Towards Abstractions for Distributed Systems

**Abstract.**
For historical, sociological and technical reasons, lambda-calculi
have been the dominant theoretical paradigm in the study of functional
computation. Similarly, but to a lesser degree, pi-calculi dominate
advanced mathematical accounts of concurrency. Alas, and despite its
ever increasing ubiquity, an equally convincing formal foundation for
distributed computing has not been forthcoming. This thesis seeks to
contribute towards ameliorating that omission. To this end, guided by
the assumption that distributed computing is concurrent computing with
partial failures of various kinds, we extend the asynchronous
pi-calculus with

- a notion of sites,
- the possibility of site failure,
- a persistence mechanism to deal with site failures,
- the distinction between inter-site and intra-site communication,
- the possibility of message loss in inter-site communication and
- a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.

The basic theory of two of the resulting augmented pi-calculi is explored in considerable detail: the asynchronous pi-calculus with timers and the asynchronous pi-calculus with timers, sites and message failure. The emphasis of this development is on soundly approximating reduction congruence, the canonical equivalence for asynchronous pi-calculi. In the case of the asynchronous pi-calculus with timers we manage to obtain a characterisation of reduction congruence as a labelled bisimilarity. Our results appear to be robust under variations of the underlying calculi. In addition, as a test to evaluate the usefulness and the integration of the aforementioned extensions, we cleanly and incrementally represent the Two Phase Commit Protocol -- an important distributed algorithm, used to ensure consistency of distributed databases in the face of various kinds of (non-byzantine) failures -- in the asynchronous pi-calculus, the asynchronous pi-calculus with timers, sites and message failure and in the asynchronous pi-calculus with timers, sites, site failure and message failure. We establish the correctness of our representations by equational reasoning.

**Update (5 May 2005).** An anonyous reviewer found a rather clever
counterexample to my Theorem 25 (the labelled characterisation of the
maximal sound theory). That does not influence the rest of the
development, as Theorem 25 is not really used anywhere. In particular,
the labelled bisimilarities are still sound, but I'm currently
investigating the source of the problem and will publish the
forensics. It seems that the problem can be overcome. Moreover, the
counterexample is such that it is irrelevant to the verification of
realistic programs. The ps.gz and pdf files below have not yet been
modified. I will update the thesis when I have some more time. For
now, my *Reply to referees* below explains the problem.

**Downloads:** PhD dissertation. BibTeX