(defun make-line (func l r b)
  (loop for x from l to r by b collect (cons x (funcall func x))))

(defun f (x) (- (- (* x x)) 3))       ; -x^2 - 3
(defun g (x) (* x x))                 ; x^2
(defun h (x) (+ (* x x) (* 10 x) 25)) ; (x + 5)^2
(defun l (x) (+ x))                   ; x
(defparameter *line1* (make-line #'f -10 10 0.1))
(defparameter *line2* (make-line #'g -10 10 0.1))
(defparameter *line3* (make-line #'h -10 10 0.1))
(defparameter *line4* (make-line #'l -10 10 0.1))

(defun dist^2 (p1 p2)
  (+ (expt (- (car p1) (car p2)) 2) (expt (- (cdr p1) (cdr p2)) 2)))

(defun mid-point (p1 p2)
  (cons (/ (+ (car p1) (car p2)) 2) (/ (+ (cdr p1) (cdr p2)) 2)))

(defun minimum (lst &key (comp< #'<) (key #'identity))
  (let* ((res (car lst))
         (min (funcall key res)))
    (loop for p in (cdr lst) do
         (when (funcall comp< (funcall key p) min)
           (setf min (funcall key p) res p)))
    (values res min)))

(defun mid-line (l1 l2)
  (sort (mapcar #'mid-point
                l1
                (loop for p1 in l1 collect
                     (minimum l2 :key (lambda (p2) (dist^2 p1 p2)))))
        (lambda (p1 p2) (< (car p1) (car p2)))))

;ex.
;(mid-line *line3* *line4*)