Sequentiality and the CPS Semantics of Fresh Names

We investigate the domain-theoretic denotational semantics of a CPS calculus with fresh name declaration. This is the target of a fully abstract CPS translation from the nu-calculus with first-class continuations. We describe a notion of “FM-categorical” model for our calculus, with a simple interpretation of name generation due to Shinwell and Pitts. We show that full abstraction fails (at order two) in the simplest instance of such a model (FM-cpos) because of the presence of parallel elements. Accordingly, we define a sequential model — FM-biorders, based on “bistable FM-bicpos” and bistable functions — and prove that it is fully abstract up to order four (our main result), but that full abstraction fails at order five.