springer, Heidelberg (2008)de Moor, O., Sereni, D., Verbaere, M., Hajiyev, E., Avgustinov, P., Ekman, T., Ongkingco, N., Tibble, J.: QL: Object-oriented queries made easy. In: Lämmel, R., Visser, J., Saraiva, J. (eds.) GTTSE 2008. LNCS, vol. 5235, pp. 78–133. Springer, Heidelberg (2008)Feliú, M., Joubert, C., Tarín, F.: Efficient BES-based Bottom-Up Evaluation of Datalog Programs. In: Gulías, V., Silva, J., Villanueva, A. (eds.) Proc. X Jornadas sobre Programación y Lenguajes (PROLE 2010), Garceta, pp. 165–176 (2010)Feliú, M., Joubert, C., Tarín, F.: Evaluation strategies for datalog-based points-to analysis. In: Bendisposto, J., Leuschel, M., Roggenbach, M. (eds.) Proc. 10th Workshop on Automated Verification of Critical Systems (AVoCS 2010), pp. 88–103. Technical Report of Düsseldorf University (2010)Garavel, H., Mateescu, R., Lang, F., Serwe, W.: CADP 2006: A Toolbox for the Construction and Analysis of Distributed Processes. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 158–163. Springer, Heidelberg (2007)Hajiyev, E., Verbaere, M., de Moor, O.: CodeQuest: Scalable Source Code Queries with Datalog. In: Hu, Q. (ed.) ECOOP 2006. LNCS, vol. 4067, pp. 2–27. Springer, Heidelberg (2006)Hanus, M.: The Integration of Functions into Logic Programming: From Theory to Practice. Journal on Logic Programming 19 & 20, 583–628 (1994)Joubert, C., Mateescu, R.: Distributed On-the-Fly Model Checking and Test Case Generation. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 126–145. Springer, Heidelberg (2006)Leeuwen, J. (ed.): Formal Models and Semantics, vol. B. Elsevier, The MIT Press (1990)Liu, X., Smolka, S.A.: Simple Linear-Time Algorithms for Minimal Fixed Points. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 53–66. Springer, Heidelberg (1998)Liu, Y.A., Stoller, S.D.: From datalog rules to efficient programs with time and space guarantees. ACM Trans. Program. Lang. Syst. 31(6) (2009)Livshits, B., Whaley, J., Lam, M.: Reflection Analysis for Java. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 139–160. Springer, Heidelberg (2005)Marchiori, M.: Logic Programs as Term Rewriting Systems. In: Rodríguez-Artalejo, M., Levi, G. (eds.) ALP 1994. LNCS, vol. 850, pp. 223–241. Springer, Heidelberg (1994)Mateescu, R.: Local Model-Checking of an Alternation-Free Value-Based Modal Mu-Calculus. In: Proc. 2nd Int’l Workshop on Verication, Model Checking and Abstract Interpretation, VMCAI 1998 (1998)Mateescu, R., Thivolle, D.: A Model Checking Language for Concurrent Value-Passing Systems. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 148–164. Springer, Heidelberg (2008)Meseguer, J.: Conditional Rewriting Logic as a Unified Model of Concurrency. Theoretical Computer Science 96(1), 73–155 (1992)Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Reddy, U.: Transformation of Logic Programs into Functional Programs. In: Proc. Symposium on Logic Programming (SLP 1984), pp. 187–197. IEEE Computer Society Press, Los Alamitos (1984)Reps, T.W.: Solving Demand Versions of Interprocedural Analysis Problems. In: Adsul, B. (ed.) CC 1994. LNCS, vol. 786, pp. 389–403. Springer, Heidelberg (1994)Rosu, G., Havelund, K.: Rewriting-Based Techniques for Runtime Verification. Autom. Softw. Eng. 12(2), 151–197 (2005)Schneider-Kamp, P., Giesl, J., Serebrenik, A., Thiemann, R.: Automated Termination Analysis for Logic Programs by Term Rewriting. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 177–193. Springer, Heidelberg (2007)Ullman, J.D.: Principles of Database and Knowledge-Base Systems, Volume I and II, The New Technologies. Computer Science Press, Rockville (1989)Vieille, L.: Recursive Axioms in Deductive Databases: The Query/Subquery Approach. In: Proc. 1st Int’l Conf. on Expert Database Systems, EDS 1986, pp. 253–267 (1986)Whaley, J.: Joeq: a Virtual Machine and Compiler Infrastructure. In: Proc. Workshop on Interpreters, Virtual Machines and Emulators, IVME 2003, pp. 58–66. ACM Press, New York (2003)Whaley, J., Avots, D., Carbin, M., Lam, M.S.: Using Datalog with Binary Decision Diagrams for Program Analysis. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 97–118. Springer, Heidelberg (2005)Zheng, X., Rugina, R.: Demand-driven alias analysis for C. In: Proc. 35th ACM SIGPLAN-SIGACT Symp. on Principles of Programming Languages, POPL 2008, pp. 197–208. ACM Press, New York (2008

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

A Termination Analyzer for Java Bytecode based on Path-Length

It is important to prove that supposedly terminating programs actuallyterminate, particularly if those programs must berun on critical systems or downloaded into a client such as a mobile phone.Although termination of computer programs is generally undecidable,it is possible and useful to provetermination of a large, non-trivial subset of the terminating programs.In this paper we present our termination analyser for sequential Java bytecode,based on a program property called path-length. We describe theanalyses which are needed before the path-length can be computed, such assharing, cyclicity and aliasing. Then weformally define the path-length analysis and prove it correct wrt areference denotational semantics of the bytecode. We show that a constraintlogic program P_CLPcan be built from the result of the path-length analysisof a Java bytecode program P andformally prove that if P_CLP terminates then also P terminates.Hence a termination prover for constraint logic programs can be appliedto prove the termination of P. We conclude with some discussion of thepossibilities and limitations of our approach.Ours is the first existing termination analyser for Java bytecodedealing with any kind of data structures dynamically allocated on the heapand which does not require any help or annotation on the part of the user

Automated Termination Analysis for Logic Programs by Term Rewriting

Abstract. There are two kinds of approaches for termination analysis of logic programs: “transformational ” and “direct ” ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.

Towards a Framework for Proving Termination of Maude Programs

Maude es un lenguaje de programación declarativo basado en la lógica de reescritura que incorpora muchas características que lo hacen muy potente. Sin embargo, a la hora de probar ciertas propiedades computacionales esto conlleva dificultades. La tarea de probar la terminación de sistemas de reesctritura es de hecho bastante dura, pero aplicada a lenguajes de programación reales se concierte en más complicada debido a estas características inherentes. Esto provoca que métodos para probar la terminación de este tipo de programas requieran técnicas específicas y un análisis cuidadoso. Varios trabajos han intentado probar terminación de (un subconjunto de) programas Maude. Sin embargo, todos ellos siguen una aproximación transformacional, donde el programa original es trasformado hasta alcanzar un sistema de reescritura capaz de ser manejado con las técnicas y herramientas de terminación existentes. En la práctica, el hecho de transformar los sistemas originales suele complicar la demostración de la terminación ya que esto introduce nuevos símbolos y reglas en el sistema. En esta tesis, llevamos a cabo el problema de probar terminación de (un subconjunto de) programas Maude mediante métodos directos. Por un lado, nos centramos en la estrategia de Maude. Maude es un lenguaje impaciente donde los argumentos de una función son evaluados siempre antes de la aplicación de la función que los usa. Esta estrategia (conocida como llamada por valor) puede provocar la no terminación si los programas no están escritos cuidadosamente. Por esta razón, Maude (en concreto) incorpora mecanismos para controlar la ejecución de programas como las anotaciones sintácticas que están asociadas a los argumentos de los símbolos. En reescritura, esta estrategia sería conocida como reescritura sensible al contexto innermost (RSCI). Por otro lado, Maude también incorpora la posibilidad de declarar atributos.Alarcón Jiménez, B. (2011). Towards a Framework for Proving Termination of Maude Programs [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11003Palanci