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A formalization of the strong normalization proof for System F in LEGO

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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

We describe a complete formalization of a strong normalization proof for the Curry style presentation of System F in LEGO. The underlying type theory is the Calculus of Constructions enriched by inductive types. The proof follows Girard et al [GLT89], i.e. we use the notion of candidates of reducibility, but we make essential use of general inductive types to simplify the presentation. We discuss extensions and variations of the proof: the extraction of a normalization function, the use of saturated sets instead of candidates, and the extension to a Church Style presentation. We conclude with some general observations about Computer Aided Formal Reasoning.

When doing this research I have been supported by a SIEMENS studentship. This research was also partially supported by the ESPRIT BRA on Logical Frameworks and a SERC grant.

This is a revision of the LFCS report ECS-LFCS-92-230 “Brewing Strong Normalization Proofs with LEGO”.

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Authors and Affiliations

  1. Laboratory for Foundations of Computer Science Department of Computer Science, University of Edinburgh, UK

    Thorsten Altenkirch

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  1. Thorsten Altenkirch
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Altenkirch, T. (1993). A formalization of the strong normalization proof for System F in LEGO. 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/BFb0037095

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  • DOI: https://doi.org/10.1007/BFb0037095

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  • Print ISBN: 978-3-540-56517-8

  • Online ISBN: 978-3-540-47586-6

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