Strong normalization of proof nets modulo structural congruences

Abstract

This paper proposes a notion of reduction for the proof nets of Linear Logic modulo an equivalence relation on the contraction links, that essentially amounts to consider the contraction as an associative commutative binary operator 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 parallel syntax for Linear Logic, and on the other side from the application of proof nets to λ-calculus with or without explicit substitutions, which needs a notion of reduction 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.