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On Correctness and Completeness of an n Queens Program

Published online by Cambridge University Press:  14 October 2021

WŁODZIMIERZ DRABENT Open the ORCID record for WŁODZIMIERZ DRABENT [Opens in a new window]
WŁODZIMIERZ DRABENT*
Affiliation:
Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland Department of Computer and Information Science, Linköping University S – 581 83 Linköping, Sweden (e-mail: drabent@ipipan.waw.pl)
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Abstract

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Thom Frühwirth presented a short, elegant, and efficient Prolog program for the n queens problem. However, the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a declarative way and provides proofs of its correctness and completeness. The specification and the proofs are declarative, that is they abstract from any operational semantics. The specification is approximate, it is unnecessary to describe the program’s semantics exactly. Despite the program works on non-ground terms, this work employs the standard semantics, based on logical consequence and Herbrand interpretations. Another purpose of the paper is to present an example of precise declarative reasoning about the semantics of a logic program.

Keywords

logic programmingdeclarative programmingprogram completenessprogram correctnessspecificationnonground answers
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 1 , January 2022 , pp. 37 - 50
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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