On Correctness and Completeness of an n Queens Program

Abstract

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.

A Note on Occur-Check

“…The core fragment of the n queens program [Frü91] will be now used as an example. We call it NQUEENS, see [Dra22] for explanations.…”