Read till 3.11
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(load "util.scm")
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(display "\nex-3.9 - draw factorial evaluation model\n")
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(display "[see comments]\n")
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(define (factorial n)
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(if (= n 1)
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1
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(* n (factorial (- n 1)))))
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(define (factorial n)
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(fact-iter 1 1 n))
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(define (fact-iter product counter max-count)
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(if (> counter max-count)
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product
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(fact-iter (* counter product)
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(+ counter 1)
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max-count)))
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; Nothing to special. I drew this out in my 2020 notebook on page 203.
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; The drawing in the Scheme-Wiki is nice too:
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; http://community.schemewiki.org/?sicp-ex-3.9
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; RECURSIVE VERSION
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;
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; global ________________________
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; env | other var. |
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; ------->| factorial : * |
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; | | |
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; |_____________|_________|
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; | ^
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; | |
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; variables : n
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; body: (if (= n 1) 1 (* n (factorial (- n 1))))
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;
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; (factorial 6)
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;
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; _______ ^
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; E1 -->| n : 6 |___________| GLOBAL
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; -------
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; (* 6 (factorial 5))
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; _______ ^
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; E2 -->| n : 5 |___________| GLOBAL
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; -------
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; (* 5 (factorial 4))
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; _______ ^
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; E3 -->| n : 4 |___________| GLOBAL
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; -------
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; (* 4 (factorial 3))
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; _______ ^
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; E4 -->| n : 3 |___________| GLOBAL
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; -------
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; (* 3 (factorial 2))
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; _______ ^
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; E5 -->| n : 2 |___________| GLOBAL
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; -------
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; (* 2 (factorial 1))
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; _______ ^
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; E6 -->| n : 1 |___________| GLOBAL
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; -------
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; 1
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;
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; ITERATIVE VERSON
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;
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; global ___________________________________
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; env | other var. |
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; ------->| factorial : * |
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; | fact-iter : | * |
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; |_____________|_______________|____|
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; | ^ | ^
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; | | | |
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; | | variable : (product counter max-count)
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; | | body: (if (> counter max-count)
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; | | prod
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; | | (fact-iter (* counter product)
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; | | (+ counter 1)
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; | | max-count))
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; | |
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; variable: n
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; body: (fact-iter 1 1 n)
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;
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; (factorial 6)
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;
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; _______ ^
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; E1 -->| n : 6 |_____________| GLOBAL
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; -------
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; (fact-iter 1 1 n)
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;
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; E2 -->| product : 1 ^
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; | counter : 1 ___| GLOBAL
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; | max-count : 6
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; (fact-iter 1 2 6)
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;
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; E3 -->| product : 1 ^
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; | counter : 2 ____| GLOBAL
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; | max-count : 6
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; (fact-iter 2 3 6)
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;
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; E4 -->| product : 2 ^
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; | counter : 3 _____| GLOBAL
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; | max-count : 6
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; (fact-iter 6 4 6)
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;
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; E5 -->| product : 6 ^
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; | counter : 4 _____| GLOBAL
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; | max-count : 6
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; (fact-iter 24 5 6)
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;
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; E6 -->| product : 24 ^
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; | counter : 5 _____| GLOBAL
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; | max-count : 6
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; (fact-iter 120 6 6)
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;
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; E7 -->| product : 120 ^
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; | counter : 6 _____| GLOBAL
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; | max-count : 6
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; (fact-iter 720 7 6)
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;
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; E8 -->| product : 720 ^
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; | counter : 7 _____| GLOBAL
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; | max-count : 6
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; 720
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(display "\nex-3.10 - nested lambdas frames\n")
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(define (make-withdraw initial-amount)
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(let ((balance initial-amount))
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(lambda (amount)
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(display initial-amount) (newline)
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(display balance) (newline)
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(if (>= balance amount)
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(begin (set! balance (- balance amount))
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balance)
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"Insufficient funds"))))
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(define W1 (make-withdraw 100))
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(W1 20)
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(W1 20)
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(W1 20)
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; The let binding creates a second lambda procedure and consequently a
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; second frame. We can use display to show that both initial-amount and balance
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; are available via the first and second frame. However, only balance is
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; affected by calls to the return procedure, as we can see.
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; This is the ascii diagram from the Scheme community wiki:
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; global->| make-withdraw : * |
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; env. | W1 : * | |
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; -------|---^-----|---^-
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; | | | |
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; | | parameter: initial-mount
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; | | body: ((lambda (balance) ((...))) initial-mount)
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; | |
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; | _|___Frame_A__________
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; | | initial-mount : 100 |<- E0
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; | -^--------------------
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; | |
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; | _|__________Frame_B______
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; | | balance : initial-mount | <- E1
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; | -^-----------------------
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; | |
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; parameter: amount
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; body: (if (>= balance amount) ... )
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;
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; (W1 50)
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;
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; Set! will affect Frame B, initial-mount remains unchanged in Frame A.
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; _______________________
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; global->| make-withdraw : * |
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; env. | W1 : * | |
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; -------|---^-----|---^-
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; | | | |
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; | | parameter: initial-mount
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; | | body: ((lambda (balance) ((...))) initial-mount)
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; | |
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; | _|___Frame_A__________
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; | | initial-mount : 100 |<- E0
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; | -^--------------------
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; | |
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; | _|__________Frame_B___
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; | | balance : 50 | <- E1
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; | -^--------------------
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; | |
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; parameter: amount
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; body: (if (>= balance amount) ... )
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(display "\nex-3.11\n")
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; Relatively clear to me what is going on. Let's move on.
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(display "[see schemewiki]\n")
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@ -1,4 +0,0 @@
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(load "util.scm")
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(display "\nex-3.9\n")
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@ -0,0 +1,3 @@
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(load "util.scm")
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(display "\nex-3.12\n")
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