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Strong Normalization of Proof NetsModulo Structural Congruences

By Roberto Di Cosmo


Abstract. This paper proposes a notion of reduction for the proof nets of LinearLogic modulo an equivalence relation on the contraction links, that essentially amounts to consider the contraction as an associative commutative binary opera-tor that can float freely in and out of proof net boxes. The need for such a system comes, on one side, from the desire to make proof nets an even more parallelsyntax for Linear Logic, and on the other side from the application of proof nets to l-calculus with or without explicit substitutions, which needs a notion of re-duction more flexible than those present in the literature. The main result of the paper is that this relaxed notion of rewriting is still strongly normalizing. Keywords: Proof Nets. Linear Logic. Strong Normalization. 1 Introduction In his seminal paper [6], Girard proposed proof nets as a parallel syntax for LinearLogic, where uninteresting permutations in the order of application of logical rules are de-sequentialised and collapsed. Nevertheless, in the presence of exponentials, thatare necessary to translate l-terms into proof nets, the traditional presentation of proof nets turns out to be inadequate: too many inessential details concerning the order ofapplication of independent structural rules (e.g., contraction) are still present

Year: 2009
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