Traces, Pomsets, Fairness and Full Abstraction for Communicating Processes

We provide a denotational trace semantics for processes with synchronous communication and a form of weakly fair parallelism. The semantics is fully abstract: processes have the same trace sets if and only if their communication behaviors are identical in all contexts. The model can easily be adapted for asynchronously communicating processes, or for shared-memory parallel programs. We also provide a partial-order semantics, using pomsets adapted for synchronization and our form of fairness. The pomset semantics can also be adjusted to model alternative paradigms. The traces of a process can be recovered from the pomset semantics by taking all fair interleavings consistent with the partial order.