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Read till 3.11

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Felix Martin 2020-12-16 12:05:38 -05:00
parent 8709aba590
commit 5366074974
3 changed files with 198 additions and 4 deletions
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ex-3_09-11.scm Normal file
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(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")

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(load "util.scm")
(display "\nex-3.9\n")

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(load "util.scm")
(display "\nex-3.12\n")