# Join-calculus

(Redirected from Join calculus)

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 $\pi$-calculus. Encodings of the $\pi$-calculus in the join-calculus, and vice versa, have been demonstrated.[2]

The join-calculus is a member of the $\pi$-calculus family of process calculi, and can be considered, at its core, an asynchronous $\pi$-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 $\pi$-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.[4]

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.
• MC# and Parallel C# extend Polyphonic C#.
• A Concurrent Basic proposal that uses Join-calculus
• JErlang (the J is for Join, erjang is Erlang for the JVM)

## 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.

## References

1. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus"., pg. 1
2. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus"., pg. 2
3. ^ Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus"., pg. 19
4. ^ Cedric Fournet, Georges Gonthier (2000). "The Join Calculus: A Language for Distributed Mobile Programming".