Advertisement

Graph-Based Shape Analysis Beyond Context-Freeness

  • Hannah Arndt
  • Christina Jansen
  • Christoph Matheja
  • Thomas Noll
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10886)

Abstract

We develop a shape analysis for reasoning about relational properties of data structures. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is parameterized by user-supplied indexed graph grammars to guide concretization and abstraction. This novel extension of context-free graph grammars is powerful enough to model complex data structures such as balanced binary trees with parent pointers, while preserving most desirable properties of context-free graph grammars.

One strength of our analysis is that no artifacts apart from grammars are required from the user; it thus offers a high degree of automation. We implemented our analysis and successfully applied it to various programs manipulating AVL trees, (doubly-linked) lists, and combinations of both.

References

  1. 1.
    Abdulla, P.A., Holík, L., Jonsson, B., Lengál, O., Trinh, C.Q., Vojnar, T.: Verification of heap manipulating programs with ordered data by extended forest automata. Acta Inf. 53(4), 357–385 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aho, A.V.: Indexed grammars - an extension of context-free grammars. J. ACM 15(4), 647–671 (1968)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Arndt, H., Jansen, C., Katoen, J.P., Matheja, C., Noll, T.: Let this graph be your witness! an attestor for verifying Java pointer programs. In: CAV (2018, to appear)Google Scholar
  4. 4.
    Arndt, H., Jansen, C., Matheja, C., Noll, T.: Heap abstraction beyond context-freeness. CoRR abs/1705.03754 (2017). http://arxiv.org/abs/1705.03754
  5. 5.
    Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple phrase structure grammars. Sprachtypologie und Universalienforschung 14, 143–172 (1961)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Calcagno, C., Distefano, D., O’Hearn, P.W., Yang, H.: Compositional shape analysis by means of bi-abduction. J. ACM 58(6), 26:1–26:66 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Chang, B.E., Rival, X.: Relational inductive shape analysis. In: POPL 2008, pp. 247–260. ACM (2008)Google Scholar
  8. 8.
    Chang, B.E., Rival, X.: Modular construction of shape-numeric analyzers. EPTCS 129, 161–185 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chang, B.-Y.E., Rival, X., Necula, G.C.: Shape analysis with structural invariant checkers. In: Nielson, H.R., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 384–401. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74061-2_24CrossRefGoogle Scholar
  10. 10.
    Chin, W., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006–1036 (2012)CrossRefGoogle Scholar
  11. 11.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL 1977, pp. 238–252. ACM (1977)Google Scholar
  12. 12.
    Cousot, P., Cousot, R.: Abstract interpretation frameworks. J. Log. Comput. 2(4), 511–547 (1992)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Ferrara, P., Fuchs, R., Juhasz, U.: TVAL+ : TVLA and value analyses together. In: Eleftherakis, G., Hinchey, M., Holcombe, M. (eds.) SEFM 2012. LNCS, vol. 7504, pp. 63–77. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33826-7_5CrossRefGoogle Scholar
  14. 14.
    Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Heidelberg (1992).  https://doi.org/10.1007/BFb0013875CrossRefzbMATHGoogle Scholar
  15. 15.
    Heinen, J., Jansen, C., Katoen, J., Noll, T.: Juggrnaut: using graph grammars for abstracting unbounded heap structures. Form. Method. Syst. Des. 47(2), 159–203 (2015)CrossRefGoogle Scholar
  16. 16.
    Jansen, C., Göbe, F., Noll, T.: Generating Inductive predicates for symbolic execution of pointer-manipulating programs. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 65–80. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-09108-2_5CrossRefGoogle Scholar
  17. 17.
    Jansen, C., Heinen, J., Katoen, J.-P., Noll, T.: A local Greibach normal form for hyperedge replacement grammars. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 323–335. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21254-3_25CrossRefGoogle Scholar
  18. 18.
    Jansen, C., Katelaan, J., Matheja, C., Noll, T., Zuleger, F.: Unified reasoning about robustness properties of symbolic-heap separation logic. In: Yang, H. (ed.) ESOP 2017. LNCS, vol. 10201, pp. 611–638. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-662-54434-1_23CrossRefGoogle Scholar
  19. 19.
    Plump, D.: Checking graph-transformation systems for confluence. In: ECEASST, vol. 26 (2010)Google Scholar
  20. 20.
    Reps, T.W., Sagiv, M., Wilhelm, R.: Shape analysis and applications. In: Srikant, Y.N., Shankar, P. (eds.) The Compiler Design Handbook, 2nd edn. CRC Press, Boca Raton (2007)Google Scholar
  21. 21.
    Sagiv, S., Reps, T.W., Wilhelm, R.: Parametric shape analysis via 3-valued logic. In: POPL 1999, pp. 105–118. ACM (1999)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hannah Arndt
    • 1
  • Christina Jansen
    • 1
  • Christoph Matheja
    • 1
  • Thomas Noll
    • 1
  1. 1.RWTH Aachen UniversityAachenGermany

Personalised recommendations