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Intuitionistic Sequent-Style Calculus with Explicit Structural Rules

Abstract : In this paper we extend the Curry-Howard correspondence to intuitionistic sequent calculus with explicit weakening and contraction. We study a system derived from /\-Gtz of Espirito Santo by adding explicit operators for weakening and contraction, which we call l/\-Gtz. This system contains only linear terms. For the proposed calculus we introduce the type assignment system with simple types. The presented system has a natural diagrammatic representation, which is used for proving the subject reduction property. We prove the strong normalisation property by embedding l/\-Gtz into the simply typed /\lxr calculus of Kesner and Lengrand.
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Contributor : Pierre Lescanne <>
Submitted on : Thursday, December 22, 2011 - 8:52:28 PM
Last modification on : Wednesday, November 20, 2019 - 3:01:26 AM


  • HAL Id : ensl-00654762, version 1



Pierre Lescanne, Silvia Ghilezan, Jelena Ivetic, Dragisa Zunic. Intuitionistic Sequent-Style Calculus with Explicit Structural Rules. Logic, Language, and Computation - 8th International Tbilisi Symposium on Logic, Language, and Computation, Sep 2009, Bakuriani, Georgia. pp.101-124. ⟨ensl-00654762⟩



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