How to shorten following program?

Question

I would like to shorten the following program. Just imaging there are tens of variables instead of just X and Y. The problem is that I need to define domain for each variable separately. I don't like it because it makes my program much longer and less transparent.

Input:

?- Dom1 in 0..2, Dom2 in 0..2, global_cardinality([X,Y], [0-Dom1,1-Dom2]), labeling([],[X,Y]).

Results:

X = 0,
Y = 0,
Dom1 = 2,
Dom2 = 0 ? ;
X = 0,
Y = 1,
Dom1 = 1,
Dom2 = 1 ? ;
X = 1,
Y = 0,
Dom1 = 1,
Dom2 = 1 ? ;
X = 1,
Y = 1,
Dom1 = 0,
Dom2 = 2 ? ;
no

At first I thought that I would solve it simply by writing:

?- Dom1 in 0..2, global_cardinality([X,Y], [0-Dom1,1-Dom1]), labeling([],[X,Y]).  

but it does not work because Dom1 unifies (is this the proper term for what happens in clpfd?) with one value and therefore the only results are:

X = 0,      
Y = 1,
Dom1 = 1 ? ;
X = 1,
Y = 0,
Dom1 = 1 ? ;
no

Thanks!

Answer 1

Suppose that L = [X1,...,Xn] and you want every variable to be in 1..10.

Alternative 1, works for intervals only:

?- domain(L, 1, 10).

Alternative 2, works for domains that are not intervals too:

?- (foreach(X,L) do X in 1..10).

Answer 2

I can't understand your use case. The result you're after seems to be the same of

?- [X,Y] ins 0..1, labeling([], [X,Y]).
X = Y, Y = 0 ;
X = 0,
Y = 1 ;
X = 1,
Y = 0 ;
X = Y, Y = 1.

Your explanation

it does not work because Dom1 unifies (...) with one value

seems clear to me. Since Dom1 means 'number of occurrences' of key and there are 2 variables with 2 possible values (the 'keys' 0, 1), Dom1 must be 1.