SICP Exercise 2.38 fold-left

Exercise 2.38.  The accumulate procedure is also known as fold-right, because it combines the first element of the sequence with the result of combining all the elements to the right. There is also a fold-left, which is similar to fold-right, except that it combines elements working in the opposite direction:

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

What are the values of

(fold-right / 1 (list 1 2 3))
(fold-left / 1 (list 1 2 3))
(fold-right list nil (list 1 2 3))
(fold-left list nil (list 1 2 3))


Give a property that op should satisfy to guarantee that fold-right and fold-left will produce the same values for any sequence.

SOLUTION
The code and tests are here.

 Notes: 'op' should satisfy the associative property to guarantee that fold-right and fold-left will produce the same values for any sequence. We can see in the above examples that for addition and multiplication which are associative operations, the same result is produced by both fold-right and fold-left. On the other hand, for division and subtraction different results are produced by fold-right and fold-left


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