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Recursive Pattern: accumulate

Another recursive pattern is called the accumulate pattern. In the accumulate recursive pattern, an action is performed on every element of a list and the result of that action is accumulated with the results of performing the action on the other elements.

This is very like the `every' pattern using cons, except that cons is not used, but some other combiner.

The pattern is:

• If a list be empty, return zero or some other constant.
• Else, act on the beginning of the list (the CAR of the list),
  • and combine that acted-on element, using + or some other combining function, with
  • a recursive call by the function on the rest (the CDR) of the list.

Here is an example:

(defun add-elements (numbers-list)
  "Add the elements of NUMBERS-LIST together."
  (if (not numbers-list)
      0
    (+ (car numbers-list) (add-elements (cdr numbers-list)))))

(add-elements '(1 2 3 4))
    => 10

See Making a List of Files, for an example of the accumulate pattern.