Prolog graph path search with cyclic path

Question

I am a complete newbie in Prolog. I am trying to figure out a problem where I need to check if path is present between edges. I am done with acyclic graph code for cyclic my code is going to infinite loop.

path(Start, End) :- edge(Start, End).
path(Start, End) :- edge(Start, Z), path(Z, End).

I need to handle this case by defining a new predicate: new_path(Start,End,path) which should eliminate infinite loop. Please let me know how to proceed with it.

Answer 1

Try

path(Start, End) :-
   closure(edge, Start, End).

using this definition for closure/3

Answer 2

You need to keep track of what nodes you've visited as you go, using a prolog list as a LIFO stack. Something along these lines:

path( A , Z , P ) :-           % to find a path from A to Z
  traverse( A , Z , [] , P ) , % take a walk, visiting A to see if we can get to Z, seeding the visited list with the empty string.
  reverse(P,Path)              % once we find a path, let's reverse it, since it's in LIFO order.
  .                            % That's all there is to it, really.

traverse( Z , Z , V , [Z|V] )     % if current node is the destination node, we've arrived.
  .                               % - just push the destination vertice onto the visited list and unify that with the path
traverse( A , Z , V , P ) :-      % Otherwise...
  edge( A , Z ) ,                 % - if the current node is directly connected to the destination node,
  traverse( Z , Z , [A|V] , P)    % - go visit the destination, marking the current node as visited
  .                               %
traverse( A, Z , V , P ) :-       % Otherwise...
  A \= Z,
  edge( A , B ) ,                 % - if the current node is connected to a node
  B \= Z ,                        % - that is not the destination node, and
  unvisited([A|V],B) ,            % - we have not yet visited that node,
  traverse( B , Z , [A|V] , P )   % - go visit the intermediate node, marking the current node as visited.
  .                               % Easy!

unvisited( []    , _ ) .                   % We succeed if the visited list is empty.
unvisited( [A|_] , A ) :- ! , fail .       % We fail deterministically if we find the node in the visited list.
unvisited( [_|L] , A ) :- unvisited(L,A) . % otherwise, we keep looking.