Accumulation

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.


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(define (inc n) (+ n 1))

(define (square x) (* x x))

(define (identity x) x)

(check-equal? (accumulate * 1 square 1 inc 3) 36)
(check-equal? (accumulate * 1 identity 3 inc 5) 60)
(check-equal? (accumulate + 0 identity 1 inc 10) 55)