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Coherence for sharing proofnets
 Proceedings of the 7th International Conference on Rewriting Techniques and Applications (RTA96), LNCS 1103
, 1996
"... Sharing graphs are an implementation of linear logic proofnets in such a way that their reduction never duplicate a redex. In their usual formulations, proofnets present a problem of coherence: if the proofnet N reduces by standard cutelimination to N 0, then, by reducing the sharing graph of N ..."
Abstract

Cited by 10 (7 self)
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Sharing graphs are an implementation of linear logic proofnets in such a way that their reduction never duplicate a redex. In their usual formulations, proofnets present a problem of coherence: if the proofnet N reduces by standard cutelimination to N 0, then, by reducing the sharing graph of N we donot obtain the sharing graph of N 0.Wesolve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is con uent and terminating. The proof of this fact exploits an algebraic semantics for sharing graphs. 1
A general theory of sharing graphs
 THEORET. COMPUT. SCI
, 1999
"... Sharing graphs are the structures introduced by Lamping to implement 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 can be used to implement a w ..."
Abstract

Cited by 4 (3 self)
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Sharing graphs are the structures introduced by Lamping to implement 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 can be used to implement a wide class of calculi. Here, we give a general characterization of sharing graphs independent from the calculus to be implemented. Such a characterization rests on an algebraic semantics of sharing graphs exploiting the methods of Geometry of Interaction. By this semantics we can de ne an unfolding partial order between proper sharing graphs, whose minimal elements are unshared graphs. The leastshared instance of a sharing graph is the unique unshared graph that the unfolding partial order associates to it. The algebraic semantics allows to prove that we can associate a semantical readback to each unshared graph and that such a readback can be computed