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Notes on the Simply Typed Lambda Calculus

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Computational Logic

Part of the book series: NATO ASI Series ((NATO ASI F,volume 165))

Abstract

The simply typed lambda calculus, of these notes, has types built up from atomic types using the function type operation that forms a new typeA→Bfrom typesA,B.The calculus can be viewed as a refined version of the purely implicational fragment of intuitionistic logic. The refinement consists in using terms of the untyped lambda calculus to represent formal derivations of the logic.

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References

  1. H. BarendregtThe Lambda CalculusNorth Holland Publishing Co., Amsterdam. 2nd edition, 1984.

    MATH  Google Scholar 

  2. J. Gallier, “On Girard’s ”Candidats de Reductibilité“, inLogic and Computer Scienceed. P. Odifreddi, Vol. 31 in APIC studies in Data Processing, pp. 123–203, Academic Press, 1990.

    Google Scholar 

  3. J. Gallier, “Constructive Logics, Part I: A tutorial on proof systems and typed A-calculi”Theoretical Computer Science 110249–339, 1991.

    Article  MathSciNet  Google Scholar 

  4. J. Girard, Y. Lafont and P. TaylorProofs and TypesCambridge Tracts in Theoretical Computer Science 7, Cambridge University Press, 1989.

    MATH  Google Scholar 

  5. J. Lambek and P.J. ScottIntroduction to higher order categorical logicCambridge Studies in Advanced Mathematics 7, Cambridge University Press, 1986.

    MATH  Google Scholar 

  6. P. Martin-LofIntuitionistic Type TheoryBibliopolis, Napoli, 1984.

    Google Scholar 

  7. B. Nordstrom, K. Petersson and J. SmithProgramming in Martin-Lof’s Type Theory An InroductionMonographs on Computer Science 7, Oxford University Press, 1990.

    Google Scholar 

  8. B. Nordstrom and K. Petersson and J. Smith, “Martin-Lof’s Type Theory.” A chapter inHandbook of Logic in Computer Sciencewritten in 1994, to appear. (Available by ftp fromftp://ftp.cs.chalmers.se)/pub/csreports/papers/smith/hlcs.ps.gz

  9. M. Takahashi, “Parallel Reductions in λ-Calculus”Information and Computation118, 120–127, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. S. Troelstra and H. Schwichtenberg, Basic Proof TheoryCambridge Tracts in Theoretical Computer Science 43Cambridge University Press, 1996.

    MATH  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Aczel, P. (1999). Notes on the Simply Typed Lambda Calculus. In: Berger, U., Schwichtenberg, H. (eds) Computational Logic. NATO ASI Series, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58622-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-58622-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63670-7

  • Online ISBN: 978-3-642-58622-4

  • eBook Packages: Springer Book Archive

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