Full Abstractness of a Metric Semantics for Action Refinement

For a process language with action refinement and synchronization both an operational and a denotational semantics are given. The operational semantics is based on an SOS-style transition system specification involving syntactical refinement sequences. The denotational semantics is an interleaving model which uses semantical refinement `environments'. It identifies those statements which are equal under all refinements. The denotational model is shown to be fully abstract with respect to the operational one. The underlying metric machinery is exploited to obtain this full abstractness result. Usually, action refinement is treated either in a model with some form of true concurrency, or, when an interleaving model is applied, by assuming that the refining statements are atomized. We argue that an interleaving model without such atomization is attractive as well.