Substructural Observed Communication Semantics

Session-types specify communication protocols for communicating processes, and session-typed languages are often specified using substructural operational semantics given by multiset rewriting systems. We give an observed communication semantics for a session-typed language with recursion, where a process's observation is given by its external communications. To do so, we introduce fair executions for multiset rewriting systems, and extract observed communications from fair process executions. This semantics induces an intuitively reasonable notion of observational equivalence that we conjecture coincides with semantic equivalences induced by denotational semantics, bisimulations, and barbed congruences for these languages.