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Equational Systems and Free Constructions (Extended Abstract)

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Automata, Languages and Programming (ICALP 2007)

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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. 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. Barr, M., Wells, C.: Toposes, Triples and Theories. Springer, Heidelberg (1985)

    MATH  Google Scholar 

  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. Day, B.: On closed categories of functors. In: Reports of the Midwest Category Seminar IV. LNM, vol. 137, pp. 1–38. Springer, Heidelberg (1970)

    Chapter  Google Scholar 

  5. Fiore, M., Moggi, E., Sangiorgi, D.: A fully abstract model for the π-calculus. Information and Computation 179(1), 76–117 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  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. Fokkinga, M.: Datatype laws without signatures. Mathematical Structures in Computer Science 6(1), 1–32 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gabbay, M.J., Pitts, A.: A new approach to abstract syntax with variable binding. Formal Aspects of Computing 13, 341–363 (2001)

    Article  Google Scholar 

  9. Ghani, N., Lüth, C.: Rewriting via coinserters. Nordic Journal of Computing 10(4), 290–312 (2003)

    MATH  MathSciNet  Google Scholar 

  10. Ghani, N., Lüth, C., De Marchi, F., Power, A.J.: Dualising initial algebras. Mathematical Structures in Computer Science 13(2), 349–370 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. 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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kock, A.: Strong functors and monoidal monads. Archiv der Mathematik 23 (1972)

    Google Scholar 

  16. Plotkin, G.: Domains. Pisa Notes on Domain Theory (1983)

    Google Scholar 

  17. Plotkin, G., Power, A.J.: Algebraic operations and generic effects. Applied Categorical Structures 11(1), 69–94 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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. Power, A.J.: Enriched Lawvere theories. Theory and Applications of Categories 6, 83–93 (1999)

    MATH  MathSciNet  Google Scholar 

  20. Robinson, E.: Variations on algebra: Monadicity and generalisations of equational theories. Formal Aspects of Computing 13(3–5), 308–326 (2002)

    Article  MATH  Google Scholar 

  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. 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 

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Lars Arge Christian Cachin Tomasz Jurdziński Andrzej Tarlecki

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Fiore, M., Hur, CK. (2007). Equational Systems and Free Constructions (Extended Abstract) . In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_53

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  • DOI: https://doi.org/10.1007/978-3-540-73420-8_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73419-2

  • Online ISBN: 978-3-540-73420-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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