Define a connectivity graph in Prolog

Question

I'm continuing some researches in lattices and semilattices and suddenly having this question.

Basically, we have a RelationList of [a,b] pairs, which means that (a,b) is an edge. Now we should know, is a graph formed by this RelationList 1-connectivity or not. By the way, we have an ordered graph, so order of (a,b) is important.

clear_link(X, Y, RelationList) :-
    (member([X,Y], RelationList)
    ;
    member([Y,X], RelationList)),
    X =\= Y.

linked(X, Y, RelationList) :-
    clear_link(X, Y, RelationList),
    !.
linked(X, Y, RelationList) :-
    clear_link(X, Z, RelationList),
    linked(Z, Y, RelationList).

simple_connect(RelationList, E) :-
    forall((member(X, E),
    member(Y, E), X < Y),
    linked(X, Y, RelationList)).

But, for 6-element graph I have stackoverflow.

?- simple_connect([[2,1],[2,3],[4,3],[4,5],[6,5]],[1,2,3,4,5,6]).
ERROR: Out of local stack

Am I defining it wrong?

Answer 1

I've correct some. Now it's fine

clear_link(X, Y, RelationList) :-
    member([X,Y], RelationList),
    X =\= Y.

linked(X, Y, RelationList) :-
    clear_link(X, Y, RelationList),
    !.
linked(X, Y, RelationList) :-
    clear_link(X, Z, RelationList),
    linked(Z, Y, RelationList),
    !.

simple_connect(RelationList, E) :-
    forall((member(X, E),
    member(Y, E), X < Y),
    linked(X, Y, RelationList)).

connective_graph(RelationList, E) :-
    findall(Relation, (
        member(X, RelationList),
        sort(X, Relation)
    ),SortRelationList),
    simple_connect(SortRelationList, E).

And

?- connective_graph([[2,1],[2,3],[4,3],[4,5],[6,5]],[1,2,3,4,5,6]).
true.

?- connective_graph([[2,1],[4,3],[4,5],[6,5]],[1,2,3,4,5,6]).
false.

Right answer (copy to post)

connected(X, Y, RelationList) :-
    (member([X,Y], RelationList);
    member([Y,X], RelationList)).

path(X, Y, RelationList, Path) :-
    travel(X, Y, RelationList, [X], ReversePath),
    reverse(ReversePath, Path),!.

travel(X, Y, RelationList, Point, [Y | Point]) :-
    connected(X, Y, RelationList).
travel(X, Y, RelationList, Visited, Path) :-
    connected(X, Z, RelationList),
    Z =\= Y,
    \+member(Z, Visited),
    travel(Z, Y, RelationList, [Z|Visited], Path).

connective_graph(RelationList, E) :-
    forall((member(X, E),
        member(Y, E),
        X < Y)
    ,path(X,Y,RelationList,_)).