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 <??> <??>))
迭代式的 sum 可以如下写：
(define (sum term a next b)
(define (iter a result)
(if (> a b)
result
(iter (next a)
(+ (term a) result))))
(iter a 0))
同样，我们需要进行测试
(load "../testframe.scm")
; cube
(define (inc n) (+ n 1))
(define (sum-cubes a b)
(sum cube a inc b))
(assert= (sum-cubes 1 10) 3025)
; sum-integers
(define (identity x) x)
(define (sum-integers a b)
(sum identity a inc b))
(assert= (sum-integers 1 10) 55)