Iterative sum using recursion

Question

Given the following recursive definition of sum:

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))

And the task:

Exercise 1.30

The sum procedure above generates a linear recursion. The procedure can be rewritten so that the sum is performed iteratively. Show how to do this by filling in the missing expressions in the following definition:

(define (sum term a next b)
  (define (iter a result)
    (if <??>
        <??>
        (iter <??> <??>)))
  (iter <??> <??>))

I wrote the following code. What do you think?

(define (i-sum term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (+ result (term a)))))
  (iter a 0))

(define (identity x) x)
(define (inc x) (+ 1 x))
(define (sum-integers a b) (i-sum identity a inc b))

Answer 1

I believe your answer is correct, although I'm not sure why you need the identity, inc, and sum-integers procedure on the bottom for your solution.