Stefano Guerrini (original) (raw)

Abstract

this paper is a solution to the coherence problem (for restricted proof-nets, see below) obtained by changing the way the information is coded into sharing graphs. This is achieved via two technical tools: (i) a new reduction rule (absorption) allowing a simplification of the net in some critical cases; (ii) a clear separation of the logical and control information in the representation of a net. The logical information takes the form of levels on the formulas of the proof-net; control is expressed by unifying fans and brackets into one single node (mux ). It is this separation to allow the formulation of the absorption reduction and to enforce coherence. Our results, like those of most of the literature, hold for restricted proof-nets, where weakening is not allowed. It should be clear that any approach to cutelimination based on a local graph exploration may work only on connected components. If the syntax allows, during reduction, the creation of distinct components out of a sing...

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