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planet/SICP/slide08.tm

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<TeXmacs|2.1.2>
<style|<tuple|beamer|no-page-numbers|chinese|python>>
<\body>
<\hide-preamble>
<assign|dfn|<macro|x|<strong|<arg|x>>>>
</hide-preamble>
<\slideshow>
<\slide>
\;
\;
\;
\;
<doc-data|<doc-title|\<#96F6\>\<#57FA\>\<#7840\>SICP
08>|<doc-author|<author-data|<author-name|>>>|<doc-author|<author-data|<author-name|\<#6C88\>\<#6D6A\>\<#718A\>\<#732B\>\<#513F\>>>>|<doc-author|<author-data|<author-name|MathAgape>>>|<doc-subtitle|\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>>>
</slide>
<\slide>
<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>8\<#8BFE\>>
<\wide-tabular>
<tformat|<cwith|2|-1|1|-1|cell-height|40px>|<cwith|2|-1|1|-1|cell-vmode|exact>|<table|<row|<\cell>
<very-large|<\sectional-normal-bold>
\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>\<#5BFC\>\<#5F15\>
</sectional-normal-bold>>
</cell>|<\cell>
<\very-large>
<strong|Introduction to Data Abstraction>
</very-large>
</cell>>|<row|<\cell>
\<#5B9E\>\<#4F8B\>\<#FF1A\>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>
</cell>|<\cell>
Example: Arithmetic Operations for Rational Numbers
</cell>>|<row|<\cell>
\<#62BD\>\<#8C61\>\<#5C42\>\<#7EA7\>
</cell>|<\cell>
Abstraction Barriers
</cell>>|<row|<\cell>
\<#6570\>\<#636E\>\<#610F\>\<#5473\>\<#7740\>\<#4EC0\>\<#4E48\>
</cell>|<\cell>
What Is Meant by Data?
</cell>>>>
</wide-tabular>
\;
<strong|\<#7F16\>\<#7A0B\>\<#7684\>\<#57FA\>\<#672C\>\<#539F\>\<#7406\>\<#662F\>\<#5BF9\>\<#6570\>\<#636E\>\<#548C\>\<#8BA1\>\<#7B97\>\<#7684\>\<#7EC4\>\<#5408\>\<#548C\>\<#62BD\>\<#8C61\>>
\;
\;
\;
</slide>
<\slide>
<tit|\<#6709\>\<#7406\>\<#6570\>\<#4E0E\>\<#5206\>\<#5F0F\>>
\<#9884\>\<#5B9A\>\<#4E49\>\<#51FD\>\<#6570\>\<#FF1A\>\<#5206\>\<#5F0F\>\<#3001\>\<#5206\>\<#5F0F\>\<#663E\>\<#3001\>\<#5206\>\<#5B50\>\<#3001\>\<#5206\>\<#6BCD\>
<\with|par-columns|2>
<\session|scheme|default>
<\folded-io|Scheme] >
(define \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\>
1 2))
<|folded-io>
(1 . 2)
</folded-io>
<\folded-io|Scheme] >
(define \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\>
1 3))
<|folded-io>
(1 . 3)
</folded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5B50\> \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>)
<|unfolded-io>
1
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#6BCD\> \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>)
<|unfolded-io>
2
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>)
<|unfolded-io>
<text|<frac|1|3>>
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>)
<|unfolded-io>
<text|<frac|1|2>>
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
</with>
<\itemize>
<item>\<#6784\>\<#9020\>\<#51FD\>\<#6570\>\<#FF1A\>\<#5206\>\<#5F0F\>
<item>\<#9009\>\<#62E9\>\<#51FD\>\<#6570\>\<#FF1A\>\<#5206\>\<#5B50\>\<#3001\>\<#5206\>\<#6BCD\>
<item>\<#663E\>\<#793A\>\<#51FD\>\<#6570\>\<#FF1A\>\<#5206\>\<#5F0F\>\<#663E\>
\<#FF08\>\<#548C\>\<#4EBA\>\<#7C7B\>\<#505A\>\<#4EA4\>\<#4E92\>\<#FF09\>
</itemize>
</slide>
<\slide>
<tit|\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>>
<\with|par-columns|2>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#52A0\>
\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
<|unfolded-io>
<text|<frac|5|6>>
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#51CF\>
\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
<|unfolded-io>
<text|<frac|1|6>>
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#4E58\>
\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
<|unfolded-io>
<text|<frac|1|6>>
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#9664\>
\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
<|unfolded-io>
<text|<frac|3|2>>
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
</with>
\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>\<#51FD\>\<#6570\>\<#FF1A\>\<#5206\>\<#5F0F\>\<#52A0\>,\<#5206\>\<#5F0F\>\<#51CF\>,\<#5206\>\<#5F0F\>\<#4E58\>,\<#5206\>\<#5F0F\>\<#9664\>
</slide>
<\slide>
<tit|\<#5206\>\<#5F0F\>\<#52A0\>>
<\equation*>
<frac|n<rsub|1>|d<rsub|1>>+<frac|n<rsub|<rsub|2>>|d<rsub|2>>=<frac|n<rsub|1>*d<rsub|2>+n<rsub|2>*d<rsub|1>|d<rsub|1>*d<rsub|2>>
</equation*>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define (\<#5206\>\<#5F0F\>\<#52A0\> x y)
\ \ (let* ((n1 (\<#5206\>\<#5B50\> x))
\ \ \ \ \ \ \ \ \ (d1 (\<#5206\>\<#6BCD\> x))
\ \ \ \ \ \ \ \ \ (n2 (\<#5206\>\<#5B50\> y))
\ \ \ \ \ \ \ \ \ (d2 (\<#5206\>\<#6BCD\> y)))
\ \ \ \ (\<#5206\>\<#5F0F\> (+ (* n1 d2) (* n2 d1))
\ \ \ \ \ \ \ \ \ \ (* d1 d2))))
<|unfolded-io>
\<#5206\>\<#5F0F\>\<#52A0\>
</unfolded-io>
<\folded-io|Scheme] >
(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#52A0\>
(\<#5206\>\<#5F0F\> 1 2) (\<#5206\>\<#5F0F\> 1 4)))
<|folded-io>
<text|<frac|6|8>>
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#62BD\>\<#8C61\>\<#5C42\>\<#7EA7\>>
<strong|\<#5C06\>\<#63A5\>\<#53E3\>\<#4E0E\>\<#5B9E\>\<#73B0\>\<#7684\>\<#9694\>\<#79BB\>>
<\itemize>
<item>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#4F7F\>\<#7528\>\<#8005\>
<\itemize>
<item>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>
\<#FF08\><with|color|#afa|\<#7528\>\<#6237\>\<#81EA\>\<#5B9A\>\<#4E49\>\<#7684\>\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>>\<#FF09\>
<\itemize>
<item>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#6784\>\<#9020\>\<#4E0E\>\<#9009\>\<#62E9\>
\<#FF08\><with|color|green|\<#7528\>\<#6237\>\<#81EA\>\<#5B9A\>\<#4E49\>\<#7684\>\<#6570\>\<#636E\>\<#7ED3\>\<#6784\>>\<#FF09\>
<\itemize>
<item>\<#6709\>\<#5E8F\>\<#5BF9\> pair
\<#FF08\><with|color|dark green|\<#7528\>\<#6237\>\<#81EA\>\<#5B9A\>\<#4E49\>\<#7684\>\<#6570\>\<#636E\>\<#7ED3\>\<#6784\>>\<#FF09\>
<\itemize>
<item>\<#57FA\>\<#7840\>\<#6570\>\<#636E\>\<#7ED3\>\<#6784\>\<#FF1A\>\<#94FE\>\<#8868\>\<#FF08\><strong|Scheme\<#8BED\>\<#8A00\>\<#5B9A\>\<#4E49\>>\<#FF09\>
<\itemize>
<item><text-dots>
<\itemize>
<item>\<#5185\>\<#5B58\>\<#3001\>\<#5BC4\>\<#5B58\>\<#5668\>\<#3001\>\<#6307\>\<#4EE4\>\<#4E2D\>\<#7684\>\<#5B9E\>\<#73B0\>\<#FF08\><todo|Scheme\<#89E3\>\<#91CA\>\<#5668\>>\<#FF09\>
</itemize>
</itemize>
</itemize>
</itemize>
</itemize>
</itemize>
</itemize>
<\itemize>
<item>\<#86CB\>\<#631E\>\<#FF08\>\<#4E0D\>\<#7528\>\<#7BA1\>\<#73B0\>\<#6709\>\<#9E21\>\<#8FD8\>\<#662F\>\<#5148\>\<#6709\>\<#86CB\>\<#FF09\>
<\itemize>
<item>\<#9E21\>\<#3001\>\<#86CB\>
</itemize>
</itemize>
\;
</slide>
<\slide>
<tit|\<#6709\>\<#5E8F\>\<#5BF9\>\<#7684\>\<#62BD\>\<#8C61\>>
<\description>
<item*|pair>\<#6784\>\<#9020\>\<#5668\>\<#FF1A\>\<#63D0\>\<#4F9B\>\<#4E24\>\<#4E2A\>\<#53C2\>\<#6570\>\<#FF0C\>\<#6784\>\<#9020\>\<#4E00\>\<#4E2A\>\<#6709\>\<#5E8F\>\<#5BF9\>
<item*|pair.x1>\<#9009\>\<#62E9\>\<#5668\>\<#FF1A\>\<#6709\>\<#5E8F\>\<#5BF9\>\<#4E2D\>\<#7684\>\<#7B2C\>\<#4E00\>\<#4E2A\>\<#5143\>\<#7D20\>
<item*|pair.x2>\<#9009\>\<#62E9\>\<#5668\>\<#FF1A\>\<#6709\>\<#5E8F\>\<#5BF9\>\<#4E2D\>\<#7684\>\<#7B2C\>\<#4E8C\>\<#4E2A\>\<#5143\>\<#7D20\>
</description>
<\session|scheme|default>
<\folded-io|Scheme] >
(define (pair x1 x2) (cons x1 x2))
<|folded-io>
pair
</folded-io>
<\folded-io|Scheme] >
(define (pair.x1 p) (car p))
<|folded-io>
pair.x1
</folded-io>
<\folded-io|Scheme] >
(define (pair.x2 p) (cdr p))
<|folded-io>
pair.x2
</folded-io>
<\folded-io|Scheme] >
(pair 1 2)
<|folded-io>
(1 . 2)
</folded-io>
<\folded-io|Scheme] >
(pair.x1 (pair 3 4))
<|folded-io>
3
</folded-io>
<\folded-io|Scheme] >
(pair.x2 (pair "\<#7236\>\<#4EB2\>" "\<#6BCD\>\<#4EB2\>"))
<|folded-io>
\<#6BCD\>\<#4EB2\>
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#57FA\>\<#7840\>\<#6570\>\<#636E\>\<#7ED3\>\<#6784\>\<#FF1A\>\<#94FE\>\<#8868\>>
<\description>
<item*|()>\<#6784\>\<#9020\>\<#5668\>\<#FF1A\>\<#8868\>\<#793A\>\<#7A7A\>\<#94FE\>\<#8868\>
<item*|cons>\<#6784\>\<#9020\>\<#5668\>\<#FF1A\>\<#63D0\>\<#4F9B\>\<#4E00\>\<#4E2A\>\<#5143\>\<#7D20\>\<#548C\>\<#4E00\>\<#4E2A\>\<#94FE\>\<#8868\>\<#FF0C\>\<#5C06\>\<#4E24\>\<#8005\>\<#7EC4\>\<#5408\>\<#6210\>\<#94FE\>\<#8868\>\<#3002\>
<item*|car>\<#9009\>\<#62E9\>\<#5668\>\<#FF1A\>\<#53D6\>\<#51FA\>\<#94FE\>\<#8868\>\<#5934\>\<#90E8\>\<#7684\>\<#5143\>\<#7D20\>\<#3002\>
<item*|cdr>\<#9009\>\<#62E9\>\<#5668\>\<#FF1A\>\<#79FB\>\<#9664\>\<#94FE\>\<#8868\>\<#5934\>\<#90E8\>\<#4E4B\>\<#540E\>\<#FF0C\>\<#5269\>\<#4E0B\>\<#7684\>\<#5143\>\<#7D20\>\<#6309\>\<#7167\>\<#539F\>\<#6765\>\<#7684\>\<#987A\>\<#5E8F\>\<#7EC4\>\<#5408\>\<#6210\>\<#7684\>\<#94FE\>\<#8868\>\<#3002\>
<item*|list>\<#6784\>\<#9020\>\<#5668\>\<#FF1A\>\<#63D0\>\<#4F9B\>\<#4E00\>\<#7EC4\>\<#5143\>\<#7D20\>\<#FF0C\>\<#53EF\>\<#4EE5\>\<#5C06\>\<#8FD9\>\<#4E00\>\<#7EC4\>\<#5143\>\<#7D20\>\<#7EC4\>\<#5408\>\<#6210\>\<#94FE\>\<#8868\>\<#3002\>
</description>
<\session|scheme|default>
<\folded-io|Scheme] >
(list 1 2 3 4) # (cons 1 (cons 2 (cons 3 (cons 4 ()))))
<|folded-io>
(1 2 3 4)
</folded-io>
<\folded-io|Scheme] >
(car (list 1 2 3 4))
<|folded-io>
1
</folded-io>
<\folded-io|Scheme] >
(cdr (list 1 2 3 4))
<|folded-io>
(2 3 4)
</folded-io>
<\folded-io|Scheme] >
(car (list ))
<|folded-io>
<errput|car argument, (), is nil but should be a pair>
</folded-io>
<\folded-io|Scheme] >
(eq? (list ) (list ))
<|folded-io>
#t
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>>
\<#901A\>\<#8FC7\>\<#5B9A\>\<#4E49\>\<#4E00\>\<#7EC4\><strong|\<#903B\>\<#8F91\>\<#81EA\>\<#6D3D\>>\<#7684\>\<#9009\>\<#62E9\>\<#51FD\>\<#6570\>\<#548C\>\<#6784\>\<#9020\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>\<#3002\>
\<#6BD4\>\<#5982\><person|Peano>\<#81EA\>\<#7136\>\<#6570\>\<#516C\>\<#7406\>\<#FF1A\>
<\axiom>
<label|axiom:zero><math|0\<in\>\<bbb-N\>>.
</axiom>
<\axiom>
<label|axiom:successor is a function>\<#82E5\><math|x\<in\>\<bbb-N\>>\<#FF0C\>\<#5219\><math|x>\<#6709\>\<#4E14\>\<#53EA\>\<#6709\>\<#4E00\>\<#4E2A\>\<#540E\>\<#7EE7\><math|x<rsup|<rprime|'>>\<in\>\<bbb-N\>>.
</axiom>
<\axiom>
<label|axiom:successor is non-zero>\<#5BF9\>\<#4EFB\>\<#610F\><math|x\<in\>\<bbb-N\>,x<rsup|<rprime|'>>\<neq\>0>.
</axiom>
<\axiom>
<label|axiom:successor is injective>\<#5BF9\>\<#4EFB\>\<#610F\><math|x<rsub|1>,x<rsub|2>\<in\>\<bbb-N\>>\<#FF0C\>\<#82E5\><math|x<rsub|1>\<neq\>x<rsub|2>>\<#FF0C\>\<#5219\><math|x<rsub|1><rsup|<rprime|'>>\<neq\>x<rsub|2><rsup|<rprime|'>>>.
</axiom>
<\axiom>
<label|axiom:induction>\<#8BBE\><math|\<bbb-M\>\<subseteq\>\<bbb-N\>>.
\<#82E5\><math|0\<in\>\<bbb-M\>>\<#FF0C\>\<#4E14\>\<#5F53\><math|x\<in\>\<bbb-M\>>\<#65F6\>\<#4E5F\>\<#6709\><math|x<rsup|<rprime|'>>\<in\>\<bbb-M\>>\<#FF0C\>\<#5219\><math|\<bbb-M\>=\<bbb-N\>>.
</axiom>
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#81EA\>\<#7136\>\<#6570\>\<#8FD9\>\<#79CD\>\<#6570\>\<#636E\>>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define \<#96F6\> (list ))
<|unfolded-io>
()
</unfolded-io>
<\unfolded-io|Scheme] >
(define (\<#540E\>\<#7EE7\> x) (cons (list ) x))\
<|unfolded-io>
\<#540E\>\<#7EE7\>
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#540E\>\<#7EE7\> \<#96F6\>)
<|unfolded-io>
(())
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#540E\>\<#7EE7\> (\<#540E\>\<#7EE7\> \<#96F6\>))
<|unfolded-io>
(() ())
</unfolded-io>
<\unfolded-io|Scheme] >
(\<#540E\>\<#7EE7\> (\<#540E\>\<#7EE7\> (\<#540E\>\<#7EE7\>
\<#96F6\>)))
<|unfolded-io>
(() () ())
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|cons/car/cdr\<#7684\>\<#5176\>\<#4E2D\>\<#4E00\>\<#79CD\>\<#5B9E\>\<#73B0\>>
<\session|scheme|default>
<\folded-io|Scheme] >
(define (cons2 x y)
\ \ (define (dispatch m)
\ \ \ \ (cond ((= m 0) x)
\ \ \ \ \ \ \ \ \ \ ((= m 1) y)
\ \ \ \ \ \ \ \ \ \ (else (error "Argument not 0 or 1 -- CONS"
m))))
\ \ dispatch)
<|folded-io>
cons2
</folded-io>
<\folded-io|Scheme] >
(define (car2 z) (z 0))
<|folded-io>
car2
</folded-io>
<\folded-io|Scheme] >
(define (cdr2 z) (z 1))
<|folded-io>
cdr2
</folded-io>
<\folded-io|Scheme] >
(car2 (cons2 1 2))
<|folded-io>
1
</folded-io>
<\folded-io|Scheme] >
(cdr2 (cons2 1 2))
<|folded-io>
2
</folded-io>
<\folded-io|Scheme] >
(car2 (cons2 1 (cons2 2 (cons2 3 ()))))
<|folded-io>
1
</folded-io>
<\folded-io|Scheme] >
(car2 (cdr2 (cons2 1 (cons2 2 (cons2 3 ())))))
<|folded-io>
2
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#603B\>\<#7ED3\>>
<\itemize>
<item>\<#4E3A\>\<#4EC0\>\<#4E48\>\<#9700\>\<#8981\>\<#62BD\>\<#8C61\>\<#5C42\>\<#7EA7\>
<item>\<#5982\>\<#4F55\>\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>
<item>Schem\<#539F\>\<#8BED\> (R7RS small)
<\itemize>
<item>\<#94FE\>\<#8868\>
<\itemize>
<item>\<#6709\>\<#5E8F\>\<#5BF9\>
<\itemize>
<item>\<#5206\>\<#5F0F\>
<\itemize>
<item>\<#6709\>\<#7406\>\<#6570\>
</itemize>
</itemize>
</itemize>
</itemize>
</itemize>
</slide>
</slideshow>
</body>
<\initial>
<\collection>
<associate|info-flag|minimal>
<associate|marked-color|pastel yellow>
<associate|page-border|attached>
<associate|page-medium|paper>
<associate|page-offset|1>
<associate|page-packet|2>
<associate|page-screen-margin|false>
<associate|par-columns|1>
<associate|preamble|false>
</collection>
</initial>
<\references>
<\collection>
<associate|axiom:induction|<tuple|5|?|slide07.tm>>
<associate|axiom:successor is a function|<tuple|2|?|slide07.tm>>
<associate|axiom:successor is injective|<tuple|4|?|slide07.tm>>
<associate|axiom:successor is non-zero|<tuple|3|?|slide07.tm>>
<associate|axiom:zero|<tuple|1|?|slide07.tm>>
</collection>
</references>
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