4 days ago

my attempt to do the exercises in sicp.

## Sunday, June 29, 2008

### sicp exercise 1.32

; Exercise 1.32. a. Show that sum and product (exercise 1.31) are both special cases of a still more

; general notion called accumulate that combines a collection of terms, using some general accumulation

; function:

;

; (accumulate combiner null-value term a next b)

;

; Accumulate takes as arguments the same term and range specifications as sum and product, together

; with a combiner procedure (of two arguments) that specifies how the current term is to be combined

; with the accumulation of the preceding terms and a null-value that specifies what base value to use

; when the terms run out. Write accumulate and show how sum and product can both be defined as simple

; calls to accumulate.

; b. If your accumulate procedure generates a recursive process, write one that generates an

; iterative process. If it generates an iterative process, write one that generates a recursive process.

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

(if (> a b)

null-value

(combiner (term a) (accumulate-recur combiner null-value term (next a) next b))))

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

(define (iter a result)

(if (> a b)

result

(iter (next a) (combiner (term a) result))))

(iter a null-value))

(define (sum term a next b)

(accumulate + 0 term a next b))

(define (product term a next b)

(accumulate * 1 term a next b))

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