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:
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References
S. Abramsky. Proofs as processes. Unpublished Lecture Notes, 1991.
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.
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.
P. Aczel. Non-well-founded sets. CSLI Lecture Notes 14. Center for the Study of Language and Information, 1988.
B. Alpern and F. B. Schneider. Defining liveness. Information Processing Letters, 21 (4): 181–185, 1985.
D. Austry and G. Boudol. Algèbres de processus et synchronisations. Theoretical Computer Science, 30: 91–131, 1984.
M. Barr. ★-autonomous categories and linear logic. Mathematical Structures in Computer Science, 1 (2): 159–178, July 1991.
G. Berry, P. Couronné, and G. Gonthier. Synchronous programming of reactive systems: An introduction to ESTEREL. Technical Report 647, INRIA, 1986.
G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20: 265–321, 1982.
A. Carboni and R.F.C.Walters. Cartesian bicategories I. Annals of Pure and Applied Algebra, 49: 11–32, 1987.
Pierre-Louis Curien. Categorical Combinators, Sequential Algorithms and Functional Programming. Research Notes in Theoretical Computer Science. Pitman, 1986.
P. J. Freyd and A. Scedrov. Categories,Allegories, volume 39 of North-Holland Mathematical Library. North-Holland, 1990.
G. Gentzen. Investigations into logical deduction. In M. E. Szabo, editor, The Collected Papers of Gerhard Gentzen. North-Holland, 1969.
J.-Y. Girard. Linear Logic. Theoretical Computer Science, 50 (1): 1–102, 1987.
C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall, 1985.
S. Mac Lane. Categories for the Working Mathematician. Springer-Verlag, Berlin, 1971.
E. Manes. Algebraic Theories, volume 26 of Graduate Texts in Mathematics. Springer-Verlag, 1976.
R. Milner.A Calculus for Communicating Systems,volume 92 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1980.
R. Milner. Calculi for synchrony and asynchrony. Theoretical Computer Science, 25: 267310, 1983.
R. Milner. Communication and Concurrency. Prentice Hall, 1989.
E. Moggi. Computational lambda calculus and monads. In Proceedings,Fourth Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, 1989.
M. Nielsen, G. D. Plotkin, and G. Winskel. Petri nets, event structures and domains I. Theoretical Computer Science, 13 (1): 85–108, 1981.
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.
G. Winskel. The Formal Semantics of Programming Languages. Foundations of Computing. The MIT Press, Cambridge, Massachusetts, 1993.
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.
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© 1993 British Computer Society
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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
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DOI: https://doi.org/10.1007/978-1-4471-3503-6_5
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