Why does my lisp code give me …should be a lambda expression?

Question

(defun helper-2 (list) 
  (if (null (first (rest list)))
      0)
  (+ (distance ((car list) (first (rest list)))) 
     (helper-2 (rest list))))

I'm new to lisp and I'm writing a program to compute the perimeter of any polygon with input following clockwise order. My logic is that I use a helper method to compute the length of two points next to each other and do the sum. After recursion is done, I will do a separate call to calculate the length from the beginning point to its end and sum everything up. I've finished the distance method which takes 2 points and return the length.

(distance '(2 0) '(4 0)) ;this will output 2

helper-2 logic: assume we have 3 points a (2 0) b (3 3) c (4 0) This method is expected to sum up the distance between ab and bc. However, I keep getting "(car head) should be a lambda expression" error. Can anyone help? Thank you. Or could anyone give me a better way to compute the perimeter of a polygon?

(defun square (n) (* n n))

(defun distance (a b)
  (let ((h (- (second b) (second a)))
        (w (- (first b) (first a))))
    (sqrt (+ (square h) (square w)))))

Answer 1

Your helper-2 function is wrong in two places:

1. You should be using a two-armed if, so that it functions as an if/else.
2. You have too many parentheses around the (car list).

Here's the fixed version:

(defun helper-2 (list) 
  (if (null (first (rest list)))
      0
      (+ (distance (car list) (first (rest list))) 
         (helper-2 (rest list)))))

Answer 2

Section 3.1.2.1.2.3 Function Forms of the HyperSpec describes how a form that is a cons, such as ((car list) (first (rest list))), is evaluated:

How a compound form is processed depends on whether it is classified as a special form, a macro form, a function form, or a lambda form.

You can read the subsections linked to from that page for more details, but the essence is that since the first element of this list is not a symbol, the form as a whole must be a lambda form. According to 3.1.2.1.2.4 Lambda Forms a lambda form is a list where the first element is a lambda expression. `However, (car list) is not a lambda expression, so you get the corresponding error message.

You claimed that (distance '(2 0) '(4 0)) will output two, but that shows distance being called with two arguments. Even if ((car list) (first (rest list))) could be evaluated, it would produce just one value, and so (distance ((car list) (first (rest list)))) would call distance with just one argument. You should be doing this instead:

(distance (car list) (first (rest list)))

Also see:

• Cannot use function call as first argument in s-exp
• Why do we need funcall in lisp
• Do any lisps have a s-expression as their head, e.g. ((f 2) 3 4)? If not, why?