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Game Semantics and Uniqueness of Type Inhabitance in the Simply-Typed λ-Calculus

  • Pierre Bourreau
  • Sylvain Salvati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6690)

Abstract

The problem of characterizing sequents for which there is a unique proof in intuitionistic logic was first raised by Mints [Min77], initially studied in [BS82] and later in [Aot99]. We address this problem through game semantics and give a new and concise proof of [Aot99]. We also fully characterize a family of λ-terms for Aoto’s theorem. The use of games also leads to a new characterization of principal typings for simply-typed λ-terms. These results show that game models can help proving strong structural properties in the simply-typed λ-calculus.

Keywords

games semantics simply-typed λ-calculus principal typing coherence theorem uniqueness of type inhabitance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pierre Bourreau
    • 1
  • Sylvain Salvati
    • 1
  1. 1.LaBRI - INRIA Sud-OuestTalence CedexFrance

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