Equational Systems and Free Constructions (Extended Abstract)

  • Marcelo Fiore
  • Chung-Kil Hur
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop a theory of free constructions for such equational systems; and to illustrate the use of equational systems as needed in modern applications, specifically to the theory of substitution in the presence of variable binding and to models of name-passing process calculi.

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References

  1. 1.
    Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, pp. 1–168. Oxford University Press, Oxford (1994)Google Scholar
  2. 2.
    Barr, M., Wells, C.: Toposes, Triples and Theories. Springer, Heidelberg (1985)MATHGoogle Scholar
  3. 3.
    Cîrstea, C.: An algebra-coalgebra framework for system specification. In: Proc. 3rd International Workshop on Coalgebraic Methods in Computer Science. ENTCS, vol. 33, pp. 80–110. Elsevier, Amsterdam (2000)Google Scholar
  4. 4.
    Day, B.: On closed categories of functors. In: Reports of the Midwest Category Seminar IV. LNM, vol. 137, pp. 1–38. Springer, Heidelberg (1970)CrossRefGoogle Scholar
  5. 5.
    Fiore, M., Moggi, E., Sangiorgi, D.: A fully abstract model for the π-calculus. Information and Computation 179(1), 76–117 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fiore, M., Plotkin, G., Turi, D.: Abstract syntax and variable binding. In: Proc. 14th IEEE Symp. Logic in Computer Science, pp. 193–202. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  7. 7.
    Fokkinga, M.: Datatype laws without signatures. Mathematical Structures in Computer Science 6(1), 1–32 (1996)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Gabbay, M.J., Pitts, A.: A new approach to abstract syntax with variable binding. Formal Aspects of Computing 13, 341–363 (2001)CrossRefGoogle Scholar
  9. 9.
    Ghani, N., Lüth, C.: Rewriting via coinserters. Nordic Journal of Computing 10(4), 290–312 (2003)MATHMathSciNetGoogle Scholar
  10. 10.
    Ghani, N., Lüth, C., De Marchi, F., Power, A.J.: Dualising initial algebras. Mathematical Structures in Computer Science 13(2), 349–370 (2003)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Goguen, J., Thatcher, J., Wagner, E.: An initial algebra approach to the specification, correctness and implementation of abstract data types. In: Yeh, R. (ed.) Current Trends in Programming Methodology: Software Specification and Design, vol. IV, chapter 5, pp. 80–149. Prentice Hall, Englewood Cliffs (1978)Google Scholar
  12. 12.
    Hamana, M.: Free Σ-monoids: A higher-order syntax with metavariables. In: Wei-Ngan Chin (ed.) Second Asian Symp. Programming Languages and Systems. LNCS, vol. 3302, pp. 348–363. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Hennessy, M., Plotkin, G.: Full abstraction for a simple parallel programming language. In: Becvar, J. (ed.) Mathematical Foundations of Computer Science. LNCS, vol. 74, pp. 108–120. Springer, Heidelberg (1979)Google Scholar
  14. 14.
    Kelly, G.M., Power, A.J.: Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads. Journal of Pure and Applied Algebra 89, 163–179 (1993)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kock, A.: Strong functors and monoidal monads. Archiv der Mathematik 23 (1972)Google Scholar
  16. 16.
    Plotkin, G.: Domains. Pisa Notes on Domain Theory (1983)Google Scholar
  17. 17.
    Plotkin, G., Power, A.J.: Algebraic operations and generic effects. Applied Categorical Structures 11(1), 69–94 (2003)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Plotkin, G., Power, A.J.: Computational effects and operations: An overview. In: Proc. Workshop on Domains VI. ENTCS, vol. 73, pp. 149–163. Elsevier, Amsterdam (2004)Google Scholar
  19. 19.
    Power, A.J.: Enriched Lawvere theories. Theory and Applications of Categories 6, 83–93 (1999)MATHMathSciNetGoogle Scholar
  20. 20.
    Robinson, E.: Variations on algebra: Monadicity and generalisations of equational theories. Formal Aspects of Computing 13(3–5), 308–326 (2002)MATHCrossRefGoogle Scholar
  21. 21.
    Stark, I.: Free-algebra models for the π-calculus. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 155–169. Springer, Heidelberg (2005)Google Scholar
  22. 22.
    Worrell, J.: Terminal sequences for accessible endofunctors. In: Proc. 2nd International Workshop on Coalgebraic Methods in Computer Science. ENTCS, vol. 19, Elsevier, Amsterdam (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Marcelo Fiore
    • 1
  • Chung-Kil Hur
    • 1
  1. 1.Computer Laboratory, University of Cambridge 

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