Game semantics and uniqueness of type inhabitance in the simply typed lambda-calculus

Pierre Bourreau (1) , Sylvain Salvati (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Mots clés: game semantics; simply-typed λ-calculus; principal typing; coherence theorem; uniqueness of type inhabitance

Domaines: Informatique et langage [cs.CL]; Logique en informatique [cs.LO]

Pierre Bourreau, Sylvain Salvati. Game semantics and uniqueness of type inhabitance in the simply typed lambda-calculus. Typed Lambda-Calculi and Applications, Apr 2011, Novi Sad, Serbia. pp.61-75. ⟨hal-00719044⟩