Intuitionistic sequent-style calculus with explicit structural rules

Authors:
Silvia Ghilezan;Jelena Ivetić;Pierre Lescanne;Dragisa Žunić
Affiliations:
Faculty of Technical Sciences, University of Novi Sad, Serbia;Faculty of Technical Sciences, University of Novi Sad, Serbia;University of Lyon, École Normal Supérieure de Lyon, France;Faculty of Economics and Management, Novi Sad, Serbia
Venue:
TbiLLC'09 Proceedings of the 8th international tbilisi conference on Logic, language, and computation
Year:
2009

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Abstract

In this paper we extend the Curry-Howard correspondence to intuitionistic sequent calculus with explicit structural rules of weakening and contraction. We present a linear term calculus derived from the calculus of Espírito Santo, which captures the computational content of the intuitionistic sequent logic, by adding explicit operators for weakening and contraction. For the proposed calculus we introduce the type assignment system with simple types and prove some operational properties, including the subject reduction and strong normalisation property. We then relate the proposed linear type calculus to the simply typed intuitionistic calculus of Kesner and Lengrand, which handles explicit operators of weakening and contraction in the natural deduction framework.