🚀 go-pugleaf

I tried to solve the 4 queens problem using the boolean constraint
solver of SICStus 2.1#1 using the cardinality predicate.

I assume that 

:- bool:sat(card([0-1],[A,B,C,D])).

that at most one of the boolean variables A, B, C and D is true.


:- fourQueens(A).

hasn't found a solution in several minutes.


fourQueens(q(r(S11, S12, S13, S14),
	     r(S21, S22, S23, S24),
	     r(S31, S32, S33, S34),
	     r(S41, S42, S43, S44))) :-
	%% rows
	bool:sat(card([0-1],[S11, S12, S13, S14])),
	bool:sat(card([0-1],[S21, S22, S23, S24])),
	bool:sat(card([0-1],[S31, S32, S33, S34])),
	bool:sat(card([0-1],[S41, S42, S43, S44])),
	%% columns
	bool:sat(card([0-1],[S11, S21, S31, S41])),
	bool:sat(card([0-1],[S12, S22, S32, S42])),
	bool:sat(card([0-1],[S13, S23, S33, S43])),
	bool:sat(card([0-1],[S14, S24, S34, S44])),
	%% diag left-right
	bool:sat(card([0-1],[S14])),
	bool:sat(card([0-1],[S13, S24])),
	bool:sat(card([0-1],[S12, S23, S34])),
	bool:sat(card([0-1],[S11, S22, S33, S44])),
	bool:sat(card([0-1],[S21, S32, S43])),
	bool:sat(card([0-1],[S31, S42])),
	bool:sat(card([0-1],[S41])),
	%% diag right-left
	bool:sat(card([0-1],[S11])),
	bool:sat(card([0-1],[S12, S21])),
	bool:sat(card([0-1],[S13, S22, S31])),
	bool:sat(card([0-1],[S14, S23, S32, S41])),
	bool:sat(card([0-1],[S24, S33, S42])),
	bool:sat(card([0-1],[S34, S43])),
	bool:sat(card([0-1],[S44])).


--
Mattias Waldau                              
Computing Science Department                mattias@emil.csd.uu.se
P.O. Box 520, S-751 20  Uppsala, Sweden     Phone: +46-18-181055