(load "util.scm")

(display "\nex-3.9 - draw factorial evaluation model\n")
(display "[see comments]\n")

(define (factorial n)
  (if (= n 1)
      1
      (* n (factorial (- n 1)))))

(define (factorial n)
  (fact-iter 1 1 n))
(define (fact-iter product counter max-count)
  (if (> counter max-count)
      product
      (fact-iter (* counter product)
                 (+ counter 1)
                 max-count)))

; Nothing to special. I drew this out in my 2020 notebook on page 203.

; The drawing in the Scheme-Wiki is nice too:
; http://community.schemewiki.org/?sicp-ex-3.9

; RECURSIVE VERSION
;
; global  ________________________
; env     | other var.            |
; ------->| factorial : *         |
;         |             |         |
;         |_____________|_________|
;                       |     ^
;                       |     |
;                 variables : n
;                 body: (if (= n 1) 1 (* n (factorial (- n 1))))
;
; (factorial 6)
;
;          _______            ^
;   E1 -->| n : 6 |___________| GLOBAL
;          -------
;         (* 6 (factorial 5))
;          _______            ^
;   E2 -->| n : 5 |___________| GLOBAL
;          -------
;         (* 5 (factorial 4))
;          _______            ^
;   E3 -->| n : 4 |___________| GLOBAL
;          -------
;         (* 4 (factorial 3))
;          _______            ^
;   E4 -->| n : 3 |___________| GLOBAL
;          -------
;         (* 3 (factorial 2))
;          _______            ^
;   E5 -->| n : 2 |___________| GLOBAL
;          -------
;         (* 2 (factorial 1))
;          _______            ^
;   E6 -->| n : 1 |___________| GLOBAL
;          -------
;          1
;
; ITERATIVE VERSON
;
; global  ___________________________________
; env     | other var.                       |
; ------->| factorial : *                    |
;         | fact-iter : |               *    |
;         |_____________|_______________|____|
;                       |       ^       |  ^
;                       |       |       |  |
;                       |       |       variable : (product counter max-count)
;                       |       |       body: (if (> counter max-count)
;                       |       |                 prod
;                       |       |                 (fact-iter (* counter product)
;                       |       |                            (+ counter 1)
;                       |       |                            max-count))
;                       |       |
;                 variable: n
;                 body: (fact-iter 1 1 n)
;
; (factorial 6)
;
;          _______              ^
;   E1 -->| n : 6 |_____________| GLOBAL
;          -------
;          (fact-iter 1 1 n)
;
;   E2 -->| product   : 1       ^
;         | counter   : 1    ___| GLOBAL
;         | max-count : 6
;          (fact-iter 1 2 6)
;
;   E3 -->| product   : 1       ^
;         | counter   : 2   ____| GLOBAL
;         | max-count : 6
;          (fact-iter 2 3 6)
;
;   E4 -->| product   : 2       ^
;         | counter   : 3  _____| GLOBAL
;         | max-count : 6
;          (fact-iter 6 4 6)
;
;   E5 -->| product   : 6       ^
;         | counter   : 4  _____| GLOBAL
;         | max-count : 6
;          (fact-iter 24 5 6)
;
;   E6 -->| product   : 24      ^
;         | counter   : 5  _____| GLOBAL
;         | max-count : 6
;          (fact-iter 120 6 6)
;
;   E7 -->| product   : 120     ^
;         | counter   : 6  _____| GLOBAL
;         | max-count : 6
;          (fact-iter 720 7 6)
;
;   E8 -->| product   : 720     ^
;         | counter   : 7  _____| GLOBAL
;         | max-count : 6
;          720

(display "\nex-3.10 - nested lambdas frames\n")

(define (make-withdraw initial-amount)
  (let ((balance initial-amount))
    (lambda (amount)
      (display initial-amount) (newline)
      (display balance) (newline)
      (if (>= balance amount)
          (begin (set! balance (- balance amount))
                 balance)
          "Insufficient funds"))))

(define W1 (make-withdraw 100))

(W1 20)
(W1 20)
(W1 20)

; The let binding creates a second lambda procedure and consequently a
; second frame. We can use display to show that both initial-amount and balance
; are available via the first and second frame. However, only balance is
; affected by calls to the return procedure, as we can see.

; This is the ascii diagram from the Scheme community wiki:

; global->| make-withdraw : *     |
; env.    | W1 :  *         |     |
;          -------|---^-----|---^-
;                 |   |     |   |
;                 |   |     parameter: initial-mount
;                 |   |     body: ((lambda (balance) ((...))) initial-mount)
;                 |   |
;                 |  _|___Frame_A__________
;                 | | initial-mount : 100  |<- E0
;                 |  -^--------------------
;                 |   |
;                 |  _|__________Frame_B______
;                 | | balance : initial-mount | <- E1
;                 |  -^-----------------------
;                 |   |
;                 parameter: amount
;                 body: (if (>= balance amount) ... )
;
; (W1 50)
;
; Set! will affect Frame B, initial-mount remains unchanged in Frame A.
;          _______________________
; global->| make-withdraw : *     |
; env.    | W1 :  *         |     |
;          -------|---^-----|---^-
;                 |   |     |   |
;                 |   |     parameter: initial-mount
;                 |   |     body: ((lambda (balance) ((...))) initial-mount)
;                 |   |
;                 |  _|___Frame_A__________
;                 | | initial-mount : 100  |<- E0
;                 |  -^--------------------
;                 |   |
;                 |  _|__________Frame_B___
;                 | | balance : 50         | <- E1
;                 |  -^--------------------
;                 |   |
;                 parameter: amount
;                 body: (if (>= balance amount) ... )


(display "\nex-3.11\n")

; Relatively clear to me what is going on. Let's move on.
(display "[see schemewiki]\n")