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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.[1] 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.[2]

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:[3]

  • 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.[4]


Languages based on the join-calculus[edit]

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 some failure-detection.[5]

  • Though not explicitly based on join-calculus, the rule system of CLIPS implements it if every rule deletes its inputs when triggered (retracts the relevant facts when fired).

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 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)[6]

Embeddings in other programming languages[edit]

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

  • The ScalaJoins and the Chymyst libraries are in Scala
  • JoinHs by Einar Karttunen and syallop/Join-Language by Samuel Yallop are DSLs for Join calculus in Haskell
  • 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
  • C++ via Boost[7] (for boost from 2009, ca. v. 40, current (Dec '19) is 72).


  1. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus". {{cite journal}}: Cite journal requires |journal= (help), pg. 1
  2. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus". {{cite journal}}: Cite journal requires |journal= (help), pg. 2
  3. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus". {{cite journal}}: Cite journal requires |journal= (help), pg. 19
  4. ^ Petricek, Tomas. "TryJoinads (IV.) - Concurrency using join calculus". Retrieved 2023-01-24.
  5. ^ Cedric Fournet, Georges Gonthier (2000). "The Join Calculus: A Language for Distributed Mobile Programming": 268–332. {{cite journal}}: Cite journal requires |journal= (help)
  6. ^ "JErlang: Erlang with Joins". Archived from the original on 2017-12-08. Retrieved 2015-04-18.
  7. ^ Yigong Liu - Join-Asynchronous Message Coordination and Concurrency Library

External links[edit]