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A Declarative Language for the Coq Proof Assistant

  • Pierre Corbineau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4941)

Abstract

This paper presents a new proof language for the Coq proof assistant. This language uses the declarative style. It aims at providing a simple, natural and robust alternative to the existing \(\mathcal{L}_{tac}\) tactic language. We give the syntax of our language, an informal description of its commands and its operational semantics. We explain how this language can be used to implement formal proof sketches. Finally, we present some extra features we wish to implement in the future.

Keywords

Operational Semantic Proof Obligation Proof Assistant Partial Conclusion Proof State 
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.

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References

  1. 1.
    Coen, C.S.: Automatic generation of declarative scripts. CHAT: Connecting Humans and Type Checkers (December 2006)Google Scholar
  2. 2.
    The Coq Development Team. The Coq Proof Assistant Reference Manual – Version V8.1 (February 2007)Google Scholar
  3. 3.
    Corbineau, P.: First-order reasoning in the calculus of inductive constructions. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 162–177. Springer, Heidelberg (2004)Google Scholar
  4. 4.
    Corbineau, P.: Deciding equality in the constructor theory. In: Altenkirch, T., McBride, C. (eds.) TYPES 2006. LNCS, vol. 4502, pp. 78–92. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Corbineau, P., Kaliszyk, C.: Cooperative repositories for formal proofs. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 221–234. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Giero, M., Wiedijk, F.: MMode, a mizar mode for the proof assistant coq. Technical report, ICIS, Radboud Universiteit Nijmegen (2004)Google Scholar
  7. 7.
    Gordon, M., Milner, R., Wadsworth, C.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)MATHGoogle Scholar
  8. 8.
    Harrison, J.: A mizar mode for HOL. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 203–220. Springer, Heidelberg (1996)Google Scholar
  9. 9.
    Harrison, J.: The HOL Light manual, Version 2.20 (2006)Google Scholar
  10. 10.
    Lamport, L.: How to write a proof. American Mathematics Monthly 102(7), 600–608 (1995)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Paulson, L.: Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)MATHGoogle Scholar
  12. 12.
    Syme, D.: DECLARE: A prototype declarative proof system for higher order logic. Technical report, University of Cambridge (1997)Google Scholar
  13. 13.
    Syme, D.: Three tactic theorem proving. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 203–220. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Wenzel, M.: Isar - A generic interpretative approach to readable formal proof documents. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 167–184. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  15. 15.
    Wenzel, M., Wiedijk, F.: A comparison of Mizar and Isar. Journal of Automated Reasoning 29(3-4), 389–411 (2002)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Wiedijk, F.: Mizar light for HOL light. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 378–394. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Wiedijk, F.: Formal proof sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pierre Corbineau
    • 1
  1. 1.Institute for Computing and Information ScienceRadboud University NijmegenNijmegenThe Netherlands

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