2.32.rkt

#lang sicp
;; Exercise 2.32:
;; 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 (lambda (x) (cons (car s) x)) rest)))))

(define (append list1 list2)
  (if (null? list1)
      list2
      (cons (car list1)
            (append (cdr list1)
                    list2))))

(define (map proc items)
  (if (null? items)
      nil
      (cons (proc (car items))
            (map proc (cdr items)))))