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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))
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migrated from stackoverflow.com Mar 30 '11 at 3:11

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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.

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  • \$\begingroup\$ Not homework - personal growth exercise :) \$\endgroup\$ – jaresty Mar 30 '11 at 2:51
  • \$\begingroup\$ @Joshua: Haha okay, just checking. :) \$\endgroup\$ – Mehrdad Mar 30 '11 at 2:57
  • \$\begingroup\$ They're there for testing purposes - I suppose maybe I should have removed them before posting the question?...hmm \$\endgroup\$ – jaresty Mar 30 '11 at 3:22

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