KA-VL4

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Archivierte Version vom 2016-04-20T15:17:11+00:00. Aktuelle Version

Streamprozeduren:

(require racket/engine)

(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 make-stream 
  (lambda (seed proc)
    (letrec 
      ((stream-builder
         (lambda (n)
           (stream-cons n (stream-builder (proc n))))))
      (stream-builder seed))))
  
(define stream-item
  (lambda (str k)
    (if (= k 0)
      (stream-car str)
      (stream-item (stream-cdr str) (- k 1)))))

(define stream-map
  (lambda (f str)
    (stream-cons
     (f (stream-car str))
     (stream-map f (stream-cdr str)))))

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



(define nat_zahlen (make-stream 0 (lambda (n) (+ n 1))))

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

Aufzählprozedur für Wortmenge A* mit A = {a,b,c}

(define g
  (lambda (n)
    (cond
      ([= n 0] "")
      ([= n 1] "a")
      ([= n 2] "b")
      ([= n 3] "c")
      ([= (modulo n 3) 0] (string-append (g (- (/ n 3) 1)) "c"))
      ([= (modulo n 3) 1] (string-append (g (- (/ (+ n 2) 3) 1)) "a"))
      ([= (modulo n 3) 2] (string-append (g (- (/ (+ n 1) 3) 1)) "b")))))

(g 0)

Cantorsche Paarungsfunktion

(define cantor
  (lambda (x y)
    (+ (/ (* (+ y x) (+ y x 1)) 2) y)))

(define getCantorX
  (lambda (z)
    (- (getCantorW z)(getCantorY z))))


(define getCantorW
  (lambda (z)
    (floor (/ (- (sqrt (+ (* 8 z) 1)) 1) 2)   )))

(define getCantorT
  (lambda (w)
    (/ (* (+ w 1) w) 2)))


(define getCantorY
  (lambda (z)
    (- z (getCantorT (getCantorW z)))))

\Chi '_M mit Hilfsprozeduren

(define fib
  (lambda (n)
    (cond
      ([= n 1] 1)
      ([= n 2] 1)
      (else (+ (fib (- n 1)) (fib (- n 2)))))))

(define countB_helper
  (lambda (ls i)
    (cond
      ([empty? ls] i)
      ([equal? (car ls) #\b] (countB_helper (cdr ls) (+ i 1)))
      (else (countB_helper (cdr ls) i)))))

(define countB
  (lambda (str)
    (countB_helper (string->list str) 0)))
      
(define chiStrichFib_helper
  (lambda (w i)
    (cond
      ([= (countB w) (fib i)] #t)
      (else (chiStrichFib_helper w (+ i 1))))))

(define chiStrichFib
  (lambda (w t)
    (chiStrichFib_helper w 1)))

(chiStrichFib "ab" #t)

Aufzählfunktion für M

(define aufzaehlKA
  (lambda (z)
    (cond
      ([equal? #t (engine-run (getCantorY z) (engine (binary->unary chiStrichFib (g(getCantorX z)))))] (g(getCantorX z)))
      (else "abb"))))

(aufzaehlKA 5)

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