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

Mitsuhiro Okada, Ryo Takemura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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

Original languageEnglish
Title of host publicationRewriting, Computation and Proof - Essays Dedicated to Jean-Pierre Jouannaud on the Occasion of His 60th Birthday
EditorsHubert Comon-Lundh, Claude Kirchner, Helene Kirchner
Pages167-181
Number of pages15
Publication statusPublished - 2007 Dec 1

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4600 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Okada, M., & Takemura, R. (2007). Remarks on semantic completeness for proof-terms with Laird's dual affine/intuitionistic λ-calculus. In H. Comon-Lundh, C. Kirchner, & H. Kirchner (Eds.), Rewriting, Computation and Proof - Essays Dedicated to Jean-Pierre Jouannaud on the Occasion of His 60th Birthday (pp. 167-181). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4600 LNCS).