Abstract
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).
This research has partly been supported by the “Deutsche Forschungsgemeinschaft” within the “Schwerpunktprogramm Deduktion”. The results were obtained in the course of [Kem98].
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Kempe, D., Schönegge, A. (1999). On the Power of Quantifiers in First-Order Algebraic Specification. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_4
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DOI: https://doi.org/10.1007/10703163_4
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