In the ic library, one can create a variable with a domain like so:
X #:: [1..10] % Variable X with domain the integers from 1 to 10.
It is also possible to create 2 variables with the same domain like so:
[X,Y] #:: [1..10]
How can I create 2 variables that have as a domain a list of integers?
More specifically, if I have a set of integers S, how can I make two variables that each has a subset (P1, P2) of S as to ensure that P1 and P2 have no common elements and that P1 + P2 = S?
You can use lib(ic_sets) in this way:
:- lib(ic).
:- lib(ic_sets).
test(X,Y):-
LT = [1,2,3,4,5,6,7],
LA in_set_range []..LT,
LB in_set_range []..LT,
length(LT,N),
#(LA /\ LB,0),
#(LA \/ LB,N),
insetdomain(LA,_,_,_),
insetdomain(LB,_,_,_),
X #:: LA,
Y #:: LB.
LT is the list with the integer you want (it doesn't have to be a list of consecutive integers). in_set_range sets the domain of the two lists. Then #(LA /\ LB,0) constraints the interseption between the two sets to be empty (no common elements) and #(LA \/ LB,N) constraints the union of the two sets to have the length N of the starting list (i.e. number of element in the domain of LA + number of element in the domain of LB must be N). insetdomain/4 instantiates the set and X #:: LA sets the domain of X.
?- test(X, Y).
X = X{1 .. 6}
Y = 7
Yes (0.00s cpu, solution 1, maybe more)
X = X{[1 .. 5, 7]}
Y = 6
Yes (0.00s cpu, solution 2, maybe more)
X = X{1 .. 5}
Y = Y{[6, 7]}
Yes (0.00s cpu, solution 3, maybe more)
and so on...