1.32.scm

;;;; 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.

;;; Answer
(load "0.util.scm")

;; a. Recursive 
(define (accumulate combiner null-value term a next b)
  (if (> a b)
    null-value
    (combiner 
      (term a)
      (accumulate combiner null-value term (next a) next b))))

(define (sum term a next b)
  (accumulate + 0 term a next b))
(define (product term a next b)
  (accumulate * 1 term a next b))

;; Test
(define (id x) x)
(define (1+ x) (+ x 1))
(test (sum id 1 1+ 10) 55)
(test (product id 1 1+ 5) 120)

;; a. Iterative
(define (accumulate combiner null-value term a next b)
  (display "Using iterative accumulate:")
  (newline)
  (define (iter a result)
    (if (> a b)
      result
      (iter (next a) (combiner result (term a)))))
  (iter a null-value))

;; Test
(define (id x) x)
(define (1+ x) (+ x 1))
(test (sum id 1 1+ 10) 55)
(test (product id 1 1+ 5) 120)