Revivals, stuckness and the hierarchy of CSP models

We give details of a new model for CSP introduced in response to work by Fournet et al [C. Fournet, C.A.R. Hoare, S.K. Rajamani and J. Rehof, Stuck-free conformance, Proceedings CAV 04, 16th International Conference on Computer Aided Verification, Boston, USA, July 2004.]. This is the stable revivals model R alluded to in Reed et al (2007, FAC, 19, 3). We provide the full semantics for CSP in this model, indicate why this is operationally congruent, and provide proofs of the full abstraction properties asserted in that paper. We study the place of R in the hierarchy of CSP models, and show how this generates several extensions of R handling infinite behaviours. In doing this we discover more about the hierarchy and several known models within it. This includes results that show that the traces model, failures model and are new one are somehow “essential” or “Platonic”. We set out a number of conjectures and challenges for future workers in this area.