A functorial semantics for observed concurrency

  • David MurphyEmail author
  • Axel PoignéEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)


This paper presents a meta-model of observation in concurrency theory; it allows us to unify notions of observation in many different behavioural settings. We treat traces, process trees and event structures, and show how observations of them fit into a common framework. Behaviour and observation will both be modeled as categories and lined using the notions of ‘functor’ and ‘adjunction’.

Timing will be our chief example of observation; we present a timed traces model, and hint how it generalises to timed process trees (branching time) and timed ‘true concurrency.’ The general setup sees timing as a way of embedding observations into time; we propose stable categories of embeddings as natural metamodels of timed observation.


Stable Category Terminal Object Concurrency Theory Finite Distributive Lattice Functorial Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    S. Abramsky and S. Vickers, Quantales, observationallogic and process semantics, Technical Report DOC 90/1, Department of Computing, Imperial College, 1991.Google Scholar
  2. 2.
    J. van Benthem, The logic of time, D. Reidel, 1983.Google Scholar
  3. 3.
    S. Brookes and A. Roscoe, An improved failures model for communicating sequential processes, in the Proceedings NSF-SERC Seminar on Concurrency, Volume 197, Springer-Verlag LNCS, 1985.Google Scholar
  4. 4.
    T. Coquand, Categories of embeddings, Theoretical Computer Science, Volume 68 (1989), Pp. 221–237.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    T. Coquand, C. Gunter, and G. Winskel, dI-domains as a model of polymorphism, in Mathematical Foundations of Programming Language Semantics, Volume 298, Springer-Verlag LNCS, 1988.Google Scholar
  6. 6.
    J. Davies and S. Schneider, An introduction to timed CSP, Technical Report Number 75, Oxford University Computer Laboratory, 1989.Google Scholar
  7. 7.
    U. Engberg and G. Winskel, Petri nets as models of linear logic, in the Proceedings of TAPSOFT (CAAP) (A. Arnold, Ed.), Volume 431, Springer-Verlag LNCS, 1990.Google Scholar
  8. 8.
    C. Hoare, Communicating sequential processes, International series on computer science, Prentice-Hall, 1985.Google Scholar
  9. 9.
    A. Jeffrey, Timed process algebra ≠ time × process algebra, Technical Report 79, Programming Methodology Group, Chalmers University, 1991.Google Scholar
  10. 10.
    J. Meseguer and U. Montanari, Petri nets are monoids: A new algebraic foundation for net theory, in Logic in Computer Science, (1988), 1988, Proceedings of the 3rd Annual IEEE Symposium, pp. 155–164.Google Scholar
  11. 11.
    D. Murphy, Time, causality, and concurrency, Ph.D. thesis, Department of Mathematics, University of Surrey, 1989, available as Technical Report CSC 90/R32, Department of Computing Science, University of Glasgow.Google Scholar
  12. 12.
    D. Murphy and A. Poigné, A functorial semantics for observed concurrency, Technical Report to appear, GMD, 1992.Google Scholar
  13. 13.
    A. Pnueli, Linear and branching structures in the semantics and logics of reactive systems, in Automata, Languages and Programming (W. Brauer, Ed.), Volume 194, Springer-Verlag LNCS, 1986, (12th Coll.).Google Scholar
  14. 14.
    S. Vickers, Topology via logic, Tracts in Theoretical Computer Science, Volume 5, Cambridge University Press, 1989.Google Scholar
  15. 15.
    G. Whitrow, The natural philosophy of time, Oxford University Press, 1980.Google Scholar
  16. 16.
    G. Winskel, Event structures, in Petri Nets: Central Models and Their Properties (W. Brauer, W. Reisig, and G. Rozenberg, Eds.), Volume 254, Springer-Verlag LNCS, 1986, Proceedings of Advances in Petri Nets. Also available as a Cambridge University Computer Laboratory Technical Report.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.GMD 15Sankt Augustin 1Germany

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