(define (sum n) 
  (insertl + (intsto n)))

(define (insertl f lst)
  (if (null? lst) 
      (f)
      (f (car lst) (insertl f (cdr lst)))))

(define (insertl2 f lst)
  (if (= (length lst) 2)
      (f (car lst) (cadr lst))
      (f (car lst) (insertl2 f (cdr lst)))))

(define (insertlg f lst start)
  (if (= (length lst) 1)
      (f (car lst) start)
      (f (car lst) (insertlg f (cdr lst) start))))

(define (intsto n)
  (if (= n 0) null
      (append (intsto (- n 1)) (list n))))

(define (doubleall lst)
  (insertlg (lambda (a b) (cons (* 2 a) b)) lst null))

(define (doubleallm lst)
  (map (lambda (s) (* 2 s)) lst))

(define (filter f lst)
  (insertlg (lambda (a b)
              (if (f a) (cons a b) b)) lst null))
            
(define (map f lst)
  (insertlg
   (lambda (a b)
     (cons (f a) b))
   lst
   null))

(define (mapr f lst)
  (if (null? lst) null 
      (cons (f (car lst))
            (map f (cdr lst)))))