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SICP 11：符号数据和符号求导
2024-05-22 20:43:04 +08:00
<TeXmacs|2.1.2>
<style|<tuple|beamer|no-page-numbers|chinese|python|s7|maxima>>
<\body>
<\hide-preamble>
<assign|dfn|<macro|x|<strong|<arg|x>>>>
</hide-preamble>
<\slideshow>
<\slide>
\;
\;
\;
<doc-data|<doc-title|\<#96F6\>\<#57FA\>\<#7840\>SICP
11>|<doc-author|<author-data|<author-name|>>>|<doc-author|<author-data|<author-name|\<#6C88\>\<#6D6A\>\<#718A\>\<#732B\>\<#513F\>>>>|<doc-author|<author-data|<author-name|MathAgape>|<\author-affiliation>
\;
\;
\;
\;
\;
\;
\;
</author-affiliation>>>|<doc-subtitle|\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#548C\>\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>>>
</slide>
<\slide>
<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>11\<#8BFE\>>
<\wide-tabular>
<tformat|<cwith|2|-1|1|-1|cell-height|40px>|<cwith|2|-1|1|-1|cell-vmode|exact>|<table|<row|<\cell>
<\large>
<strong|\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>\<#5BFC\>\<#5F15\>>
</large>
</cell>|<\cell>
<\large>
<strong|Introduction to Data Abstraction>
</large>
</cell>>|<row|<\cell>
\;
</cell>|<\cell>
\;
</cell>>|<row|<\cell>
<large|<strong|\<#5C42\>\<#6B21\>\<#6027\>\<#6570\>\<#636E\>\<#548C\>\<#95ED\>\<#5305\>\<#6027\>\<#8D28\>>>
</cell>|<\cell>
<large|<strong|Hierarchical Data and the Closure Property>>
</cell>>|<row|<\cell>
\;
</cell>|<\cell>
\;
</cell>>|<row|<\cell>
<large|<strong|\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>>>
</cell>|<\cell>
<large|<strong|Symbolic Data>>
</cell>>|<row|<\cell>
\<#5F15\>\<#53F7\>
</cell>|<\cell>
Quotation
</cell>>|<row|<\cell>
\<#5B9E\>\<#4F8B\>\<#FF1A\>\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>
</cell>|<\cell>
Example: Symbolic Differentiation
</cell>>>>
</wide-tabular>
\;
\<#56DE\>\<#987E\>\<#FF1A\>\<#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\>
\;
</slide>
<\slide>
<tit|\<#56DE\>\<#987E\>\<#FF1A\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>>
\<#7279\>\<#6B8A\>\<#5F62\>\<#5F0F\>\<#4E0D\>\<#7B26\>\<#5408\>\<#5E94\>\<#7528\>\<#5E8F\>\<#6C42\>\<#503C\>\<#FF0C\>\<#6BD4\>\<#5982\><scm|define>\<#FF0C\><scm|cond>\<#FF0C\><scm|if>\<#FF08\>\<#96F6\>\<#57FA\>\<#7840\>SICP\<#7B2C\>\<#4E00\>\<#8BB2\>\<#7684\>\<#5185\>\<#5BB9\>\<#FF09\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (myabs x) (if (\<gtr\> x 0) x (- x)))
<|folded-io>
myabs
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(myabs -1)
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
((lambda (x) (if (\<gtr\> x 0) x (- x))) -1)
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
-1
<|folded-io>
-1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(- 1)
<|folded-io>
-1
</folded-io>
<\input>
\<gtr\>\
<|input>
(list? )
</input>
</session>
\<#5373\>\<#4F7F\>\<#6211\>\<#4EEC\>\<#7684\>Scheme\<#89E3\>\<#91CA\>\<#5668\>\<#4E0D\>\<#652F\>\<#6301\><scm|-1>\<#FF0C\><scm|define>\<#FF0C\>\<#6211\>\<#4EEC\>\<#4E5F\>\<#53EF\>\<#4EE5\>\<#4F7F\>\<#7528\>\<#66F4\>\<#52A0\>\<#7E41\>\<#7410\>\<#7684\>\<#8BED\>\<#6CD5\>\<#6765\>\<#8868\>\<#793A\>\<#540C\>\<#6837\>\<#7684\>\<#542B\>\<#4E49\>\<#3002\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>\<#5E76\>\<#6CA1\>\<#6709\>\<#7ED9\>\<#6211\>\<#4EEC\>\<#5E26\>\<#6765\>\<#65B0\>\<#7684\>\<#80FD\>\<#529B\>\<#FF0C\>\<#4F46\>\<#80FD\>\<#5E2E\>\<#52A9\>\<#6211\>\<#4EEC\>\<#7B80\>\<#5316\>\<#4EE3\>\<#7801\>\<#3002\>
\<#5229\>\<#7528\>\<#5B8F\>\<#7F16\>\<#7A0B\>\<#7684\>\<#7279\>\<#6027\>\<#FF0C\>\<#6211\>\<#4EEC\>\<#53EF\>\<#4EE5\>\<#81EA\>\<#5B9A\>\<#4E49\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>\<#3002\>
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\V\<#6784\>\<#9020\>\<#51FD\>\<#6570\>quote>
<marked|<scm|'>>\<#662F\>\<#4E00\>\<#79CD\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>\<#FF0C\>\<#5982\>\<#679C\>\<#6CA1\>\<#6709\><marked|<scm|'>>\<#FF0C\>\<#4E5F\>\<#53EF\>\<#4EE5\>\<#4F7F\>\<#7528\><scm|quote>\<#3002\>Scala\<#91CC\>\<#9762\>\<#4E5F\>\<#6709\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#3002\>SRFI-1
List
<\with|par-columns|2>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
'a
<|folded-io>
a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(quote a)
<|folded-io>
a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
''a
<|folded-io>
'a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(quote (quote a))
<|folded-io>
'a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'1
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eq? 1 (quote 1))
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'#t
<|folded-io>
#t
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eq? #t `#t)
<|folded-io>
#t
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'+
<|folded-io>
+
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eq? + '+)
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
''
<|folded-io>
#\<eof\>
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</with>
\<#5B57\>\<#9762\>\<#91CF\>\<#FF08\>literally\<#FF09\>\<#5728\>\<#5F15\>\<#7528\>\<#FF08\>\<#4E24\>\<#6B21\>\<#5F15\>\<#7528\>\<#FF1F\>\<#FF09\>\<#4E4B\>\<#540E\>\<#FF0C\>\<#8FD8\>\<#662F\>\<#5B57\>\<#9762\>\<#91CF\>\<#3002\>\<#7B26\>\<#53F7\>\<#5728\>\<#5F15\>\<#7528\>\<#4E4B\>\<#540E\>\<#FF0C\>\<#5219\>\<#53D8\>\<#6210\>\<#4E86\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#3002\>
\;
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\V\<#9009\>\<#62E9\>\<#51FD\>\<#6570\>unquote>
<marked|<scm|,>>\<#662F\>\<#4E00\>\<#79CD\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>\<#FF0C\>\<#5982\>\<#679C\>\<#6CA1\>\<#6709\><marked|<scm|,>>\<#FF0C\>\<#4E5F\>\<#53EF\>\<#4EE5\>\<#4F7F\>\<#7528\><scm|unquote>\<#3002\>unquote\<#53EA\>\<#80FD\>\<#5728\><marked|<scm|`>>\<#FF08\>quasiquote\<#FF09\>\<#4E0B\>\<#4F7F\>\<#7528\>\<#3002\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define a 1)
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
a
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'a
<|folded-io>
a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(quote a)
<|folded-io>
a
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
`,a
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(quasiquote (unquote a))
<|folded-io>
1
</folded-io>
</session>
\<#8BD5\>\<#8BD1\>\<#FF1A\>quote\<#4E3A\>\<#5F15\>\<#7528\>\<#FF0C\>unquote\<#4E3A\>\<#89E3\>\<#5F15\>\<#7528\>\<#FF0C\>quasiquote\<#4E3A\>\<#51C6\>\<#5F15\>\<#7528\>\<#3002\><marked|<scm|'>>
\<#662F\>\<#5F15\>\<#53F7\>\<#FF0C\><marked|<scm|,>>
\<#662F\>\<#89E3\>\<#5F15\>\<#53F7\>\<#FF0C\><marked|<scm|`>>
\<#662F\>\<#51C6\>\<#5F15\>\<#53F7\>\<#3002\>
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\V\<#53C2\>\<#6570\>\<#4E3A\>\<#5217\>\<#8868\>\<#7684\>\<#6784\>\<#9020\>\<#51FD\>\<#6570\>>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
'(a b c)
<|folded-io>
(a b c)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(list 'a 'b 'c)
<|folded-io>
(a b c)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'(a b (c d))
<|folded-io>
(a b (c d))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(list 'a 'b (list 'c 'd))
<|folded-io>
(a b (c d))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
'(+ 1 2)
<|folded-io>
(+ 1 2)
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<\scm-code>
' ; quote
` ; quasiquote
, ; unquote
</scm-code>
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\V\<#5728\>\<#5217\>\<#8868\>\<#4E2D\>\<#7406\>\<#89E3\>\<#9009\>\<#62E9\>\<#51FD\>\<#6570\>>
<\with|par-columns|2>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
'(+ a 1)
<|folded-io>
(+ a 1)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define a 4)
<|folded-io>
4
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
`(+ ,(+ a 1) 1)
<|folded-io>
(+ 5 1)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
`(+ ,a 1)
<|folded-io>
(+ 4 1)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eval `(+ ,a 1))
<|folded-io>
5
</folded-io>
</session>
<\equation*>
<frac|5+4+0*<around*|(|2-<around*|(|3-<around*|(|6+<frac|4|5>|)>|)>|)>|3<around*|(|6-2|)><around*|(|2-7|)>>
</equation*>
</with>
\<#7528\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#53EF\>\<#4EE5\>\<#5EF6\>\<#8FDF\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\>\<#3002\>\<#5EF6\>\<#8FDF\>\<#8BA1\>\<#7B97\>\<#8FC7\>\<#7A0B\>\<#FF0C\>\<#53EF\>\<#4EE5\>\<#907F\>\<#514D\>\<#65E0\>\<#6548\>\<#8BA1\>\<#7B97\>\<#548C\>\<#91CD\>\<#590D\>\<#8BA1\>\<#7B97\>\<#3002\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define \<#5206\>\<#5B50\> `(+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5))))))
<|folded-io>
(+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define \<#5206\>\<#6BCD\> `(* 3 (- 6 2) (- 2 7)))
<|folded-io>
(* 3 (- 6 2) (- 2 7))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
`(/ ,\<#5206\>\<#5B50\> ,\<#5206\>\<#6BCD\>)
<|folded-io>
(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5))))) (* 3 (- 6 2) (- 2 7)))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eval `(/ ,\<#5206\>\<#5B50\> ,\<#5206\>\<#6BCD\>))
<|folded-io>
-37/150
</folded-io>
</session>
\<#FF08\>\<#8FD9\>\<#4E2A\>\<#4F8B\>\<#5B50\>\<#6765\>\<#81EA\>\<#4E8E\>\<#300A\>\<#96F6\>\<#57FA\>\<#7840\>SICP\<#300B\>\<#7B2C\>2.1\<#8BFE\>
00:12:00\<#FF09\>
</slide>
<\slide>
<tit|\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>>
<\eqnarray*>
<tformat|<table|<row|<cell|<frac|\<mathd\>c|\<mathd\>x>>|<cell|=>|<cell|0>>|<row|<cell|<frac|\<mathd\>x|\<mathd\>x>>|<cell|=>|<cell|1>>|<row|<cell|<frac|d<around*|(|u+v|)>|\<mathd\>x>>|<cell|=>|<cell|<frac|\<mathd\>u|\<mathd\>x>+<frac|\<mathd\>v|\<mathd\>x>>>|<row|<cell|<frac|\<mathd\><around*|(|u*v|)>|\<mathd\>x>>|<cell|=>|<cell|u*<frac|\<mathd\>v|\<mathd\>x>+v*<frac|\<mathd\>u|\<mathd\>x>>>>>
</eqnarray*>
<\remark*>
<math|c>\<#662F\>\<#4E00\>\<#4E2A\>\<#5E38\>\<#6570\>\<#6216\>\<#8005\>\<#662F\>\<#4E00\>\<#4E2A\>\<#548C\><math|x>\<#65E0\>\<#5173\>\<#7684\>\<#53D8\>\<#91CF\>\<#3002\>
</remark*>
</slide>
<\slide>
<tit|\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>\V\<#5E94\>\<#7528\>>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(deriv '(+ x 3) 'x)
<|folded-io>
(+ 1 0)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(deriv '(* x y) 'x)
<|folded-io>
(+ (* x 0) (* 1 y))
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(deriv '(* (* x y) (+ x 3)) 'x)
<|folded-io>
(+ (* (* x y) (+ 1 0)) (* (+ (* x 0) (* 1 y)) (+ x 3)))
</folded-io>
</session>
<\session|maxima|default>
<\output>
Maxima 5.46.0 https://maxima.sourceforge.io
using Lisp GNU Common Lisp (GCL) GCL 2.6.14 git tag
Version_2_6_15pre3
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
</output>
<\folded-io>
<with|color|red|(<with|math-font-family|rm|%i>4) >
<|folded-io>
diff(<math|x+3>)
<|folded-io>
<math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o4>)
>>d*x>>
</folded-io>
<\folded-io>
<with|color|red|(<with|math-font-family|rm|%i>5) >
<|folded-io>
diff(<math|x*y>,x)
<|folded-io>
<math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o5>)
>>y>>
</folded-io>
<\folded-io>
<with|color|red|(<with|math-font-family|rm|%i>6) >
<|folded-io>
diff(<math|x*y*<around*|(|x+3|)>>,x)
<|folded-io>
<math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o6>)
>><around*|(|x+3|)>*y+x*y>>
</folded-io>
<\input>
<with|color|red|(<with|math-font-family|rm|%i>7) >
<|input>
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>\V\<#5B9E\>\<#73B0\>>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (deriv exp var)
\ \ (cond ((number? exp) 0)
\ \ \ \ \ \ \ \ ((variable? exp)
\ \ \ \ \ \ \ \ \ (if (same-variable? exp var) 1 0))
\ \ \ \ \ \ \ \ ((sum? exp)
\ \ \ \ \ \ \ \ \ (make-sum (deriv (addend exp) var)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (deriv (augend exp) var)))
\ \ \ \ \ \ \ \ ((product? exp)
\ \ \ \ \ \ \ \ \ (make-sum
\ \ \ \ \ \ \ \ \ \ \ (make-product (multiplier exp)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (deriv
(multiplicand exp) var))
\ \ \ \ \ \ \ \ \ \ \ (make-product (deriv (multiplier exp) var)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (multiplicand
exp))))
\ \ \ \ \ \ \ \ (else
\ \ \ \ \ \ \ \ \ (error "unknown expression type -- DERIV" exp))))
<|unfolded-io>
deriv
</unfolded-io>
</session>
</slide>
<\slide>
<tit|\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>\V\<#57FA\>\<#7840\>\<#51FD\>\<#6570\>>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (variable? x) (symbol? x)) ;
\<#5224\>\<#65AD\>x\<#662F\>\<#4E0D\>\<#662F\>\<#53D8\>\<#91CF\>
<|folded-io>
variable?
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (same-variable? v1 v2) ;
v1\<#548C\>v2\<#662F\>\<#4E0D\>\<#662F\>\<#540C\>\<#4E00\>\<#4E2A\>\<#53D8\>\<#91CF\>
\ \ (and (variable? v1) (variable? v2) (eq? v1 v2)))
<|folded-io>
same-variable?
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (make-sum a1 a2) (list '+ a1 a2)) ;\
<|folded-io>
make-sum
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (make-product m1 m2) (list '* m1 m2))
<|folded-io>
make-product
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (sum? x) (and (pair? x) (eq? (car x) '+))) ;
x\<#662F\>\<#548C\>\<#5F0F\>\<#4E48\>\<#FF1F\>
<|folded-io>
sum?
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (addend s) (cadr s)) ; s\<#7684\>\<#88AB\>\<#52A0\>\<#6570\>\<#FF08\>\<#52A0\>\<#53F7\>\<#5DE6\>\<#8FB9\>\<#90A3\>\<#4E2A\>\<#6570\>\<#FF09\>
<|folded-io>
addend
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (augend s) (caddr s)) ;
s\<#7684\>\<#52A0\>\<#6570\>\<#FF08\>\<#52A0\>\<#53F7\>\<#53F3\>\<#8FB9\>\<#90A3\>\<#4E2A\>\<#6570\>\<#FF09\>
<|folded-io>
augend
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (product? x) ; x\<#662F\>\<#5426\>\<#662F\>\<#4E00\>\<#4E2A\>\<#4E58\>\<#5F0F\>
\ \ (and (pair? x) (eq? (car x) '*)))
<|folded-io>
product?
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (multiplier p) (cadr p)) ;
p\<#7684\>\<#88AB\>\<#4E58\>\<#6570\>\<#FF08\>\<#4E58\>\<#53F7\>\<#5DE6\>\<#8FB9\>\<#FF09\>
<|folded-io>
multiplier
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (multiplicand p) (caddr p)) ;
p\<#7684\>\<#4E58\>\<#6570\>\<#FF08\>\<#4E58\>\<#53F7\>\<#53F3\>\<#8FB9\>\<#FF09\>
<|folded-io>
multiplicand
</folded-io>
</session>
</slide>
<\slide>
<tit|\<#5C0F\>\<#7ED3\>>
<\itemize>
<item>\<#56DE\>\<#987E\>\<#8BED\>\<#6CD5\>\<#7CD6\>\<#8863\>\<#8FD9\>\<#4E2A\>\<#6982\>\<#5FF5\>
<item>\<#9488\>\<#5BF9\>\<#539F\>\<#8BED\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>
<item>\<#9488\>\<#5BF9\>\<#590D\>\<#5408\>\<#8868\>\<#8FBE\>\<#5F0F\>\<#5B9A\>\<#4E49\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>
<item>\<#7406\>\<#89E3\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#FF1A\>\<#5B9E\>\<#73B0\>\<#5EF6\>\<#8FDF\>\<#8BA1\>\<#7B97\>
<item>\<#5E94\>\<#7528\>\<#7B26\>\<#53F7\>\<#6570\>\<#636E\>\<#FF1A\>\<#7B26\>\<#53F7\>\<#6C42\>\<#5BFC\>
</itemize>
</slide>
</slideshow>
</body>
<\initial>
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