Categorical Semantics, Or Extending Data Types to Include Memory

  • Eric G. Wagner
Part of the Informatik-Fachberichte book series (INFORMATIK, volume 116)


This paper extends the algebraic theory of data types so that it can deal with issues, such as those involving memory, that can not be easily treated within the usual algebraic specification framework. The result is a simple, uniform, mathematical framework in which we can treat, not only data types and their operations, but also, the semantics of imperative languages with assignment, conditionals, while-do’s, and elementary exception handling.


Data Type Category Theory Finite Type Unique Morphism Abstract Data Type 
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  1. [1]
    ADJ (Goguen, J. A., Thatcher, J.W., Wagner, E.G.), “An Initial Algebra Approach to the Specification, Correctness, and Implementation of Abstract Data Types,” in Current Trends in Programming Methodology, Volume IV, (R. Yeh, Editor), Prentice-Hall, Inc. Englewood Cliffs, NJ, 1978.Google Scholar
  2. [2]
    MacLane, S. Categories for the Working Mathematician, Springer-Verlag, New York, Heidelberg, Berlin, 1971.Google Scholar
  3. [3]
    Wagner, E.G., “Categorical Semantics, or Extending Data Types to Include Memory,” presented at the 3rd Workshop on Theory and Applicatons of Abstract Data Types, in Bremen, West Germany, 12–16 November, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Eric G. Wagner
    • 1
  1. 1.Computing Technology DepartmentIBM Thomas J. Watson Research CenterYorktown HeightsUSA

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