Common Lisp Error: Expected-type: REAL datum: NIL

I'm working on actually writing something on my own in Common Lisp for once, implementing the Shunting-yard Algorithm. I thought it went okay, even if it came out rather ugly and if I doubt its Lispy-ness, but upon testing out the function in the REPL, I get the error in the title.

The code is as follows, with the test case being (shunting-yard '(3 + 5)).

(defparameter *output-queue*   nil)
(defparameter *operator-stack* nil)

(defun determine-precedence (operator)
  (case operator
    (('+ '-) 2)
    (('* '/) 3)
    ('^      4)))

(defun shunting-yard (stmt)
  (loop until (null stmt) do
       (let ((token (car stmt)))
         (cond ((or (numberp token)
            (eq token '\())
            (setf *output-queue* (cons token *output-queue*)))
               ((mapcar #'(lambda (x) (eq token x)) '(+ - * / ^))
            (let* ((token-precedence (determine-precedence token))
                   (stack-topmost (car *operator-stack*))
                   (stack-precedence (determine-precedence stack-topmost)))
              (when (< token-precedence stack-precedence)
                (setf *output-queue* (cons stack-topmost *output-queue*))
                (setf *operator-s开发者_Go百科tack* (cdr *operator-stack*)))
              (setf *operator-stack* (cons token *operator-stack*))))
               ((eq token '\))
            (loop for stack-topmost in *operator-stack*
               until (eq stack-topmost '\()
               do (progn
                (setf *output-queue* (cons stack-topmost *output-queue*))
                (setf *operator-stack* (cdr *operator-stack*)))
               finally (setf *operator-stack* (cdr *operator-stack*)))))
         (setf stmt (cdr stmt))))
  (loop while (not (null *operator-stack*))
     do (progn
      (setf *output-queue* (cons (car *operator-stack*) *output-queue*))
      (setf *operator-stack* (cdr *operator-stack*))))
  (nreverse *output-queue*))

Is the error in the code itself (my guess) or is it in my test case?

Thanks so much in advance, this was REALLY fun to write and I can't wait to work on something else, but only after I get this working.

There are several errors:

First:

(defun determine-precedence (operator)
  (case operator
    (('+ '-) 2)
    (('* '/) 3)
    ('^      4)))

The quotes need to go. All.

Second:

(mapcar #'(lambda (x) (eq token x)) '(+ - * / ^))

Above is not doing what you think. Replace it with a call to MEMBER.

Third:

 (when (< token-precedence stack-precedence)

You need to make sure that the variables are really bound to numbers. Use something like

 (check-type token-precedence number)
 (check-type stack-precedence number)

before as a check.

Happy further debugging...