Puneet Varma (Editor)

Join calculus

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The join-calculus is a process calculus developed at INRIA. The join-calculus was developed to provide a formal basis for the design of distributed programming languages, and therefore intentionally avoids communications constructs found in other process calculi, such as rendezvous communications, which are difficult to implement in a distributed setting. Despite this limitation, the join-calculus is as expressive as the full π-calculus. Encodings of the π-calculus in the join-calculus, and vice versa, have been demonstrated.


The join-calculus is a member of the π-calculus family of process calculi, and can be considered, at its core, an asynchronous π-calculus with several strong restrictions:

  • Scope restriction, reception, and replicated reception are syntactically merged into a single construct, the definition;
  • Communication occurs only on defined names;
  • For every defined name there is exactly one replicated reception.
  • However, as a language for programming, the join-calculus offers at least one convenience over the π-calculus — namely the use of multi-way join patterns, the ability to match against messages from multiple channels simultaneously.

    Languages based on the join-calculus

    The join-calculus programming language is a new language based on the join-calculus process calculus. It is implemented as an interpreter written in OCaml, and supports statically typed distributed programming, transparent remote communication, agent-based mobility, and failure-detection.

    Many implementations of the join-calculus were made as extensions of existing programming languages:

  • JoCaml is a version of OCaml extended with join-calculus primitives.
  • Polyphonic C# and its successor Cω extend C#.
  • MC# and Parallel C# extend Polyphonic C#.
  • Join Java extends Java.
  • A Concurrent Basic proposal that uses Join-calculus
  • JErlang (the J is for Join, erjang is Erlang for the JVM))
  • C++ via Boost
  • Embeddings in other programming languages

    These implementations do not change the underlying programming language but introduce join calculus operations through a custom library:

  • The Boost.Join library is an implementation in C++ within the Boost framework.
  • The ScalaJoins library is in Scala.
  • Joinads - various implementations of join calculus in F#.
  • CocoaJoin is an experimental implementation in Objective-C for iOS and Mac OS X.
  • The Join Python library is in Python 3.
  • References

    Join-calculus Wikipedia

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