BuK/IIm20/Vorlesung 2 Grüning

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<language>SchemeJS</language>
== Absolute Unlösbarkeit ==
'''Seite 7'''

<code id="605f350395747">
(define f
  (lambda (n)
    (if (= n 1)
        1
        (if (even? n)
            (+ (f (/ n 2)) 1)
            (/ 1 (f (- n 1)))
            )
        )
    )
  )
</code>
<run id="605f35039582a">
(f 1)
</run>

<code id="605f3503957bb">
(define f^-
  (lambda (n)
    (if (= n 1)
        1
        (if (> n 1)
            (* (f^- (- n 1)) 2)
            (+ (f^- (/ 1 n)) 1)
            )
        )
    )
  )
</code>
<run id="605f350395882">
(f^- 1)
</run>


== Hilbert Hotel ==
<code id="605dd0651e5eb">
(define stream-car car)

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

(define-macro (stream-cons head tail)
  `(cons ,head (delay ,tail)))

(define stream?
  (lambda (stm)
    (and (pair? stm) (promise? (cdr stm)))))

(define stream-map
  (lambda (proz stm)
    (stream-cons (proz (stream-car stm)) (stream-map proz (stream-cdr stm)))))

(define show-stream
  (lambda (stm n)
    (letrec
        ([show
          (lambda (stm n ls)
            (if (= n 0)
                (apply display (append ls (list "...")))
                (show (stream-cdr stm) (- n 1) (append ls (list (stream-car stm) ", ")))))])
      (show stm n ()))))

(define zeige-mir show-stream)

</code>

<code id="605dd0651e650">

(define baue-hilberthotel
  (lambda ()
    (stream-cons #f (baue-hilberthotel)))
  )

(define hilberthotel (baue-hilberthotel))
</code>

<run id="605dd0651e6ad">
(zeige-mir hilberthotel 11)
</run>

<code id="605dd4de3e11c">
(define einzelbuchung
  (lambda (val stm pos)
    (let ([old-pos pos])
      (letrec
          ([shorten
            (lambda (val stm pos)
              (if (= pos 0)
                  (if (eq? #f (stream-car stm))
                      (stream-cons val (stream-cdr stm))
                      (raise (string-append (number->string old-pos) " schon belegt mit: " (stream-car stm))))
                  (stream-cons (stream-car stm) (shorten val (stream-cdr stm) (- pos 1)))
                  ))
            ])
        (shorten val stm pos)
        )
      )
    )
  )
</code>
<run id="605dd4de3e1e0">
(set! hilberthotel (einzelbuchung "Otto Grundmann" hilberthotel 3))
(zeig-mir hilberthotel 12)
</run>

<code id="605ded6247d06">
(define baue-kleinbus
  (lambda (numb pers)
    (list numb pers)))


(define kleinbus815 (baue-kleinbus 815 8))
</code>
<run id="605ded74e3e0f">
(zeig-mir kleinbus815)
</run>

<code id="605dff4adf833">
(define kleingruppenbuchung
  (lambda (hotel finite-bus)
    (letrec
        ([helper
          (lambda (hotel finite-bus pos)
            (if (not (empty? finite-bus))
                (helper (einzelbuchung (car finite-bus) hotel pos) (+ pos 1))
                (hotel)
                )
            )
          ])
      (hotel finite-bus 0)
      )
    )
  )

(set! hilberthotel (kleingruppenbuchung kleinbus815 hilberthotel))
</code>

<run id="605dff4adf8c7">
(zeig-mir hilberthotel 12)
</run>