% Figure 9.21   Path-finding in a graph:  Path is 
% an acyclic path with cost Cost from A to Z in Graph.

:- op( 900, fy, not).

% path( A, Z, Graph, Path, Cost):
%    Path is an acyclic path with cost Cost from A to Z in Graph

path( A, Z, Graph, Path, Cost)  :-
  path1( A, [Z], 0, Graph, Path, Cost).

path1( A, [A | Path1], Cost1, Graph, [A | Path1], Cost1).

path1( A, [Y | Path1], Cost1, Graph, Path, Cost)  :-
   adjacent( X, Y, CostXY, Graph),
   not member( X, Path1),
   Cost2 is Cost1 + CostXY,
   path1( A, [X, Y | Path1], Cost2, Graph, Path, Cost).

% not Goal): negation as failure; 
%   Note: This is often available as a built-in predicate,
%   often written as prefix operator "\+", e.g. \+ likes(mary,snakes)

not Goal  :-
  Goal, !, fail
  ; 
  true.