Client Server Systems

A Distributed Pi-Calculus by Matthew Hennessy

By Matthew Hennessy

Dispensed platforms are quick changing into the norm in machine technology. Formal mathematical versions and theories of allotted habit are wanted so one can comprehend them. This ebook proposes a disbursed pi-calculus referred to as Dpi, for describing the habit of cellular brokers in a disbursed global. it truly is in accordance with an latest formal language, the pi-calculus, to which it provides a community layer and a primitive migration build. A mathematical thought of the habit of those disbursed platforms is constructed, within which the presence of sorts performs an important function. it's also proven how in precept this thought can be utilized to boost verification thoughts for making certain the habit of allotted brokers. The textual content is out there to machine scientists with a minimum heritage in discrete arithmetic. It includes an basic account of the pi-calculus, and the linked idea of bisimulations. It additionally develops the kind conception required by means of Dpi from first ideas.

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Example text

The continuation R is then only executed once an acknowledgement has been received on ack. The receiving process is expected to send this acknowledgement, via the simple process ack! () , whenever a value is received on c. 1 The language aPi 13 tuple of values; that is no value is sent and the channel ack is simply used for synchronisation. However in future, to avoid the proliferation of brackets, we will render the transmission along these synchronisation channels simply by ack! This also explains the input notation.

X) (c! x | z) is the body of the recursive definition. (x) (c! (x) (c! x | F1 (b, c)). So in summary one application of (r-unwind) gives F1 (b, c) −→ B(b, c) Let us now see how this reduction can take place as part of the larger system FF1 . 4 may be applied anywhere under occurrences of the static operators | and (new n): (r-par) (r-new) P −→ P P | Q −→ P | Q Q | P −→ Q | P P −→ P (new n) P −→ (new n) P So we have the following formal derivation, where the inferences are justified by the rules used: 1 F1 (b, c) −→ B(b, c) 2 F1 (b, c) | F1 (c, d ) −→ B(b, c) | F1 (c, d ) 3 FF1 −→ (new c)(B(b, c) | F1 (c, d )) (r-unwind) (r-par) to 1 (r-new) to 2 In other words one possible computation step from the system FF1 is given by FF1 −→ (new c)(B(b, c) | F1 (c, d )) Nevertheless these unwindings, even within static contexts, do not lead to interesting computations.

3), followed by (r-par), gives the reduction Sys2 −→ (new c)(c! (x) print! x (Sys3 ) At this point, in Sys3 , communication is possible along the channel c, at least intuitively, but to formally derive it we again need various applications of the rules. The basic axiom used is c! v | B(c, d ) −→ d ! v | F1 (c, d ) an instance of (r-comm). An application of (r-par), then (r-struct), then (r-new), then (r-par), gives: Sys3 −→ FF1 | d ! (x) print! 2 Reduction semantics for aPi 21 In a similar manner the communication of v on d can be derived, cumulating in the overall derivation Sys1 −→∗ FF1 | print!

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