Question 3: Higher order functions [4]

Below we show specifications for two functions, validPoint and addPoints, and an implementation of function sumPoints. 

   ; (validPoint point)
   ; ------------------
   ; returns true if point is a valid x,y point,
   ;     i.e. a list of two numbers,
   ; returns nil otherwise
   ; e.g. (validPoint '(10 2)) returns t
   ;      (validPoint '(x))   returns nil


   ; (addPoints point1 point2)
   ; -------------------------
   ; if point1 is a valid point, (x1 y1), and
   ;    point2 is a valid point, (x2 y2),
   ;    then return the point (x1+x2, y1+y2)
   ; otherwise return nil
   ; e.g. (addPoints '(1 2) '(10 20)) returns (11 22)


   ; (sumPoints pointList)
   ; ---------------------
   (defun sumPoints (pointsList)
      (cond
          ((not (listp pointsList)) nil)
          ((null pointsList) nil)
          (t (reduce 'addPoints pointsList))))

Assuming our points list contained points (1 1) (2 5) and (-1 3) (in that order) show the results of each of the three calls below: 

       ; call #1
       (mapcar 'validPoint pointsList)

       ; call #2
       (sumPoints pointsList)

       ; call #3
       (maplist 'sumPoints pointsList)