By Matthew Hennessy

ISBN-10: 0511275641

ISBN-13: 9780511275647

ISBN-10: 0521873304

ISBN-13: 9780521873307

Disbursed structures are speedy changing into the norm in machine technology. Formal mathematical versions and theories of dispensed habit are wanted which will comprehend them. This e-book proposes a allotted pi-calculus known as Dpi, for describing the habit of cellular brokers in a dispensed global. it really is in response to an current formal language, the pi-calculus, to which it provides a community layer and a primitive migration build. A mathematical idea of the habit of those allotted structures is built, within which the presence of sorts performs a massive position. it's also proven how in precept this idea can be utilized to enhance verification suggestions for ensuring the habit of disbursed brokers. The textual content is available to desktop scientists with a minimum heritage in discrete arithmetic. It comprises an effortless account of the pi-calculus, and the linked concept of bisimulations. It additionally develops the sort concept required through Dpi from first rules.

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**Extra resources for A Distributed Pi-Calculus**

**Sample text**

Z, y ) where the new variable w is chosen to be different from the existing free and bound variables. Intuitively the behaviour of a process is independent of the actual identity of bound variables as they are merely place-holders. So here we have renamed the bound variable y so that when the substitution of y for x is made, what was previously a free variable, x, is not transformed into a bound variable. This is generalised to the substitution of a structured value V for a pattern, denoted R{|V/X |}; again for this to be well-defined we require at least that the structure of V and X match.

W, x ) as only the place-holders for incoming values have been changed. (y, z) (d ! y, x | b! (z, w) (d ! z, x | b! w, x ) In a similar manner, assuming m does not appear in P, (new n)(c! (x) P) ≡α (new m)(c! (x) (P{|m/n|})) We will identify terms up to α-equivalence, or more formally use terms as representatives of their α-equivalence classes. 4 (Barendregt) This identification of terms up to α-equivalence allows us to use a very convenient convention when writing terms. We will always ensure all bound identifiers are distinct, and chosen to be different from all free identifiers.

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.

### A Distributed Pi-Calculus by Matthew Hennessy

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