Actor model theory

In theoretical computer science, Actor model theory concerns theoretical issues for the Actor model. Actors are the primitives that form the basis of the Actor model of concurrent digital computation. In response to a message that it receives, an Actor can make local decisions, create more Actors, send more messages, and designate how to respond to the next message received. Actor model theory incorporates theories of the events and structures of Actor computations, their proof theory, and denotational models. From the definition of an Actor, it can be seen that numerous events take place: local decisions, creating Actors, sending messages, receiving messages, and designating how to respond to the next message received. However, this article focuses on just those events that are the arrival of a message sent to an Actor. This article reports on the results published in Hewitt [2006]. Law of Countability: There are at most countably many events. The activation ordering (-≈→) is a fundamental ordering that models one event activating another (there must be energy flow in the message passing from an event to an event which it activates). Because of the transmission of energy, the activation ordering is relativistically invariant; that is, for all events e1.e2, if e1 -≈→ e2, then the time of e1 precedes the time of e2 in the relativistic frames of reference of all observers. Law of Strict Causality for the Activation Ordering: For no event does e -≈→ e. Law of Finite Predecession in the Activation Ordering: For all events e1 the set {e|e -≈→ e1} is finite. The arrival ordering of an Actor x ( -x→ ) models the (total) ordering of events in which a message arrives at x. Arrival ordering is determined by arbitration in processing messages (often making use of a digital circuit called an arbiter). The arrival events of an Actor are on its world line. The arrival ordering means that the Actor model inherently has indeterminacy (see Indeterminacy in concurrent computation).