Actor model and process calculi history

The Actor model and process calculi
Actor model and process calculi
In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation...

share an interesting history and co-evolution.

Early work

The Actor model

Actor model

In computer science, the Actor model is a mathematical model of concurrent computation that 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...

, first published in 1973, 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

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,...

.

Robin Milner

Robin Milner

Arthur John Robin Gorell Milner FRS FRSE was a prominent British computer scientist.-Life, education and career:...

's initial published work on concurrency 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:

There are a fixed number of processes as opposed to the Actor model which allows the number of Actors to vary dynamically
The only quantities that can be passed in messages are integers and strings as opposed to the Actor model which allows the addresses of Actors to be passed in messages
The processes have a fixed topology as opposed to the Actor model which allows varying topology
Communication is synchronous as opposed to the Actor model in which an unbounded time can elapse between sending and receiving a message.
The semantics provided bounded nondeterminism unlike the Actor model with unbounded nondeterminism. However, with bounded nondeterminism is impossible for a server to guarantee service to its clients, i.e., a client might starve
Resource starvation
In computer science, starvation is a multitasking-related problem, where a process is perpetually denied necessary resources. Without those resources, the program can never finish its task....

.

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

Communicating sequential processes

In computer science, Communicating Sequential Processes is a formal language for describing patterns of interaction in concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi...

was different from the Actor model which states:

This paper suggests that input and output are basic primitives of programming and that parallel composition of communicating sequential processes is a fundamental program structuring method. When combined with a development of Dijkstra's guarded command, these concepts are surprisingly versatile. Their use is illustrated by sample solutions of a variety of familiar programming exercises.

...

The programs expressed in the proposed language are intended to be implementable both by a conventional machine with a single main store, and by a fixed network of processors connected by input/output channels (although very different optimizations are appropriate in the different cases). It is consequently a rather static language: The text of a program determines a fixed upper bound on the number of processes operating concurrently; there is no recursion and no facility for process-valued variables. In other respects also, the language has been stripped to the barest minimum necessary for explanation of its more novel features.

...

This paper has suggested that input, output, and concurrency should be regarded as primitives of programming, which underlie many familiar and less familiar programming concepts. However, it would be unjustified to conclude that these primitives can wholly replace the other concepts in a programming language. Where a more elaborate construction (such as a procedure or a monitor) is frequently useful, has properties which are more simply provable, and can also be implemented more efficiently than the general case, there is a strong reason for including in a programming language a special notation for that construction. The fact that the construction can be defined in terms of simpler underlying primitives is a useful guarantee that its inclusion is logically consistent with the remainder of the language.

The 1978 version of CSP differed from the Actor model in the following respects [Clinger 1981]:

The concurrency primitives of CSP were input, output, guarded commands, and parallel composition whereas the Actor model is based on asynchronous one-way messaging.
The fundamental unit of execution was a sequential process in contrast to the Actor model in which execution was fundamentally concurrent. Sequential execution is problematical because multi-processor computers are inherently concurrent.
The processes had a fixed topology of communication whereas Actors had a dynamically changing topology of communications. Having a fixed topology is problematical because it precludes the ability to dynamically adjust to changing conditions.
The processes were hierarchically structured using parallel composition whereas Actors allowed the creation of non-hierarchical execution using futures
Future (programming)
In computer science, future, promise, and delay refer to constructs used for synchronization in some concurrent programming languages. They describe an object that acts as a proxy for a result that is initially not known, usually because the computation of its value has not yet completed.The term...

[Baker and Hewitt 1977]. Hierarchical parallel composition is problematical because it precludes the ability to create a process that outlives its creator. Also message passing is the fundamental mechanism for generating parallelism in the Actor model; sending more messages generates the possibility of more parallelism.
Communication was synchronous whereas Actor communication was asynchronous. Synchronous communication is problematical because the interacting processes might be far apart.
Communication was between processes whereas in the Actor model communications are one-way to Actors. Synchronous communication between processes is problematical by requiring a process to wait on multiple processes (see Actor model and process calculi
Actor model and process calculi
In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation...

).
Data structures consisted of numbers, strings, and arrays whereas in the Actor model data structures were Actors. Restricting data structures to numbers, strings, and arrays is problematical because it prohibits programmable data structures.
Messages contain numbers and strings whereas in the Actor model messages could include the addresses of Actors. Not allowing addresses in messages is problematical because it precludes flexibility in communication because there is no way to supply another process with the ability to communicate with an already known process.
The model of CSP deliberately had bounded nondeterminism [Francez, Hoare, Lehmann, and de Roever 1979] whereas the Actor model had unbounded nondeterminism
Unbounded nondeterminism
In computer science, unbounded nondeterminism or unbounded indeterminacy is a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be...

. Dijkstra [1976] had convinced Hoare that a programming language with unbounded nondeterminism could not be implemented. Consequently it was not possible to guarantee that servers implemented using CSP would provide service to multiple clients.

Milner, et al.

In his Turing lecture, Milner remarked as follows:

Now, the pure lambda-calculus is built with just two kinds of thing: terms and variables. Can we achieve the same economy for a process calculus? Carl Hewitt, with his Actors model, responded to this challenge long ago; he declared that a value, an operator on values, and a process should all be the same kind of thing: an Actor. This goal impressed me, because it implies the homogeneity and completeness of expression ... But it was long before I could see how to attain the goal in terms of an algebraic calculus...So, in the spirit of Hewitt, our first step is to demand that all things denoted by terms or accessed by names--values, registers, operators, processes, objects--are all of the same kind of thing; they should all be processes. Thereafter we regard access-by-name as the raw material of computation...

In 2003, Ken Kahn recalled in a message about the Pi calculus:

Pi calculus is based upon synchronous (hand-shake) communication. About 25 years ago I went to dinner with Carl Hewitt and Robin Milner (of CSS and pi calculus fame) and they were arguing about synchronous vs. asynchronous communication primitives. Carl used the post office metaphor while Robin used the telephone. Both quickly admitted that one can implement one in the other.

Hoare, et al.

Tony Hoare, Stephen Brookes, and A. W. Roscoe

Bill Roscoe

A. William "Bill" Roscoe is a Scottish computer scientist. He is Head of the Department of Computer Science, University of Oxford and a Professor of Computing Science...

developed and refined the theory of CSP into its modern form. The approach taken in developing the theoretical version of CSP was heavily influenced by Robin Milner

Robin Milner

Arthur John Robin Gorell Milner FRS FRSE was a prominent British computer scientist.-Life, education and career:...

's work on the Calculus of Communicating Systems

Calculus of Communicating Systems

The Calculus of Communicating Systems is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. Its actions model indivisible communications between exactly two participants. The formal language includes primitives for describing parallel...

(CCS), and vice versa. Over the years there have been many fruitful exchanges of ideas between the researchers working on both CSP and CCS.

Hewitt, et al.

Will Clinger [1981] developed the first denotational Actor model for concurrent computation that embodied unbounded nondeterminism

Unbounded nondeterminism

In computer science, unbounded nondeterminism or unbounded indeterminacy is a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be...

. Bill Kornfeld and Carl Hewitt [1981] showed that the Actor model could encompass large-scale concurrency. Agha

Gul Agha (computer scientist)

Gul Agha is a Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign, and Director of the Open Systems Laboratory. He is known for his work on the Actor model of concurrent computation, and was also Editor-in-Chief of ACM Computing Surveys from 1999 to...

developed Actors as a fundamental model for concurrent computation. His work on representing Actor abstraction and composition, and on developing an operational semantics

Operational semantics

In computer science, operational semantics is a way to give meaning to computer programs in a mathematically rigorous way. Operational semantics are classified into two categories: structural operational semantics formally describe how the individual steps of a computation take place in a...

for Actors based on asynchronous communications trees was explicitly influenced by Milner's work on the Calculus of Communicating Systems

Calculus of Communicating Systems

(CCS). as well the work of Clinger.

Further co-evolution

The π-calculus

Pi-calculus

In theoretical computer science, the π-calculus is a process calculus originally developed by Robin Milner, and David Walker as a continuation of work on the process calculus CCS...

, 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

Channel (communications)

In telecommunications and computer networking, a communication channel, or channel, refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel...

(see Actor model and process calculi

Actor model and process calculi

In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation...

). 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 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 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:

Gaspari and Zavattaro
Agha and Thati

Early work

Milner, et al.

Hoare, et al.

Hewitt, et al.

Further co-evolution

Further reading