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

**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} }