Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8312))

Abstract

We describe new extensions of the Vampire theorem prover for computing tree interpolants. These extensions generalize Craig interpolation in Vampire, and can also be used to derive sequence interpolants. We evaluated our implementation on a large number of examples over the theory of linear integer arithmetic and integer-indexed arrays, with and without quantifiers. When compared to other methods, our experiments show that some examples could only be solved by our implementation.

This research was partly supported by the Austrian National Research Network RiSE (FWF grants S11402-N23 and S11410-N23) and the WWTF PROSEED grant (ICT C-050).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. iZ3 Documentation, http://research.microsoft.com/en-us/um/redmond/projects/z3/old/iz3documentation.html

  2. Albarghouthi, A., Gurfinkel, A., Chechik, M.: Craig Interpretation. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 300–316. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Craig, W.: Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. J. of Symbolic Logic 22(3), 269–285 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  4. de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Gupta, A., Popeea, C., Rybalchenko, A.: Predicate Abstraction and Refinement for Verifying Multi-Threaded Programs. In: Proc. of POPL, pp. 331–344 (2011)

    Google Scholar 

  6. Gupta, A., Thevenet-Montagne, A.: Tree Interpolants via Localized Proofs (2012), http://pub.ist.ac.at/~agupta/papers/localize-draft.pdf

  7. Gurfinkel, A., Rollini, S.F., Sharygina, N.: Interpolation Properties and SAT-Based Model Checking. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 255–271. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Heizmann, M., Hoenicke, J., Podelski, A.: Nested Interpolants. In: Proc. of POPL, pp. 471–482 (2010)

    Google Scholar 

  9. Hoder, K., Kovács, L., Voronkov, A.: Playing in the Grey Area of Proofs. In: Proc. of POPL, pp. 259–272 (2012)

    Google Scholar 

  10. Jhala, R., McMillan, K.L.: A Practical and Complete Approach to Predicate Refinement. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 459–473. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. 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 

  12. McMillan, K., Rybalchenko, A.: Solving Constrained Horn Clauses using Interpolation. Technical report, MSR (2013)

    Google Scholar 

  13. 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 

  14. McMillan, K.L.: Interpolants from Z3 Proofs. In: Proc. of FMCAD, pp. 19–27 (2011)

    Google Scholar 

  15. Srivastava, S., Gulwani, S.: Program Verification using Templates over Predicate Abstraction. In: Proc. of PLDI, pp. 223–234 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blanc, R., Gupta, A., Kovács, L., Kragl, B. (2013). Tree Interpolation in Vampire. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45221-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45220-8

  • Online ISBN: 978-3-642-45221-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics