research-article

Calculi for interaction

Author:

Robin MilnerAuthors Info & Claims

Acta Informatica, Volume 33, Issue 5

Pages 707 - 737

https://doi.org/10.1007/BF03036472

Published: 01 August 1996 Publication History

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 calledaction 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 ofmolecules; the syntactic binding ofnames 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, calledcontrols.

Action calculi generalise a previously defined action structure PIC for the π- calculus. Several extensions to PIC are given as action calculi, giving essentially the same power as the π-calculus. An action calculus is also given for the typed λ-calculus, and for Petri nets parametrized on their places and transitions.

An equational characterization of action calculi is given: each action calculusA 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 toA; the equations are the basic axioms of action structures together with four additional axiom schemata.

References

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Gardner, P.: A name-free account of action calculi. Proc. 11th Conference on Mathematical Foundations of Programming Semantics, Tulane, 1995

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Hermida, C., Power, J.: Fibrational control structures, Proc CONCUR ’95: Concurrency theory. Lecture Notes in Computer Science, Vol 962, pp. 117–129, Springer 1995

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Mifsud, A., Milner, R, Power, J.: Control structures. Proceedings of LICS ’95, 10th Annual IEEE Symposium on Logic in Computer Science, ed. D. Kozen, IEEE Computer Society Press, pp. 188–198, 1995

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Milner, R.: The polyadic π-calculus: a tutorial. In: Logic and Algebra of Specification (ed. F.L. Bauer, W. Brauer and H. Schwichtenberg) Springer Verlag, 1993, pp 203–246

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Milner R. Functions as processes Math. Struct. in Comp. Science 1992 2 119-141

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Milner, R.: Action structures and the π-calculus. In: Proof and Computation (ed. H. Schwichtenberg) Series F: Computer and Systems Sciences, NATO Advanced Study Institute, (Proceedings of International Summer School held in Marktoberdorf, Germany, 1993), Springer Verlag 1994, pp 219–280

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Milner, R.: Action structures for the π-calculus. Research Report ECS-LFCS-93-264, Laboratory for Foundations of Computer Science, Computer Science Department, Edinburgh University, 1992

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Milner, R., Action calculi, or concrete action structures. Proc. MFCS Conference, Gdansk, Poland, Lecture Notes in Computer Science, Vol 711, pp. 105–121. Springer-Verlag 1993

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Milner, R.: Higher-order action calculi. Proc. Computer Science Logic 1992 (ed. Karl Meinke) Lecture Notes in Computer Science, Vol 832, pp. 238–260. Springer-Verlag 1994

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Petri, C.A.: Fundamentals of a theory of asynchronous information flow. Proc. IFIP Congress ’62, pp. 386–390. North Holland 1962

Cited By

Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 2: The Axiomatic PresentationFundamenta Informaticae10.5555/2365216.236522197:4(439-470)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.5555/2365216.2365221
Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive PresentationFundamenta Informaticae10.5555/2365176.236518597:1-2(235-273)Online publication date: 1-Jan-2009
https://dl.acm.org/doi/10.5555/2365176.2365185
Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 2: The Axiomatic PresentationFundamenta Informaticae10.5555/1737924.173792997:4(439-470)Online publication date: 1-Dec-2009
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Index Terms

Calculi for interaction
1. Mathematics of computing
  1. Continuous mathematics
    1. Calculus
      1. Lambda calculus
  2. Mathematical analysis
    1. Calculus
      1. Lambda calculus
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
  2. Semantics and reasoning
    1. Program semantics

Index terms have been assigned to the content through auto-classification.

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cover image Acta Informatica

Acta Informatica Volume 33, Issue 5

Aug 1996

381 pages

ISSN:0001-5903

Issue’s Table of Contents

© Springer-Verlag 1996.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 1996

Received: 07 August 1995

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Cited By

Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 2: The Axiomatic PresentationFundamenta Informaticae10.5555/2365216.236522197:4(439-470)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.5555/2365216.2365221
Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive PresentationFundamenta Informaticae10.5555/2365176.236518597:1-2(235-273)Online publication date: 1-Jan-2009
https://dl.acm.org/doi/10.5555/2365176.2365185
Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 2: The Axiomatic PresentationFundamenta Informaticae10.5555/1737924.173792997:4(439-470)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.5555/1737924.1737929
Winkowski J(2009)An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive PresentationFundamenta Informaticae10.5555/1735979.173598997:1-2(235-273)Online publication date: 1-Jan-2009
https://dl.acm.org/doi/10.5555/1735979.1735989
Winkowski J(2007)Towards a Framework for Modelling Behaviours of Hybrid SystemsFundamenta Informaticae10.5555/2367430.236744780:1-3(311-332)Online publication date: 1-Jan-2007
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Winkowski J(2007)Behaviour AlgebrasFundamenta Informaticae10.5555/2366376.236640275:1-4(537-560)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/2366376.2366402
Winkowski J(2007)Towards a Framework for Modelling Behaviours of Hybrid SystemsFundamenta Informaticae10.5555/1366708.136672580:1-3(311-332)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/1366708.1366725
Leifer JMilner R(2006)Transition systems, link graphs and Petri netsMathematical Structures in Computer Science10.1017/S096012950600566416:6(989-1047)Online publication date: 1-Dec-2006
https://dl.acm.org/doi/10.1017/S0960129506005664
Baldan PCorradini AEhrig HHeckel R(2005)Compositional semantics for open Petri nets based on deterministic processesMathematical Structures in Computer Science10.5555/1047125.104712615:1(1-35)Online publication date: 1-Feb-2005
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Milner R(2005)Axioms for bigraphical structureMathematical Structures in Computer Science10.1017/S096012950500480915:6(1005-1032)Online publication date: 1-Dec-2005
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