Advertisement

Automated Real Proving in PVS via MetiTarski

  • William Denman
  • César Muñoz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8442)

Abstract

This paper reports the development of a proof strategy that integrates the MetiTarski theorem prover as a trusted external decision procedure into the PVS theorem prover. The strategy automatically discharges PVS sequents containing real-valued formulas, including transcendental and special functions, by translating the sequents into first order formulas and submitting them to MetiTarski. The new strategy is considerably faster and more powerful than other strategies for nonlinear arithmetic available to PVS

Keywords

Theorem Prover Interval Arithmetic Proof Strategy Proof Rule Interactive Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akbarpour, B., Paulson, L.C.: MetiTarski: An automatic theorem prover for real-valued special functions. Journal of Automated Reasoning 44, 175–205 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Daumas, M., Lester, D., Muñoz, C.: Verified real number calculations: A library for interval arithmetic. IEEE Transactions on Computers 58(2), 226–237 (2009)CrossRefGoogle Scholar
  3. 3.
    Di Vito, B.: A PVS prover strategy package for common manipulations. Technical Memorandum NASA/TM-2002-211647, NASA Langley Research Center (2002)Google Scholar
  4. 4.
    Muñoz, C., Carreño, V., Dowek, G., Butler, R.: Formal verification of conflict detection algorithms. International Journal on Software Tools for Technology Transfer 4(3), 371–380 (2003)CrossRefGoogle Scholar
  5. 5.
    Muñoz, C., Mayero, M.: Real automation in the field. Contractor Report NASA/CR-2001-211271, ICASE, Langley Research Center, Hampton VA 23681-2199, USA (December 2001)Google Scholar
  6. 6.
    Muñoz, C., Narkawicz, A.: Formalization of a representation of Bernstein polynomials and applications to global optimization. Journal of Automated Reasoning 51(2), 151–196 (2013), http://dx.doi.org/10.1007/s10817-012-9256-3 CrossRefMathSciNetGoogle Scholar
  7. 7.
    Narkawicz, A., Muñoz, C.: A formally verified generic branching algorithm for global optimization. In: Cohen, E., Rybalchenko, A. (eds.) VSTTE 2013. LNCS, vol. 8164, pp. 326–343. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  8. 8.
    Owre, S., Rushby, J., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • William Denman
    • 1
  • César Muñoz
    • 2
  1. 1.Computer LaboratoryUniversity of CambridgeUK
  2. 2.Langley Research CenterNASAUS

Personalised recommendations