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International Workshop on Verification, Model Checking, and Abstract Interpretation

VMCAI 2011: Verification, Model Checking, and Abstract Interpretation pp 278–293Cite as

Towards Complete Reasoning about Axiomatic Specifications

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6538))

Abstract

To support verification of expressive properties of functional programs, we consider algebraic style specifications that may relate multiple user-defined functions, and compare multiple invocations of a function for different arguments. We present decision procedures for reasoning about such universally quantified properties of functional programs, using local theory extension methodology. We establish new classes of universally quantified formulas whose satisfiability can be checked in a complete way by finite quantifier instantiation. These classes include single-invocation axioms that generalize standard function contracts, but also certain many-invocation axioms, specifying that functions satisfy congruence, injectivity, or monotonicity with respect to abstraction functions, as well as conjunctions of some of these properties. These many-invocation axioms can specify correctness of abstract data type implementations as well as certain information-flow properties. We also present a decidability-preserving construction that enables the same function to be specified using different classes of decidable specifications on different partitions of its domain.

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References

  1. Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Ge, Y., de Moura, L.: Complete instantiation for quantified SMT formulas. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 306–320. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Gligoric, M., Gvero, T., Jagannath, V., Khurshid, S., Kuncak, V., Marinov, D.: Test generation through programming in UDITA. In: International Conference on Software Engineering, ICSE (2010)

    Google Scholar 

  5. Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On local reasoning in verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Jacobs, S.: Incremental instance generation in local reasoning. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 368–382. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Jacobs, S.: Hierarchic Decision Procedures for Verification. PhD thesis, Saarland University, Germany (2010)

    Google Scholar 

  8. Jacobs, S., Kuncak, V.: On complete reasoning about axiomatic specifications. Technical Report EPFL-REPORT-151486, EPFL (2010)

    Google Scholar 

  9. Jacobs, S., Sofronie-Stokkermans, V.: Applications of hierarchical reasoning in the verification of complex systems. Electronic Notes in Theoretical Computer Science 174(8), 39–54 (2007)

    Article  MATH  Google Scholar 

  10. Lam, P., Kuncak, V., Rinard, M.: Generalized typestate checking for data structure consistency. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 430–447. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. McPeak, S., Necula, G.C.: Data structure specifications via local equality axioms. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 476–490. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Podelski, A., Wies, T.: Counterexample-guided focus. In: 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (2010)

    Google Scholar 

  13. Sofronie-Stokkermans, V.: Hierarchic reasoning in local theory extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Sofronie-Stokkermans, V.: Efficient hierarchical reasoning about functions over numerical domains. In: Dengel, A.R., Berns, K., Breuel, T.M., Bomarius, F., Roth-Berghofer, T.R. (eds.) KI 2008. LNCS (LNAI), vol. 5243, pp. 135–143. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Sofronie-Stokkermans, V.: Locality results for certain extensions of theories with bridging functions. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 67–83. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Sofronie-Stokkermans, V., Ihlemann, C.: Automated reasoning in some local extensions of ordered structures. Journal of Multiple-Valued Logic and Soft Computing 13(4-6), 397–414 (2007)

    MathSciNet  MATH  Google Scholar 

  17. Suter, P., Dotta, M., Kuncak, V.: Decision procedures for algebraic data types with abstractions. In: 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (2010)

    Google Scholar 

  18. Wies, T., Kuncak, V., Lam, P., Podelski, A., Rinard, M.: Field constraint analysis. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 157–173. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  19. Zhang, T., Sipma, H.B., Manna, Z.: Decision procedures for recursive data structures with integer constraints. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 152–167. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

    Swen Jacobs & Viktor Kuncak

Authors
  1. Swen Jacobs
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  2. Viktor Kuncak
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Editor information

Editors and Affiliations

  1. UC San Diego, USA

    Ranjit Jhala

  2. Department of Computing and Information Sciences, Kansas State University, 234 Nichols Hall, 66506, Manhattan, KS, USA

    David Schmidt

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Jacobs, S., Kuncak, V. (2011). Towards Complete Reasoning about Axiomatic Specifications. In: Jhala, R., Schmidt, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2011. Lecture Notes in Computer Science, vol 6538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18275-4_20

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  • DOI: https://doi.org/10.1007/978-3-642-18275-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18274-7

  • Online ISBN: 978-3-642-18275-4

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