Actor Model

Origin. Hewitt, Bishop, Steiger (1973). Concurrent computation via actors. Message passing only. No shared state. Foundation for distributed systems.

Models. Actors: concurrent entities. Mailbox: message queue. Behavior: response to messages. Create, send, become. Asynchronous, location-transparent.

Formalism.

Actor: Independent computational entity. Has: address, behavior, mailbox. Responds to messages one at a time.

Primitive operations: send(a, m): send message m to actor a create(b): create new actor with behavior b become(b): change own behavior to b

Message delivery: Asynchronous: send doesn't wait. Guaranteed delivery (in model). Order not guaranteed between actors.

Behavior: Function from message to actions. b(m) = {send(...), create(...), become(...)}

Operational semantics: Configuration: set of actors + messages in transit. Step: actor processes message, performs actions.

Event ordering: Happens-before: causal ordering. a sends to b happens-before b receives. Local ordering within actor.

Properties: No shared state. Location transparency. Encapsulation. Fairness: messages eventually processed.

Formal models: Agha's actor algebra. Configuration structures. Denotational: powerdomain.

Symbols.

Symbol	Unicode	Name	Meaning
a, b	—	Actors	Entity addresses
m	—	Message	Communication
→	U+2192	Send	Message passing
⟨⟩	—	Behavior	Response function

Metatheory. Turing complete. Expressing concurrency. Bisimulation. Fairness properties.

Applies to. Erlang/OTP. Akka. Distributed systems. Cloud computing. Fault tolerance.

Limitations. Ordering challenges. Debugging distributed. Deadlock possible. Performance overhead.