Fairness and Communication-Based Semantics for Session-Typed Languages

Abstract: We give communication-based semantics and reasoning techniques for Polarized SILL, a rich session-typed programming language with general recursion. Its features include channel and code transmission, synchronous and asynchronous communication, and functional programming. Our contributions are distinguished by their faithfulness to the process abstraction, i.e., to the premise that communication is the only observable phenomenon of processes. We give the first observed communication semantics that supports general recursion and code transmission. Observed communication semantics define the meaning of processes in terms of their observed communications. We use this observational semantics to define experiments on processes, and we give a communication-based testing equivalences framework for defining observational simulations and equivalences on processes. This framework captures several natural equivalences, and we show that one of these coincides with barbed congruence, the canonical notion of process equivalence. Polarized SILL is defined using a substructural operational semantics based on multiset rewriting. To ensure that our contributions are well-defined in the presence of non-termination, we introduce fairness for multiset rewriting systems. We construct a fair scheduler, we give sufficient conditions for traces to be fair, and we study the effects of permutation on fair traces.