To cite this version: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. 6878, pp.61-75, 2011 Game semantics and uniqueness of type inhabitance in the simply-typed λ-calculus 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.
The class of mildly context-sensitive languages is commonly accepted as fulfilling the requirements to describe natural language. Many formalisms are known to generate languages which belong to this class, such as tree-adjoining grammars, multiple context-free grammars or abstract categorial grammars. All these formalisms share the property of being describe thanks to linear transformations, i.e. which avoid erasing or copying of material along derivations. We show that restricted copying operations allow defining mildly context-sensitive languages, thanks to the introduction of a new operation: IO-substition of languages.
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