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

摘要

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 A-terms for Aoto's theorem. The use of games also leads to a new characterization of principal typings for simply-typed A-terms. These results show that game models can help proving strong structural properties in the simply-typed A-calculus.