Structured reasoning about actor systems

The actor model of distributed computing imposes important restrictions on concurrent computations in order to be valid. In particular, an actor language implementation must provide fairness, the property that if a system transition is infinitely often enabled, the transition must eventually happen. Fairness is fundamental to proving progress properties. We show that many properties of actor computation can be expressed and proved at an abstract level, independently of the details of a particular system of actors. As in abstract algebra, we formulate and prove theorems at the most abstract level possible, so that they can be applied at all more refined levels of the theory hierarchy. Our most useful abstract-level theorems concern persistence of actors, conditional persistence of messages, preservation of unique actor identifiers, monotonicity properties of actor local states, guaranteed message delivery, and general consequences of fairness. We apply the general actor theory to a concrete ticker and clock actor system, proving several system-specific properties, including conditional invariants and a progress theorem. We develop our framework within the Athena proof system, in which proofs are both human-readable and machine-checkable, taking advantage of it library of algebraic and relational theories.