Experiments on Supporting Interactive Proof Using Resolution

  • Jia Meng
  • Lawrence C. Paulson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3097)


Interactive theorem provers can model complex systems, but require much effort to prove theorems. Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications. This paper reports a series of experiments designed to determine whether resolution can support interactive proof as it is currently done. In particular, we present a sound and practical encoding in first-order logic of Isabelle’s type classes.


Theorem Prover Type Class Conjunctive Normal Form Type Information 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahrendt, W., Beckert, B., Hähnle, R., Menzel, W., Reif, W., Schellhorn, G., Schmitt, P.H.: Integrating automated and interactive theorem proving. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction— A Basis for Applications, Systems and Implementation Techniques, vol. II, pp. 97–116. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  2. 2.
    Bezem, M., Hendriks, D., de Nivelle, H.: Automatic proof construction in type theory using resolution. Journal of Automated Reasoning 29(3-4), 253–275 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chang, C.-L., Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, London (1973)zbMATHGoogle Scholar
  4. 4.
    Gordon, M.J.C., Melham, T.F.: Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, Cambridge (1993)zbMATHGoogle Scholar
  5. 5.
    Hurd, J.: Integrating Gandalf and HOL. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 311–321. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Hurd, J.: An LCF-style interface between HOL and first-order logic. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 134–138. Springer, Heidelberg (2002)Google Scholar
  7. 7.
    Meng, J.: Integration of interactive and automatic provers. In: Carro, M., Correas, J. (eds.) Second CologNet Workshop on Implementation Technology for Computational Logic Systems (2003), On the Internet at
  8. 8.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHCrossRefGoogle Scholar
  9. 9.
    Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson and Voronkov [17], ch. 6. pp. 335–367Google Scholar
  10. 10.
    Owre, S., Rajan, S., Rushby, J.M., Shankar, N., Srivas, M.K.: PVS: Combining specification, proof checking, and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 411–414. Springer, Heidelberg (1996)Google Scholar
  11. 11.
    Paulson, L.C.: Generic automatic proof tools. In: Veroff, R. (ed.) Automated Reasoning and its Applications: Essays in Honor of Larry Wos, ch. 3. MIT Press, Cambridge (1997)Google Scholar
  12. 12.
    Paulson, L.C.: The inductive approach to verifying cryptographic protocols. Journal of Computer Security 6, 85–128 (1998)Google Scholar
  13. 13.
    Paulson, L.C.: A generic tableau prover and its integration with Isabelle. Journal of Universal Computer Science 5(3), 73–87 (1999)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Paulson, L.C.: Isabelle’s isabelle’s logics: FOL and ZF. Technical report, Computer Laboratory, University of Cambridge (2003), On the Internet at
  15. 15.
    Riazanov, A., Voronkov, A.: Efficient checking of term ordering constraints. Preprint CSPP-21, Department of Computer Science, University of Manchester (February 2003)Google Scholar
  16. 16.
    Riazanov, A., Voronkov, A.: Vampire 1.1 (system description). In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 376–380. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Robinson, A., Voronkov, A. (eds.): Handbook of Automated Reasoning. Elsevier Science, Amsterdam (2001)zbMATHGoogle Scholar
  18. 18.
    Siekmann, J., Benzmüller, C., Fiedler, A., Meier, A., Normann, I., Pollet, M.: Proof development with ωmega: The irrationality of \(\sqrt{2}\). In: Kamareddine, F. (ed.) Thirty Five Years of Automating Mathematics, pp. 271–314. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  19. 19.
    Sutcliffe, G., Suttner, C.: The TPTP problem library: CNF Release v1.2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson and Voronkov [17], ch. 27. pp. 1965–2013Google Scholar
  21. 21.
    Wenzel, M.: Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 307–322. Springer, Heidelberg (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jia Meng
    • 1
  • Lawrence C. Paulson
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridge(UK)

Personalised recommendations