Free-Style Theorem Proving

  • David Delahaye
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2410)


We propose a new proof language based on well-known existing styles such as procedural and declarative styles but also using terms as proofs, a specific feature of theorem provers based on the Curry-Howard isomorphism. We show that these three styles are really appropriate for specific domains and how it can be worth combining them to benefit from their advantages in every kind of proof. Thus, we present, in the context of the Coq proof system, a language, called L pdt , which is intended to make a fusion between these three styles and which allows the user to be much more free in the way of building his/her proofs. We provide also a formal semantics of L pdt for the Calculus of Inductive Constructions, as well as an implementation with a prototype for Coq, which can already run some relevant examples.


Theorem Prover Proof System Formal Semantic Implicit Argument Inductive Case 
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.
    Thierry Coquand, Catarina Coquand, Thomas Hallgren, and Aarne Ranta. The Alfa Home Page, 2001.
  2. 2.
    Yann Coscoy. A Natural Language Explanation for Formal Proofs. In C. Retoré, editor, Proceedings of Int. Gonf. on Logical Aspects of Computational Linguistics (LAGL), Nancy, volume 1328. Springer-Verlag LNCS/LNAI, September 1996.Google Scholar
  3. 3.
    Judy Crow, Sam Owre, John Rushby, Natarajan Shankar, and Mandayam Srivas. A Tutorial Introduction to PVS. In Workshop on Industrial-Strength Formal Specification Techniques, Boca Raton, Florida, April 1995.Google Scholar
  4. 4.
    David Delahaye. Conception de langages pour décrire les preuves et les automatisations dans les outils d’aide à la preuve: une étude dans le cadre du système Coq. PhD thesis, Université Pierre et Marie Curie (Paris 6), Décembre 2001.Google Scholar
  5. 5.
    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.CrossRefGoogle Scholar
  6. 6.
    John Harrison. A Mizar Mode for HOL. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics: TPHOLs’96, volume 1125 of LNCS, pages 203–220, 1996.Google Scholar
  7. 7.
    Lena Magnusson. The Implementation of ALF—a Proof Editor Based on Martin-Löf’s Monomorphic Type Theory with Explicit Substitution. PhD thesis, Chalmers University of Technology, 1994.Google Scholar
  8. 8.
    Don Syme. Declarative Theorem Proving for Operational Semantics. PhD thesis, University of Cambridge, 1998.Google Scholar
  9. 9.
    The Coq Development Team. The Coq Proof Assistant Reference Manual Version 1.3. INRIA-Rocquencourt, May 2002.
  10. 10.
    Andrzej Trybulec. The Mizar-QC/6000 logic information language. In ALLC Bulletin (Association for Literary and Linguistic Computing), volume 6, pages 136–140, 1978.Google Scholar
  11. 11.
    Markus Wenzel. Isar-A Generic Interpretative Approach to Readable Formal Proof Documents. In Yves Bertot, Gilles Dowek, André Hirschowitz, Christine Paulin-Mohring, and Laurent Théry, editors, Theorem Proving in Higher Order Logics: TPHOLs’99, volume 1690 of LNCS, pages 167–184. Springer-Verlag, 1999.CrossRefGoogle Scholar
  12. 12.
    Vincent Zammit. On the Readability of Machine Checkable Formal Proofs. PhD thesis, University of Kent, Canterbury, October 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • David Delahaye
    • 1
  1. 1.Department of Computing ScienceProgramming Logic Group Chalmers University of TechnologyGothenburgSweden

Personalised recommendations