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The polyadic π-calculus: a tutorial (1991)
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| Venue: | LOGIC AND ALGEBRA OF SPECIFICATION |
| Citations: | 186 - 1 self |
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@TECHREPORT{Milner91thepolyadic,
author = {Robin Milner},
title = {The polyadic π-calculus: a tutorial},
institution = {LOGIC AND ALGEBRA OF SPECIFICATION},
year = {1991}
}
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Abstract
The π-calculus is a model of concurrent computation based upon the notion of naming. It is first presented in its simplest and original form, with the help of several illustrative applications. Then it is generalized from monadic to polyadic form. Semantics is done in terms of both a reduction system and a version of labelled transitions called commitment; the known algebraic axiomatization of strong bisimilarity isgiven in the new setting, and so also is a characterization in modal logic. Some theorems about the replication operator are proved. Justification for the polyadic form is provided by the concepts of sort and sorting which it supports. Several illustrations of different sortings are given. One example is the presentation of data structures as processes which respect a particular sorting; another is the sorting for a known translation of the λ-calculus into π-calculus. For this translation, the equational validity of β-conversion is proved with the help of replication theorems. The paper ends with an extension of the π-calculus to ω-order processes, and a brief account of the demonstration by Davide Sangiorgi that higher-order processes maybe faithfully encoded at first-order. This extends and strengthens the original result of this kind given by Bent Thomsen for second-order processes.
Keyphrases
polyadic calculus different sorting known translation replication operator bent thomsen several illustrative application algebraic axiomatization particular sorting original form order process davide sangiorgi original result concurrent computation several illustration new setting replication theorem labelled transition modal logic brief account data structure strong bisimilarity higher-order process polyadic form reduction system second-order process equational validity
