A Mixed λ-calculus

Studia Logica 87 (2-3):269-294 (2007)
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Abstract

The aim of this paper is to define a λ-calculus typed in aMixed (commutative and non-commutative) Intuitionistic Linear Logic. The terms of such a calculus are the labelling of proofs of a linear intuitionistic mixed natural deduction NILL, which is based on the non-commutative linear multiplicative sequent calculus MNL [RuetAbrusci 99]. This linear λ-calculus involves three linear arrows: two directional arrows and a nondirectional one (the usual linear arrow). Moreover, the -terms are provided with seriesparallel orders on free variables. We prove a normalization theorem which explicitly gives the behaviour of the order during the normalization procedure.

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Myriam Quatrini
Aix-Marseille University

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References found in this work

Non-commutative logic I: the multiplicative fragment.V. Michele Abrusci & Paul Ruet - 1999 - Annals of Pure and Applied Logic 101 (1):29-64.
Lambda Grammars and the Syntax-Semantics Interface.Reinhard Muskens - 2001 - In Robert Van Rooij & Martin Stokhof, Proceedings of the Thirteenth Amsterdam Colloquium. Amsterdam: ILLC. pp. 150-155.
The logic of types.Wojciech Buszkowski - 1987 - In Jan T. J. Srzednicki, Initiatives in logic. Boston: M. Nijhoff. pp. 180--206.

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