A Tactic Language for the System Coq

  • David Delahaye
Conference paper
Part of the Lecture Notes in Artificial Intelligence book series (LNCS, volume 1955)


We propose a new tactic language for the system Coq, which is intended to enrich the current tactic combinators (tacticals). This language is based on a functional core with recursors and matching operators for Coq terms but also for proof contexts. It can be used directly in proof scripts or in toplevel definitions (tactic definitions). We show that the implementation of this language involves considerable changes in the interpretation of proof scripts, essentially due to the matching operators. We give some examples which solve small proof parts locally and some others which deal with non-trivial problems. Finally, we discuss the status of this meta-language with respect to the Coq language and the implementation language of Coq.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bruno Barras et al. The Coq Proof Assistant Reference Manual Version 6.3.1. INRIA-Rocquencourt, May 2000. 86
  2. 2.
    Yann Coscoy. A natural language explanation for formal proofs. In C. Retoré, editor, Proceedings of Int. Conf. on Logical Aspects of Computational Liguistics (LACL), Nancy, volume 1328. Springer-Verlag LNCS/LNAI, September 1996. 85Google Scholar
  3. 3.
    Roberto Di Cosmo. Isomorphisms of Types: from λ-calculus to information retrieval and language design. Progress in Theoretical Computer Science. Birkhauser, 1995. ISBN-0-8176-3763-X. 92Google Scholar
  4. 4.
    Roy Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. In The Journal of Symbolic Logic, volume 57(3), September 1992. 91Google Scholar
  5. 5.
    M. J. C. Gordon and T. F. Melham. Introduction to HOL: a Theorem ProvingEnvironment for Higher Order Logic. Cambridge University Press, 1993. 86Google Scholar
  6. 6.
    M. J. C. Gordon, R. Milner, and C. P. Wadsworth. Edinburgh LCF: a mechanised logic of computation. In Lectures Notes in Computer Science, volume 78. Springer-Verlag, 1979. 86Google Scholar
  7. 7.
    John Harrison. Proof style. In Eduardo Giménez and Christine Paulin-Mohring, editors, Types for Proofs and Programs: International Workshop TYPES’96, volume 1512 of LNCS, pages 154–172, Aussois, France, 1996. Springer-Verlag. 85Google Scholar
  8. 8.
    Xavier Leroy et al. The Objective Caml system release 3.00. INRIA-Rocquencourt, April 2000. 87
  9. 9.
    César Muñoz. Démonstration automatique dans la logique propositionnelle intuitionniste. Mémoire du DEA d'informatique fondamentale, Université Paris 7, Septembre 1994. 91Google Scholar
  10. 10.
    Sam Owre, Natarajan Shankar, and John Rushby. PVS: A prototype verification system. In Proceedings of CADE 11, Saratoga Springs, New York, June 1992. 85Google Scholar
  11. 11.
    Don Syme. Declarative Theorem Proving for Operational Semantics. PhD thesis, University of Cambridge, 1998. 85Google Scholar
  12. 12.
    Andrzej Trybulec. The Mizar-QC/6000 logic information language. In ALLC Bulletin (Association for Literary and Linguistic Computing), volume 6, pages 136–140, 1978. 85Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • David Delahaye
    • 1
  1. 1.Project CoqINRIA-RocquencourtRocquencourt

Personalised recommendations