About data type genericity

  • Didier Bert
  • Roger Soler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 107)


The notion of genericity and polymorphism is of main interest in the field of abstract data types. Semantic models based on a domain of retracts and continuous functions (theory of Strachey-Scott) are not sufficient to describe some specific aspects of genericity. Other models using categories (Burstall-Goguen) are more appropriate but less conventional. This paper is an attempt to extend the model of Strachey-Scott by techniques used in the categorical approach, that is to say the notion of satisfaction, in order to define a semantic of generic abstract data types The main result is that, as well as typing ensures the validity of the utilisation of values, "typing of types" ensures the validity of the utilisation of types.


abstract data types algebraic specification universal domain polymorphism genericity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. D. Bert, P. Jacquet [1977]. "Generic abstract data types". Proc. 5th Annual III Conference, WG.2.1. IFIP.Google Scholar
  2. D. Bert, P. Jacquet [1978]. "Some validation problems with parameterized types and generic functions". 3rd International Symposium on Programming, IP, Paris (Dunod)Google Scholar
  3. R. Burstall, J.A. Goguen [1980]. "The Semantics of CLEAR, a specification Language". Lecture Notes in Computer Science, no 86 (Springer Verlag).Google Scholar
  4. J. Donahue [1979]. "On the Semantics of Data Type". Siam J. Comput., Vol. 8, no 4, pp. 546–560.Google Scholar
  5. H. Ganzinger, K. Ripken [1980]. "Operator Identification in ADA: Formal Specification, Complexity, and concrete Implementation", Sigplan Notices 15, 2.Google Scholar
  6. J.A. Goguen, J.W. Thatcher, E.G. Wagner [1978]. "An initial algebra approach to the correctness, and implementation of abstract data types". In Current Trends in Programming Methodology, Vol IV, (ed. Yeh) Prentice Hall.Google Scholar
  7. J.V. Guttag, J.J. Horning [1978]. "The algebraic specification of abstract data types". Acta Informatica, 10, pp. 27–52.CrossRefGoogle Scholar
  8. C.A.R. Hoare [1972]. "Proof of Correctness of Data Representations". Acta Informatica, 1, pp. 271–281.CrossRefGoogle Scholar
  9. A. Kanda [1978]. "Data Types as Initial Algebras: An Unification of Scottery and ADJery". 19th Annual Symposium on Foundations of Computer Science, pp 221–230.Google Scholar
  10. J. Mc Carthy [1963]. "A basis for a mathematical theory of computation". In Computer Programming and Formal Systems. P. Braffort and D. Hirschberg (eds.), Amsterdam, North-Holland.Google Scholar
  11. N.J. Mc Cracken [1979]. "An Investigation of a Programming Language with a Polymorphic Type Structure". Ph.D. Syracuse University.Google Scholar
  12. R. Milner [1977]. "A Theory of Type Polymorphism in Programming". Report CSR-9-77, Univ. of Edinburgh, Dpt. of Computer Science.Google Scholar
  13. ML [1979]. M.J. Gordon, A.J. Milner, C.P. Wadsworth. "Edimburgh LCF". Lecture Notes in Computer Science, no 78, Springer Verlag.Google Scholar
  14. D.R. Musser [1980]. "On proving inductive properties of abstract data types". Conference Record of the 7th annual ACM Symposium on Principles of Programming Languages.Google Scholar
  15. R. Nakajima, M. Honda, H. Nakahara [1977]. "Describing and Verifying Programs with Abstract Types". Formal Description of Programming Concepts (ed. Neuhold), North-Holland.Google Scholar
  16. J.C. Reynolds [1974]. "Towards a Theory of type structure". Colloquium of Programming, Paris.Google Scholar
  17. L.E. Sanchis [1977]. "Data Types as Lattices: Retractions, Closures and Projections". R.A.I.R.O. Informatique Théorique, vol. 11, no 4.Google Scholar
  18. D. Scott [1974]. "Data Types as lattices". Logic Conference-Kiel-Lecture Notes in Mathematics, Springer Verlag (eds. A. Dold and B. Eckmann), New York 1975.Google Scholar
  19. A. Shamir, W.W. Wadge [1977]. "Data Types as Objects". Automata Languages and Programming, 4th Colloquium, Lecture Notes in Computer Science, no 52.Google Scholar
  20. J.W. Thatcher, E.G. Wagner, J. Wright [1978]. "Data-type specification: parameterisation and the power of specification techniques". Proc. of the SIGACT, 10th Annual Symposium on Theory of Computing.Google Scholar
  21. D.J. Lehmann, M.B. Smyth [1977]. "Data Types". 18th Annual Symposium on Fondations of Computer Science, pp. 7–12.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Didier Bert
    • 1
  • Roger Soler
    • 2
    • 3
  1. 1.Laboratoire IMAGGrenobleFrance
  2. 2.Universidad Central de VenezuelaCaracasVenezuela
  3. 3.Laboratoire IMAGGrenobleFrance

Personalised recommendations