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Program Extraction from Normalization Proofs

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Abstract

This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.

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Authors and Affiliations

  1. Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK

    Ulrich Berger

  2. Institut für Informatik, Technische Universität München, Boltzmannstr. 3, D-85748, Garching, Germany

    Stefan Berghofer

  3. Laboratoire P.P.S., Université Denis Diderot, Case 7014, 2 Place Jussieu, F-75251, Paris, Cedex 05, France

    Pierre Letouzey

  4. Mathematisches Institut der Universität München, Theresienstr. 39, D-80333, München, Germany

    Helmut Schwichtenberg

Authors
  1. Ulrich Berger
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  2. Stefan Berghofer
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  3. Pierre Letouzey
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  4. Helmut Schwichtenberg
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Corresponding author

Correspondence to Ulrich Berger.

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Berger, U., Berghofer, S., Letouzey, P. et al. Program Extraction from Normalization Proofs. Stud Logica 82, 25–49 (2006). https://doi.org/10.1007/s11225-006-6604-5

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  • DOI: https://doi.org/10.1007/s11225-006-6604-5

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