A decidability result about sufficient-completeness of axiomatically specified abstract data types

  • Tobias Nipkow
  • Gerhard Weikum
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 145)


The problem of deciding whether an axiomatic specification of an abstract data type is sufficiently-complete is known to be in general unsolvable. Regarding axioms as directed rewrite rules instead of symmetric equations a specification defines a reduction relation on terms. It is proved that in the subclass of left-linear axiomatic specifications the property of sufficient-completeness is decidable, if the corresponding reduction relation is normalizing and confluent. The presented algorithm can also be used to determine a set of constructors for a specified data type.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Tobias Nipkow
    • 1
  • Gerhard Weikum
    • 1
  1. 1.Institut für Praktische InformatikTechnische Hochschule DarmstadtDarmstadt

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