Calculi for interaction
type: Item
instance of: scholarly article
title: Calculi for interaction
zbMATH Open document ID: 0853.68123
author: Robin Milner
published in: Acta Informatica
publication date: 1995-11-15T00:00:00Z
review text: 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 PIC for the pi calculus. Several extensions to 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.
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 68Q10
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 814166
zbMATH Keywords: interactive computation
zbMATH Keywords: pi calculus
zbMATH Keywords: action calculi
zbMATH Keywords: typed lambda calculus
zbMATH Keywords: Petri nets
zbMATH Keywords: term algebra
MaRDI profile type: Publication
full work available at URL: s002360050067
OpenAlex ID: W4246926559
DOI: 10.1007/S002360050067
description: scientific article; zbMATH DE number 814166