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Reports Year : 2011

Jump from Parallel to Sequential Proofs: Additives

Abstract

In previous work, we introduced a framework for proof nets of the multiplicative fragment of Linear Logic, where \emph{partially sequentialized} nets are allowed. In this paper we extend this result to include additives, using a definition of proof net, called \emph{J-proof net}, which is the typed version of an L-net of Faggian and Maurel. In J-proof nets, we can characterize nets with different degrees of sequentiality, by gradual insertion of sequentiality constraints (jumps). As a byproduct, we obtain a simple proof of the sequentialization theorem. Moreover, we provide a denotational semantics for J-proof nets which is an extension of the relational model, using pointed sets, and we prove that such a semantics is injective with respect to J-proof nets.
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Dates and versions

hal-00616386 , version 1 (22-08-2011)
hal-00616386 , version 2 (28-09-2011)

Identifiers

  • HAL Id : hal-00616386 , version 2

Cite

Paolo Di Giamberardino. Jump from Parallel to Sequential Proofs: Additives. 2011. ⟨hal-00616386v2⟩
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