sicp-exercise-1.32-1.33

Exercise 1.32

Recursive process

(define (accumulate combiner null-value a b term next)
  (if (> a b)
    null-value
    (combiner (term a)
              (accumulate combiner null-value (next a) b term next))))

Iterative process

(define (accumulate combiner null-value a b term next)
  (define (iter a result)
    (if (> a b)
      result
      (iter (next a) (combiner (term a) result))))
  (iter a null-value))

Define sum and product.

(define (sum a b term next)
  (define (add x y) (+ x y))
  (accumulate add 0 a b term next))


(define (product a b term next)
  (define (mul x y) (* x y))
  (accumulate mul 1 a b term next))

Exercise 1.33

(define (filtered-accumulate pass-filter? combiner null-value term a next b)
  (if (> a b)
    null-value
    (combiner (if (pass-filter? a)
                (term a)
                null-value)
              (filtered-accumulate pass-filter?
                                   combiner
                                   null-value
                                   term
                                   (next a)
                                   next
                                   b))))

Define sum of the squares of the prime numbers in [a, b],
and product of all positive integers less than n that are relatively prime to n.

(define (sum-prime-squares a b)
  (filtered-accumulate prime? add 0 square a inc b))

;;;;;;;;;;;;;
(define (relative-prime? x y)
  (= (gcd x y) 1))

(define (product-reletive-prime n)
  (define (filter x)
    (relative-prime? x n))
  (filtered-accumulate filter mul 1 identity 1 inc n))