Quick Take on the Pi Calculus

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Take a couple of management consultants from the same firm as Michael Champy (i.e. Reengineering fame), couple that with a new mathematical formulation of computation and mix in some java technology from an open source proponent (i.e. Intalio) and you not only turn heads but brew controversy rivaling the cold fusion “discoveries”.

Pi calculus is a fairly recent formulation of computation that strives to take into account mobile processes. So if you could extrapolate that the lambda calculus modeled recursive computation, the relational calculus modeled data and now you have the Pi calculus models process. Looks pretty enticing doesn’t it? Well just like any formal treatements that have come and gone (remember the Object calculi by Abadi and Cardelli ) some have extreme impact and some are complete duds.

In my explorations to figure this out, I’ve come upon this short explanation:

Now, as for the suitability of the framework to this domain, it turns out that the mobile process algebras are the first model of computation to simultaneously enjoy four features:

  1. Completeness — i.e. Turing complete
  2. Compositionality — the model is an algebra, the practical advantage of which is that large(r) programs are built from small(er) ones
  3. Concurrency — the model has an explicit account of autonomous execution
  4. Cost — the model has an explicit account of resources like time and space

Turing machines, for example, fail on features 2 and 3. Lambda calculus fails on 3 and 4. Petri nets fail on 2. CCS, CSP fail on 4

(remind me later where I dug this up) Well that certainly clears it up a bit. But what’s in it for me? Well another piece I dug up:

From our discussion I hear that pi gives me: 1) automatic deadlock detection, 2) a formal composition model that let me describe that how messages are interchaged 3) automatic verification (simulation) that something is going to work. That said, the pi-calculus provides a *framework* in which to develop the appropriate formalism. This framework is objectively and demonstrably different from the other models of computation put forward. And, it is better suited to the modeling of domains like workflow than any other model put forward so far.

Well then, are we emerging into a new formalism that intends to shake the very foundations of enterprise development? Stay tuned!

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