P93

(de infix (E)
   (if (atom E)
      E
      (list
         (infix (cadr E))
         (car E)
         (infix (caddr E)) ) ) )

(de expressions (X)
   (if (cdr X)
      (mapcan
         '((I)
            (mapcan
               '((A)
                  (mapcan
                     '((B)
                        (mapcar
                           '((Op) (list Op A B))
                           '(+ - * /) ) )
                     (expressions (tail (- I) X)) ) )
               (expressions (head I X)) ) )
         (range 1 (dec (length X))) )
      (list (car X)) ) )

(de equations (Lst)
   (use /
      (redef / (A B)
         (and (n0 B) (=0 (% A B)) (/ A B)) )
      (for (I 1  (> (length Lst) I)  (inc I))
         (for A (expressions (head I Lst))
            (for B (expressions (tail (- I) Lst))
               (let? N (eval A)
                  (when (= N (eval B))
                     (println (infix A) '= (infix B)) ) ) ) ) ) ) )

Test:

: (equations (2 3 5 7 11))
2 = (3 - (5 + (7 - 11)))
2 = (3 - ((5 + 7) - 11))
2 = ((3 - 5) - (7 - 11))
2 = ((3 - (5 + 7)) + 11)
2 = (((3 - 5) - 7) + 11)
2 = (((3 * 5) + 7) / 11)
(2 * (3 - 5)) = (7 - 11)
(2 - (3 - (5 + 7))) = 11
(2 - ((3 - 5) - 7)) = 11
((2 - 3) + (5 + 7)) = 11
((2 - (3 - 5)) + 7) = 11
(((2 - 3) + 5) + 7) = 11
-> NIL

http://picolisp.com/wiki/?99pp93

23jul10

abu