Logic Form of Rules

Our rule in logic form is:

cartesian(p) ∧ cartesian(q)
         → distance(p, q, euclidist(p,q))

For backchaining, we put the conclusion on the left:

((distance p1 p2 (euclidist p1c p2c))  ; dist is
   (cartesian p1 p1c)   ; if p1c is cart of p1
   (cartesian p2 p2c))  ;  and p2c is cart of p2

cartesian is now a two-place predicate:
cartesian(p, pc) is true if pc is the Cartesian form of p.