On the Power of Quantifiers in First-Order Algebraic Specification

  • David Kempe
  • Arno Schönegge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)


The well-known completeness theorem of Bergstra & Tucker [BT82,BT97] states that all computable data types can be specified without quantifiers, i.e., quantifiers can be dispensed with–at least if the introduction of auxiliary (hidden) functions is allowed.

However, the situation concerning the specification without hidden functions is quite different. Our main result is that, in this case, quantifiers do contribute to expressiveness. More precisely, we give an example of a computable data type that has a monomorphic first-order specification (without hidden functions) and prove that it fails to possess a monomorphic quantifier-free specification (without hidden functions).


Data Type Conjunctive Normal Form Ground Term Abstract Data Type Primality Predicate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • David Kempe
    • 1
  • Arno Schönegge
    • 2
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruheGermany

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