Remarks on semantic completeness for proof-terms with Laird's dual affine/intuitionistic λ-Calculus

Authors:
Mitsuhiro Okada;Ryo Takemura
Affiliations:
Department of Philosophy, Keio University, Tokyo, Japan;Department of Philosophy, Keio University, Tokyo, Japan
Venue:
Rewriting Computation and Proof
Year:
2007

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Abstract

The purpose of this note is to give a demonstration of the completeness theorem of type assignment system for λ-terms of [Hindley 83] and [Coquand 05] with two directions of slight extensions. Firstly, using the idea of [Okada 96], [Okada-Terui 99] and [Hermant-Okada 07], we extend their completeness theorem to a stronger form which implies a normal form theorem. Secondly, we extend the simple type (the implicational fragment of intuitionistic logic) framework of [Hindley 83] and [Coquand 05] to a linear (affine) types (the {-,&,→}-fragment of affine logic) framework of [Laird 03, 05].