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Proof, Language, and Interaction: Essays in Honour of Robin Milner (Foundations of Computing)

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The work of Robin Milner is widely known by anyone who stays current with developments in theoretical computer science, especially in the field of concurrency theory. This sizable volume contains a collection of articles written both by some of his collaborators and students, and others who have extended his work. The brief biography that begins the volume is especially helpful to those readers that need an introduction to his general work. Robin Milner is remembered by most primarily because of his development, along with J. Parrow and D. Walker, of the `pi-calculus'. There are several articles in this volume that discuss the pi-calculus, with one of particular interest being the one by Benjamin C. Pierce and David N. Turner on a programming language called `Pict' that is based on it (this was the only article in the book studied by this reviewer). Since the pi-calculus has been shown to encapsulate the lambda calculus, and the latter serves as the foundation for sequential/functional programming, it is not surprising to learn that the pi-calculus can serve as a basis for a possibly useful programming language. But the pi-calculus, unlike the lambda calculus, was designed to model the concurrency and interaction of processes, instead of sequential ones as is done in the lambda calculus. The authors of this article therefore propose that Pict is such a language, and they discuss in fair detail in this article. In their view the function calls in the lambda calculus should be replaced, in terms of a computational scheme, by process creation, context switching, and communications on channels. At first glance, Pict is an exciting proposal, but one should remember that it, and the pi-calculus that underlies it, does not go beyond the Turing notion of computability. One should therefore not expect that it would change significantly the impact of such issues as computational complexity in Turing machines. The pi-calculus though is still being developed and has been applied to many different areas, such as computational biology and genomics. It's most prevalent application though has been in business process modeling, and many industries now use software packages for this that are based on the pi-calculus.