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A Simple Abstraction of Arrays and Maps by Program Translation

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Static Analysis (SAS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9291))

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Abstract

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,...). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the “Dutch flag” algorithm.

D. Monniaux—The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement nr. 306595 “STATOR”

F. Alberti—This work has been carried out while the author was affiliated to the Università della Svizzera Italiana and supported by the Swiss National Science Foundation under grant no. P1TIP2_152261.

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Notes

  1. 1.

    [7, 8, 15] http://www.astree.ens.fr, http://absint.de/astree/.

  2. 2.

    Possible since Astrée targets safety-critical embedded systems where array sizes are typically fixed at system design and dynamic memory allocation is prohibited.

  3. 3.

    We have left out, for the sake of brevity, tests for array accesses out of bounds.

  4. 4.

    We implemented a simplification algorithm for quantifier-free Presburger arithmetic inspired by [37] so as to understand the output of Flata and ConcurInterproc.

  5. 5.

    http://cpachecker.sosy-lab.org/.

  6. 6.

    scripts/cpa.sh -predicateAnalysis after preprocessing with assert.h.

  7. 7.

    All timings using one core of a 2.4 GHz Intel ® Core™ i3 running 32-bit Linux.

  8. 8.

    http://pop-art.inrialpes.fr/people/bjeannet/bjeannet-forge/interproc/.

  9. 9.

    http://apron.cri.ensmp.fr/library/.

  10. 10.

    http://pop-art.inrialpes.fr/interproc/concurinterprocweb.cgi.

  11. 11.

    From Presburger arithmetic, a decidable theory.

References

  1. Alberti, F., Ghilardi, S., Sharygina, N.: Decision procedures for flat array properties. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 15–30. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  2. Alberti, F., et al.: An extension of lazy abstraction with interpolation for programs with arrays. Form. Methods Syst. Des. 45(1), 63–109 (2014)

    Article  MATH  Google Scholar 

  3. Alberti, F., Ghilardi, S., Sharygina, N.: Definability of accelerated relations in a theory of arrays and its applications. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS, vol. 8152, pp. 23–39. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Alberti, F., Ghilardi, S., Sharygina, N.: Decision procedures for flat array properties. J. Autom. Reasoning 54(4), 327–352 (2015)

    Article  MathSciNet  Google Scholar 

  5. Alberti, F., Monniaux, D.: Polyhedra to the rescue of array interpolants. In: Symposium on applied computing (Software Verification & Testing). ACM (2015)

    Google Scholar 

  6. Bjørner, N., McMillan, K., Rybalchenko, A.: On solving universally quantified horn clauses. In: Logozzo, F., Fähndrich, M. (eds.) Static Analysis. LNCS, vol. 7935, pp. 105–125. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Blanchet, et al.: A static analyzer for large safety-critical software. In: PLDI, pp. 196–207. ACM (2003)

    Google Scholar 

  8. Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Design and implementation of a special-purpose static program analyzer for safety-critical real-time embedded software. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds.) The Essence of Computation. LNCS, vol. 2566, pp. 85–108. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Bozga, M., Habermehl, P., Iosif, R., Konečný, F., Vojnar, T.: Automatic verification of integer array programs. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 157–172. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Bozga, M., Iosif, R., Konečný, F.: Fast acceleration of ultimately periodic relations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 227–242. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Bozga, M., Iosif, R., Lakhnech, Y.: Flat parametric counter automata. Fundamenta Informaticae 91, 275–303 (2009)

    MathSciNet  MATH  Google Scholar 

  12. Cousot, P., Cousot, R.: Abstract interpretation frameworks. J. Log. Comput. 2(4), 511–547 (1992)

    Article  MathSciNet  MATH  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. Cousot, P., Cousot, R.: Invited talk: Higher order abstract interpretation. In: IEEE International Conference on Computer Languages, pp. 95–112. IEEE Computer Society (1994)

    Google Scholar 

  15. Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Rival, X.: Why does Astrée scale up? Form. Methods Syst. Des. 35(3), 229–264 (2009)

    Article  MATH  Google Scholar 

  16. Cousot, P., Cousot, R., Logozzo, F.: A parametric segmentation functor for fully automatic and scalable array content analysis. In: POPL, pp. 105–118. ACM (2011)

    Google Scholar 

  17. Cox, A., Chang, B.-Y.E., Rival, X.: Automatic analysis of open objects in dynamic language programs. In: Müller-Olm, M., Seidl, H. (eds.) Static Analysis. LNCS, vol. 8723, pp. 134–150. Springer, Heidelberg (2014)

    Google Scholar 

  18. Dijkstra, E.W.: A discipline of programming. Prentice-Hall, Upper Saddle River (1976)

    MATH  Google Scholar 

  19. Dillig, I., Dillig, T., Aiken, A.: Fluid updates: beyond strong vs. weak updates. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 246–266. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: POPL, pp. 191–202 (2002)

    Google Scholar 

  21. Gopan, D., Reps, T., Sagiv, S.: A framework for numeric analysis of array operations. In: POPL, pp. 338–350 (2005)

    Google Scholar 

  22. Halbwachs, N.: Détermination automatique de relations linéaires vérifiées par les variables d’un programme. Ph.D. thesis, Univ. Grenoble (Mar 1979). https://tel.archives-ouvertes.fr/tel-00288805

  23. Halbwachs, N., Péron, M.: Discovering properties about arrays in simple programs. In: PLDI, pp. 339–348. ACM (2008)

    Google Scholar 

  24. Halpern, J.: Presburger arithmetic with unary predicates is \(\Pi ^1_1\) complete. J. Symbolic Log. 56(2), 637–642 (1991)

    Article  MATH  Google Scholar 

  25. Hoder, K., Kovács, L., Voronkov, A.: Invariant generation in vampire. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 60–64. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  26. Hoder, K., Kovács, L., Voronkov, A.: Interpolation and symbol elimination in vampire. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 188–195. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 247–251. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  28. Jeannet, B., Gopan, D., Reps, T.: A relational abstraction for functions. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 186–202. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  29. Jeannet, B., Miné, A.: Apron: a library of numerical abstract domains for static analysis. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 661–667. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  30. Jhala, R., McMillan, K.L.: Array abstractions from proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  31. Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  32. McMillan, K.L.: Applications of craig interpolation to model checking. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 15–16. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  33. McMillan, K.L.: Quantified invariant generation using an interpolating saturation prover. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 413–427. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  34. McMillan, K.L.: Lazy abstraction with interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  35. McMillan, K.: Interpolants from Z3 proofs. In: FMCAD, pp. 19–27 (2011)

    Google Scholar 

  36. Miné, A.: The octagon abstract domain. High. Order Symbolic Comput. 19(1), 31–100 (2006)

    Article  MATH  Google Scholar 

  37. Monniaux, D.: A quantifier elimination algorithm for linear real arithmetic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 243–257. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  38. Péron, M.: Contributions to the Static Analysis of Programs Handling Arrays. Theses, Université de Grenoble (September 2010). https://tel.archives-ouvertes.fr/tel-00623697

  39. Perrelle, V.: Analyse statique de programmes manipulant des tableaux. Theses, Université de Grenoble (February 2013). https://tel.archives-ouvertes.fr/tel-00973892

  40. Rival, X., Mauborgne, L.: The trace partitioning abstract domain. ACM Trans. Program Lang. Syst. 29(5), 26 (2007)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Université Grenoble Alpes, VERIMAG, 38000, Grenoble, France

    David Monniaux

  2. CNRS, VERIMAG, 38000, Grenoble, France

    David Monniaux

  3. Fondazione Centro San Raffaele, Milan, Italy

    Francesco Alberti

Authors
  1. David Monniaux
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  2. Francesco Alberti
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Correspondence to Francesco Alberti .

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Editors and Affiliations

  1. Université Rennes 1, Rennes, France

    Sandrine Blazy

  2. Inria, Rennes, France

    Thomas Jensen

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Monniaux, D., Alberti, F. (2015). A Simple Abstraction of Arrays and Maps by Program Translation. In: Blazy, S., Jensen, T. (eds) Static Analysis. SAS 2015. Lecture Notes in Computer Science(), vol 9291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48288-9_13

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  • DOI: https://doi.org/10.1007/978-3-662-48288-9_13

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