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On the design of algebraic data structures with the approach of abstract data types

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

Abstract

The problem of giving a formal definition of the representation of algebraic data structures is considered and developped in the frame work of the abstract data types approach. Such concepts as canonical form and simplification are formalized and related to properties of the abstract specification and of the associated term rewriting system.

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Bibliography

  1. (JAG,JWT,ECW) J.A.Goguen, J.W.Thatcher, E.G.Wagner "An initial algebra approach to the specification, correctness, and implementation of abstract data types" IBM Research Report RC-6487, October 1976.

    Google Scholar 

  2. (JAG) J.A.Goguen "Abstract errors for abstract data types". UCLA Semantics Theory of Computation Report 6, February 1977. Proceedings IFIP Working Conference on Formal Description of Programming Concepts. St. Andrews, New Brusswick, pp. 21.1–21.32. August 1977.

    Google Scholar 

  3. R.M. Burstall and J.A.Goguen "Putting Theories together to make Specifications". Proceedings 1977 IJCAI,MIT, Cambridge, MA, August 1977.

    Google Scholar 

  4. H.Ehrig, H.J.Kreowski and P.Padawitz "Stepwise specification and implementation of abstract data types". Technical University of Berlin, Report, March 1978.

    Google Scholar 

  5. R.Fateman "Essays in algebraic simplification". Ph.D. diss, Harward U., Cambridge, Mass., 1971.

    Google Scholar 

  6. M.Griss "The Definition and Use of Data Structures in Reduce". Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation.

    Google Scholar 

  7. J.V.Guttag "The specification and application to programming of abstract data types". University of Toronto, Computer Systems Research Group, Technical Report CSRG-59, September 1975.

    Google Scholar 

  8. A.C.Hearn "A new REDUCE model for Algebraic Simplification". Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation.

    Google Scholar 

  9. G.Huet "Confluent reductions: abstract properties and applications to term rewriting systems". Rapport de Recherche — IRIA.

    Google Scholar 

  10. E.Horowitz and S. Sahni "Fundamentals of Data Structures". Computer Science Press, Inc., 1976.

    Google Scholar 

  11. R.Loos "Toward a Formal Implementation of Computer Algebra". Symsam 1974.

    Google Scholar 

  12. G.Levi, and F.Sirovich "Proving program properties, symbolic evaluation and logical procedural semantics". Mathematical Foundations of Computer Science 1975. Lecture Notes in Computer Science, Springer Verlag, pp. 294–301.

    Google Scholar 

  13. B.H. Liskov, S.N. Zilles "Programming with abstract data types". Proc. of ACM Symp. on Very High Level Languages, SIGPLAN Notices 9, pp. 50–59 (1974).

    Google Scholar 

  14. J.Moses "Algebraic Simplification: A Guide for the Perplexed". Communications of ACM August 1971, Vol. 14, N.8.

    Google Scholar 

  15. J.W.Thatcher, E.G.Wagner, J.B.Wright "Data Type Specification: Parameterization and the Power of Specification Techniques". Report IBM Laboratories. Yorktown Heights.

    Google Scholar 

  16. S.N.Zilles "Algebraic Specification of data types". Project MAC Progress Report 11, MIT, Cambridge, Mass.

    Google Scholar 

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Edward W. Ng

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© 1979 Springer-Verlag Berlin Heidelberg

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Ausiello, G., Mascari, G.F. (1979). On the design of algebraic data structures with the approach of abstract data types. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_100

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  • DOI: https://doi.org/10.1007/3-540-09519-5_100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

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