Advertisement

A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity

  • Serge Autexier
  • Christoph Benzmüller
  • Dominik Dietrich
  • Andreas Meier
  • Claus-Peter Wirth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)

Abstract

A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components including the human user. We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants. It supports and bridges the gap between abstract level proof explanation and low-level proof verification. The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts.

Keywords

Proof Assistant Proof Tree Automate Theorem Prover Automate Deduction Proof Step 
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.
    Andrews, P.B., Bishop, M., Brown, C.E.: System description: TPS: A theorem proving system for type theory. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 164–169. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Autexier, S., Hutter, D., Langenstein, B., Mantel, H., Rock, G., Schairer, A., Stephan, W., Vogt, R., Wolpers, A.: VSE: Formal methods meet industrial needs. In: International Journal on Software Tools for Technology Transfer, Special issue on Mechanized Theorem Proving for Technology. Springer, Heidelberg (1998)Google Scholar
  3. 3.
    Avenhaus, J., Kühler, U., Schmidt-Samoa, T., Wirth, C.-P.: How to prove inductive theorems? QUODLIBET! In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 328–333. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development — Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science, An EATCS Series. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  5. 5.
    Cheikhrouhou, L., Sorge, V.: PDS — A Three-Dimensional Data Structure for Proof Plans. In: Proc. of the Int. Conf. on Artificial and Computational Intelligence for Decision, Control and Automation in Engineering and Industrial Applications, ACIDCA 2000 (2000)Google Scholar
  6. 6.
    Dixon, L.: Interactive and hierarchical tracing of techniques in IsaPlanner. In: Proc. of UITP 2005 (2005)Google Scholar
  7. 7.
    Fiedler, A.: Dialog-driven adaptation of explanations of proofs. In: Proc. of the 17th International Joint Conference on Artificial Intelligence (IJCAI), Seattle, WA, pp. 1295–1300. Morgan Kaufmann, San Francisco (2001)Google Scholar
  8. 8.
    The OMEGA Group: Proof development with ΩMEGA. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 143–148. Springer, Heidelberg (2002)Google Scholar
  9. 9.
    Huang, X.: Reconstructing proofs at the assertion level. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 738–752. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Hübner, M., Autexier, S., Benzmüller, C., Meier, A.: Interactive theorem proving with tasks. Electronic Notes in Theoretical Computer Science 103(C), 161–181 (2004)CrossRefGoogle Scholar
  11. 11.
    Hutter, D., Sengler, C.: INKA - The Next Generation. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, Springer, Heidelberg (1996)Google Scholar
  12. 12.
    Kreitz, C., Lorigo, L., Eaton, R., Constable, R.L., Allen, S.F.: The nuprl open logical environment (2000)Google Scholar
  13. 13.
    Meier, A.: Proof Planning with Multiple Strategies. PhD thesis, Saarland Univ (2004)Google Scholar
  14. 14.
    Melis, E., Siekmann, J.: Knowledge-Based Proof Planning. Artificial Intelligence 115(1), 65–105 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Paulson, L.C.: Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)CrossRefzbMATHGoogle Scholar
  16. 16.
    Siekmann, J., Benzmüller, C., Fiedler, A., Meier, A., Normann, I., Pollet, M.: Proof Development in OMEGA: The Irrationality of Square Root of 2, pp. 271–314. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  17. 17.
    Siekmann, J., Benzmüller, C., Fiedler, A., Meier, A., Pollet, M.: Proof development with OMEGA: Sqrt(2) is irrational. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 367–387. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Wirth, C.-P.: Descente infinie + Deduction. Logic J. of the IGPL 12(1), 1–96 (2004)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Serge Autexier
    • 1
    • 2
  • Christoph Benzmüller
    • 1
  • Dominik Dietrich
    • 1
  • Andreas Meier
    • 2
  • Claus-Peter Wirth
    • 1
  1. 1.FR InformatikSaarland UniversitySaarbrückenGermany
  2. 2.DFKI GmbHSaarbrückenGermany

Personalised recommendations