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Program extraction from normalization proofs

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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

From a constructive proof of strong normalization plus uniqueness of the long beta-normal form for the simply typed lambda-calculus a normalization program is extracted using Kreisel's modified realizability interpretation for intuitionistic logic. The proof — which uses Tait's computability predicates — is not completely formalized: Induction is done on the meta level, and therefore not a single program but a family of program, one for each term is obtained. Nevertheless this may be used to write a short and efficient normalization program in a type free programming functional programming language (e.g. LISP) which has the interesting feature that it first evaluates a term r of type π to a functional ¦r¦ of type p and then collapses ¦r¦ to the normal form of r.

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References

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Authors and Affiliations

  1. Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, 8000, München 2, Germany

    Ulrich Berger

Authors
  1. Ulrich Berger
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Berger, U. (1993). Program extraction from normalization proofs. 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/BFb0037100

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  • DOI: https://doi.org/10.1007/BFb0037100

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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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