Question

I need to implement something like this:

(loop for i from 1 to N sum (f i))

except that accumulated values are represent lists of numbers like (1 2 3)
and they are added element-wise. In other words I would like to initialize summation
with (zerov N) and use (v+) to add subsequent elements:

(defun v+ (a b) (mapcar '+ a b))
(defun zerov (n) (loop for i from 1 to n collect 0))

Is it possible to do something like this with loop macro? I can implement it as a
separate function, but I would like to use loop or loop-like macro for expressiveness.
Perhaps there is a way to define simple loop-like macro just for this case?

Answer 1

LOOP as defined in the Common Lisp standard is not extensible.

I would write it with the normal LOOP functionality:

(let ((result (zerov n)))
  (loop for i from 1 to N
        do (setf result (v+ result (f i))))
  result)

The I would write it as a function:

(defun sum (n f init sum)
  (let ((result (funcall init n)))
    (loop for i from 1 to n
          do (setf result (funcall sum result (funcall f i))))
    result))

If you want such a functionality as a direct language feature of a loopy macro, then an alternative would be the ITERATE macro, which is more powerful than the LOOP macro and it is also extensible.