016: Traffic Lights

% 
% Traffic lights problem in ASP.
% 
% CSPLib problem 16
% http://www.csplib.org/Problems/prob016
% """
% Specification:
% Consider a four way traffic junction with eight traffic lights. Four of 
% the traffic lights are for the vehicles and can be represented by the 
% variables V1 to V4 with domains 
% {r,ry,g,y} (for red, red-yellow, green and yellow). 
%  The other four traffic lights are for the pedestrians and can be 
%  represented by the variables P1 to P4 with domains {r,g}.
% 
% The constraints on these variables can be modelled by quaternary 
% constraints on 
% (Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples 
% {(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}.
%
% It would be interesting to consider other types of junction (e.g. five roads 
% intersecting) as well as modelling the evolution over time of the 
% traffic light sequence. 
% ...
%
% Results
% Only 2^2 out of the 2^12 possible assignments are solutions.
% 
% (V1,P1,V2,P2,V3,P3,V4,P4) = 
%    {(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r), (y,r,ry,r,y,r,ry,r)}
%    [(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1, 2,1)}
%
%
% The problem has relative few constraints, but each is very tight. 
% Local propagation appears to be rather ineffective on this problem.
%   
% """
% 
% This was created by Hakan Kjellerstrand, hakank@gmail.com
% See also http://www.hakank.org/answer_set_programming/
%

% Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

% r:red, g:green
% y:yello, ry: red-yellow
% 
cars(r;g;ry;y).
pedestrians(r;g).
ix(1..4).

allowed(r,r,g,g).
allowed(ry,r,y,r).
allowed(g,g,r,r).
allowed(y,r,ry,r).

% cars
1 { v(Ix, Car) : cars(Car) } 1 :- ix(Ix).

% pedestrians
1 { p(Ix, Pedestrian) : pedestrians(Pedestrian) } 1 :- ix(Ix).

:- ix(I), ix(J), J == (1+I) \ 4, v(I, VI), v(J, VJ), p(I, PI), p(J,PJ),
    not allowed(VI,PI,VJ,PJ).

% combined for #show
all(V1,P1,V2,P2,V3,P3,V4,P4) :-
    v(1,V1), v(2,V2), v(3,V3),v(4,V4), 
    p(1,P1), p(2,P2), p(3,P3),p(4,P4). 

% #show v/2.
% #show p/2.
#show all/8.