## Section: Scientific Foundations

### Concurrency theory

Milner started the theory of concurrency in 1980 at Edinburgh. He proposed the calculus of communicating systems (CCS) as an algebra modeling interaction [25] . This theory was amongst the most important to present a compositional process language. Furthermore, it included a novel definition of operational equivalence, which has been the source of many articles, most of them quite subtle. In 1989, R. Milner, J. Parrow and D. Walker [26] introduced a new calculus, the pi-calculus , capable of handling reconfigurable systems. This theory has been refined by D. Sangiorgi (Edinburgh/INRIA Sophia/Bologna) and others. Many variants of the pi-calculus have been developed since 1989.

We developed a variant, called the Join-calculus [4] , [5] , a variant easier to implement in a distributed environment. Its purpose is to avoid the use of atomic broadcast to implement fair scheduling of processes. The Join-calculus allows concurrent and distributed programming, and simple communication between remote processes. It was designed with locations of processes and channels. It leads smoothly to the design and implementation of high-level languages which take into account low-level features such as the locations of objects.

The Join-calculus has higher-order channels as in the pi-calculus; channels names can be passed as values. However there are several restrictions: a channel name passed as argument cannot become a receiver; a receiver is permanent and has a single location, which allows one to identify channel names with their receivers. The loss of expressibility induced by these restrictions is compensated by joined receivers. A guard may wait on several receivers before triggering a new action. This is the way to achieve rendez-vous between processes. In fact, the notation of the Join-calculus is very near the natural description of distributed algorithms.

The second important feature of the Join-calculus is the concept of location. A location is a set of channels co-residing at the same place. The unit of migration is the location. Locations are structured as trees. When a location migrates, all of its sub-locations move too.

The Join-calculus, renamed Jocaml, has been fully integrated into Ocaml. Locations and channels are new features; they may be manipulated by or can handle any Ocaml values. Unfortunately the newer versions of Ocaml do not support them. We are still planning for both systems to converge.

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