#lang sicp

(define (fold-right op initial sequence)
  (if (null? sequence)
    initial
    (op (car sequence)
        (fold-right op initial (cdr sequence)))))

(define (fold-left op initial sequence)
  (define (iter result rest)
    (if (null? rest)
        result
        (iter (op result (car rest))
              (cdr rest))))
  (iter initial sequence))

; (fold-right / 1 (list 1 2 3)) -> (1/(2/(3/1))) = 3/2
; (fold-left / 1 (list 1 2 3)) -> (((1/1)/2)/3) = 1/6
; (fold-right list nil (list 1 2 3)) -> (1 (2 (3 ())))
; (fold-left list nil (list 1 2 3)) -> (((() 1) 2) 3)
; in order to produce the same results, the operation
; must be associative.