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Explanation in Natural Language of λ̄μμ͂-Terms

  • Claudio Sacerdoti Coen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)

Abstract

The λ̄μμ͂-calculus, introduced by Curien and Herbelin, is a calculus isomorphic to (a variant of) the classical sequent calculus LK of Gentzen. As a proof format it has very remarkable properties that we plan to study in future works. In this paper we embed it with a rendering semantics that provides explanations in pseudo-natural language of its proof terms, in the spirit of the work of Yann Coscoy [3] for the λ-calculus. The rendering semantics unveils the richness of the calculus that allows to preserve several proof structures that are identified when encoded in the λ-calculus.

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References

  1. 1.
    Asperti, A., Guidi, F., Padovani, L., Sacerdoti Coen, C., Schena, I.: Mathematical Knowledge Management in HELM. Annals of Mathematics and Artificial Intelligence 38(1), 27–46 (2003)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Asperti, A., Sacerdoti Coen, C.: Stylesheets to intermediate representation (prototypes D2.c-D2.d) and I. Loeb, Presentation stylesheets (prototypes D2.e-D2.f), technical reports of MoWGLI (project IST-2001-33562)Google Scholar
  3. 3.
    Coscoy, Y.: Explication textuelles de preuves pour le calcul des constructions inductives. PhD. thesis, Université de Nice-Sophia-Antipolis (2000)Google Scholar
  4. 4.
    Crolard, T.: Subtractive logic. Theoretical computer science 254(1-2), 151–185 (2001)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Curien, P., Herbelin, H.: The duality of computation. In: Proceedings of the Fifth ACM SIGPLAN International Conference on Functional Programming (ICFP 2000). SIGPLAN Notices, vol. 35(9), pp. 233–243. ACM, New York (2000), ISBN:1-58113-2-2-6Google Scholar
  6. 6.
    Herbelin, H.: Séquents qu’on calcule: de l’interprétation du calcul des séquents comme calcul de lambda-terms et comme calcul de stratégies gagnantes. PhD. thesis (1995)Google Scholar
  7. 7.
    Kohlhase, M.: OMDoc: An Open Markup Format for Mathematical Documents (Version 1.2)Google Scholar
  8. 8.
    Lengrand, S.: Call-by-value, call-by-name, and strong normalization for the classical sequent calculus. In: Gramlich, B., Lucas, S. (eds.) Electronic Notes in Theoretical Computer Science, vol. 86(4). Elsevier, Amsterdam (2003)Google Scholar
  9. 9.
    Parigot, M.: λμ-calculus: An algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624. Springer, Heidelberg (1992)Google Scholar
  10. 10.
    Wiedijk, F.: Formal Proof Sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Claudio Sacerdoti Coen
    • 1
  1. 1.Project PCRI, CNRSÉcole Polytechnique, INRIA, Université Paris-Sud 

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