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Modularly Combining Numeric Abstract Domains with Points-to Analysis, and a Scalable Static Numeric Analyzer for Java

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8318))

Abstract

This paper contributes to a new abstract domain that combines static numeric analysis and points-to analysis. One particularity of this abstract domain lies in its high degree of modularity, in the sense that the domain is constructed by reusing its combined components as black-boxes. This modularity dramatically eases the proof of its soundness and renders its algorithm intuitive. We have prototyped the abstract domain for analyzing real-world Java programs. Our experimental results show a tangible precision enhancement compared to what is possible by traditional static numeric analysis, and this at a cost that is comparable to the cost of running the numeric and pointer analyses separately.

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References

  1. Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Technical Report 457, Dipartimento di Matematica, Università di Parma, Italy (2006)

    Google Scholar 

  2. Bagnara, R.: A hierarchy of constraint systems for data-flow analysis of constraint logic-based languages. Sci. Comput. Program. 30(1-2), 119–155 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bertrane, J., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Rival, X.: Static analysis by abstract interpretation of embedded critical software. ACM SIGSOFT Software Engineering Notes 36(1), 1–8 (2011)

    Article  Google Scholar 

  4. Blackburn, S.M., Garner, R., Hoffman, C., Khan, A.M., McKinley, K.S., Bentzur, R., Diwan, A., Feinberg, D., Frampton, D., Guyer, S.Z., Hirzel, M., Hosking, A., Jump, M., Lee, H., Moss, J.E.B., Phansalkar, A., Stefanović, D., VanDrunen, T., von Dincklage, D., Wiedermann, B.: The DaCapo benchmarks: Java benchmarking development and analysis. In: OOPSLA 2006: Proceedings of the 21st Annual ACM SIGPLAN Conference on Object-Oriented Programing, Systems, Languages, and Applications, pp. 169–190. ACM Press, New York (2006)

    Google Scholar 

  5. Calcagno, C., Distefano, D., O’Hearn, P.W., Yang, H.: Compositional shape analysis by means of bi-abduction. J. ACM 58(6), 26 (2011)

    Article  MathSciNet  Google Scholar 

  6. Chang, B.-Y.E., Rival, X.: Relational inductive shape analysis. In: POPL, pp. 247–260 (2008)

    Google Scholar 

  7. Chang, B.-Y.E., Rival, X., Necula, G.C.: Shape analysis with structural invariant checkers. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 384–401. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Cortesi, A., Le Charlier, B., Van Hentenryck, P.: Combinations of abstract domains for logic programming: open product and generic pattern construction. Sci. Comput. Program. 38(1-3), 27–71 (2000)

    Article  MATH  Google Scholar 

  9. Cousot, P., Cousot, R.: Static determination of dynamic properties of programs. In: Proceedings of the Second International Symposium on Programming, pp. 106–130, Dunod, Paris (1976)

    Google Scholar 

  10. Cousot, P., Cousot, R.: Abstract interpretation frameworks. Journal of Logic and Computation 2(4), 511–547 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252 (1977)

    Google Scholar 

  12. Cousot, P., Cousot, R., Mauborgne, L.: The reduced product of abstract domains and the combination of decision procedures. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 456–472. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL, pp. 84–96 (1978)

    Google Scholar 

  14. Deutsch, A.: A storeless model of aliasing and its abstractions using finite representations of right-regular equivalence relations. In: ICCL, pp. 2–13 (1992)

    Google Scholar 

  15. Emami, M., Ghiya, R., Hendren, L.J.: Context-sensitive interprocedural points-to analysis in the presence of function pointers. In: PLDI, pp. 242–256 (1994)

    Google Scholar 

  16. Fähndrich, M., Logozzo, F.: Static contract checking with abstract interpretation. In: Beckert, B., Marché, C. (eds.) FoVeOOS 2010. LNCS, vol. 6528, pp. 10–30. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Fu, Z.: Static Analysis of Numerical Properties in the Presence of Pointers. PhD thesis, Université de Rennes 1 – INRIA, France (2013)

    Google Scholar 

  18. Gopan, D., DiMaio, F., Dor, N., Reps, T., Sagiv, M.: Numeric domains with summarized dimensions. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 512–529. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Lev-Ami, T., Sagiv, M.: TVLA: A system for implementing static analyses. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 280–302. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  20. Lhoták, O., Hendren, L.: Scaling java points-to analysis using SPARK. In: Hedin, G. (ed.) CC 2003. LNCS, vol. 2622, pp. 153–169. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. McCloskey, B., Reps, T., Sagiv, M.: Statically inferring complex heap, array, and numeric invariants. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 71–99. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Miné, A.: Weakly Relational Numerical Abstract Domains. PhD thesis, École Polytechnique, Palaiseau, France (December 2004)

    Google Scholar 

  23. Miné, A.: Field-sensitive value analysis of embedded c programs with union types and pointer arithmetics. In: LCTES, pp. 54–63 (2006)

    Google Scholar 

  24. Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31–100 (2006)

    Article  MATH  Google Scholar 

  25. Pioli, A., Hind, M.: Combining interprocedural pointer analysis and conditional constant propagation. Technical report, IBM T. J. Watson Research Center (1999)

    Google Scholar 

  26. Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. In: Proceedings of the 26th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 1999, pp. 105–118. ACM, New York (1999)

    Chapter  Google Scholar 

  27. Simon, A.: Value-Range Analysis of C Programs. Springer (August 2008)

    Google Scholar 

  28. Toubhans, A., Chang, B.-Y.E., Rival, X.: Reduced product combination of abstract domains for shapes. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 375–395. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  29. Vallée-Rai, R., Co, P., Gagnon, E., Hendren, L., Lam, P., Sundaresan, V.: Soot - a java bytecode optimization framework. In: Proceedings of the 1999 Conference of the Centre for Advanced Studies on Collaborative Research, CASCON 1999, p. 13. IBM Press (1999)

    Google Scholar 

  30. Vallee-Rai, R., Hendren, L.J.: Jimple: Simplifying java bytecode for analyses and transformations. Technical report, Sable Research Group, McGill University (July 1998)

    Google Scholar 

  31. Venet, A.: Towards the integration of symbolic and numerical static analysis. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 227–236. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  32. Yang, H., Lee, O., Berdine, J., Calcagno, C., Cook, B., Distefano, D., O’Hearn, P.W.: Scalable shape analysis for systems code. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 385–398. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Fu, Z. (2014). Modularly Combining Numeric Abstract Domains with Points-to Analysis, and a Scalable Static Numeric Analyzer for Java. In: McMillan, K.L., Rival, X. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2014. Lecture Notes in Computer Science, vol 8318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54013-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-54013-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54012-7

  • Online ISBN: 978-3-642-54013-4

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