Quasiprobability distribution

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

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:

• 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 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.

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.

The Boost.Join library is an implementation in C++.

A Concurrent Basic proposal that uses Join-calculus

External links

• INRIA, Join Calculus homepage

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