The set of all subsets

We can represent a set as a list of distinct elements, and we can represent the set of all subsets of the set as a list of lists. For example, if the set is (1 2 3) , then the set of all subsets is (() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)) . Complete the following definition of a procedure that generates the set of subsets of a set and give a clear explanation of why it works:

(define (subsets s)
  (if (null? s)
      (list nil)
      (let ((rest (subsets (cdr s))))
        (append rest (map <??> rest)))))

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(define l (list 1 2 3))

(check-equal? (subsets l) '(() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)))