Advertisement

Existential quantifiers in abstract data types

  • M. Broy
  • W. Dosch
  • H. Partsch
  • P. Pepper
  • M. Wirsing
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)

Abstract

Hierarchies of abstract data types are specified by axioms which are positive formulas consisting of universally and existentially quantified disjunctions and conjunctions of equations. Necessary and sufficient conditions for the existence of terminal algebras are investigated. Furthermore, some advantages of disjunctions and existential quantifiers within the laws are discussed and the usefulness of terminal algebras is demonstrated by a few examples.

Keywords

Function Symbol Primitive Type Existential Quantifier Abstract Data Type Positive Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. /Birkhoff, Lipson 70/.
    G. Birkhoff, J.D. Lipson: Heterogeneous Algebras. Journal of Combinatorial Theory 8, 115–133 (1970).Google Scholar
  2. /Broy et al. 79/
    M. Broy, W. Dosch, H. Partsch, P. Pepper, M. Wirsing: Abstract Data Types: Some Theoretical Aspects and their Practical Consequences. To appear.Google Scholar
  3. /Goguen et al. 78/
    J. Goguen, J.W. Thatcher, E.G. Wagner: An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types. In: R.T. Yeh (ed.): Current trends in programming methodology, 4, Data Structuring, N.J.: Prentice-Hall, 1978.Google Scholar
  4. /Guttag 75/.
    J.V. Guttag: The Specification and Application to Programming of Abstract Data Types. Ph. D. Th., Univ. of Toronto, Dept. of Comp. Sci., Rep. CSRG-59, 1975.Google Scholar
  5. /Guttag et al. 76a/
    J.V. Guttag, E. Horowitz, D.R. Musser: Abstract Data Types and Software Validation. USC/Information Sciences Institute, RR-76-48 (1976).Google Scholar
  6. /Guttag et al. 76b/
    J.V. Guttag, E. Horowitz, D.R. Musser: The Design of Data Type Specifications. USC/Information Sciences Institute, RR-76-49 (1976).Google Scholar
  7. /Majster 77/.
    M. Majster: Data Types, Abstract Data Types and their Specification Problem. Technische Universität München, Institut für Informatik, TUM-INFO-7740, 1977.Google Scholar
  8. /Partsch, Broy 79/.
    H. Partsch, M. Broy: Examples for Change of Types and Object Structures. In: F.L. Bauer, M. Broy (eds.): Proc. of the International Summer School on Program Construction, Marktoberdorf 1978, LNCS, Springer Verlag 1979. To appear.Google Scholar
  9. /Thatcher et al. 77/
    J.W. Thatcher, E.G. Wagner, J.B. Wright: Specification of Abstract Data Types Using Conditional Axioms. IBM Research Report RC-6214, 1977.Google Scholar
  10. /Wand 78/.
    M. Wand: Final Algebra Semantics and Data Type Extensions. Indiana University, Comp. Science Department, Technical Report No. 65, 1978.Google Scholar
  11. /Zilles 74/.
    S. Zilles: Algebraic Specification of Data Types. Computation Structures Group Memo 119, MIT, Cambridge, Mass., 1974.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • M. Broy
    • 1
  • W. Dosch
    • 1
  • H. Partsch
    • 1
  • P. Pepper
    • 1
  • M. Wirsing
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2

Personalised recommendations