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]}

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 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)
^{[6]}

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 in Python 3
^{[7]} - C++ via Boost
^{[8]}(for boost from 2009, ca. v. 40, current (Dec '19) is 72).

**^**Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus".`((cite journal))`

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(help), pg. 1**^**Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus".`((cite journal))`

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(help), pg. 2**^**Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus".`((cite journal))`

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(help), pg. 19**^**Petricek, Tomas. "TryJoinads (IV.) - Concurrency using join calculus".*tomasp.net*. Retrieved 2023-01-24.**^**Cedric Fournet, Georges Gonthier (2000). "The Join Calculus: A Language for Distributed Mobile Programming": 268–332.`((cite journal))`

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(help)**^**"JErlang: Erlang with Joins". Archived from the original on 2017-12-08. Retrieved 2015-04-18.**^**Join Python, Join-calculus for Python by Mattias Andree**^**Yigong Liu - Join-Asynchronous Message Coordination and Concurrency Library

- INRIA, Join Calculus homepage
- Microsoft Research, The Join Calculus: a Language for Distributed Mobile Programming

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Process calculi | |

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