A Fair Power Domain for Actor Computations

Abstract

Actor-based languages feature extreme concurrency, allow side effects, and specify a form of fairness which permits unbounded nondeterminism. This makes it difficult to provide a satisfactory mathematical foundation for the semantics. Due to the high degree of parallelism, an oracle semantics would be intractable. A weakest precondition semantics is out of the question because of the possibility of unbounded nondeterminism. The most attractive approach, fixed point semantics using power domains, has not been helpful because the available power domain constructions, although very general, seemed to deal inadequately with fairness. By taking advantage of the relatively complex structure of the actor computation domain C, however, a power domain P(C) can be defined which is similar to Smyth's weak power domain but richer. Actor systems, which are collections of mutually recursive primitive actors with side effects, may be assigned meanings as least fixed points of their associated continuous functions acting on this power domain. Given a denotation A ∈ P(C), the set of possible complete computations of the actor system it represents is the set of least upper bounds of a certain set of "fair" chain in A, and this set of chains is definable within A itself without recourse to oracles or an auxiliary interpretive semantics. It should be emphasized that this power domain construction is not nearly as generally applicable as those of the Plotkin [Pl] and Smyth [Sm], which can be used with any complete partial order. Fairness seems to require that the domain from which the power domain is to be constructed contain sufficient operational information.