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The conservation theorem revisited

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Typed Lambda Calculi and Applications (TLCA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 664))

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Abstract

This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call βs, and we prove that any λ-term that has a β 1 β s-normal form is strongly β-normalizable. We show how to use this result to prove the strong normalization of different typed λ-calculi.

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References

  1. H.P. Barendregt. The lambda calculus, its syntax and semantics. North-Holland, revised edition, 1984.

    Google Scholar 

  2. H.P. Barendregt. Introduction to Generalised Type Systems. Journal of Functional Programming, 1(2):125–154, 1991.

    Google Scholar 

  3. H.P. Barendregt. Lambda calculi with types. In S. Abramsky, D. Gabbai, and T. Maibaum, editors, Handbook of Logic in Computer Science. Oxford University Press, 1992.

    Google Scholar 

  4. Th. Coquand. Metamathematical investigations of a calculus of constructions. In P. Odifreddi, editor, Logic and Computer Science, pages 91–122. Academic Press, 1990.

    Google Scholar 

  5. N.G. de Bruijn. Lambda calculus notations with nameless dummies, a tool for automatic formula manipulation, with an application to the Church-Rosser theorem. Indigationes Mathematicae, 34:381–392, 1972.

    Google Scholar 

  6. N.G. de Bruijn. A survey of the project Automath. In J.P. Seldin and J.R. Hindley, editors, to H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 579–606. Academic Press, 1980.

    Google Scholar 

  7. Ph. de Groote. Définition et Propriétés d'un métacalcul de représentation de théories. PhD thesis, Université Catholique de Louvain, Unité d'Informatique, 1991.

    Google Scholar 

  8. J.H. Gallier. On Girard's “Candidats de Réductibilité”. In P. Odifreddi, editor, Logic and Computer Science, pages 123–203. Academic Press, 1990.

    Google Scholar 

  9. R.O. Gandy. Au early proof of normalization by A.M. Turing. In J. P. Seldin and J. R. Hindley, editors, to H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 453–455. Academic Press, 1980.

    Google Scholar 

  10. R.O. Gandy. Proofs of strong normalization. In J. P. Seldin and J. R. Hindley, editors, to H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 457–478. Academic Press, 1980.

    Google Scholar 

  11. H. Geuvers and M.-J. Ncderhof. Modular proof of strong normalization for the calculus of construction. Journal of Functional Programming, 1(2):155–189, 1991.

    Google Scholar 

  12. J.-Y. Girard. The system F of variable types, fifteen years later. Theoretical Computer Science, 45:159–192, 1986.

    Google Scholar 

  13. J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989.

    Google Scholar 

  14. R. Harper, F. Housel, and G. Plotkin. A framework for defining logics. In Proceedings of the second annual IEEE symposium on logic in computer science, pages 194–204, 1987.

    Google Scholar 

  15. J.R. Hindley and J.P. Seldin. Introduction to combinators and λ-calculus. London Mathematical Society Student Texts. Cambridge University Press, 1986.

    Google Scholar 

  16. J.W. Klop. Combinatory Reduction Systems. PhD thesis, CWI, Amsterdam, Mathematical Centre Tracts Nr. 127, 1980.

    Google Scholar 

  17. R.P. Nederpelt. Strong normalization in a typed lambda calculus with lambda structured types. PhD thesis, Technische hogeschool Eindhoven, 1973.

    Google Scholar 

  18. A. Scedrov. Normalization revisited. In J.W. Gray and A. Scedrov, editors, Proceedings of the AMS research conference, pages 357–369. American Mathematical Society, 1987.

    Google Scholar 

  19. D.T. van Daalen. The language theory of Automath. PhD thesis, Technische hogeschool Eindhoven, 1980.

    Google Scholar 

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Authors and Affiliations

  1. Campus Scientifique, INRIA-Lorraine-CRIN-CNRS, B.P. 239, 54506, Vandœuvre-les-Nancy Cedex, France

    Philippe Groote

Authors
  1. Philippe Groote
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Groote, P. (1993). The conservation theorem revisited. In: Bezem, M., Groote, J.F. (eds) Typed Lambda Calculi and Applications. TLCA 1993. Lecture Notes in Computer Science, vol 664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037105

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  • DOI: https://doi.org/10.1007/BFb0037105

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56517-8

  • Online ISBN: 978-3-540-47586-6

  • eBook Packages: Springer Book Archive

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