Computational flux

Lecture summary The lecture will be about a simple graphical model for mobile computing. Graphical or geometric models of computing are probably as old as the stored-program computer, possibly older. I do not know when the first flowchart was drawn. Though undeniably useful, flowcharts were denigrated because vital notions like parametric computing-the procedure, in Algol terms-found no place in them. But a graphical reduction model was devised by Wadsworth [15] for the lambda calculus, the essence of parametric (functional) computing. Meanwhile, Patti nets [13] made a breakthrough in understanding synchronization and concurrent control flow. Later, the chemical abstract machine (Chain) [2]-employing chemical analogy but clearly a spatial concept-clarified and generalised many features of process calculi. Before designing CCS, I definedflowgraphs [9] as a graphical presentation offlow algebra, an early form of what is now called structural congruence; it represented the static geometry of interactive processes. The pi calculus and related calculi are all concerned with a form of mobility; they all use some form of structural congruence , but are also informed by a kind of dynamic geometrical intuition, even if not expressed formally in those terms. There are now many such calculi and associated languages. Exam-pies are the pi calculus [11], the fusion calculus [12], the join calculus [5], the spi calculus [1], the ambient calculus [3], Pict [14], nomadic Pitt [16], explicit fusions [6]. While these calculi were evolving, in the action calculus project [10] we tried to distill their shared mobile geometry into the notion of action graph. This centred around a notion of molecule, a node in which further graphs may nest. All action calculi share this kind of geometry, and are distinguished only by a signature (a set of molecule types) and a set of reaction rules. The latter determine what configurations of molecules can react, and the contexts in which these reactions can take place. Such a framework does not necessarily help in designing and analysing a calculus for a particular purpose. It becomes useful when it supplies non-trivial theory relevant to all, or a specific class Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post …