SWISH -- SWI-Prolog for SHaring

arc( a , b ).
arc( a , f ).
arc( b , c ).
arc( b , d ).
arc( b , e ).
arc( f , g ).
arc( f , i ).
arc( i , j ).
arc( i , k ).

% --- traverse/3 -----------------------
% 
% Traverses a directed graph
%
% traverse( Origin, Destination, Path ).
%---------------------------------------
traverse(A,Z,P) :-
    traverse(A,Z,[],Vs),
    reverse(Vs,P).

% --- traverse/4 --------------------------------------------
%
% private helper for traverse/3
%
% traverse( Origin, Destination, Visited, Path).
%
% Note that  Path is returned in most recently visited order.
%
%------------------------------------------------------------
traverse(A,Z,Vs,[Z,A|Vs]) :-  % we can get from A to Z
    arc(A,Z).                 % - if A and Z are directly connected
traverse(A,Z,Vs,P) :-         % otherwise, we can get from A to Z, if...
    arc(A,B),                 % - A is connected to some B
    \+ member(B,Vs),          % - that we have not yet visited
    traverse(B,Z,[A|Vs],P).   % - and we can get from B to Z (recording that A has been visited).