defun vs defmacro and backquote vs list

Question

While looking to exclude the uses of the list function through the backquote substitutes in defmacros, my attempt failed when combined with the let and `let* recipe, together with the gensym function (as a source of uninterned symbols, as illustrated somewhere else), to create temporary variables - but the latter is not the issue.

A running MWE [EDITED: inserted macroexpand] is the following.

(defun w (a &optional b) ; line 1
  (let ((z (gensym)))
   `(let* ((,z (if (integerp ,b) '((,a ,b)) '((,a))))) ,z)))
    ⇒ w

(eval (w 3)) ; line 2
    ⇒ ((3))
(eval (w 3 0)) ; line 3
    ⇒ ((3 0))

The w is a defun above: when the optional integerp second argument is present, return the pair as a "doubled" list; otherwise return only the first argument, also inside two pairs of parentheses.

Now comes the tricky part: need to replace the defun with a defmacro (m for w).

(defmacro m (a &optional b) ; line 4
  (let ((z (gensym)))
   `(let* ((,z (if (integerp ,b) `((,a ,b)) `((,a))))) ,z)))
    ⇒ m

(macroexpand (m (+ 1 2) 0)) ; line 5
    ⇒ list: Symbol's value as variable is void: a

And also attempt to return the evaluation of (+ 1 2), i.e., ((3 0)). The loop shows the above line #4 is faulty.

Next use instead simple quotes, i.e., '((,a ,b)).

(defmacro m (a &optional b) ; line 6
  (let ((z (gensym)))
   `(let* ((,z (if (integerp ,b) '((,a ,b)) '((,a))))) ,z)))
    ⇒ m

(macroexpand (m (+ 1 2) 0)) ; line 7
    ⇒ (((+ 1 2) 0))

Okay, but there is no evaluation of the argument: not acceptable.

(defmacro m (a &optional b) ; line 8
  (let ((z (gensym)))
   `(let* ((,z (if (integerp ,b) (list (list ,a ,b)) (list (list ,a))))) ,z)))
    ⇒ m

(macroexpand (m (+ 1 2) 0)) ; line 9
    ⇒ ((3 0))

Finally, use the list function for a change: this time it works, yet there is one list too many.

The problem is then how can line #4 keep its minimalistic form using (back)quotes, so that line #5 would result as line #3 - using defmacro versus defun. There is a `(... within `(--- pattern. that might be the cause.

Appreciate all answers. Thank s.

Answer 1

It's not necessary to use a backquote inside another, that's the beauty of it.

(defmacro m1 (a &optional b)
  (let ((z (gensym)))
    `(let ((,z (if (integerp ,b)
                   (list ,a ,b)
                 (list ,a))))
       ,z)))

But that isn't correct yet. The purpose of z isn't to add another variable for the fun of it, but to protect b from being evaluated more than once (because doing that might have side-effects or be costly). You are not doing that. Here's how to do it.

(defmacro m2 (a &optional b)
  (let ((z (gensym)))
    `(let ((,z ,b))
       (if (integerp ,z)
           (list ,a ,z)
         (list ,a)))))

This demonstrates the difference:

(let ((v 1)) (m1 1 (cl-incf v))) => (1 3)
(let ((v 1)) (m2 1 (cl-incf v))) => (1 2)

You do not have to do the same for a because, even though it appears twice, only ever one occurrence is evaluated.

Answer 2

Nested backquotes require more commas.

(defmacro m (a &optional b) ; line 4
  (let ((z (gensym)))
   `(let* ((,z ,b)) (if (integerp ,z) `((,,a ,,z)) `((,,a))))))