Abstract

Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets without boxes. Proof nets are translated into graphs of the sort used in optimal -calculus implementations; computation is performed by simple graph rewriting. This graph implementation helps in understanding optimal reductions in the -calculus and in the various programming languages inspired by linear logic. 1 Beyond the -calculus The -calculus is not entirely explicit about the operations of erasing and duplicating arguments. These operations are important both in the theory of the - calculus and in its implementations, yet they are typically treated somewhat informally, implicitly. The proof nets of linear logic [1] provide a refinement of the -calculus where these operations become explici...

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