How can I reverse a list?

Use:

(define (reverse1 l)
  (if (null? l)
     nil
     (append (reverse1 (cdr l)) (list (car l)))
  )
)

Explanation:

Rules:

1. If the list is empty, then the reverse list is also empty
2. Else behind the reverse tail of the list, add the first element of the list

Look at this code this way:

reverse1 is name of the function and l is a parameter. If the list is empty then the reverse is also empty. Else call the reverse1 function with (cdr l) which is the tail of the list and append that to the first alement (car l) that you make as a list.

In your example (pseudocode):

1st iteration
l=>(a (bcd)e)
car l => a
cdr l => (bcd)e
list(car l) =>(a)
------------------
reverse( cdr l)"+"(a)
------------------
2nd iteration
l=>((bcd)e)
car l => (bcd)
cdr l =>e
list(car l)=>(bcd)
--------------------
reverse(cdr l)"+"((bcd))+(a)
-----------------------
3rd iteration
l=>e
car l=> e
cdr l => nil
list (car l) =>(e)
-------------------------
(e (bcd)a)

(define (my-reverse ls)
  (define (my-reverse-2 ls acc)
    (if (null? ls)
      acc
      (my-reverse-2 (cdr ls) (cons (car ls) acc))))
  (my-reverse-2 ls '()))

This uses an accumulator variable to reverse the list, taking the first element off the incoming list and consing it to the front of the accumulator. It hides the accumulator taking function and just exposes the function that takes a list, so the caller doesn't have to pass in the empty list. That's why I have my-reverse-2.

(my-reverse-2 '(a (b c d) e) '()); will call
(my-reverse-2 '((b c d) e)  '(a)); which will call
(my-reverse-2 '(e)  '((b c d) a)); which will call
(my-reverse-2 '() '(e (b c d) a)); which will return
'(e (b c d) a)

Because the last function call in my-reverse-2 is a call to my-reverse-2, and the return value is passed right through (the return value of the first call is the return value of the second call, and so on) my-reverse-2 is tail optimized, which means it will not run out of room on the stack. So it is safe to call this with a list as long as you like.

If you want it to apply to nested lists use something like this:

(define (deep-reverse ls)
  (define (deep-reverse-2 ls acc)
    (if (null? ls)
        acc
        (if (list? (car ls))
            (deep-reverse-2 (cdr ls) (cons (deep-reverse (car ls)) acc))
            (deep-reverse-2 (cdr ls) (cons (car ls) acc)))))
  (deep-reverse-2 ls '()))

This checks to see if the element is a list before adding it to the list, and if it is, reverses it first. Since it calls itself to revers the inner list, it can handle arbitrary nesting.

(deep-reverse '(a (b c d) e)) -> '(e (d c b) a) which is in reverse alphabetical order, despite the fact that there is a nested list. It evaluates as so:

(deep-reverse-2 '(a (b c d) e) '()); Which calls
(deep-reverse-2 '((b c d) e)  '(a))
(deep-reverse-2 '(e) (cons (deep-reverse-2 '(b c d) '()) '(a)))
(deep-reverse-2 '(e) (cons (deep-reverse-2 '(c d)  '(b)) '(a)))
(deep-reverse-2 '(e) (cons (deep-reverse-2 '(d)  '(c b)) '(a)))
(deep-reverse-2 '(e) (cons '(d c b) '(a)))
(deep-reverse-2 '(e)  '((d c b) a))
(deep-reverse-2 '() '(e (d c b) a))
'(e (d c b) a)

This is one way that you can make a reverse function that applies to nested lists:

(define (reverse-deep l)
  (map (lambda (x) (if (list? x) (reverse-deep x) x)) (reverse l)))

Explanation in pseudo-code:
Start by reversing the list as you would normally do
Then for each element in the reversed list:
- If the element is a list itself: Apply the procedure recursively
- Else: Don't touch the element