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Applications of the calculus of trees to process description languages

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Category Theory and Computer Science (CTCS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 530))

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Abstract

Bénabou's notion of motor is extended to cover labelled finite trees. Operations on them are defined that permit to easily define the semantics for a finite concurrent calculus. Then, suitable motors that constructively define canonical representatives for strong and observational congruence based on the notion of bisimulation are introduced in a clean and straightforward way. This enables us to provide the calculus with a fully abstract semantics up to the above congruences.

“Other maps are such shapes, with their islands and capes! But we've got our brave captain to thank” (So the crew would protest) “that he's bought us the best—A perfect and absolute blank!” (Lewis Carroll The Hunting of the Snark Fit the Second, 4)

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References

  1. J. Bénabou. Lectures held at the Mathematics and Computer Science Departments of the University of Milano, and talk at the Category Theory '90 Conference in Como. 1990.

    Google Scholar 

  2. J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77–121, 1985.

    Google Scholar 

  3. I. Castellani. Bisimulations and abstraction homomorphisms. Journal of Computer and System Sciences, 34:210–235, 1987.

    Google Scholar 

  4. Ph. Darondeau and P. Degano. Causal trees. In Proc. 11th Int. Coll. on Automata and Languages ICALP, number 372 in Lecture Notes in Computer Science, pages 234–248, 1989.

    Google Scholar 

  5. P. Degano, R. De Nicola, and U. Montanari. A partial ordering semantics for CCS. Theoretical Computer Science, 75:223–262, 1990.

    Google Scholar 

  6. M. Hennessy and R. Milner. Algebraic laws for nondeterminism and concurrency. Journal of Assoc. Comput. Mach., 32:137–161, 1985.

    Google Scholar 

  7. P. Inverardi and M. Nesi. A rewriting strategy to verify observational equivalence. Info. Proc. Letters, 35:191–199, 1990.

    Google Scholar 

  8. D.E. Knuth. The Art of Computer Programming. Addison-Wesley, 1973.

    Google Scholar 

  9. S. Kasangian and S. Vigna. Trees in a distributive category. To appear in Proceedings CT '90.

    Google Scholar 

  10. S. Kasangian and S. Vigna. Introducing a calculus of trees. In Proceedings of the International Joint Conference on Theory and Practice of Software Development (TAPSOFT/CAAP '91), number 493 in Lecture Notes in Computer Science, pages 215–240, 1991.

    Google Scholar 

  11. R. Milner. Processes, a mathematical model of computing agents. In Logic Colloquium, Bristol 1973, pages 157–174. North-Holland, 1975.

    Google Scholar 

  12. R. Milner. A Calculus of Communicating Systems. Number 92 in Lecture Notes in Computer Science. Springer-Verlag, 1980.

    Google Scholar 

  13. R. Milner. A complete inference system for a class of regular behaviours. Journal of Computer and System Sciences, 28:439–466, 1984.

    Google Scholar 

  14. R. Milner. Communication and Concurrency. International Series in Computer Science. Prentice Hall, 1989.

    Google Scholar 

  15. U. Montanari and M. Sgamma. Canonical representatives for observational equivalence classes. In Proceedings Colloquium on the resolution of equations in algebraic structures, pages 293–319. Academic Press, Inc., 1989.

    Google Scholar 

  16. D. Park. Concurrency and automata on infinite sequences. In Proc. Theoretical Computer Science, number 104 in Lecture Notes in Computer Science, pages 167–183. Springer-Verlag, 1981.

    Google Scholar 

  17. C.A. Petri. Concurrency. In Net Theory and Applications, number 84 in Lecture Notes in Computer Science, pages 1–19. Springer-Verlag, 1980.

    Google Scholar 

  18. C. Pair and A. Quere. Définition et étude des bilangages réguliers. Information and Control, 13:565–593, 1968.

    Google Scholar 

  19. V.R. Pratt. Modeling concurrency with partial orders. International Journal of Parallel Programming, 15(1):33–71, February 1986.

    Google Scholar 

  20. J.J.M.M. Rutten. Explicit canonical representatives for weak bisimulation equivalence and congruence. Technical Report CS-R9062, CWI, 1990.

    Google Scholar 

  21. R.F.C. Walters. Data types in a distributive category. Bull. Austr. Math. Soc., 40:79–82, 1989.

    Google Scholar 

  22. G. Winskel. Synchronization trees. Theoretical Computer Science, 34:33–82, 1984.

    Google Scholar 

  23. G. Winskel. Petri nets, algebras, morphisms and compositionality. Info. and Co., 72:197–238, 1987.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125, Pisa PI, Italy

    P. Degano

  2. Dipartimento di Matematica, Università di Parma, Via M. d'Azeglio 85, I-43100, Parma PR, Italy

    P. Degano

  3. Dipartimento di Matematica, Università di Milano, Via Saldini 50, I-20133, Milano MI, Italy

    S. Kasangian & S. Vigna

Authors
  1. P. Degano
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  2. S. Kasangian
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  3. S. Vigna
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Editor information

David H. Pitt Pierre-Louis Curien Samson Abramsky Andrew M. Pitts Axel Poigné David E. Rydeheard

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© 1991 Springer-Verlag Berlin Heidelberg

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Degano, P., Kasangian, S., Vigna, S. (1991). Applications of the calculus of trees to process description languages. In: Pitt, D.H., Curien, PL., Abramsky, S., Pitts, A.M., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. CTCS 1991. Lecture Notes in Computer Science, vol 530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013471

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  • DOI: https://doi.org/10.1007/BFb0013471

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54495-1

  • Online ISBN: 978-3-540-38413-7

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