How to do a powerset in DrRacket?

htdp, powerset, racket, scheme

Solution

            What's in a powerset? A set's subsets! 
            An empty set is any set's subset,
            so powerset of empty set's not empty. 
            Its (only) element it is an empty set:

(define
  (powerset aL)
  (cond
    [(empty? aL) (list empty)]
    [else

            As for non-empty sets, there is a choice,
            for each set's element, whether to be
            or not to be included in subset
            which is a member of a powerset. 
            We thus include both choices when combining 
            first element with smaller powerset, 
            that, which we get recursively applying 
            the same procedure to the rest of input:

       (combine (first aL)
                (powerset (rest aL)))]))

(define
  (combine a r)                      ; `r` for Recursive Result
  (cond
    [(empty? r)  empty]              ; nothing to combine `a` with
    [else
      (cons (cons a (first r))       ; Both add `a` and
          (cons (first r)            ;   don't add, to first subset in `r`
              (combine               ; and do the same
                    a                ;   with 
                    (rest r))))]))   ;   the rest of `r`

            "There are no answers, only choices". Rather, 
            the choices made, are what the answer's made of.

Problem

I'm using the beginning language with list abbreviations for DrRacket and want to make a powerset recursively but cannot figure out how to do it. I currently have this much ``` (define (powerset aL) (cond [(empty? aL) (list)] ``` any help would be good.

Original source