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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 communication 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.[1]

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:[1]

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.[2]

Implementations<br>[edit]

Languages based on the join-calculus<br>[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.[3]

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)[4]

Embeddings in other programming languages<br>[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 in Python 3[5]

C++ via Boost[6] (for boost from 2009, ca. v. 40, current (Dec '19) is 72).

References<br>[edit]

^ a b c Cedric Fournet, Georges Gonthier (1995). "The reflexive CHAM and the join-calculus". Proceedings of POPL., pg. 1

^ 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". Applied Semantics. International Summer School, APPSEM 2000: 268–332.

^ "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

External links<br>[edit]

INRIA, Join Calculus homepage

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

Concurrent computing<br>General<br>Concurrency

Concurrency control

Concurrent data structures<br>Concurrent hash tables

Concurrent users

Indeterminacy

Linearizability

Process calculi<br>CSP

CCS

ACP

LOTOS

π-calculus

Ambient calculus

API-Calculus

PEPA

Join-calculus

Classic problems<br>ABA problem

Cigarette smokers problem

Deadlock

Dining philosophers problem

Producer–consumer problem

Race condition

Readers–writers problem

Sleeping barber problem

Category: Concurrent computing

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