The Cut-Elimination Theorem for Differential Nets with Promotion

Authors:
Michele Pagani
Affiliations:
Laboratoire Preuves, Programmes et Systèmes, Université Paris Diderot, Paris 7, and Dipartimento di Informatica, Università degli Studi di Torin,
Venue:
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Year:
2009

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Abstract

Recently Ehrhard and Regnier have introduced Differential Linear Logic, DiLL for short -- an extension of the Multiplicative Exponential fragment of Linear Logic that is able to express non-deterministic computations. The authors have examined the cut-elimination of the promotion-free fragment of DiLL by means of a proofnet-like calculus: differential interaction nets. We extend this analysis to exponential boxes and prove the Cut-Elimination Theorem for the whole DiLL: every differential net that is sequentializable can be reduced to a cut-free net.