(module towers-alist mzscheme
  
  (require (planet "inference.ss" ("williams" "inference.plt")))
    
  ;; Example Inference Model
  
  ;; Towers of Hanoi from Artificial Intelligence: Tools, Techniques,
  ;; and Applications, Tim O'Shea and Marc Eisenstadt, Harper & Rowe,
  ;; 1984, pp.45
  ;;
  ;; The rules of the game are: (1) move one ring at a time and (2)
  ;; never place a larger ring on top of a smaller ring.  The object
  ;; ive isto transfer the entire pile of rings from its starting
  ;; peg to either of the other pegs - the target peg.
  (define-ruleset towers-rules)
  
  ;; If the target peg hld all the rings 1 to n, stop because according
  ;; to game rule (2) they must be in their original order and so the
  ;; problem is solved.
  (define-rule (rule-1 towers-rules)
      (all (ring ? (on . right)))
     ==>
      (printf "Problem solved!~n"))
  
  ;; If there is no current goal - that is, if a ring has just been
  ;; successfully moved, or if no rings have yet to be moved - generate
  ;; a goal.  In this case the goal is to be that of moving to the
  ;; target peg the largest ring that is not yet on the target peg.
  (define-rule (rule-2 towers-rules)
      (no (move . ?))
      (ring ?size (on ?peg (not (eq? ?peg 'right))))
      (no (ring (?size-1 (> ?size-1 ?size))
                (on ?peg-1 (not (eq? ?peg-1 'right)))))
    ==>
      (assert `(move (size . ,?size) (from . ,?peg) (to . right))))
  
  ;; If there is a current goal, it can be achieved at once of there is
  ;; no small rings on top of the ring to be moved (i.e. if the latter
  ;; is at the top of its pile), and there are no small rings on the
  ;; peg to which it is to be moved (i.e. the ring to be moved is
  ;; smaller that the top ring on the peg we intend to move it to).  If
  ;; this is the case, carry out the move and then delete the current
  ;; goal so that rule 2 will apply next time.
   (define-rule (rule-3 towers-rules)
       (?move <- (move (size . ?size) (from . ?from) (to . ?to)))
       (?ring <- (ring ?size (on . ?from)))
       (no (ring (?size-1 (< ?size-1 ?size)) (on . ?from)))
       (no (ring (?size-2 (< ?size-2 ?size)) (on . ?to)))
     ==>
       (printf "Move ring ~a from ~a to ~a.~n" ?size ?from ?to)
       (replace ?ring `(ring ,?size (on . ,?to)))
       (retract ?move))
  
  ;; If there is a current goal but its disc cannot be moved as in rule
  ;; 3, set up a new goal: that of moving the largest of the obstructing
  ;; rings to the peg that is neither of those specified in the current
  ;; goal (i.e. well out of the way of the current goal).  Delete the
  ;; current goal, so that rule 2 will apply to the new goal next time.
  (define-rule (rule-4 towers-rules)
      (?move <- (move (size . ?size) (from . ?from) (to . ?to)))
      (peg (?other (not (memq ?other (list ?from ?to)))))
      (ring (?size-1 (< ?size-1 ?size))
            (on ?peg-1 (not (eq? ?peg-1 ?other))))
      (no (ring (?size-2 (< ?size-1 ?size-2 ?size))
                (on ?peg-2 (not (eq? ?peg-2 ?other)))))
    ==>
      (replace ?move `(move (size . ,?size-1) (from . ,?peg-1) (to . ,?other))))
  
  (define (solve-towers n)
    (with-new-inference-environment
     (activate towers-rules)
     ;(current-inference-trace #t)
     ;; Create pegs.
     (assert '(peg left))
     (assert '(peg middle))
     (assert '(peg right))
     ;; Create rings.
     (do ((i 1 (+ i 1)))
       ((> i n) (void))
       (assert `(ring ,i (on . left))))
     ;; Start inferencing.
     (start-inference)))
  
  (solve-towers 6)

  )