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About permutation algebras, (pre)sheaves and named sets

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Higher-Order and Symbolic Computation

Abstract

In this paper we survey some well-known approaches proposed as general models for calculi dealing with names (like for example process calculi with name-passing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets, studying the relationships among these models, thus allowing techniques and constructions to be transferred from one model to the other.

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References

  1. Bucalo, A., Hofmann, M., Honsell, F., Miculan, M., Scagnetto, I.: Consistency of the Theory of Contexts. J. Funct. Progr. 16, 327–395 (2006)

    Article  MATH  Google Scholar 

  2. Corradini, A., Heckel, R., Montanari, U.: Compositional SOS and Beyond: A Coalgebraic View of Open Systems. Theor. Comp. Sci. 280, 163–192 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ferrari, G., Montanari, U., Pistore, M.: Minimizing Transition Systems for Name Passing Calculi: A Co-Algebraic Formulation. In: Nielsen. M., Engberg, U. (eds.), Foundations of Software and Computer Science, vol. 2303, Lect. Notes in Comp. Sci., Springer, pp. 129–143 (2002)

  4. Fiore, M.: Notes on combinatorial functors (draft). Unpublished manuscript available from the author’s web page (2001)

  5. Fiore, M., Moggi, E., Sangiorgi, D.: A fully abstract model for the calculus. In: Clarke, E. (ed.), Logic in Computer Science, IEEE, pp. 43–54 (1996)

    Google Scholar 

  6. Fiore, M., Staton, S.: Comparing Operational Models of Name-Passing Process Calculi. In: Adámek, J., Milius, S. (eds.), Coalgebraic Methods in Computer Science, vol. 106, Electr. Notes in Theor. Comp. Sci., Elsevier Science (2004)

  7. Fiore, M., Turi, D.: Semantics of Name and Value Passing. In: Maierson, H. (ed.), Logic in Computer Science. IEEE, pp. 93–104 (2001)

    Google Scholar 

  8. Gabbay, M.J., Pitts, A.M.: A New Approach to Abstract Syntax wit Variable Binding. Formal Aspects of Computing 13, 341–363 (2002)

    Article  Google Scholar 

  9. Gadducci, F., Miculan, M., Montanari, U.: Some Characterization Results for Permutation Algebras. In: Honsell, F., Lenisa, M., Miculan, M. (eds.), Computational Metamodels, Workshop of the sc cometa Project, vol. 104, Electr. Notes in Theor. Comp. Sci., Elsevier Science (2004)

  10. Hofmann, M.: Semantical analysis of higher-order abstract syntax. In: Longo, G. (ed.), Logic in Computer Science, IEEE, pp. 204–213 (1999) Computer Society Press.

    Google Scholar 

  11. Honsell, F., Miculan, M., Scagnetto, I.: An Axiomatic Approach to Metareasoning on Nominal Algebras in HOAS. In: Orejas, F., Spirakis, P., van Leeuwen, J. (eds.), Automata, Languages and Programming, vol. 2076, Lect. Notes in Comp. Sci., Springer, pp. 963–978 (2001)

  12. Kelley, J.: General topology. Springer (1975)

  13. MacLane, S.: Categories for the Working Mathematician. Springer (1971)

  14. McLane, S., Moerdijk, I.: Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Springer (1994)

  15. Miculan, M., Yemane, K.: A Unifying Model of Variables and Names. In: Sassone, V. (ed.), Foundations of Software Science and Computational Structures, vol. 3441, Lect. Notes in Comp. Sci., Springer, pp. 170–186 (2005)

  16. Moggi, E.: Notions of computation and monads. Information and Computation 93, 55–92 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  17. Montanari, U., Pistore, M.: Structured Coalgebras and Minimal HD-automata for the calculus. Theor. Comp. Sci. 340, 539–576.

  18. Montanari, U., Pistore, M.: Calculus, Structured Coalgebras, and Minimal HD-automata. In: Nielsen, M., Rovan, B. (eds.), Mathematical Foundations of Computer Science, vol. 1893, Lect. Notes in Comp. Sci., Springer, pp. 569–578 (2000)

  19. O’Hearn, P., Tennent, R.: Parametricity and Local Variables. In: O’Hearn, P., Tennent, R. (eds.), Algol-like Languages, Birkhauser, pp. 109–164 (1997)

    Google Scholar 

  20. Pitts, A.M.: Nominal Logic, A First Order Theory of Names and Binding. Information and Computation 186, 165–193 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Plotkin, G., Power, J.: Semantics for Algebraic Operations. In: Brookes, S., Mislove, M. (eds.), Mathematical Foundations of Programming Semantics, vol.45, Electr. Notes in Theor. Comp. Sci., Elsevier Science (2001)

  22. Rutten, J.: Universal coalgebra: A theory of systems. Theor. Comp. Sci. 249, 3–80 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Stark, I.: Names and Higher-Order Function. Ph.D. thesis, University of Cambridge, Cambridge Computer Laboratory (1994)

  24. Stark, I.: A fully abstract domain model for the calculus. In: Clarke, E. (ed.), Logic in Computer Science. IEEE, pp. 36–42 (1996) Computer Society Press.

    Google Scholar 

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Correspondence to Fabio Gadducci.

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Research partially supported by the EU IST-2004-16004 SENSORIA.

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Gadducci, F., Miculan, M. & Montanari, U. About permutation algebras, (pre)sheaves and named sets. Higher-Order Symb Comput 19, 283–304 (2006). https://doi.org/10.1007/s10990-006-8749-3

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