% Given a number of satisfiable inequalites, this program
% returns an integer solution, if any.
% Sample usage:
%
% ?- X + 2 * Y <= 7, 2*X - Y<=3, X>=0, Y>=0, intsoln([X,Y]).
%
% X=2
% Y=2
%
% *** Retry?
%
% The program will generate all possible integer solutions.
%


intsoln([]).
intsoln([X|R]) :-
	dump([X],[n],C),
	b(C,X),
	intsoln(R).

b(C,X) :- get_integer_ub(C,U), !, c(U,X).
b(C,X) :- get_integer_lb(C,L), !, d(L,X).
b(_,X) :- d(0,X).
b(_,X) :- c(-1,X).

c(U,X) :- floor(U,X).
c(U,X) :- c(U,X+1).

d(L,X) :- floor(-L,-X).
d(L,X) :- d(L,X-1).

get_integer_ub([quote(n<=B)|_], B) :- !.
get_integer_ub([quote(n<B)|_], B) :- !.
get_integer_ub([_|R], B) :- get_integer_ub(R, B).

get_integer_lb([quote(-(n)<=B)|_], 0-B) :- !.
get_integer_lb([quote(-(n)<B)|_], 0-B) :- !.
get_integer_lb([_|R], B) :- get_integer_lb(R, B).