The Polyadic Pi-calculus (Abstract)

The ~'-calculus is a calculus of concurrent processes based upon the idea of namira3. It modeIs dynamically changing concurrent systems, has a rich algebraic theory, and c o n t ~ s in a precise way both functions (the)`-calculus) and data structures, represented as processes. The calculus is a generalization of CCS, and was introduced by Robin Milner, Joachim Parrow and David Walker, based on important ideas of biogens Nielsen and Ufl'e Engberg. The way in which everything is built upon nsmlng is this: When two processes interact, they use a name (which can be thought of as a channel). This name is called the subjeei of the interaction. The object of an interaction its information content i s also a name; this is the mention of a name, not the use ofit. To receive s name is to acquire the ability to use it, perhaps to interact with a process which was previously inaccessible. This process may indeed represent a datum, as explained above; then one can think of the datum itself having been received. In this lecture I shall discuss the polyadic version of the x-calculus, which supports a very fruitful notion of sort and sorting, Akln to simple typing in the )`calculus. It will be seen how different sortings are appropriate for different applications. The encoding of the ),-calculus into ~r-calculus, and the uniform representation of data structures, are best seen in the polyadic setting with suitable sortings.