Process algebras crumble

September 15th, 2009 • review
Tags: concurrency

Samson Abramsky states in “What are the fundamental structures of concurrency? We still don’t know!” what is obvious about what appears to be a fundamental subject. As Robin Milner points out, it is appears to be blindingly obvious that this is a world where concurrent processes in information systems are now unavoidable in our daily lives. The reality is that the languages and tools built to tackel this subject, which were in the 1980 buzzing with promise, have failed systematically, on every avenue, to take any realistic steps.

But from what appears lost there are messages to harvest. Concurrency models break from the world of Bertrand Russell, as demonstrated by the inadequacy of denotational models; a view is shared by the direction of abstract algebra. Concurrency models do not directly tackle concrete problems; there remains a gulf between the model and the implementation which is not systematically transcended. Such transcendence appears equally in logic, where often barely a cut elimination theorem can be achieved. Direct lifting into a field associated with higher levels of abstraction — categories of bigraphs, relative pushouts … — have added definitions but not insight.

The path is not staring us in our face. The path of elegance does not repeat the same questions over and over again. Not even for a handful of decades. Let us select a stronger branch but do not grapple it.