TY - GEN

T1 - Remarks on semantic completeness for proof-terms with Laird's dual affine/intuitionistic λ-calculus

AU - Okada, Mitsuhiro

AU - Takemura, Ryo

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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 {-o, &, →;}-fragment of affine logic) framework of [Laird 03, 05].

AB - 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 {-o, &, →;}-fragment of affine logic) framework of [Laird 03, 05].

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M3 - Conference contribution

AN - SCOPUS:38149033062

SN - 9783540731467

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 167

EP - 181

BT - Rewriting, Computation and Proof - Essays Dedicated to Jean-Pierre Jouannaud on the Occasion of His 60th Birthday

A2 - Comon-Lundh, Hubert

A2 - Kirchner, Claude

A2 - Kirchner, Helene

ER -