Verification of Certifying Computations through AutoCorres and Simpl

  • Lars Noschinski
  • Christine Rizkallah
  • Kurt Mehlhorn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8430)

Abstract

Certifying algorithms compute not only an output, but also a witness that certifies the correctness of the output for a particular input. A checker program uses this certificate to ascertain the correctness of the output. Recent work used the verification tools VCC and Isabelle to verify checker implementations and their mathematical background theory. The checkers verified stem from the widely-used algorithms library LEDA and are written in C. The drawback of this approach is the use of two different tools. The advantage is that it could be carried out with reasonable effort in 2011. In this article, we evaluate the feasibility of performing the entire verification within Isabelle. For this purpose, we consider checkers written in the imperative languages C and Simpl. We re-verify the checker for connectedness of graphs and present a verification of the LEDA checker for non-planarity of graphs. For the checkers written in C, we translate from C to Isabelle using the AutoCorres tool set and then reason in Isabelle. For the checkers written in Simpl, Isabelle is the only tool needed. We compare the new approach with the previous approach and discuss advantages and disadvantages. We conclude that the new approach provides higher trust guarantees and it is particularly promising for checkers that require domain-specific reasoning.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall (1993)Google Scholar
  2. 2.
    Alkassar, E., Böhme, S., Mehlhorn, K., Rizkallah, C.: A framework for the verification of certifying computations. JAR (2013), doi:10.1007/s10817-013-9289-2Google Scholar
  3. 3.
    Back, R.J.R.: Correctness preserving program refinements: Proof theory and applications. Mathematical Centre tracts. Mathematisch centrum (1980)Google Scholar
  4. 4.
    de Berg, M., Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer (1997)Google Scholar
  5. 5.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development—Coq’Art: The Calculus of Inductive Constructions. Springer (2004)Google Scholar
  6. 6.
    Besson, F., Jensen, T., Pichardie, D., Turpin, T.: Certified result checking for polyhedral analysis of bytecode programs. In: Wirsing, M., Hofmann, M., Rauschmayer, A. (eds.) TGC 2010, LNCS, vol. 6084, pp. 253–267. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Blum, M., Kannan, S.: Designing programs that check their work. In: STOC, pp. 86–97 (1989)Google Scholar
  8. 8.
    Böhme, S., Leino, K.R.M., Wolff, B.: HOL-Boogie—An interactive prover for the Boogie program-verifier. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 150–166. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Bright, J.D., Sullivan, G.F., Masson, G.M.: A formally verified sorting certifier. IEEE Transactions on Computers 46(12), 1304–1312 (1997)CrossRefGoogle Scholar
  10. 10.
    Charguéraud, A.: Characteristic formulae for the verification of imperative programs. In: ICFP, pp. 418–430 (2011)Google Scholar
  11. 11.
    Cock, D., Klein, G., Sewell, T.: Secure microkernels, state monads and scalable refinement. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 167–182. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Cohen, E., Dahlweid, M., Hillebrand, M., Leinenbach, D., Moskal, M., Santen, T., Schulte, W., Tobies, S.: VCC: A practical system for verifying concurrent C. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 23–42. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Dijkstra, E.W.: Notes on structured programming. Technological University Eindhoven Netherlands (1970)Google Scholar
  14. 14.
    Gordon, M.J., Milner, A.J., Wadsworth, C.P.: Edinburgh LCF: A Mechanised Logic of Computation. LNCS, vol. 78. Springer, Heidelberg (1979)Google Scholar
  15. 15.
    Greenaway, D., Andronick, J., Klein, G.: Bridging the gap: Automatic verified abstraction of C. In: Beringer, L., Felty, A. (eds.) ITP 2012. LNCS, vol. 7406, pp. 99–115. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Greenaway, D., Lim, J., Andronick, J., Klein, G.: Don’t sweat the small stuff: Formal verification of c code without the pain. In: PLDI (2014) (to appear)Google Scholar
  17. 17.
    Klein, G., Andronick, J., Elphinstone, K., Heiser, G., Cock, D., Derrin, P., Elkaduwe, D., Engelhardt, K., Kolanski, R., Norrish, M., Sewell, T., Tuch, H., Winwood, S.: seL4: Formal verification of an operating-system kernel. CACM 53(6), 107–115 (2010)CrossRefGoogle Scholar
  18. 18.
    Leroy, X.: Formal verification of a realistic compiler. CACM 52(7), 107–115 (2009)CrossRefGoogle Scholar
  19. 19.
    McConnell, R.M., Mehlhorn, K., Näher, S., Schweitzer, P.: Certifying algorithms. Computer Science Review 5(2), 119–161 (2011)CrossRefGoogle Scholar
  20. 20.
    Mehlhorn, K., Näher, S.: From algorithms to working programs: On the use of program checking in LEDA. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 84–93. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  21. 21.
    Mehlhorn, K., Näher, S.: The LEDA Platform for Combinatorial and Geometric Computing. Cambridge University Press (1999)Google Scholar
  22. 22.
    Mehta, F., Nipkow, T.: Proving pointer programs in higher-order logic. Information and Computation 199, 200–227 (2005)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL — A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)Google Scholar
  24. 24.
    Noschinski, L.: A graph library for Isabelle (2013), http://www21.in.tum.de/~noschinl/documents/noschinski2013graphs.pdf (submitted)
  25. 25.
    Schirmer, N.: Verification of sequential imperative programs in Isabelle/HOL. Ph.D. thesis, Technische Universität München (2006)Google Scholar
  26. 26.
    Sullivan, G.F., Masson, G.M.: Using certification trails to achieve software fault tolerance. In: FTCS, pp. 423–431 (1990)Google Scholar
  27. 27.
    Winwood, S., Klein, G., Sewell, T., Andronick, J., Cock, D., Norrish, M.: Mind the gap: A verification framework for low-level C. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 500–515. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  28. 28.
    Wirth, N.: Program development by stepwise refinement. CACM 14(4), 221–227 (1971)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lars Noschinski
    • 1
  • Christine Rizkallah
    • 1
  • Kurt Mehlhorn
    • 2
  1. 1.Institut für InformatikTechnische Universität MünchenGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations