mirror of https://gitee.com/XmacsLabs/planet.git
零基础SICP08
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<TeXmacs|2.1.2>
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<style|<tuple|generic|no-page-numbers|chinese>>
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<\body>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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(define (make-rat n d) (cons n d))
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<|unfolded-io>
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make-rat
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (numer x) (car x))
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<|unfolded-io>
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numer
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (denom x) (cdr x))
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<|unfolded-io>
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denom
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\> n d) (make-rat n d))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5B50\> x) (numer x))
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<|unfolded-io>
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\<#5206\>\<#5B50\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#6BCD\> x) (denom x))
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<|unfolded-io>
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\<#5206\>\<#6BCD\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f z var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#5B50\>"))))
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<|unfolded-io>
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("f z tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#5F0F\>"))))
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<|unfolded-io>
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("f s tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f m var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#6BCD\>"))))
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<|unfolded-io>
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("f m tab")
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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<\with|prog-scripts|scheme>
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(define (add-rat x y)
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\ \ (make-rat (+ (* (numer x) (denom y))
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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (* (numer y) (denom x)))
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\ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
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</with>
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<|unfolded-io>
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add-rat
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (sub-rat x y)
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\ \ (make-rat (- (* (numer x) (denom y))
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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (* (numer y) (denom x)))
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\ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
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<|unfolded-io>
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sub-rat
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (mul-rat x y)
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\ \ (make-rat (* (numer x) (numer y))
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\ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
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<|unfolded-io>
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mul-rat
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (div-rat x y)
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\ \ (make-rat (* (numer x) (denom y))
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\ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (numer y))))
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<|unfolded-io>
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div-rat
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (equal-rat? x y)
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\ \ (= (* (numer x) (denom y))
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\ \ \ \ \ (* (numer y) (denom x))))
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<|unfolded-io>
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equal-rat?
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s + var" (insert (utf8-\<gtr\>cork
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"\<#5206\>\<#5F0F\>\<#52A0\>"))))
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<|unfolded-io>
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("f s + tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s - var" (insert (utf8-\<gtr\>cork
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"\<#5206\>\<#5F0F\>\<#51CF\>"))))
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<|unfolded-io>
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("f s - tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s * var" (insert (utf8-\<gtr\>cork
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"\<#5206\>\<#5F0F\>\<#4E58\>"))))
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<|unfolded-io>
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("f s * tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s / var" (insert (utf8-\<gtr\>cork
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"\<#5206\>\<#5F0F\>\<#9664\>"))))
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<|unfolded-io>
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("f s / tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(kbd-map ("f s x var" (insert (utf8-\<gtr\>cork
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"\<#5206\>\<#5F0F\>\<#663E\>"))))
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<|unfolded-io>
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("f s x tab")
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\>\<#52A0\> x y) (add-rat x y))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>\<#52A0\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\>\<#51CF\> x y) (sub-rat x y))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>\<#51CF\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\>\<#4E58\> x y) (mul-rat x y))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>\<#4E58\>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\>\<#9664\> x y) (div-rat x y))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>\<#9664\>
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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(define x (cons 1 2))
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<|unfolded-io>
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(1 . 2)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(car x)
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<|unfolded-io>
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1
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(cdr x)
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<|unfolded-io>
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2
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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(define x (cons 1 2))
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<|unfolded-io>
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(1 . 2)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define y (cons 3 4))
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<|unfolded-io>
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(3 . 4)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define z (cons x y))
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<|unfolded-io>
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((1 . 2) 3 . 4)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(car (car z))
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<|unfolded-io>
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1
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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\;
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<\session|scheme|default>
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<\input|Scheme] >
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(define (print-rat x)
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\ \ (newline)
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\ \ (display (numer x))
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\ \ (display "/")
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\ \ (display (denom x)))
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</input>
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<\unfolded-io|Scheme] >
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(define (\<#5206\>\<#5F0F\>\<#663E\> x)
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\ \ (stree-\<gtr\>tree `(frac ,(\<#5206\>\<#5B50\> x)
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,(\<#5206\>\<#6BCD\> x))))
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<|unfolded-io>
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\<#5206\>\<#5F0F\>\<#663E\>
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|scheme|default>
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<\unfolded-io|Scheme] >
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(define \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\> 1 2))
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<|unfolded-io>
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(1 . 2)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(define \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\> 1 3))
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<|unfolded-io>
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(1 . 3)
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>)
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<|unfolded-io>
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<text|<frac|1|3>>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>)
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<|unfolded-io>
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<text|<frac|1|2>>
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</unfolded-io>
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<\folded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#52A0\>
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\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
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\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
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<|folded-io>
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<text|<frac|5|6>>
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</folded-io>
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<\unfolded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#51CF\>
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\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
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\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
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<|unfolded-io>
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<text|<frac|1|6>>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#4E58\>
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\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
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\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
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<|unfolded-io>
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<text|<frac|1|6>>
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</unfolded-io>
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<\unfolded-io|Scheme] >
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(\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#9664\>
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\<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
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\<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
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<|unfolded-io>
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<text|<frac|3|2>>
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</unfolded-io>
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<\input|Scheme] >
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\;
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</input>
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</session>
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<\session|scheme|default>
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<\input>
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Scheme]\
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<|input>
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(define (make-rat n d)
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\ \ (let ((g (gcd n d)))
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\ \ \ \ (cons (/ n g) (/ d g))))
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</input>
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</session>
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<\session|scheme|default>
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<\input|Scheme] >
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(print-rat (add-rat one-third one-third))
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</input>
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<\input|Scheme] >
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\;
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</input>
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</session>
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</body>
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<\initial>
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<\collection>
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<associate|page-medium|papyrus>
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<associate|page-screen-margin|false>
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</collection>
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</initial>
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<\references>
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<\collection>
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<associate|auto-1|<tuple|?|?|code07.tm>>
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<associate|auto-2|<tuple|?|?|code07.tm>>
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<associate|auto-3|<tuple|?|?|code07.tm>>
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</collection>
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</references>
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<\auxiliary>
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<\collection>
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<\associate|toc>
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<with|par-left|<quote|1tab>|2.1.1 <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-1>>
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<with|par-left|<quote|1tab>|2.1.2 <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-2>>
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||||||
|
<with|par-left|<quote|1tab>|2.1.3 <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
|
||||||
|
<no-break><pageref|auto-3>>
|
||||||
|
</associate>
|
||||||
|
</collection>
|
||||||
|
</auxiliary>
|
||||||
|
|
@ -24,6 +24,12 @@
|
||||||
<item>\<#76EE\>\<#6807\>\<#90AE\>\<#7BB1\>\<#FF1A\>shenda AT ustc.edu
|
<item>\<#76EE\>\<#6807\>\<#90AE\>\<#7BB1\>\<#FF1A\>shenda AT ustc.edu
|
||||||
</itemize>
|
</itemize>
|
||||||
|
|
||||||
|
<item>\<#7B2C\>8\<#8BFE\>\<#FF1A\>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>
|
||||||
|
|
||||||
|
\<#8BFE\>\<#4EF6\>\<#FF1A\><hlink|\<#5E7B\>\<#706F\>\<#7247\>08|slide08.tm>
|
||||||
|
|
||||||
|
\<#4EE3\>\<#7801\>\<#FF1A\><hlink|\<#4EE3\>\<#7801\>\<#6E05\>\<#5355\>08|code08.tm>
|
||||||
|
|
||||||
<item>\<#7B2C\>7\<#8BFE\>\<#FF1A\>\<#9AD8\>\<#9636\>\<#51FD\>\<#6570\>
|
<item>\<#7B2C\>7\<#8BFE\>\<#FF1A\>\<#9AD8\>\<#9636\>\<#51FD\>\<#6570\>
|
||||||
|
|
||||||
\<#7EC3\>\<#4E60\>\<#FF1A\>\<#8BFE\>\<#540E\>\<#4E60\>\<#9898\>\<#7684\>\<#6570\>\<#5B66\>\<#542B\>\<#91CF\>\<#6BD4\>\<#8F83\>\<#91CD\>\<#FF0C\>\<#53EF\>\<#81EA\>\<#884C\>\<#9009\>\<#62E9\>\<#4E00\>\<#4E9B\>\<#4E60\>\<#9898\>\<#7EC3\>\<#4E60\>\<#4E00\>\<#4E0B\>
|
\<#7EC3\>\<#4E60\>\<#FF1A\>\<#8BFE\>\<#540E\>\<#4E60\>\<#9898\>\<#7684\>\<#6570\>\<#5B66\>\<#542B\>\<#91CF\>\<#6BD4\>\<#8F83\>\<#91CD\>\<#FF0C\>\<#53EF\>\<#81EA\>\<#884C\>\<#9009\>\<#62E9\>\<#4E00\>\<#4E9B\>\<#4E60\>\<#9898\>\<#7EC3\>\<#4E60\>\<#4E00\>\<#4E0B\>
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,546 @@
|
||||||
|
<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>
|
||||||
Loading…
Reference in New Issue