3.1 Assignment and Local State

Exercise 3.1

(define (make-accumulator value)
  (lambda (num)
    (begin (set! value (+ value num))
           value)))

Exercise 3.2

(define (make-monitored f)
  (let ((counter 0))
    (lambda (arg)
      (if (eq? arg 'how-many-calls?)
          counter
          (begin (set! counter (inc counter))
                 (f arg))))))

Exercise 3.3

(define (make-account balance password)
  (lambda (given-password method)
    (if (eq? given-password password)
        (lambda (amount)
          (cond ((eq? method 'deposit)
                 (begin (set! balance (+ balance amount))
                        balance))
                ((eq? method 'withdraw)
                 (if (< balance amount)
                     "Insufficient funds"
                     (begin (set! balance (- balance amount))
                            balance)))))
        (lambda (amount) "Incorrect password"))))

Exercise 3.4

(define (make-account balance password)
  (let ((incorrect-times 0))
    (lambda (given-password method)
      (if (eq? given-password password)
          (lambda (amount)
            (cond ((eq? method 'deposit)
                  (begin (set! balance (+ balance amount))
                          balance))
                  ((eq? method 'withdraw)
                  (if (< balance amount)
                      "Insufficient funds"
                      (begin (set! balance (- balance amount))
                              balance)))))
          (begin (set! incorrect-times (inc incorrect-times))
                 (if (>= incorrect-times 7) (call-the-cops))
                 (lambda (amount) "Incorrect password"))))))

Exercise 3.5

(define (random-in-range low high)
  (+ (random (- high low)) low))

(define (estimate-integral pred x1 x2 y1 y2 trials)
  (define (experiment)
    (pred (random-in-range x1 x2)
          (random-in-range y1 y2)))
  (let ((ratio (monte-carlo trials experiment)))
    (* ratio (- x2 x1) (- y2 y1))))

(define (in-unit-circle? x y)
  (< (+ (* x x) (* y y)) 1.0))

(define (estimate-pi)
  (estimate-integral in-unit-circle?
                     -1.0 1.0 -1.0 1.0
                     1000000)

Exercise 3.6

(define (rand action)
  (let ((x rand-init))
    (define (rand-generate)
      (set! x (rand-update x))
      x)
    (define (rand-reset new-random-init)
      (set! x new-rand-init))
    (cond ((eq? action 'generate)
           (rand-generate))
          ((eq? action 'reset)
           rand-reset))))))

Exercise 3.7

Making no modifications to my solution to Exercise 3.3, I wrote make-joint as a “wrap” around the original account, and if joint-password is correct, it will provide the original password.

(define (make-joint account password joint-password)
  (lambda (given-password method)
    (if (eq? given-password joint-password)
        (account password method)
        (account given-password method))))

Exercise 3.8

(define (f-obj)
  (let ((last-x 0))
    (lambda (x)
      (let ((result last-x))
      (set! last-x x)
      result))))

(define f (f-obj))

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