State Oriented Linear Logic: for Hermann's birthday

Early last year I was invited to contribute to a volume celebrating Hermann Haeusler's 50th birthday. Hermann is a good friend and collaborator of mine and it's always fun to think of stuff that we have done together.

In particular many  moons ago, when Marcelo Correa was his phd student, we wrote a paper together A Dialectica Model of State. (Correa, Haeusler and de Paiva) which appeared in CATS'96, Computing: The Australian Theory Symposium Proceedings, Melbourne, Australia, January 1996, and which we never got around to publishing in a journal. 
Since I also had a phd student (Alex Tucker, in Birmingham) who did some work on this problem  but decided to quit the doctoral programme, just after getting a paper (Categorical Modelling of a State Oriented version of Linear Logic), in the Student Session of ESSLLI 1998, this seemed an ideal work to try to bring to the table as a present for Hermann.

Here's the newer version of the paper (Linear Logic Model of State Revisited), it's still very rough, I haven't had the time to make sure that I read all the good work that came after it, maybe I should try to talk about it in the BACAT meetings...