## Olivier Laurent and Lorenzo Tortora de Falco.
Slicing polarized additive normalization.
Quaderno 12, Istituto per le Applicazioni del Calcolo, Roma, Italy,
June 2001.
To appear in `Linear Logic in Computer Science`, Thomas
Ehrhard, Jean-Yves Girard, Paul Ruet and Phil Scott editors, London
Mathematical Society Lecture Notes Series, Cambridge University Press.

To attack the problem of ``computing with the additives'',
we introduce a notion of sliced proof-net for the polarized fragment of
linear logic. We prove that this notion yields computational objects,
sequentializable in the absence of cuts. We then show how the
injectivity property of denotational semantics guarantees the
``canonicity'' of sliced proof-nets, and prove injectivity for the
fragment of polarized linear logic corresponding to simply typed
lambda-calculus with pairing.

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