Dan's Thoughts Thinking somewhat carefully

Exercise 1.9 of SICP

Exercise 1.9: Each of the following two procedures defines a method for adding two positive integers in terms of the procedures inc, which increments its argument by 1, and dec, which decrements its argument by 1.

Recursive:

(define (+ a b)
  (if (= a 0)
      b
      (inc (+ (dec a) b))))

(+ 4 5)
(inc (+ 3 5))
(inc (inc (+ 2 5)))
(inc (inc (inc (+ 1 5))))
(inc (inc (inc (inc (+ 0 5)))))
(inc (inc (inc (inc 5))))
(inc (inc (inc 6)))
(inc (inc 7))
(inc 8)
9

Iterative:

(define (+ a b)
  (if (= a 0)
      b
      (+ (dec a) (inc b))))

(+ 4 5)
(+ 3 6)
(+ 2 7)
(+ 1 8)
(+ 0 9)
9