diff --git a/SICP/code08.tm b/SICP/code08.tm
new file mode 100644
index 0000000..146cdd7
--- /dev/null
+++ b/SICP/code08.tm
@@ -0,0 +1,383 @@
+<TeXmacs|2.1.2>
+
+<style|<tuple|generic|no-page-numbers|chinese>>
+
+<\body>
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define (make-rat n d) (cons n d))
+    <|unfolded-io>
+      make-rat
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (numer x) (car x))
+    <|unfolded-io>
+      numer
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (denom x) (cdr x))
+    <|unfolded-io>
+      denom
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\> n d) (make-rat n d))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5B50\> x) (numer x))
+    <|unfolded-io>
+      \<#5206\>\<#5B50\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#6BCD\> x) (denom x))
+    <|unfolded-io>
+      \<#5206\>\<#6BCD\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f z var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#5B50\>"))))
+    <|unfolded-io>
+      ("f z tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#5F0F\>"))))
+    <|unfolded-io>
+      ("f s tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f m var" (insert (utf8-\<gtr\>cork "\<#5206\>\<#6BCD\>"))))
+    <|unfolded-io>
+      ("f m tab")
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      <\with|prog-scripts|scheme>
+        (define (add-rat x y)
+
+        \ \ (make-rat (+ (* (numer x) (denom y))
+
+        \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (* (numer y) (denom x)))
+
+        \ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
+      </with>
+    <|unfolded-io>
+      add-rat
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sub-rat x y)
+
+      \ \ (make-rat (- (* (numer x) (denom y))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (* (numer y) (denom x)))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
+    <|unfolded-io>
+      sub-rat
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (mul-rat x y)
+
+      \ \ (make-rat (* (numer x) (numer y))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (denom y))))
+    <|unfolded-io>
+      mul-rat
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (div-rat x y)
+
+      \ \ (make-rat (* (numer x) (denom y))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ (* (denom x) (numer y))))
+    <|unfolded-io>
+      div-rat
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (equal-rat? x y)
+
+      \ \ (= (* (numer x) (denom y))
+
+      \ \ \ \ \ (* (numer y) (denom x))))
+    <|unfolded-io>
+      equal-rat?
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s + var" (insert (utf8-\<gtr\>cork
+      "\<#5206\>\<#5F0F\>\<#52A0\>"))))
+    <|unfolded-io>
+      ("f s + tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s - var" (insert (utf8-\<gtr\>cork
+      "\<#5206\>\<#5F0F\>\<#51CF\>"))))
+    <|unfolded-io>
+      ("f s - tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s * var" (insert (utf8-\<gtr\>cork
+      "\<#5206\>\<#5F0F\>\<#4E58\>"))))
+    <|unfolded-io>
+      ("f s * tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s / var" (insert (utf8-\<gtr\>cork
+      "\<#5206\>\<#5F0F\>\<#9664\>"))))
+    <|unfolded-io>
+      ("f s / tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (kbd-map ("f s x var" (insert (utf8-\<gtr\>cork
+      "\<#5206\>\<#5F0F\>\<#663E\>"))))
+    <|unfolded-io>
+      ("f s x tab")
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\>\<#52A0\> x y) (add-rat x y))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>\<#52A0\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\>\<#51CF\> x y) (sub-rat x y))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>\<#51CF\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\>\<#4E58\> x y) (mul-rat x y))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>\<#4E58\>
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\>\<#9664\> x y) (div-rat x y))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>\<#9664\>
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define x (cons 1 2))
+    <|unfolded-io>
+      (1 . 2)
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (car x)
+    <|unfolded-io>
+      1
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (cdr x)
+    <|unfolded-io>
+      2
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define x (cons 1 2))
+    <|unfolded-io>
+      (1 . 2)
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define y (cons 3 4))
+    <|unfolded-io>
+      (3 . 4)
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define z (cons x y))
+    <|unfolded-io>
+      ((1 . 2) 3 . 4)
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (car (car z))
+    <|unfolded-io>
+      1
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  \;
+
+  <\session|scheme|default>
+    <\input|Scheme] >
+      (define (print-rat x)
+
+      \ \ (newline)
+
+      \ \ (display (numer x))
+
+      \ \ (display "/")
+
+      \ \ (display (denom x)))
+    </input>
+
+    <\unfolded-io|Scheme] >
+      (define (\<#5206\>\<#5F0F\>\<#663E\> x)
+
+      \ \ (stree-\<gtr\>tree `(frac ,(\<#5206\>\<#5B50\> x)
+      ,(\<#5206\>\<#6BCD\> x))))
+    <|unfolded-io>
+      \<#5206\>\<#5F0F\>\<#663E\>
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\> 1 2))
+    <|unfolded-io>
+      (1 . 2)
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\> (\<#5206\>\<#5F0F\> 1 3))
+    <|unfolded-io>
+      (1 . 3)
+    </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>
+
+    <\folded-io|Scheme] >
+      (\<#5206\>\<#5F0F\>\<#663E\> (\<#5206\>\<#5F0F\>\<#52A0\>
+      \<#4E8C\>\<#5206\>\<#4E4B\>\<#4E00\>
+      \<#4E09\>\<#5206\>\<#4E4B\>\<#4E00\>))
+    <|folded-io>
+      <text|<frac|5|6>>
+    </folded-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>
+
+  <\session|scheme|default>
+    <\input>
+      Scheme]\ 
+    <|input>
+      (define (make-rat n d)
+
+      \ \ (let ((g (gcd n d)))
+
+      \ \ \ \ (cons (/ n g) (/ d g))))
+    </input>
+  </session>
+
+  <\session|scheme|default>
+    <\input|Scheme] >
+      (print-rat (add-rat one-third one-third))
+    </input>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+</body>
+
+<\initial>
+  <\collection>
+    <associate|page-medium|papyrus>
+    <associate|page-screen-margin|false>
+  </collection>
+</initial>
+
+<\references>
+  <\collection>
+    <associate|auto-1|<tuple|?|?|code07.tm>>
+    <associate|auto-2|<tuple|?|?|code07.tm>>
+    <associate|auto-3|<tuple|?|?|code07.tm>>
+  </collection>
+</references>
+
+<\auxiliary>
+  <\collection>
+    <\associate|toc>
+      <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>>
+      <no-break><pageref|auto-1>>
+
+      <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>>
+      <no-break><pageref|auto-2>>
+
+      <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>
\ No newline at end of file
diff --git a/SICP/index.tm b/SICP/index.tm
index d23bf70..e189efa 100644
--- a/SICP/index.tm
+++ b/SICP/index.tm
@@ -24,6 +24,12 @@
       <item>\<#76EE\>\<#6807\>\<#90AE\>\<#7BB1\>\<#FF1A\>shenda AT ustc.edu
     </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\>
 
     \<#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\>
diff --git a/SICP/slide08.tm b/SICP/slide08.tm
new file mode 100644
index 0000000..a207f5e
--- /dev/null
+++ b/SICP/slide08.tm
@@ -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>
\ No newline at end of file