BuK/IIm11/Studenten/sirorose/uebung4

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<language>Scheme</language>
= Übung 4, Aufgabe 4 (Teilaufgabe 3) =

Illustrieren Sie den Beweis (Aufgabe 4.2) durch ein Scheme-Programm. 

<code id="4f8da37d4debf" hidden>
(define stream-car car)

(define stream-cdr
  (lambda (stm)
    (force (cdr stm))))

(define-syntax stream-cons
  (syntax-rules ()
    ((_ head tail) (cons head (delay tail)))))


  
(define stream-item
  (lambda (str k)
    (if (= k 0)
      (stream-car str)
      (stream-item (stream-cdr str) (- k 1)))))

(define stream->list
  (lambda (str n)
    (if (<= n 0)
      '()
      (cons 
        (stream-car str) 
        (stream->list (stream-cdr str) (- n 1))))))


(define print-stream
  (lambda (stm n)
    (cond
      ((<= n 0) (display "...\n"))
      (else
       (display (stream-car stm))
       (display ", ")
       (print-stream (stream-cdr stm) (- n 1))))))

(define stream-map
  (lambda (stm proc)
    (stream-cons
     (proc (string->number (stream-car stm)))
     (stream-map (stream-cdr stm) proc))))

(define natstream
  (lambda (start)
    (stream-cons (number->string start) (natstream (+ 1 start)))))

(define natzahlstream (stream-cons (number->string 0) (natstream 1)))
</code>



<code id="4f8da37d4df0b">
; Aufzählfunktion f für alle ungerade Zahlen (hier für M)
(define f
  (lambda (n)
    (number->string (+ 1 (* n 2)))))

; Aufzählfunktion g für alle gerade Zahle (hier für A*/M)
(define g
  (lambda (n)
    (number->string (* 2 n))))

(define generiere_aufzaehlbare_menge 
  (lambda (f)
    (stream-map natzahlstream f)))

(define menge-bis print-stream)

(define M (generiere_aufzaehlbare_menge f))
(define A*-M (generiere_aufzaehlbare_menge g))

(define chi_M
  (lambda (w)
    (letrec
        ((chihelper
          (lambda (i)
            (cond
              ((string=? (f i) w) #t)
              ((string=? (g i) w) #f)
              (else
               (chihelper (+ i 1)))))))
         (chihelper 0))))

</code>
<run id="4f8da37d4dfa8">
(menge-bis M 10) 
</run>
<run id="4f8da37d4e023">
(menge-bis A*-M 10) 
</run>
<run id="4f8da37d4e0a4">
(chi_M "9199")
</run>