;; Answer = (union 'correct 'lower 'higher)
(define answer=? symbol=?)

(define HI 100)
(define LO   0)

;; Number -> Answer
;; returns a function that consumes a number -- g -- and
;; returns whether n is g, n if lower than g, or n is
;; higher than g.  This of this function as someone who
;; is keeping a secret number
(define (oracle n)
  (lambda (g)
    (cond
      [(= (abs (- g n)) 1) 'correct]
      [(< n g) 'lower]
      [(> n g) 'higher])))

;; Example: A person with the secret number 10
(define person-with-10 (oracle 10))

;; Ask the oracle about certain number compared to 10
;; is the number 17
(answer=? (person-with-10 17) 'higher)  ;; nope 17 is higher than secret number
(answer=? (person-with-10  9) 'lower)   ;; nope 9 is lower than the secret number
(answer=? (person-with-10 10) 'correct) ;; nope 9 is lower than than the secret number

;; guess: (Number -> Answer) Number Number -> 
;; returns true if we guess the correct number according to
;; an oracle p, starting with number n
(define (guess p n)
  (guess* p n -1))

(define (guess* p n last)
  (cond
    [(symbol=? (p n) 'higher) (guess* p (round (/ (+ (if (or (= last -1) (< last n)) HI last) n) 2)) n)]
    [(symbol=? (p n) 'lower)  (guess* p (round (/ (+ n (if (or (= last -1 ) (> last n)) LO last)) 2)) n)]
    [else true]))

(guess (oracle 17) 97)