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We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar deened by such a rewriting system (connuent and strong normalizing on the new proof nets) gives a correctness criterion that we show equivalent to the… (More)

We reformulate Danos contractibility criterion in terms of a sort of unification. As for term unification , a direct implementation of the unification criterion leads to a quasi-linear algorithm. Linearity is obtained after observing that the disjoint-set union-find at the core of the unification criterion is a special case of union-find with a real linear… (More)

Sharing graphs are an implementation of linear logic proof-nets in such a way that their reduction never duplicate a redex. In their usual formulations, proof-nets present a problem of coherence: if the proof-net N reduces by standard cut-elimination to N 0 , then, by reducing the sharing graph of N we d o not obtain the sharing graph of N 0. W e s o l v e… (More)

We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty is in a complete set of rewriting rules for cut-elimination in presence of weakening (which requires garbage collection). The proposed reduction system is strongly normalizing and confluent. The are all… (More)

The paper presents in full details the first linear algorithm given in the literature [6] implementing proof structure correctness for multiplicative linear logic without units. The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the… (More)

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… (More)

Sharing graphs are the structures introduced by Lamping for the implementation of optimal reductions of lambda-calculus. Gonthier's reformulation of Lamping's technique inside Geometry of Interaction and Asperti and Laneve's work on Interaction Systems have shown that sharing graphs implement a wide class of calculi. We give a semantical characterization of… (More)