Prolog falling into infinite loop

Question

I have two problems that have bugged me for hours. connected/2 is supposed to judge whether two people are connected or not; distance/3 is supposed to measure the kinship. But:

1. I keep getting trues infinitely for the query connected(x,y);
2. and I'm getting infinitely increasing N for distance(x,y,N) query. Any suggestions?

Here are my facts:

male(ted).
male(barney).
male(ranjit).
male(marshall).
male(tony).
male(swarley).
male(steve).
male(chuck).
male(john).
male(devon).
male(morgan).

female(robin).
female(lily).
female(wendy).
female(stellar).
female(abby).
female(victoria).
female(carina).
female(sarah).
female(ellie).

married(ted,      robin).
married(marshall, lily).
married(ranjit,   wendy).
married(stellar,  tony).
married(steve,    carina).
married(sarah,    chuck).
married(ellie,    devon).

father(ted,      barney).
father(ted,      ranjit).
father(marshall, wendy).
father(ranjit,   stellar).
father(tony,     abby).
father(tony,     swarley).
father(tony,     victoria).
father(steve,    chuck).
father(steve,    ellie).
father(chuck,    john).
father(devon,    morgan).

mother(robin,    barney).
mother(robin,    ranjit).
mother(lily,     wendy).
mother(wendy,    stellar).
mother(stellar,  abby).
mother(stellar,  swarley).
mother(stellar,  victoria).
mother(carina,   chuck).
mother(carina,   ellie).
mother(sarah,    john).
mother(ellie,    morgan).

Now, my predicates:

parent(X,Y) :- father(X,Y).
parent(X,Y) :- mother(X,Y).

son(X,Y) :-
    male(X),
    parent(Y,X).

daughter(X,Y) :-
    female(X),
    parent(Y,X).

sibling(X,Y) :-
    parent(Z,X),
    parent(Z,Y).

cousin(X,Y) :-
    parent(Z,X),
    parent(W,Y),
    parent(G,Z),
    parent(G,W).

ancestor(X,Y) :-
    parent(X,Z),
    ancestor(Z,Y).
ancestor(X,Y) :- parent(X,Y).

notmember(X,[]).
notmember(X,[H|T]) :- 
    X \= H,
    notmember(X,T).

connected(X,Y,_) :- X == Y.
connected(X,Y,Visited) :- 
    ancestor(X,Z),
    notmember(Z,Visited),
    connected(Z,Y,[Z|Visited]).
connected(X,Y,Visited) :- 
    ancestor(Z,X),
    notmember(Z,Visited),
    connected(Z,Y,[Z|Visited]).
connected(X,Y,Visited) :- 
    sibling(X,Z),
    notmember(Z,Visited),
    connected(Z,Y,[Z|Visited]).
connected(X,Y,Visited) :- 
    married(X,Z),
    notmember(Z,Visited),
    connected(Z,Y,[Z|Visited]).
connected(X,Y) :- connected(X,Y,[X]).

minimum(X,[X]).
minimum(X,[M,H|T]) :- 
    M =< H,
    minimum(X,[M|T]).
minimum(X,[M,H|T]) :-
    M > H,
    minimum(X,[H|T]).

distance(X,X,_,0).
distance(X,Y,Visited,N) :- 
    parent(X,Z),
    notmember(Z,Visited),
    distance(Z,Y,[Z|Visited],N1),
    N is N1+1.
distance(X,Y,Visited,N) :- 
    parent(Z,X),
    notmember(Z,Visited),
    distance(Z,Y,[Z|Visited],N1),
    N is N1+1.
distance(X,Y,N) :- distance(X,Y,[],N).

EDIT: Thank you, i think i've managed to solve half way through the problems now. Taking @twinterer's advice, I have fixed the predicates like this

connected(X,Y,_) :- X == Y.
connected(X,Y,V) :-
    married(X,Z),
    notmember(Z,V),
    connected(Z,Y,[Z|V]),!.
connected(X,Y,V) :-
    sibling(X,Z),
    notmember(Z,V),
    connected(Z,Y,[Z|V]),!.
connected(X,Y,V) :-
    parent(X,Z),
    notmember(Z,V),
    connected(Z,Y,[Z|V]),!.
connected(X,Y,V) :-
    parent(Z,X),
    notmember(Z,V),
    connected(Z,Y,[Z|V]),!.
connected(X,Y) :- connected(X,Y,[X]).

minimum(X,[X]).
minimum(X,[M,H|T]) :- 
    M =< H,
    minimum(X,[M|T]).
minimum(X,[M,H|T]) :-
    M > H,
    minimum(X,[H|T]).

count(X,[],0).
count(X,[X|T],N) :-
    count(X,T,N1),
    N is N1+1.
count(X,[H|T],N) :-
    X \== H,
    count(X,T,N1),
    N is N1.

distance(X,X,Visited,0) :-
    count(X,Visited,N),
    N =< 1, !.
distance(X,Y,Visited,N) :- 
    parent(X,Z),
    (notmember(Z,Visited)->
        distance(Z,Y,[Z|Visited],N1),
        N is N1+1
    ;
        fail
    ),!.
distance(X,Y,Visited,N) :- 
    parent(Z,X),
    (notmember(Z,Visited)->
        distance(Z,Y,[Z|Visited],N1),
        N is N1+1
    ;
        fail
    ),!.
distance(X,Y,N) :- 
    findall(N1,distance(X,Y,[X],N1),L),!,
    minimum(N,L),!.

But there is a new set of problems now

1. it can't take arbitrary queries like distance(X,y,n)
2. queries like connected(X,y) return duplicate results

I think removing duplicate results can be achieved by using that findall/3 predicate, but I am clueless as to how I can actually implement it.

Answer 1

1) I don't think that you end in an infinite loop, but you let your program explore all ways that two people are connected, which will be a very large number. Since you probably are only interested in whether they are connected at all, you should add cuts at the end of the connected/3 clauses that will prevent backtracking once you have successfully determined that two people are connected, e.g.:

connected(X,Y,_) :- X == Y,!.
connected(X,Y,Visited) :- 
    ancestor(X,Z),
    notmember(Z,Visited),
    connected(Z,Y,[Z|Visited]),!.
...

2) I didn't get infinitely increasing values for N when I tested your code, but still the distance/3 predicate would determine different paths how two people are connected. Depending on the people, the minimum distance would not be the first to be computed. I would change the definition of distance/3 to something like this:

distance(X,Y,N) :- 
    findall(N0, distance(X,Y,[],N0), Ns), !,
    minimum(N, Ns).

This is reusing your minimum/2 predicate. Note that you should add cuts to the first two clauses of this predicate in order to avoid spurious choicepoints.

Regarding your additional questions:

3) you have to distinguish between looking for the smallest N and looking for people matching degree N:

distance(X,Y,N) :-
  nonground(N),!,
  findall(N0, distance(X,Y,[],N0), Ns), !,
  minimum(N, Ns).
distance(X,Y,N) :-
  distance(X,Y,[X],N).

Also, you need to remove the cuts that you added to distance/4. This is different from the cuts added to connected/3!

There's probably a better way that avoids distinguishing between these two modes, but all I can think of at the moment is using some kind of breadth-first-search (in order to guarantee the minimum degree)...

4) I don't get duplicate answers for queries like ?- connected(X,victoria). Do you have an example?