Abstract Continuation Semantics for Asynchronous Concurrency.

We investigate the abstractness of denotational models designed with continuation semantics for concurrency over metric spaces. Although there exist papers using continuations in the denotational semantics of concurrent languages, we are not aware of any full abstractness result for a concurrent language designed with continuations. Therefore we introduce a new criterion that we name weak abstractness; it preserves the correctness condition, but relaxes the completeness condition of the full abstractness criterion. Weak abstractness may be useful for a wide class of denotational models designed with continuations in which full abstractness is difficult (or impossible) to achieve. To illustrate this approach we present a denotational semantics for a simple asynchronous concurrent language designed with continuation semantics over metric spaces. We show that this denotational semantics is weakly abstract with respect to a corresponding operational model.