(define (string-lengths some-list #!optional (lengths '()))
  ; some-list - the list of strings.
  ; lengths - the length of the strings we've calc'd so far : initially '().
  (if (null? somelist)
    (begin ; "base case" - we're at the end of some-list.
      (display "Got empty list: ending")
      (newline)
      (reverse lengths))
    (begin ; take the first element in the list and work out the length.
      (display (string-length (car some-list)))
      (newline)
      (string-lengths ; pass on the rest of the list and the list of lengths.
        (cdr some-list) ; the tail of some-list
        (cons - place the string-length of list list at the head of the list of lengths.
          (string-length (car some-list))
          lengths)))))