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Higher-order action calculi

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Book cover Computer Science Logic (CSL 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 832))

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Abstract

Action calculi are a broad class of algebraic structures, including a formulation of Petri nets as well as a formulation of the π-calculus. Each action calculus HAC(K) is generated by a particular set K of operators called controls. The purpose of this paper is to extend action calculi in a uniform manner to higher-order. A special case is essentially the extension of the π-calculus to higher order by Sangiorgi. To establish a link between the interactive and functional paradigms of computation, a variety of the λ-calculus is obtained as the extension of the smallest action calculus HAC(θ).

The dynamics of higher-order action calculi is presented, blending communication -for example in process calculi- with reduction as in the λ-calculus. Strong normalisation is obtained for reduction. A set of equational axioms is given for higher-order action calculi. Taking the quotient of HAC(θ) by a single extra axiom η, a cartesian-closed category is obtained.

An ultimate goal of the paper is to combine process calculi and functional calculi, both in their formulation and in their semantics.

This work was done with the support of a Senior Fellowship from the Science and Engineering Research Council, UK.

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Authors and Affiliations

  1. Laboratory for Foundations of Computer Science Computer Science Department, University of Edinburgh, The King's Buildings, EH9 3JZ, Edinburgh, UK

    Robin Milner

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  1. Robin Milner
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Egon Börger Yuri Gurevich Karl Meinke

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© 1994 Springer-Verlag Berlin Heidelberg

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Milner, R. (1994). Higher-order action calculi. In: Börger, E., Gurevich, Y., Meinke, K. (eds) Computer Science Logic. CSL 1993. Lecture Notes in Computer Science, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049335

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  • DOI: https://doi.org/10.1007/BFb0049335

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58277-9

  • Online ISBN: 978-3-540-48599-5

  • eBook Packages: Springer Book Archive

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