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.
Partially supported by MSTD, Serbia, grant ON 144029 and MSTD, Serbia and CNRS, France, bilateral grant “TLIT”.
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Ghilezan, S., Ivetić, J., Lescanne, P., Žunić, D. (2011). Intuitionistic Sequent-Style Calculus with Explicit Structural Rules. In: Bezhanishvili, N., Löbner, S., Schwabe, K., Spada, L. (eds) Logic, Language, and Computation. TbiLLC 2009. Lecture Notes in Computer Science(), vol 6618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22303-7_7
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DOI: https://doi.org/10.1007/978-3-642-22303-7_7
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