Skip to main content

Interaction Categories

Extended Abstract

  • Conference paper

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

We propose Interaction Categories as a new paradigm for the semantics of computation. In place of the standard paradigm for categories qua universes for denotational semantics:

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky. Proofs as processes. Unpublished Lecture Notes, 1991.

    Google Scholar 

  2. S. Abramsky and R. Jagadeesan. Games and full completeness for multiplicative linear logic. Technical Report DoC 92/24, Department of Computing, Imperial College of Science Technology and Medicine, 1992.

    Google Scholar 

  3. S. Abramsky and R. Jagadeesan. New foundations for the geometry of interaction. In Proceedings,Seventh Annual IEEE Symposium on Logic in Computer Science, pages 211–222. IEEE Computer Society Press, 1992.

    Google Scholar 

  4. P. Aczel. Non-well-founded sets. CSLI Lecture Notes 14. Center for the Study of Language and Information, 1988.

    Google Scholar 

  5. B. Alpern and F. B. Schneider. Defining liveness. Information Processing Letters, 21 (4): 181–185, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Austry and G. Boudol. Algèbres de processus et synchronisations. Theoretical Computer Science, 30: 91–131, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Barr. ★-autonomous categories and linear logic. Mathematical Structures in Computer Science, 1 (2): 159–178, July 1991.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Berry, P. Couronné, and G. Gonthier. Synchronous programming of reactive systems: An introduction to ESTEREL. Technical Report 647, INRIA, 1986.

    Google Scholar 

  9. G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20: 265–321, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Carboni and R.F.C.Walters. Cartesian bicategories I. Annals of Pure and Applied Algebra, 49: 11–32, 1987.

    Article  MATH  Google Scholar 

  11. Pierre-Louis Curien. Categorical Combinators, Sequential Algorithms and Functional Programming. Research Notes in Theoretical Computer Science. Pitman, 1986.

    Google Scholar 

  12. P. J. Freyd and A. Scedrov. Categories,Allegories, volume 39 of North-Holland Mathematical Library. North-Holland, 1990.

    Google Scholar 

  13. G. Gentzen. Investigations into logical deduction. In M. E. Szabo, editor, The Collected Papers of Gerhard Gentzen. North-Holland, 1969.

    Google Scholar 

  14. J.-Y. Girard. Linear Logic. Theoretical Computer Science, 50 (1): 1–102, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  15. C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall, 1985.

    Google Scholar 

  16. S. Mac Lane. Categories for the Working Mathematician. Springer-Verlag, Berlin, 1971.

    Book  MATH  Google Scholar 

  17. E. Manes. Algebraic Theories, volume 26 of Graduate Texts in Mathematics. Springer-Verlag, 1976.

    Book  MATH  Google Scholar 

  18. R. Milner.A Calculus for Communicating Systems,volume 92 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1980.

    Book  Google Scholar 

  19. R. Milner. Calculi for synchrony and asynchrony. Theoretical Computer Science, 25: 267310, 1983.

    Google Scholar 

  20. R. Milner. Communication and Concurrency. Prentice Hall, 1989.

    Google Scholar 

  21. E. Moggi. Computational lambda calculus and monads. In Proceedings,Fourth Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, 1989.

    Google Scholar 

  22. M. Nielsen, G. D. Plotkin, and G. Winskel. Petri nets, event structures and domains I. Theoretical Computer Science, 13 (1): 85–108, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  23. D.S. Scott. Domains for denotational semantics. In M. Nielson and E. M. Schmidt, editors, Automata, Languages and Programming: Proceedings 1982. Springer-Verlag, Berlin, 1982. Lecture Notes in Computer Science 140.

    Google Scholar 

  24. G. Winskel. The Formal Semantics of Programming Languages. Foundations of Computing. The MIT Press, Cambridge, Massachusetts, 1993.

    MATH  Google Scholar 

  25. G. Winskel and M. Nielsen. Models for concurrency. In S. Abramsky, D. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science. Oxford University Press. To appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 British Computer Society

About this paper

Cite this paper

Abramsky, S. (1993). Interaction Categories. In: Burn, G., Gay, S., Ryan, M. (eds) Theory and Formal Methods 1993. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3503-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-3503-6_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19842-0

  • Online ISBN: 978-1-4471-3503-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics