Abstract.
Action structures have previously been proposed as an algebra for both the syntax and the semantics of interactive computation. Here, a class of concrete action structures called action calculi is identified, which can serve as a non-linear syntax for a wide variety of models of interactive behaviour. Each action in an action calculus is represented as an assembly of molecules; the syntactic binding of names is the means by which molecules are bound together. A graphical form, action graphs, is used to aid presentation. One action calculus differs from another only in its generators, called controls. Action calculi generalise a previously defined action structure \(\mbox{\sf PIC}\) for the \(\pi\)-calculus. Several extensions to \(\mbox{\sf PIC}\) are given as action calculi, giving essentially the same power as the \(\pi\)-calculus. An action calculus is also given for the typed \(\lambda\)-calculus, and for Petri nets parametrized on their places and transitions. An equational characterization of action calculi is given: each action calculus \(A\) is the quotient of a term algebra by certain equations. The terms are generated by a set of operators, including those basic to all action structures as well as the controls specific to \(A\); the equations are the basic axioms of action structures together with four additional axiom schemata.
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Received May 12, 1995 / August 7, 1995
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Milner, R. Calculi for interaction . Acta Informatica 33, 707–737 (1996). https://doi.org/10.1007/s002360050067
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DOI: https://doi.org/10.1007/s002360050067