Given a line in one dimension from p1 to p2, we can find the line of length 1/2 (p2-p1) centered around the midpoint of the first line in MLPQ as follows: 

begin%RECURSIVE%

/*  
     First we must build the diff relation. It is interesting  
     to note that this relation is what will limit the other  
     relations 
*/ 
 
diff(x,y,z) :- x-y>=0, -x+y>=0, z>=0, -z>=0. 
diff(x,y,z) :- diff(x1,y,z1), x-x1<=1, x-x1>=1, z-z1<=1, z-z1>=1. 
diff(x,y,z) :- diff(x,y1,z1), y-y1<=1, y-y1>=1, z1-z<=1, z1-z>=1.

/* Our initial line */
line(0,6, 0). 

/* Recursive line definition */
line(x,y,d) :- line(p1,p2,d1),  
               diff(p,p1,z1), diff(p2,p,z),  
               diff(x,p1,z2), diff(p,x,z2), 
               diff(p2,y,z3), diff(y,p,z3), 
               d-d1 = 1.

end%RECURSIV%