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Linear Logic Without Boxes Georges Gonthier \Lambda Mart'in Abadi y JeanJacques L'evy \Lambda

Summary: Linear Logic Without Boxes
Georges Gonthier \Lambda Mart'in Abadi y Jean­Jacques L'evy \Lambda
\Lambda INRIA y Digital Equipment Corporation
Domaine de Voluceau Systems Research Center
Rocquencourt, B.P. 105 130 Lytton Avenue
78153 Le Chesnay Cedex, France Palo Alto, CA 94301, USA
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 com­
pletely 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 op­
timal –­calculus implementations; computation is per­
formed by simple graph rewriting. This graph imple­
mentation helps in understanding optimal reductions
in the –­calculus and in the various programming lan­
guages inspired by linear logic.
1 Beyond the –­calculus


Source: Abadi, Martín - Department of Computer Science, University of California at Santa Cruz


Collections: Computer Technologies and Information Sciences