%% Imagine that the following knowledge base describes a maze. The
%% facts determine which points are connected, that is, from which
%% points you can get to which other points in one step. Furthermore,
%% imagine that all paths are one-way streets, so that you can only
%% walk them in one direction. So, you can get from point 1 to point
%% 2, but not the other way round.
connected(1,2).
connected(3,4).
connected(5,6).
connected(7,8).
connected(9,10).
connected(12,13).
connected(13,14).
connected(15,16).
connected(17,18).
connected(19,20).
connected(4,1).
connected(6,3).
connected(4,7).
connected(6,11).
connected(14,9).
connected(11,15).
connected(16,12).
connected(14,17).
connected(16,19).


%% Write a predicate path/2 that tells you from which points in the
%% maze you can get to which other points when chaining together
%% connections given in the above knowledge base. Can you get from
%% point 5 to point 10? Which other point can you get to when starting
%% at point 1? And which points can be reached from point 13?

path(X, Y) :- connected(X, Y).
path(X, Y) :- connected(X, Z),
	      path(Z, Y).

%% Questions:
%% 1. Can you get from point 5 to point 10? Yes:
%%
%%     ?- path(5, 10).
%%     true .
%%
%% 2. Which other point can you get when starting at point 1? You can't
%%    get to any other points:
%%
%%     ?- path(1, P).
%%     P = 2 ;
%%     false.
%%
%% 3. Which points can be reached from point 13? Points 9, 10, 14, 17,
%%    18.
%%
%%     ?- path(13, P).
%%     P = 14 ;
%%     P = 9 ;
%%     P = 17 ;
%%     P = 10 ;
%%     P = 18 ;
%%     false.