From 4f17ed85b08cd06e537167e544fad0dba982eb11 Mon Sep 17 00:00:00 2001
From: Darcy Shen <da@liii.pro>
Date: Thu, 11 Apr 2024 17:22:26 +0800
Subject: [PATCH] SICP 07: slides and code snippets

---
 SICP/code07.tm  | 333 +++++++++++++++++++++++++++++++++++++++++
 SICP/index.tm   |   8 +
 SICP/slide07.tm | 387 ++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 728 insertions(+)
 create mode 100644 SICP/code07.tm
 create mode 100644 SICP/slide07.tm

diff --git a/SICP/code07.tm b/SICP/code07.tm
new file mode 100644
index 0000000..d3ee7f5
--- /dev/null
+++ b/SICP/code07.tm
@@ -0,0 +1,333 @@
+<TeXmacs|2.1.2>
+
+<style|<tuple|generic|no-page-numbers|chinese>>
+
+<\body>
+  <subsection*|1.3.1>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define (cube x) (* x x x))
+    <|unfolded-io>
+      cube
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sum-integers a b)
+
+      \ \ (if (\<gtr\> a b)
+
+      \ \ \ \ \ \ 0
+
+      \ \ \ \ \ \ (+ a (sum-integers (+ a 1) b))))
+    <|unfolded-io>
+      sum-integers
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sum-cubes a b)
+
+      \ \ (if (\<gtr\> a b)
+
+      \ \ \ \ \ \ 0
+
+      \ \ \ \ \ \ (+ (cube a) (sum-cubes (+ a 1) b))))
+    <|unfolded-io>
+      sum-cubes
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (pi-sum a b)
+
+      \ \ (if (\<gtr\> a b)
+
+      \ \ \ \ \ \ 0
+
+      \ \ \ \ \ \ (+ (/ 1.0 (* a (+ a 2))) (pi-sum (+ a 4) b))))
+    <|unfolded-io>
+      pi-sum
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (sum-integers 1 3)
+    <|unfolded-io>
+      6
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (sum-cubes 1 3)
+    <|unfolded-io>
+      36
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (pi-sum 1 3)
+    <|unfolded-io>
+      0.3333333333333333
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sum term a next b)
+
+      \ \ (if (\<gtr\> a b)
+
+      \ \ \ \ \ \ 0
+
+      \ \ \ \ \ \ (+ (term a)
+
+      \ \ \ \ \ \ \ \ \ (sum term (next a) next b))))
+    <|unfolded-io>
+      sum
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (inc n) (+ n 1))
+    <|unfolded-io>
+      inc
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sum-cubes-2 a b)
+
+      \ \ (sum cube a inc b))
+    <|unfolded-io>
+      sum-cubes-2
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (sum-cubes-2 1 3)
+    <|unfolded-io>
+      36
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+
+    <\unfolded-io|Scheme] >
+      (define (identity x) x)
+    <|unfolded-io>
+      identity
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (sum-integers-2 a b)
+
+      \ \ (sum identity a inc b))
+    <|unfolded-io>
+      sum-integers-2
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (sum-integers-2 1 10)
+    <|unfolded-io>
+      55
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (define (pi-sum-2 a b)
+
+      \ \ (define (pi-term x)
+
+      \ \ \ \ (/ 1.0 (* x (+ x 2))))
+
+      \ \ (define (pi-next x)
+
+      \ \ \ \ (+ x 4))
+
+      \ \ (sum pi-term a pi-next b))
+    <|unfolded-io>
+      pi-sum-2
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (* 8 (pi-sum-2 1 1000))
+    <|unfolded-io>
+      3.139592655589783
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <subsection*|1.3.2>
+
+  <\session|scheme|default>
+    <\unfolded-io|Scheme] >
+      (define (square x) (* x x))
+    <|unfolded-io>
+      square
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      ((lambda (x y z) (+ x y (square z))) 1 2 3)
+    <|unfolded-io>
+      12
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+
+  <subsection*|1.3.3>
+
+  <\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>
+
+    <\unfolded-io|Scheme] >
+      (define (close-enough? x y)
+
+      \ \ (\<less\> (abs (- x y)) 0.001))
+    <|unfolded-io>
+      close-enough?
+    </unfolded-io>
+
+    <\unfolded-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)))))
+    <|unfolded-io>
+      half-interval-method
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (half-interval-method sin 2.0 4.0)
+    <|unfolded-io>
+      3.14111328125
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0
+
+      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.0)
+    <|unfolded-io>
+      1.89306640625
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+
+    <\unfolded-io|Scheme] >
+      (define tolerance 0.00001)
+    <|unfolded-io>
+      0.00001
+    </unfolded-io>
+
+    <\unfolded-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))
+    <|unfolded-io>
+      fixed-point
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (fixed-point cos 1.0)
+    <|unfolded-io>
+      0.7390822985224024
+    </unfolded-io>
+
+    <\unfolded-io|Scheme] >
+      (fixed-point (lambda (y) (+ (sin y) (cos y)))
+
+      \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0)
+    <|unfolded-io>
+      1.2587315962971173
+    </unfolded-io>
+
+    <\input|Scheme] >
+      \;
+    </input>
+  </session>
+</body>
+
+<\initial>
+  <\collection>
+    <associate|page-medium|papyrus>
+    <associate|page-screen-margin|false>
+  </collection>
+</initial>
+
+<\references>
+  <\collection>
+    <associate|auto-1|<tuple|?|?>>
+    <associate|auto-2|<tuple|?|?>>
+    <associate|auto-3|<tuple|?|?>>
+  </collection>
+</references>
+
+<\auxiliary>
+  <\collection>
+    <\associate|toc>
+      <with|par-left|<quote|1tab>|1.3.1 <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>|1.3.2 <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>|1.3.3 <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 9e9ce4c..d23bf70 100644
--- a/SICP/index.tm
+++ b/SICP/index.tm
@@ -24,6 +24,14 @@
       <item>\<#76EE\>\<#6807\>\<#90AE\>\<#7BB1\>\<#FF1A\>shenda AT ustc.edu
     </itemize>
 
+    <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\>
+
+    \<#8BFE\>\<#4EF6\>\<#FF1A\><hlink|\<#5E7B\>\<#706F\>\<#7247\>07|slide07.tm>
+
+    \<#4EE3\>\<#7801\>\<#FF1A\><hlink|\<#4EE3\>\<#7801\>\<#6E05\>\<#5355\>07|code07.tm>
+
     <item>\<#7B2C\>6\<#8BFE\>\<#FF1A\>\<#7B97\>\<#6CD5\>\<#7684\>\<#65F6\>\<#7A7A\>\<#590D\>\<#6742\>\<#5EA6\>\<#FF08\>\<#4E60\>\<#9898\>\<#8BFE\>\<#FF09\>
 
     \<#7EC3\>\<#4E60\>\<#FF1A\><hlink|\<#4E60\>\<#9898\>\<#8BFE\>\<#8BFE\>\<#4EF6\>06|https://gitee.com/XmacsLabs/interactive-sicp/raw/main/exercise06.tm>
diff --git a/SICP/slide07.tm b/SICP/slide07.tm
new file mode 100644
index 0000000..c2c72ca
--- /dev/null
+++ b/SICP/slide07.tm
@@ -0,0 +1,387 @@
+<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>
\ No newline at end of file