Scheme problem (using a function as a parameter)

I'm a Scheme newbie and trying to make sense of my homework. I've a function I made earlier called duplicate, and it looks like this:

( DEFINE ( duplicate lis )
          (IF (NULL? lis) '())
          ((CONS (CAR l开发者_JAVA百科is) (CONS (CAR lis) (duplicate (CDR lis))))
         ))

A typical i/o from this would be i: (duplicate '(1 2 3 4)) o: (1 1 2 2 3 3 4 4), so basicly it duplicates everything in the list. Moving on: Now I'm supposed to make a function that's called comp. It's supposed to be built like this:

(DEFINE (comp f g) (lambda (x) (f (g (x))))

Where I could input '(1 2 3 4) and it would return (1 1 4 4 9 9 16 16)

so f = duplicate and g = lambda. I know lambda should probably look like this:

(lambda (x) (* x x))

But here's where the problem starts, I've already spent several hours on this, and as you can see not made much progress.

Any help would be appreciated. Best regards.

Use map:

> (map (lambda (x) (* x x)) (duplicate '(1 2 3 4)))
=> (1 1 4 4 9 9 16 16)

or, modify duplicate to take a procedure as its second argument and apply it to each element of the list:

(define (duplicate lst p)
  (if (null? lst) ()
      (append (list (p (car lst)) (p (car lst))) (duplicate (cdr lst) p))))

> (duplicate '(1 2 3 4) (lambda (x) (* x x)))
=> (1 1 4 4 9 9 16 16)

One way to do is as follows:

(define (comp f g) (lambda (x) (f (g x))))
(define (square x) (* x x))
(define (dup x) (list x x))
(define (duplicate-square lst)
  (foldr append '() (map (comp dup square) lst)))

Now at the repl, do:

> (duplicate-square '(1 2 3 4))
'(1 1 4 4 9 9 16 16)