Better Eight Queens program

[lambdacalculator]

The Eight Queens program included in Examples (citation: O'Keefe, The Craft of Prolog) is unnecessarily complicated and wasteful in its data structure. Here is a much simpler program that uses the same idea (diagonals as lists of logic variables shared with columns), adapted from a program in Chapter 9 of van Roy and Haridi, Concepts, Techniques, and Models of Computer Programming, 2004:

queens(N, Queens) :-
    length(Queens, N),
    place_queens(N, Queens, _, _).

place_queens(0, _, _, _) :- !.
place_queens(N, Cs, Us, [_|Ds]) :-
    M is N - 1,
    place_queens(M, Cs, [_|Us], Ds),
    place_queen(N, Cs, Us, Ds).

place_queen(N, [N|_], [N|_], [N|_]).
place_queen(N, [_|Cs], [_|Us], [_|Ds]) :-
    place_queen(N, Cs, Us, Ds).