;;; add-pairs: add the elements of a given list, two by two, and
;;; construct a list of the results

;;; John David Stone
;;; Department of Mathematics and Computer Science
;;; Grinnell College
;;; stone@cs.grinnell.edu

;;; created February 2, 2000
;;; last revised February 2, 2000

;;; Given:
;;;   LS, a list of numbers.

;;; Result:
;;;   SUMS, a list of numbers.

;;; Precondition:
;;;   The length of LS is even.

;;; Postconditions:
;;;   Let |LS| be the length of LS.
;;;   (1) The length of SUMS is |LS| / 2.
;;;   (2) For every natural number k less than |LS| / 2, the element
;;;       at position k of SUMS is the sum of the elements at positions
;;;       2k and 2k + 1 of LS.

(define add-pairs
  (lambda (ls)
    (if (null? ls)
        null
        (cons (+ (car ls) (car (cdr ls)))
              (add-pairs (cdr (cdr ls)))))))