The Geometry of Interaction of Differential Interaction Nets
Abstract
The Geometry of Interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the lambdacalculus optimal reduction. Recently Ehrhard and Regnier have introduced an extension of the Multiplicative Exponential fragment of Linear Logic (MELL) that is able to express nondeterministic behaviour of programs and a proofnetlike calculus: Differential Interaction Nets. This paper constructs a proper Geometry of Interaction (GoI) for this extension. We consider it both as an algebraic theory and as a concrete reversible computation. We draw links between this GoI and the one of MELL. As a byproduct we give for the first time an equational theory suitable for the GoI of the Multiplicative Additive fragment of Linear Logic.
 Publication:

arXiv eprints
 Pub Date:
 April 2008
 arXiv:
 arXiv:0804.1435
 Bibcode:
 2008arXiv0804.1435D
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Programming Languages
 EPrint:
 20 pagee, to be published in the proceedings of LICS08