;; CMPU 145, Spring 2019
;; Lab 7

#lang racket
(include "asmt-helper.scm")
(include "lab6-solns.scm")

(header "Lab 7" "YOUR NAME")

(problem "Introduction")

;; GEN-AND-TEST
;; ------------
;; INPUTS: N, a non-negative integer
;;         GEN, a function of one input that is used to generate random
;;              instances of some event (e.g., tossing a die, dealing a card)
;;         TEST, a function that tests whether some given instance has some
;;              property (e.g., die > three, or card is a face card)
;; OUTPUT: The fraction of N random trials in which the randomly generated
;;         instances satisfied the TEST.
(define gen-and-test
  (lambda (n gen test [print #f])
    ;; COUNT is a counter variable
    (let ((count 0))
      ;; FOR executes its body N times
      (for ((i n))
        ;; Use (GEN) to generate a random instance;
        ;; Use TEST to determine whether that instance has the
        ;; desired property
        (let* ((rnd (gen))
               (result (test rnd)))
          (when print
            (printf "[~A: ~A] " rnd result))
          (when result
            ;; If it does, then destructively increment the counter!
            (set! count (+ count 1)))))
      ;; After the FOR loop finishes, return the fraction of the
      ;; trials that satisfied the TEST.
      (/ count n 1.0))))

;; TOSS-DIE
;; --------
;; INPUTS: None
;; OUTPUT: A randomly generated number from 1 to 6
(define toss-die
  (lambda ()
    (+ 1 (random 6))))

;; TEST-DIE
;; --------
;; INPUT: A number from 1 to 6
;; OUTPUT: #t if that number is either 5 or 6
(define test-die
  (lambda (die)
    (or (= die 5) (= die 6))))

(tester '(gen-and-test 1000 toss-die test-die))
(tester '(gen-and-test 10000 toss-die test-die))
(newline)


(problem "1. Pair of dice")

;; ...


(problem "2. Properties of natural numbers")

;; Generate a natural number between 0 and 99, represented as a list of 1s
(define random-nn
  (lambda ()
    (make-nn (random 100))))

(define test-claim1
  (lambda (nn)
    (equal? (nn-addn nn0 nn)
            nn)))

(tester '(gen-and-test 10 random-nn test-claim1))
(tester '(gen-and-test 100 random-nn test-claim1))

;; ...