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The Actor model and process calculi share an interesting history and co-evolution.
The Actor model, first published in 1973,^{[1]} is a mathematical model of concurrent computation. The Actor model treats “Actors” as the universal primitives 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 determine how to respond to the next message received.
As opposed to the previous approach based on composing sequential processes, the Actor model was developed as an inherently concurrent model. In the Actor model sequentiality was a special case that derived from concurrent computation as explained in Actor model theory.
Robin Milner's initial published work on concurrency^{[2]} was also notable in that it positions mathematical semantics of communicating processes as a framework to understand a variety of interaction agents including the computer's interaction with memory. The framework of modelling was based on Scott's model of domains and as such was not based on sequential processes. His work differed from the Actor model in the following ways:
Milner later removed some of these restrictions in his work on the Pi calculus (see section Milner, et al. below).
The publication by Tony Hoare in 1978 of the original Communicating Sequential Processes was different from the Actor model which states:^{[3]}
The 1978 version of CSP differed from the Actor model in the following respects [Clinger 1981]:
In his Turing lecture,^{[4]} Milner remarked as follows:
In 2003, Ken Kahn recalled in a message about the Pi calculus:
Tony Hoare, Stephen Brookes, and A. W. Roscoe developed and refined the theory of CSP into its modern form.^{[5]} The approach taken in developing the theoretical version of CSP was heavily influenced by Robin Milner's work on the Calculus of Communicating Systems (CCS), and vice versa. Over the years there have been many fruitful exchanges of ideas between the researchers working on both CSP and CCS.
Will Clinger [1981] developed the first denotational Actor model for concurrent computation that embodied unbounded nondeterminism. Bill Kornfeld and Carl Hewitt [1981] showed that the Actor model could encompass large-scale concurrency. Agha developed Actors as a fundamental model for concurrent computation. His work on representing Actor abstraction and composition, and on developing an operational semantics for Actors based on asynchronous communications trees was explicitly influenced by Milner's work on the Calculus of Communicating Systems (CCS).^{[6]} as well the work of Clinger.
The π-calculus, partially inspired by the Actor model as described by Milner above, introduced dynamic topology into the process calculi by allowing dynamic creation of processes and for the names to be passed among different processes. However, the goal of Milner and Hoare to attain an algebraic calculus led to a critical divergence from the Actor model: communication in the process calculi is not direct as in the Actor model but rather indirectly through channels (see Actor model and process calculi). In contrast, recent work on the Actor model [Hewitt 2006, 2007a] has emphasized denotational models and the Representation Theorem.
Nevertheless there are interesting co-evolutions between the Actor Model and Process Calculi. Montanari and Talcott^{[7]} discussed whether the Actor Model and π-calculus were compatible with each other. Sangiorgi and Walker showed how Actor work on treating control structures as patterns of passing messages^{[8]} could be modeled using the π-calculus.
Although algebraic laws have been developed for the Actor model, they do not capture the crucial property of guaranteed delivery of messages sent to Serializers. For example see the following:
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