sol-1.33.tex

Here is a `filtered-accumulate` procedure (that generates an iterative process):
\begtt\scm
(define (filtered-accumulate filter combiner null-value term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a)
              (if (filter a)
                  (combiner result (term a))
                  result))))
  (iter a null-value))
\endtt
\begitems\style a
* The sum of the squares of the prime numbers in the interval $a$ to $b$ can be expressed by
\begtt\scm
(define (s a b)
  (filtered-accumulate prime? + 0 square a inc b))
\endtt
* The product of all positive integers less than $n$ that are relatively prime to $n$ can be expressed by
\begtt\scm
(define (p n)
  (define (relatively-prime? i)
    (= 1 (gcd i n)))
  (filtered-accumulate relatively-prime? * 1 identity 1 inc (- n 1)))
\endtt
\enditems