The queen piece combines the power of the bishop piece and the rook piece. Our riddle asks for the placement of eight queens so that they don’t attack each other. We have already introduced this problem in the benchmark for the Jekejeke Runtime. We use the same pure Prolog solution here. The solution does not represent the whole board. Only the distinct positions of the placed queens are remembered in a list, which makes the check for horizontal and vertical obsolete. The diagonal check is then implemented via arithmetic.
The CLP(FD) solution resembles the pure Prolog solution. It uses again the integer values 1..8 to represent queen positions and imposes the horizontal and vertical conditions via a global constraint all_distinct/1 of the constraint system. The diagonal check is then implemented via the delayed arithmetic of the constraint system. The backtracking through the possible solution space if at all is then left to the constraint system.
Both solutions find the same number of solution board configurations:
?- findall(-, queens(_), L), length(L, N).
N = 92.
?- findall(-, queens3(_), L), length(L, N).
N = 92.