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Generating Type Systems for Process Graphs

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Abstract

We introduce a hypergraph-based process calculus with a generic type system. That is, a type system checking an invariant property of processes can be generated by instantiating the original type system. We demonstrate the key ideas behind the type system, namely that there exists a hypergraph morphism from each process graph into its type, and show how it can be used for the analysis of processes. Our examples are input/output-capabilities, secrecy conditions and avoiding vicious circles occurring in deadlocks.

In order to specify the syntax and semantics of the process calculus and the type system, we introduce a method of hypergraph construction using concepts from category theory.

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References

  1. Martín Abadi. Secrecy by typing in security protocols. In Theoretical Aspects of Computer Software, pages 611–638. Springer-Verlag, 1997.

    Google Scholar 

  2. Michel Bauderon and Bruno Courcelle. Graph expressions and graph rewritings. Mathematical Systems Theory, 20:83–127, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  3. Gérard Berry and Gérard Boudol. The chemical abstract machine. Theoretical Computer Science, 96:217–248, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chiara Bodei, Pierpaolo Degano, Flemming Nielson, and Hanne Riis Nielson. Control flow analysis for the pi-calculus. In CONCUR’ 98, pages 84–98. SpringerVerlag, 1998. LNCS 1466.

    Google Scholar 

  5. Roy L. Crole. Categories for Types. Cambridge University Press, 1993.

    Google Scholar 

  6. H. Ehrig. Introduction to the algebraic theory of graphs. In Proc. 1st International Workshop on Graph Grammars, pages 1–69. Springer-Verlag, 1979. LNCS 73.

    Google Scholar 

  7. Annegret Habel. Hyperedge Replacement: Grammars and Languages. SpringerVerlag, 1992. LNCS 643.

    MATH  Google Scholar 

  8. Kohei Honda. Composing processes. In Proc. of POPL’96, pages 344–357. ACM Press, 1996.

    Google Scholar 

  9. Kohei Honda and Nobuko Yoshida. Combinatory representation of mobile processes. In POPL’ 94, pages 348–360. ACM Press, 1994.

    Google Scholar 

  10. Naoki Kobayashi. A partially deadlock-free typed process calculus. In LICS’ 97, pages 128–139. IEEE, Computer Society Press, 1997.

    Google Scholar 

  11. Naoki Kobayashi, Benjamin C. Pierce, and David N. Turner. Linearity and the pi-calculus. In POPL’ 96, pages 358–371. ACM SIGACT/SIGPLAN, 1996.

    Google Scholar 

  12. Yves Lafont. Interaction nets. In POPL’ 90, pages 95–108. ACM Press, 1990.

    Google Scholar 

  13. R. Milner, J. Parrow, and D. Walker. A calculus of mobile processes, Part I. Tech. Rep. ECS-LFCS-89-85, University of Edinburgh, Laboratory for Foundations of Computer Science, 1989.

    Google Scholar 

  14. Robin Milner. Operational and algebraic semantics of concurrent processes. In Jan van Leeuwen, editor, Formal Models and Semantics, Handbook of Theoretical Computer Science, volume B, pages 1201–1242. Elsevier, 1990.

    Google Scholar 

  15. Robin Milner. The polyadic π-calculus: a tutorial. Tech. Rep. ECS-LFCS-91-180, University of Edinburgh, Laboratory for Foundations of Computer Science, 1991.

    Google Scholar 

  16. Robin Milner. Pi-nets: a graphical form of pi-calculus. In European Symposium on Programming, pages 26–42. Springer-Verlag, 1994. LNCS 788.

    Google Scholar 

  17. Uwe Nestmann and Martin Steén. Typing confluence. In ERCIM Workshop on Formal Methods in Industrial Critical Systems, pages 77–101, 1997.

    Google Scholar 

  18. Joachim Parrow. Interaction diagrams. Nordic Journal of Computing, 2:407–443, 1995.

    MathSciNet  Google Scholar 

  19. Benjamin Pierce and Davide Sangiorgi. Typing and subtyping for mobile processes. In LICS’ 93, pages 376–385, 1993.

    Google Scholar 

  20. Antonio Ravara and Vasco T. Vasconcelos. Behavioural types for a calculus of concurrent objects. In Euro-Par’ 97. Springer-Verlag, 1997.

    Google Scholar 

  21. David Turner. The Polymorphic Pi-Calculus: Theory and Implementation. PhD thesis, University of Edinburgh, 1995. ECS-LFCS-96–345.

    Google Scholar 

  22. P. Urzyczyn. Positive recursive type assignment. In J. Wiedermann and P. Hájek, editors, Mathematical Foundations of Computer Science 1995. Springer-Verlag, 1995. LNCS 969.

    Google Scholar 

  23. Nobuko Yoshida. Graph types for monadic mobile processes. In FST/TCS’ 96, pages 371–386. Springer-Verlag, 1996.

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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König, B. (1999). Generating Type Systems for Process Graphs. In: Baeten, J.C.M., Mauw, S. (eds) CONCUR’99 Concurrency Theory. CONCUR 1999. Lecture Notes in Computer Science, vol 1664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48320-9_25

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  • DOI: https://doi.org/10.1007/3-540-48320-9_25

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  • Print ISBN: 978-3-540-66425-3

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