016: Traffic Lights

language ESSENCE 1.2.0
$ prob016.essence: Traffic Lights
$ Problem details available at http://www.csplib.org/Problems/prob016/
$ 04 September 2007
$

$ n_roads; the number of roads
given n_roads : int(1..)

$ Road: road identifers are between 1 and n_roads
$ VCol: colours for vehicle traffic lights
$ PCol: colours for pedestrian traffic lights
letting Road be domain int(1..n_roads),
        VCol be new type enum {r,ry,g,y},
        PCol be new type enum {pr,pg}

$ valid: the valid traffic light combinations
find valid : set of function (total) Road --> (VCol,PCol)

$ all combinations obey the problem constraints
such that forAll c in valid . forAll rd : Road .
    {c(rd),c((rd % n_roads)+1)} in {{(r,pr),(g,pg)},{(ry,pr),(y,pr)}}