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Remarks on Semantic Completeness for Proof-Terms with Laird’s Dual Affine/Intuitionistic λ-Calculus

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Rewriting, Computation and Proof

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4600))

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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 \(\{\mathbin{-\mkern-3mu\circ} ,{\rm \&},\rightarrow\}\)-fragment of affine logic) framework of [Laird 03, 05].

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Authors and Affiliations

  1. Department of Philosophy, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan

    Mitsuhiro Okada & Ryo Takemura

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  1. Mitsuhiro Okada
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  2. Ryo Takemura
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Hubert Comon-Lundh Claude Kirchner Hélène Kirchner

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Okada, M., Takemura, R. (2007). Remarks on Semantic Completeness for Proof-Terms with Laird’s Dual Affine/Intuitionistic λ-Calculus. In: Comon-Lundh, H., Kirchner, C., Kirchner, H. (eds) Rewriting, Computation and Proof. Lecture Notes in Computer Science, vol 4600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73147-4_8

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  • DOI: https://doi.org/10.1007/978-3-540-73147-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73146-7

  • Online ISBN: 978-3-540-73147-4

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