clpfd:tuples

tuples_in(+Tuples, +Relation)

True iff all Tuples are elements of Relation. Each element of the list Tuples is a list of integers or finite domain variables. Relation is a list of lists of integers. Arbitrary finite relations, such as compatibility tables, can be modeled in this way. For example, if 1 is compatible with 2 and 5, and 4 is compatible with 0 and 3:

?- tuples_in([[X,Y]], [[1,2],[1,5],[4,0],[4,3]]), X = 4.
X = 4,
Y in 0\/3.

As another example, consider a train schedule represented as a list of quadruples, denoting departure and arrival places and times for each train. In the following program, Ps is a feasible journey of length 3 from A to D via trains that are part of the given schedule.

trains([[1,2,0,1],
        [2,3,4,5],
        [2,3,0,1],
        [3,4,5,6],
        [3,4,2,3],
        [3,4,8,9]]).

threepath(A, D, Ps) :-
        Ps = [[A,B,_T0,T1],[B,C,T2,T3],[C,D,T4,_T5]],
        T2 #> T1,
        T4 #> T3,
        trains(Ts),
        tuples_in(Ps, Ts).

In this example, the unique solution is found without labeling:

?- threepath(1, 4, Ps).
Ps = [[1, 2, 0, 1], [2, 3, 4, 5], [3, 4, 8, 9]].