The Geometry of Interaction of Differential Interaction Nets

Marc de Falco
2008 Logic in Computer Science  
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 λ-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
more » ... teraction 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.
doi:10.1109/lics.2008.23 dblp:conf/lics/Falco08 fatcat:oewu66c4abhopgnjokmn3n42om