weima learns to program

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))