Solution to SICP Exercise 1.31

Structure and Interpretation of Computer Programs

Solution to Exercise 1.31:

; part a (recursive process)
(define (product-r term a next b)
(if (> a b)
(* (term a)
(product-r term (next a) next b))))

(define (identity i) i)
(define (inc i) (+ i 1))

(define (factorial n)
(product-r identity 1 inc n))

(define (pi-approximator terms)
(define (numerator i)
(+ i (if (odd? i) 1 2)))
(define (denominator i)
(+ i (if (odd? i) 2 1)))
(define (pi-term i)
(/ (numerator i) (denominator i)))
(* 4.0 (product-r pi-term 1 inc terms)))

; part b (iterative process)
(define (product-i term a next b)
(define (iter a result)
(if (> a b)
(iter (next a) (* result (term a)))))
(iter a 1))