;; Magic Squares

;;  
(deffacts init
;; init the array elements
  (element 1 1 2)		;; changing any val =>  NOT MAGIC
  (element 1 2 1)		;;  fact is: element <row> <col> <val>
  (element 1 3 1)
  (element 2 1 1)
  (element 2 2 1)
  (element 2 3 1)
  (element 3 1 1)
  (element 3 2 1)
  (element 3 3 1)
;; init the array size
  (size 3)
;; init the accumulators
  (sum row 1 0)
  (sum row 2 0)
  (sum row 3 0)
  (sum col 1 0)
  (sum col 2 0)
  (sum col 3 0)
  (sum diag 1 0)
  (sum diag 2 0)
)

;; ==================================
;; make a 'addition' term's for for rows, cols and diags (2)
(defrule make-terms
  (declare (salience 300))
  (size ?n)
  (element ?r ?c ?v)
=>
  (assert (term row ?r ?c ?v)		;; addends for rows and col
          (term col ?c ?r ?v))
  (if (= ?r ?c)
    then (assert (term diag 1 ?r ?v)))	;; addend for diag2
  (if (= (+ ?r ?c) (+ 1 ?n))
    then (assert (term diag 2 ?r ?v))))	;; addend for diag2

;;==================================
;; add ?val of term on {row | col | diag} ?i ?j   
;;     to sum of {row | col | diag } ?i
(defrule addem
  (declare (salience 300))
?f1<-(sum ?type ?i ?sv)
?f2<-(term ?type ?i ? ?ev)
=>
  (retract ?f1 ?f2)
  (assert (sum ?type ?i (+ ?sv ?ev))))

;; check if not magic
(defrule not-magic
  (declare (salience 200))
  (sum ?x ?i ?s)
  (sum ?y ?l ?r)
  (test (<> ?r ?s))
=>
  (printout t "Not Magic." crlf)
  (halt))

(defrule magic
  (declare (salience 100))
  (not (term $?))
=>
 (printout t "Magic!!" crlf)
)