The Pi Calculus: Towards Global Computing


Check out the video of Christian Williams’’s talk in the Applied Category Theory Seminar here at U. C. Riverside. It was nicely edited by Paola Fernandez and uploaded by Joe Moeller.

Abstract. Historically, code represents a sequence of instructions for a single machine. Each computer is its own world, and only interacts with others by sending and receiving data through external ports. As society becomes more interconnected, this paradigm becomes more inadequate – these virtually isolated nodes tend to form networks of great bottleneck and opacity. Communication is a fundamental and integral part of computing, and needs to be incorporated in the theory of computation.

To describe systems of interacting agents with dynamic interconnection, in 1980 Robin Milner invented the pi calculus: a formal language in which a term represents an open, evolving system of processes (or agents) which communicate over names (or channels). Because a computer is itself such a system, the pi calculus can be seen as a generalization of traditional computing languages; there is an embedding of lambda into pi – but there is an important change in focus: programming is less like controlling a machine and more like designing an ecosystem of autonomous organisms.

We review the basics of the pi calculus, and explore a variety of examples which demonstrate this new approach to programming. We will discuss some of the history of these ideas, called “process algebra”, and see exciting modern applications in blockchain and biology.

“… as we seriously address the problem of modelling mobile communicating systems we get a sense of completing a model which was previously incomplete; for we can now begin to describe what goes on outside a computer in the same terms as what goes on inside – i.e. in terms of interaction. Turning this observation inside-out, we may say that we inhabit a global computer, an informatic world which demands to be understood just as fundamentally as physicists understand the material world.” — Robin Milner

The talks slides are here.

Reading material:

• Robin Milner, The polyadic pi calculus: a tutorial.

• Robin Milner, Communicating and Mobile Systems.

• Joachim Parrow, An introduction to the pi calculus.

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