Terminal algebra semantics and retractions for abstract data types

  • Günter Hornung
  • Peter Raulefs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


Very often, the terminal algebra semantics of an algebraic specification of an abstract data type is more important than the initial algebra semantics. This paper develops a theory of terminal algebra semantics. The notion of terminal (t-) abstract data type is introduced, and it is shown that a t-abstract data type is a terminal object in the categories of terminal models and implementations of an abstract data type specification. Many, but not all notions and properties of initial algebra semantics have their dual analogue in terminal algebra semantics.

The connection between t-abstract data types and Scott's notation of a data type being a retract on a universal domain is explored. The main result is that for the class of recognizable t-specifications retracts constituting terminal models of respective t-specifications can be explicitly constructed.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Günter Hornung
    • 1
  • Peter Raulefs
    • 1
  1. 1.Institut für Informatik IIIUniversität BonnBonn 1West Germany

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