Four-color theorem in Prolog (using a dynamic predicate)

Posted by outa on Stack Overflow See other posts from Stack Overflow or by outa
Published on 2010-06-13T14:36:35Z Indexed on 2010/06/13 14:42 UTC
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Hi,

I'm working on coloring a map according to the four-color theorem (http://en.wikipedia.org/wiki/Four_color_theorem) with SWI-Prolog. So far my program looks like this:

colour(red).
colour(blue).

map_color(A,B,C) :- colour(A),
         colour(B),
         colour(C),
         C \= B,
         C \= A.

(the actual progam would be more complex, with 4 colors and more fields, but I thought I'd start out with a simple case)

Now, I want to avoid double solutions that have the same structure. E.g. for a map with three fields, the solution "red, red, blue" would have the same structure as "blue, blue, red", just with different color names, and I don't want both of them displayed.

So I thought I would have a dynamic predicate solution/3, and call assert(solution(A,B,C)) at the end of my map_color predicate. And then, for each solution, check if they already exist as a solution/3 fact. The problem is that I would have to assert something like solution(Color1,Color1,Color2), i.e. with variables in order to make a unification check. And I can't think of a way to achieve this.

So, the question is, what is the best way to assert a found solution and then make a unification test so that "red, red, blue" would unify with "blue, blue, red"?

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