combination.lisp

(defun comb2 (f x y)
  (funcall f (+ x y))
  (funcall f (- x y))
  (funcall f (- y x))
  (funcall f (* x y))
  (when (not (zerop y))
    (funcall f (/ x y)))
  (when (not (zerop x))
    (funcall f (/ y x))))

(defun comb3 (f x y z)
  (comb2 (lambda (q) (comb2 f q z)) x y)
  (comb2 (lambda (q) (comb2 f q y)) x z)
  (comb2 (lambda (q) (comb2 f q x)) y z))

(defun count-evaluating-to (k x y z)
  (let ((count 0))
    (comb3 (lambda (n)
             (when (= n k)
               (incf count)))
           x y z)
    count))