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A Uniform Model Theory for the Specification of Data and Process Types

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Recent Trends in Algebraic Development Techniques (WADT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1827))

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Abstract

Generalizing products in Lawvere’s algebraic theories to projective and injective Kan extensions and their conjunctive combinations one gets a powerful categorical model theory. Based on this categorical model theory the foundations of a uniform axiomatic specification formalism for data and process types is developed.

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References

  1. Astesiano, E., Kreowski, H.-J., Krieg-Brücker, B. (eds.): Algebraic Foundations of Systems Specification. IFIP state-of-the-art reports. Springer, Heidelberg (1999)

    Google Scholar 

  2. Barr, M., Wells, C.: Category Theory for Computing Science, 2nd edn. International series in computer science. Prentice Hall, Englewood Cliffs (1996)

    Google Scholar 

  3. Cockett, J.R.B., Fukushima, T.: About charity. Technical Report 92/480/18, Department of Computer Science, University of Calgary (1992)

    Google Scholar 

  4. Cockett, J.R.B., Spencer, D.: Strong categorical datatypes i. In: Seely, R.A.G. (ed.) Canadian Mathematical Society Proceedings, Montreal (1992)

    Google Scholar 

  5. Cockett, J.R.B., Spencer, D.: Strong categorical datatypes ii: A term logic for categorical programming. Theoretical Computer Science 139, 69–113 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Freyd, P.: Algebraically complete categories. In: Carboni, A., et al. (eds.) 1990 Como Category Theory Conference. Lecture Notes in Math., vol. 1488, pp. 95–104. Springer, Berlin (1990)

    Google Scholar 

  7. Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39, 95–146 (1992)

    MathSciNet  MATH  Google Scholar 

  8. Goguen, J., Rosu, G.: Hiding more of hidden algebra. In: Wing, J.M., Woodcock, J., Davies, J. (eds.) FM 1999. LNCS, vol. 1709, pp. 1704–1719. Springer, Berlin (1999)

    Google Scholar 

  9. Jacobs, B., Rutten, J.: A tutorial on (co)algebras and (co)induction. Bulletin of the EATCS 62, 222–259 (1997)

    MATH  Google Scholar 

  10. Lair, C.: Trames et semantiques categoriques des systems de trames. Diagrammes, 19 (1987)

    Google Scholar 

  11. Lawvere, F.W.: Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. U. S. A. 50, 869–873 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  12. Milner, R.: A Calculus of Communicating Systems. In: Milner, R. (ed.) A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)

    Google Scholar 

  13. Lane, S.M.: Categories for the Working Mathematician. Springer, Heidelberg (1971)

    MATH  Google Scholar 

  14. Meseguer, J., Montanari, U.: Petri nets are monoids. Information and Computation 88, 105–155 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  15. CoFI Task Group on Langugage Design. Casl, the common algebraic specification language (summary). Technical report, CoFI: The Common Framework Initiative (1998)

    Google Scholar 

  16. Reichel, H.: Nested sketches. Technical Report ECS-LFCS-98-401, Edinburgh University, Laboratory for Foundations of Computer Science (December 1998)

    Google Scholar 

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Reichel, H. (2000). A Uniform Model Theory for the Specification of Data and Process Types. In: Bert, D., Choppy, C., Mosses, P.D. (eds) Recent Trends in Algebraic Development Techniques. WADT 1999. Lecture Notes in Computer Science, vol 1827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44616-3_20

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  • DOI: https://doi.org/10.1007/978-3-540-44616-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67898-4

  • Online ISBN: 978-3-540-44616-3

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