The Separation Theorem for Differential Interaction Nets [chapter]

Damiano Mazza, Michele Pagani
Logic for Programming, Artificial Intelligence, and Reasoning  
Differential interaction nets (DIN) have been introduced by Thomas Ehrhard and Laurent Regnier as an extension of linear logic proof-nets. We prove that DIN enjoy an internal separation property: given two different normal nets, there exists a dual net separating them, in analogy with Böhm's theorem for the λ-calculus. Our result implies in particular the faithfulness of every non-trivial denotational model of DIN (such as Ehrhard's finiteness spaces). We also observe that internal separation
more » ... es not hold for linear logic proof-nets: our work points out that this failure is due to the fundamental asymmetry of linear logic exponential modalities, which are instead completely symmetric in DIN.
doi:10.1007/978-3-540-75560-9_29 dblp:conf/lpar/MazzaP07 fatcat:3dvo35zhnjhd7d2fp7rctkdnye