typos
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Matthias Felleisen
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collects/realm/chapter2/source.rkt
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206
collects/realm/chapter2/source.rkt
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#lang racket
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(require rackunit rackunit/text-ui)
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;; Play a Guess my Number game at the REPL.
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;; Run program.
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;; Pick a number X between <n> and <m>.
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;; Evaluate
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;; (start <n> <m>)
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;; The program will respond with a number.
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;; Use
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;; (bigger)
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;; and
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;; (smaller)
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;; to let it know what you think of the guess.
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;; Watch how qiuckly the program guesses X.
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;
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;
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;
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; ;
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; ;
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; ;;; ;;;
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; ;; ;;
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; ; ; ; ; ;;;; ;;; ;; ;;;
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; ; ; ; ; ; ; ; ;; ;
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; ; ; ; ; ; ; ; ;
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; ; ; ; ;;;;;; ; ; ;
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; ; ; ; ; ; ; ;
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; ; ; ; ;; ; ; ;
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; ;;; ;;; ;;;; ;; ;;;;;;; ;;; ;;;
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;
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;
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;
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;
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;; Example:
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;; > (start 0 100) ; [0,100]
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;; 50
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;; > (bigger) ; [51,100]
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;; 75
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;; > (bigger) ; [76,100]
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;; 88
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;; > (smaller) ; [76,87]
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;; 82
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;; Number Number -> Number
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;; Start a new game in [n,m] and make a guess.
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;; > (start 0 100)
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;; 50
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(define (start n m)
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(set! lower (min n m))
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(set! upper (max n m))
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(guess))
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;; Lower and upper bounds on the number
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(define lower 1)
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(define upper 100)
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;; -> Nuber Number
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;; Guess half-way between lower and upper bounds.
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;; > (begin (start 0 100) (guess))
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;; 50
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(define (guess)
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(quotient (+ lower upper) 2))
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;; -> Number
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;; Lower the upper bound and guess again.
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;; > (begin (start 0 100) (smaller))
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;; 24
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(define (smaller)
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(set! upper (max lower (sub1 (guess))))
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(guess))
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;; -> Number
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;; Raise the lower bound and guess again.
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;; > (begin (start 0 100) (bigger))
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;; 75
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(define (bigger)
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(set! lower (min upper (add1 (guess))))
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(guess))
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;
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;
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;
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;
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;
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; ;;;;;;; ;
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; ; ; ; ;
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; ; ; ; ;;; ;;;; ; ;;;;;;; ;;;; ;
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; ; ; ; ; ; ; ;; ; ; ;;
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; ; ; ; ; ; ;
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; ; ;;;;;;; ;;;;; ; ;;;;;
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; ; ; ; ; ;
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; ; ; ; ; ; ; ; ; ;
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; ;;;;; ;;;; ;;;;;; ;;;; ;;;;;;
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;
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;
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;
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;
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(module+ test
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;; basic guesses
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(check-equal? (guess) 50)
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(check-equal? (start 0 100) 50)
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(check-equal? (begin (start 0 100) lower) 0)
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(check-equal? (begin (start 0 100) upper) 100)
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(check-equal? (begin (start 0 100) (smaller)) 24)
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(check-equal? (begin (start 0 000) (smaller)) 0)
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(check-equal? (begin (start 0 100) (smaller) lower) 0)
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(check-equal? (begin (start 0 100) (smaller) upper) 49)
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(check-equal? (begin (start 0 100) (bigger)) 75)
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(check-equal? (begin (start 0 000) (bigger)) 0)
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;; testing a sequence of interactions with expected intermediate states
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(test-begin (start 0 100)
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(bigger)
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(check-equal? lower 51)
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(check-equal? upper 100)
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(bigger)
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(check-equal? lower 76)
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(check-equal? upper 100)
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(smaller)
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(check-equal? lower 76)
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(check-equal? upper 87))
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;; doing it all over for negative numbers
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(check-equal? (start -100 0) -50)
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(check-equal? (begin (start -100 0) lower) -100)
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(check-equal? (begin (start -100 0) upper) 0)
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(check-equal? (begin (start -100 0) (smaller)) -75)
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(check-equal? (begin (start -100 0) (smaller)) -75)
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(check-equal? (begin (start -100 0) (smaller) lower) -100)
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(check-equal? (begin (start -100 0) (smaller) upper) -51)
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(check-equal? (begin (start -100 0) (bigger)) -24)
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(check-equal? (begin (start -100 0) (bigger)) -24)
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(test-begin (start -100 0)
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(bigger)
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(check-equal? lower -49)
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(check-equal? upper 0)
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(bigger)
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(check-equal? lower -23)
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(check-equal? upper 0)
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(smaller)
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(check-equal? lower -23)
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(check-equal? upper -12))
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;; ---------------------------------------------------------------------------
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;; testing random properties of our functions
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;; Property:
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;; For all games starting in [n,m] after any number of moves,
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;; lower <= upper.
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(define (prop:ordered n m i)
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(check-true
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(begin (start n m)
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(random-moves i)
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(<= lower upper))))
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;; Property:
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;; For all games starting in [n,m], for any number of moves,
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;; lower grows up, upper grows down, or they are equal.
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(define (prop:monotonic n m i)
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(check-true
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(begin (start n m)
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(for/and ([i (in-range i)])
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(define l lower)
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(define u upper)
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(random-move)
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(or (and (< l lower) (= u upper))
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(and (= l lower) (> u upper))
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(and (= l lower) (= u upper)))))))
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;; Number -> Void
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;; Move randomly n times.
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(define (random-moves i)
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(unless (zero? i)
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(random-move)
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(random-moves (sub1 i))))
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;; -> Void
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;; Move randomly once.
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(define (random-move)
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(if (zero? (random 2))
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(smaller)
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(bigger)))
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;; property tests
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(for ([i (in-range 1000)])
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(prop:ordered (random 1000) (random 1000) (random 100))
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(prop:monotonic (random 1000) (random 1000) (random 100)))
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;; reset the boundaries to defaults
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(start 1 100)
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"all tests run")
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