I was checking some references for a paper Frank and I are working on, and I came across this Lamarche and DeGroote paper (non-paywall version) which is sort of blowing my mind.

It's so close to exactly what I was trying to work out near the beginning of grad school, which I think still puts me at about three years too late. There's a peculiar way things start to look with both this funky graphical notation and with the evisceratingly unsubstructuralizing sort of translations our paper is concerned with, where you start doubting you're so sure you understand what "classical" and "intuitionistic" really mean.