Paper: The Geometry of Interaction of Differential Interaction Nets (at LICS 2008)

Authors: Marc de Falco

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 \lambda-calculus optimal reduction. Recently Ehrhard and Regnier have introduced an extension of the Multiplicative Exponential fragment of Linear Logic (MELL) that is able to express non-deterministic behaviour of programs and a proofnet-like 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 by-product we give for the first time an equational theory suitable for the GoI of the Multiplicative Additive fragment of Linear Logic.

BibTeX

  @InProceedings{deFalco-TheGeometryofIntera,
    author = 	 {Marc de Falco},
    title = 	 {The Geometry of Interaction of Differential Interaction Nets},
    booktitle =  {Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008)},
    year =	 {2008},
    month =	 {June}, 
    pages =      {465--475},
    location =   {Pittsburgh, PA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }