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planet/SICP/slide07.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
07>|<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|\<#7528\>\<#9AD8\>\<#9636\>\<#51FD\>\<#6570\>\<#505A\>\<#62BD\>\<#8C61\>>>
</slide>
<\slide>
<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>7\<#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>
\<#7528\>\<#9AD8\>\<#9636\>\<#51FD\>\<#6570\>\<#505A\>\<#62BD\>\<#8C61\>
</sectional-normal-bold>>
</cell>|<\cell>
<\very-large>
<strong|Formulating Abstractions with Higher-Order Procedures>
</very-large>
</cell>>|<row|<\cell>
\<#5728\>\<#53C2\>\<#6570\>\<#4E2D\>\<#4F20\>\<#9012\>\<#51FD\>\<#6570\>\<#503C\>
</cell>|<\cell>
Procedures as Arguments
</cell>>|<row|<\cell>
\<#7528\><scm|lambda>\<#6784\>\<#9020\>\<#533F\>\<#540D\>\<#51FD\>\<#6570\>
</cell>|<\cell>
Constructing Procedures Using <scm|lambda>
</cell>>|<row|<\cell>
\<#51FD\>\<#6570\>\<#4F5C\>\<#4E3A\>\<#4E00\>\<#822C\>\<#6027\>\<#7684\>\<#65B9\>\<#6CD5\>
</cell>|<\cell>
Procedures as General Methods
</cell>>|<row|<\cell>
\<#5728\>\<#51FD\>\<#6570\>\<#4E2D\>\<#8FD4\>\<#56DE\>\<#51FD\>\<#6570\>\<#503C\>
</cell>|<\cell>
Procedures as Returned Values
</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|\<#5728\>\<#53C2\>\<#6570\>\<#4E2D\>\<#4F20\>\<#9012\>\<#51FD\>\<#6570\>\<#503C\>>
<\with|par-columns|2>
<\equation*>
<big|sum><rsub|i=a><rsup|b>f<around*|(|i|)>=f<around*|(|a|)>+\<cdots\>+f<around*|(|b|)>
</equation*>
<\equation*>
<big|sum><rsup|100><rsub|i=1>i=1+2+\<cdots\>+100=5050<rsup|>
</equation*>
<\equation*>
lim<rsub|n\<rightarrow\>+\<infty\>><big|sum><rsup|n><rsub|i=1><frac|1|n*<around*|(|n+2|)>>=<frac|\<pi\>|8>
</equation*>
<\session|scheme|default>
<\folded-io|Scheme] >
(define (sum f a next b)
\ \ (if (\<gtr\> a b)
\ \ \ \ \ \ 0
\ \ \ \ \ \ (+ (f a)
\ \ \ \ \ \ \ \ \ (sum f (next a) next b))))
<|folded-io>
sum
</folded-io>
<\folded-io|Scheme] >
(define (inc n) (+ n 1))
<|folded-io>
inc
</folded-io>
<\folded-io|Scheme] >
(define (same x) x)
<|folded-io>
same
</folded-io>
<\folded-io|Scheme] >
\;
<|folded-io>
5050
</folded-io>
</session>
</with>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(sum <with|color|red|same> 1 <with|color|red|inc> 100)
<|unfolded-io>
5050
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
\;
</slide>
<\slide>
<tit|\<#7528\><scm|lambda>\<#6784\>\<#9020\>\<#533F\>\<#540D\>\<#51FD\>\<#6570\>>
<\equation*>
<big|sum><rsup|10><rsub|i=1>i<rsup|2>=1<rsup|2>+2<rsup|2>+\<cdots\>+10<rsup|2><rsup|>
</equation*>
\;
<\session|scheme|default>
<\folded-io|Scheme] >
(sum (lambda (x) (* x x)) 1 <with|color|red|inc> 10)
<|folded-io>
385
</folded-io>
<\input|Scheme] >
\;
</input>
</session>
\;
<\equation*>
1<rsup|2>+3<rsup|2>+5<rsup|2>+7<rsup|2>+9<rsup|2>
</equation*>
<\session|scheme|default>
<\folded-io|Scheme] >
(sum (lambda (x) (* x x)) 1 (lambda (x) (+ x 2)) 10)
<|folded-io>
165
</folded-io>
<\unfolded-io|Scheme] >
(sum (lambda (x) (* x x)) 2 (lambda (x) (+ x 2)) 10)
<|unfolded-io>
220
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#7528\><scm|let>\<#521B\>\<#5EFA\>\<#5C40\>\<#90E8\>\<#53D8\>\<#91CF\>>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define (fib-once pair)
\ \ (let ((a (first pair))
\ \ \ \ \ \ \ \ (b (second pair)))
\ \ \ (list b (+ a b))))
<|unfolded-io>
fib-once
</unfolded-io>
<\unfolded-io|Scheme] >
(fib-once (fib-once (list 1 1)))
<|unfolded-io>
(2 3)
</unfolded-io>
<\input|Scheme] >
\;
</input>
</session>
\;
</slide>
<\slide>
<tit|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#533A\>\<#95F4\>\<#6298\>\<#534A\>\<#6CD5\>>
<\gr-screen>
<with|gr-mode|<tuple|edit|line>|gr-frame|<tuple|scale|1cm|<tuple|-0.119993gw|1gh>>|gr-geometry|<tuple|geometry|1gpar|1gpag|axis>|gr-grid|<tuple|cartesian|<point|0|0>|1>|gr-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-edit-grid-aspect|<tuple|<tuple|axes|none>|<tuple|1|none>|<tuple|10|none>>|gr-edit-grid|<tuple|cartesian|<point|0|0>|1>|gr-edit-grid-old|<tuple|cartesian|<point|0|0>|1>|gr-color|magenta|<graphics||<spline|<point|4.4|-5.2>|<point|6.6|-4.0>|<point|7.8|-5.0>|<point|11.6|-1.0>|<point|12.4|0.0>>|<with|arrow-end|\<gtr\>|<line|<point|1|-3>|<point|13.3|-3.0>>>|<point|7|-4.00193>|<point|12|-0.521792>|<point|9.5|-3.4>|<math-at|A|<point|6.7|-4.4>>|<math-at|B|<point|12.4|-0.5>>|<math-at|F<rsub|1>|<point|9.5|-4>>|<point|10.7|-2.04495>|<math-at|F<rsub|2>|<point|11|-2.2>>|<point|10.2|-2.61703>|<math-at|F<rsub|3>|<point|9.8|-2.35403>>|<with|color|red|<line|<point|6.99434|-4>|<point|7.0|-3.0>>>|<with|color|red|<line|<point|12|-0.521792>|<point|12.0|-3.0>>>|<with|color|magenta|<line|<point|9.5|-3.4>|<point|9.5|-3.0>>>|<with|color|magenta|<line|<point|10.7|-2.04495>|<point|10.7|-3.0>>>>>
</gr-screen>
</slide>
<\slide>
<tit|\<#5B9E\>\<#73B0\>\<#FF1A\>\<#4E8C\>\<#5206\>\<#67E5\>\<#627E\>\<#6CD5\>>
<\session|scheme|default>
<\unfolded-io|Scheme] >
(define (average x y) (/ (+ x y) 2))
<|unfolded-io>
average
</unfolded-io>
<\unfolded-io|Scheme] >
(define (search f neg-point pos-point)
\ \ (let ((midpoint (average neg-point pos-point)))
\ \ \ \ (if (close-enough? neg-point pos-point)
\ \ \ \ \ \ \ \ midpoint
\ \ \ \ \ \ \ \ (let ((test-value (f midpoint)))
\ \ \ \ \ \ \ \ \ \ (cond ((positive? test-value)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (search f neg-point midpoint))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ((negative? test-value)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (search f midpoint pos-point))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (else midpoint))))))
<|unfolded-io>
search
</unfolded-io>
</session>
</slide>
<\slide>
<tit|\<#5B9E\>\<#73B0\>\<#FF1A\>\<#533A\>\<#95F4\>\<#6298\>\<#534A\>\<#6CD5\>>
<\session|scheme|default>
<\folded-io|Scheme] >
(define (close-enough? x y)
\ \ (\<less\> (abs (- x y)) 0.001))
<|folded-io>
close-enough?
</folded-io>
<\folded-io|Scheme] >
(define (half-interval-method f a b)
\ \ (let ((a-value (f a))
\ \ \ \ \ \ \ \ (b-value (f b)))
\ \ \ \ (cond ((and (negative? a-value) (positive? b-value))
\ \ \ \ \ \ \ \ \ \ \ (search f a b))
\ \ \ \ \ \ \ \ \ \ ((and (negative? b-value) (positive? a-value))
\ \ \ \ \ \ \ \ \ \ \ (search f b a))
\ \ \ \ \ \ \ \ \ \ (else
\ \ \ \ \ \ \ \ \ \ \ (error "Values are not of opposite sign" a
b)))))
<|folded-io>
half-interval-method
</folded-io>
<\unfolded-io|Scheme] >
(half-interval-method sin 2.0 4.0)
<|unfolded-io>
3.14111328125
</unfolded-io>
</session>
</slide>
<\slide>
<tit|\<#6848\>\<#4F8B\>\<#5206\>\<#6790\>\<#FF1A\>\<#5BFB\>\<#627E\>\<#4E0D\>\<#52A8\>\<#70B9\>>
<\equation*>
f<around*|(|x|)>,f<around*|(|f<around*|(|x|)>|)>,f<around*|(|f<around*|(|f<around*|(|x|)>|)>|)>,\<ldots\>
</equation*>
<\session|scheme|default>
<\folded-io|Scheme] >
(define tolerance 0.00001)
<|folded-io>
0.00001
</folded-io>
<\folded-io|Scheme] >
(define (fixed-point f first-guess)
\ \ (define (close-enough? v1 v2)
\ \ \ \ (\<less\> (abs (- v1 v2)) tolerance))
\ \ (define (try guess)
\ \ \ \ (let ((next (f guess)))
\ \ \ \ \ \ (if (close-enough? guess next)
\ \ \ \ \ \ \ \ \ \ next
\ \ \ \ \ \ \ \ \ \ (try next))))
\ \ (try first-guess))
<|folded-io>
fixed-point
</folded-io>
<\folded-io|Scheme] >
(fixed-point cos 1.0)
<|folded-io>
0.7390822985224024
</folded-io>
<\folded-io|Scheme] >
(fixed-point (lambda (y) (+ (sin y) (cos y))) 1.0)
<|folded-io>
1.2587315962971173
</folded-io>
</session>
</slide>
<\slide>
<tit|\<#603B\>\<#7ED3\>>
\<#4EE3\>\<#7801\>\<#5373\>\<#6570\>\<#636E\>\<#FF0C\>\<#6570\>\<#636E\>\<#5373\>\<#4EE3\>\<#7801\>\<#3002\>
\<#51FD\>\<#6570\>\<#503C\>\<#53EF\>\<#4EE5\>\<#50CF\>\<#6570\>\<#636E\>\<#4E00\>\<#6837\>\<#FF0C\>\<#4F5C\>\<#4E3A\>\<#53C2\>\<#6570\>\<#4F20\>\<#5165\>\<#51FD\>\<#6570\>\<#FF0C\>\<#4F5C\>\<#4E3A\>\<#8FD4\>\<#56DE\>\<#503C\>\<#4ECE\>\<#51FD\>\<#6570\>\<#4E2D\>\<#4F20\>\<#51FA\>\<#3002\>
<scm|define>\<#FF0C\><scm|lambda>\<#FF0C\><scm|let>
<\scm-code>
(define (<with|color|red|\<langle\>\<#51FD\>\<#6570\>\<#540D\>\<rangle\>
><with|color|brown|\<langle\>\<#5F62\>\<#5F0F\>\<#53C2\>\<#6570\>\<#5217\>\<#8868\>\<rangle\>>)
<with|color|dark cyan|\<langle\>\<#4E3B\>\<#4F53\>\<rangle\>>)
(lambda (<with|color|brown|\<langle\>\<#5F62\>\<#5F0F\>\<#53C2\>\<#6570\>\<#5217\>\<#8868\>\<rangle\>>)
<with|color|dark cyan|\<langle\>\<#4E3B\>\<#4F53\>\<rangle\>>)
\;
(let ((<with|color|red|\<less\>\<#53D8\>\<#91CF\>1\<gtr\>>
<with|color|dark cyan|\<less\>\<#8868\>\<#8FBE\>\<#5F0F\>1\<gtr\>>)
\ \ \ \ \ \ (<with|color|red|\<less\>\<#53D8\>\<#91CF\>2\<gtr\>>
<with|color|dark cyan|\<less\>\<#8868\>\<#8FBE\>\<#5F0F\>2\<gtr\>>)
\ \ \ \ \ \ ...
\ \ \ \ \ \ (<with|color|red|\<less\>\<#53D8\>\<#91CF\>n\<gtr\>>
<with|color|dark cyan|\<less\>\<#8868\>\<#8FBE\>\<#5F0F\>n\<gtr\>>))
\ \ \ <with|color|dark cyan|\<langle\>\<#4E3B\>\<#4F53\>\<rangle\>>)
</scm-code>
</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>
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