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

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

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.

Keywords

  • Type Theory
  • Formal Proof
  • Logical Framework
  • Elimination Rule
  • Inductive Type

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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© 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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