### 2Using the Inference Collection

This chapter describes how to use the PLT Scheme Inference Collection and introduces its conventions.

#### 2.1An Example

The following code demonstrates the use of the PLT Scheme Inference Collection by solving the Towers of Hanoi problem using a rule-based inference system.

 #lang scheme/base ; PLT Scheme Inference Collection ; towers-alist.ss ; ; 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 ; is to transfer the entire pile of rings from its starting ; peg to either of the other pegs - the target peg. (require (planet williams/inference/inference)) (define-ruleset towers-rules) ; If the target peg holds 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))) ==> (succeed)) ; 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)))) ; The main routine: ; In a new inference environment: ;  Activate the towers rule set. ;  Optionally, turn on tracing. ;  Create the three pegs - left, middle, and right. ;  Create the n rings. ;  Start the inference. ; The rules will print the solution to the problem. (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. (for ((i (in-range 1 n))) (assert `(ring ,i (on . left)))) ; Start inferencing. (start-inference))) ; Test with 6 disks. (solve-towers 6)

The following shows the resulting printed output.

 Move ring 1 from left to right. Move ring 2 from left to middle. Move ring 1 from right to middle. Move ring 3 from left to right. Move ring 1 from middle to left. Move ring 2 from middle to right. Move ring 1 from left to right. Move ring 4 from left to middle. Move ring 1 from right to middle. Move ring 2 from right to left. Move ring 1 from middle to left. Move ring 3 from right to middle. Move ring 1 from left to right. Move ring 2 from left to middle. Move ring 1 from right to middle. Move ring 5 from left to right. Move ring 1 from middle to left. Move ring 2 from middle to right. Move ring 1 from left to right. Move ring 3 from middle to left. Move ring 1 from right to middle. Move ring 2 from right to left. Move ring 1 from middle to left. Move ring 4 from middle to right. Move ring 1 from left to right. Move ring 2 from left to middle. Move ring 1 from right to middle. Move ring 3 from left to right. Move ring 1 from middle to left. Move ring 2 from middle to right. Move ring 1 from left to right. #t