;; Die ersten drei Zeilen dieser Datei wurden von DrRacket eingefügt. Sie enthalten Metadaten
;; über die Sprachebene dieser Datei in einer Form, die DrRacket verarbeiten kann.
#reader(lib "DMdA-vanilla-reader.ss" "deinprogramm")((modname o-set) (read-case-sensitive #f) (teachpacks ()) (deinprogramm-settings #(#f write repeating-decimal #f #t none explicit #f ())))
; Schnittstelle fuer Mengen
(provide set empty-set elem? add-set intersect)

(: empty-set set)
(: elem? (real set -> boolean))
(: add-set (real set -> set))
;(: union   (set set -> set))
(: intersect (set set -> set))


;Signatur fuer Mengen
(define set (signature (list-of real)))

; Die leere Menge
(define empty-set empty)

;Teste of ein Element in der Menge ist
(define elem?
  (lambda (x s)
    (cond ((empty? s) #f)
          ((= (first s) x) #t)
          ((< x (first s)) #f)
          (else (elem? x (rest s))))))

; Hinzufuegen eines Elements zu einer Menge
(define add-set
  (lambda (x s)
    (cond ((empty? s) (cons x empty))
          ((= x (first s)) s)
          ((< x (first s)) (cons x s))
          (else (cons (first s) (add-set x (rest s)))))))

;Schnitt zweier Mengen
(define intersect
  (lambda (s1 s2)
    (cond ((or (empty? s1) (empty? s2)) empty)
          ((= (first s1) (first s2)) 
           (cons (first s1) (intersect (rest s1) (rest s2))))
           ((< (first s1) (first s2)) (intersect (rest s1) s2))
           (else (intersect s1 (rest s2))))))

;Die Menge mit den Elementen 1 und 2 
(define set12 (add-set 2 (add-set 1 empty-set)))

;Die Menge mit den Elementen 1 und 3 
(define set13 (add-set 3 (add-set 1 empty-set)))

(check-expect (elem? 1 set12) #t)
(check-expect (elem? 3 set12) #f)
(check-expect (elem? 1 (intersect set12 set13)) #t)
(check-expect (elem? 3 (intersect set12 set13)) #f)