A Distributed Pi-Calculus by Matthew Hennessy

By Matthew Hennessy

Dispensed structures are quick turning into the norm in desktop technology. Formal mathematical types and theories of dispensed habit are wanted on the way to comprehend them. This booklet proposes a dispensed pi-calculus referred to as Dpi, for describing the habit of cellular brokers in a dispensed global. it truly is in accordance with an current 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 dispensed platforms is constructed, during which the presence of sorts performs an enormous position. it's also proven how in precept this conception can be utilized to strengthen verification recommendations for ensuring the habit of allotted brokers. The textual content is obtainable to desktop scientists with a minimum history in discrete arithmetic. It includes an easy account of the pi-calculus, and the linked idea of bisimulations. It additionally develops the kind conception required by means of Dpi from first rules.

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Now we can see that a relation R over processes is contextual if and only if it is preserved by (static contexts); that is P R Q implies C[P] R C[Q] for every static context C[−]; see Question 1 at the end of the chapter. e. 3. The condition (i) is only mentioned for emphasis; in reality, since we view terms as representing equivalence classes, it is redundant. Condition (ii) means that ≡ acts like an identity relation over terms. 3 can be applied anywhere in static contexts. 4 Reduction semantics for aPi form of garbage collection; it is possible to derive a more general form of garbage collection, namely (new n) P ≡ P if n ∈ fn(P) See Question 6 at the end of the chapter.

1 below. if v1 = v2 then R1 else R2 is a test for the identity of simple values. R1 | R2 represents two processes running in parallel; they may exchange values using input/output on channels. (new n) R is a scoping mechanism for names. For example in the process R1 | (new n) R2 the name n is known to R2 but not to R1 ; of course names are values and so in the course of a computation n may be made known to R1 as the result of a communication; this will be referred to as the scope extrusion of the name n.

15 ˜ (b)c! V ˜ • If P −−−−→ Q then P is structurally equivalent to (new b)(c! V | Q). (X ) R). • If P − −→ Q then P is structurally equivalent to a term of the form (new b)(P ˜ ∩ n(V ) = ∅, and Q is structurally equivalent to (new b)(P ˜ where (b) | R{|V/X |}). τ • P− → Q implies P −→ Q. V inference of the actions P − −−→ Q and P − −→ Q. The final statement, which is the most interesting, is also by induction on the τ inference of P −→ Q. If this is an instance of the axioms (l-eq), (l-neq) or (l-unwind) then the result is immediate since these axioms are also used in the definition of reduction.

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