(define (reduce-right f lst)
  (if (null? (cdr lst))
      (car lst)
      (f (car lst) 
         (reduce-right f (cdr lst)))))

(define (reduce-left f lst)
  (reduce-help-left f (cdr lst) (car lst)))

(define (reduce-help-left f lst res)
  (if (null? lst)
      res
      (reduce-help-left f (cdr lst) (f res (car lst)))))

(define (accumulate-right f init lst)
  (if (null? lst)
      init
      (f (car lst) (accumulate-right f init (cdr lst)))))