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On the Values of Reducibility Candidates

  • Colin Riba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5608)

Abstract

The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction.

We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard’s reducibility candidates. We show that these rules remedy the above mentioned difficulties, for strong normalization and, for the existential quantification, for subject reduction as well.

Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals.

Keywords

Closure Operator Union Type Intuitionistic Logic Typing Rule Elimination Rule 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Colin Riba
    • 1
  1. 1.Laboratoire de l’Informatique du ParallélismeENS Lyon – Université de LyonFrance

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