PROLOG all different

Question

Hello SO,

I have a very weird problem with PROLOG. I have used it before, but it's been a while and I'm rusty. I have a list of variables and I need to ensure that none of them are the same.

I have tried:

use_module(library(bounds)). all_different(A, B, C, D, 6, 8).

However, when I try this, I get an error saying that all_different/6 is undefined.

How can I go about solving this issue? Is there any library function that I can call directly for this?

I am VERY stuck and would greatly appreciate any help.

Thanks in advance.

solve([
    [A, 6, 1],

    [B, 5, C, 2, D, E, F, G, 6],

    [6, H, I, 5, J, K, 2, L, 3],

    [5, M, 6, N, O, 4, P, Q, 5],

    [4, R, S, T, U, 6, V, 4, W],

    [2, 0, X]
  ]) :-
     all_different([A,6,1,2,D,E]),
     all_different([B,5,C,6,H,I]),
     all_different([C,2,D,I,5,J]),
     all_different([D,E,F,J,K,2]),
     all_different([F,G,6,2,L,3]),
     all_different([H,I,5,M,6,N]),
     all_different([5,J,K,N,O,4]),
     all_different([K,2,L,4,P,Q]),
     all_different([5,M,6,4,R,S]),
     all_different([6,N,O,S,T,U]),
     all_different([O,4,P,U,6,V]),
     all_different([P,Q,5,V,4,W]),
     all_different([T,U,6,2,1,X]),

     A<7, A>0,       B<7, B>0,       C<7, C>0,       D<7, D>0,
     E<7, E>0,       F<7, F>0,       G<7, G>0,       H<7, H>0,
     I<7, I>0,       J<7, J>0,       K<7, K>0,       L<7, L>0,
     M<7, M>0,       N<7, N>0,       O<7, O>0,       P<7, P>0,
     Q<7, Q>0,       R<7, R>0,       S<7, S>0,       T<7, T>0,
     U<7, U>0,       V<7, V>0,       W<7, W>0,       X<7, X>0.

Answer 1

all_different([A,B,C,D,6,8]).

I believe that only a List can be passed into all_different.

Answer 2

I guess that >/2 and </2 may know nothing about attributes that all_different/1 applied to the vars in list. In SWI-Prolog that predicate is provided by library(clpfd) and among other predicates in that library there is #</2 .

        ?- all_different([X,Y]), 0 #< X, X #< 3, 1 #< Y, Y #< 4, indomain(X), indomain(Y). 
        X = 1,
        Y = 2 ;
        X = 1,
        Y = 3 ;
        X = 2,
        Y = 3.

P.S. indomain/1 from the same library yields all feasible values within applied constraints.

Answer 3

The "ic" constraint library of Eclipse Prolog provides the predicate alldifferent/1, which takes a list of variables as its argument, e.g., alldifferent([X,Y]) and computes what you are looking for.