Studia Logica

, Volume 87, Issue 2, pp 269–294

A Mixed λ-calculus

Authors

    • IML-CNRS, Aix-Marseille Université
  • Myriam Quatrini
    • IML-CNRS, Aix-Marseille Université
Article

DOI: 10.1007/s11225-007-9089-y

Cite this article as:
Fleury, M. & Quatrini, M. Stud Logica (2007) 87: 269. doi:10.1007/s11225-007-9089-y
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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.

Keywords

Typed λ-calculusnon-commutative linear logicorder varietiesseries-parallel ordersnormalization

Copyright information

© Springer Science+Business Media B.V. 2007