SICP - Solution: Exercise 1.9
Oct 1, 2018 21:03 · 187 words · 1 minute read
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.
(define (+ a b)
(if (= a 0)
b
(inc (+ (dec a) b))))
(define (+ a b)
(if (= a 0)
b
(+ (dec a) (inc b))))
Using the substitution model, illustrate the process generated by each procedure in evaluating (+ 4 5)
. Are these processes iterative or recursive?
Solution
First procedure
The procedure:
(define (+ a b)
(if (= a 0)
b
(inc (+ (dec a) b))))
have a recursive process:
(+ 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
Second procedure
The procedure:
(define (+ a b)
(if (= a 0)
b
(+ (dec a) (inc b))))
have an iterative process:
(+ 4 5)
(+ 3 6)
(+ 2 7)
(+ 1 8)
(+ 0 9)
9