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Add description for Delta
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Thu, 22 Jan 2015 10:49:27 +0900
parents 780eab85e724
children 40344cc2c590
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1 <!DOCTYPE HTML>
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2
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3 <html lang="Japanese">
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4 <head>
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5 <title>形式手法を広めるには</title>
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6 <meta charset="UTF-8">
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7 <meta name="viewport" content="width=1274, user-scalable=no">
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8 <meta name="generator" content="Slide Show (S9)">
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9 <meta name="author" content="河野真治 <br> 比嘉健太">
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10 <link rel="stylesheet" href="themes/ribbon/styles/style.css">
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11 <link rel="stylesheet" href="slide.css">
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12 </head>
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13 <body class="list">
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14 <header class="caption">
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15 <h1>形式手法を広めるには</h1>
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16 <p>河野真治 <br> 比嘉健太</p>
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17 </header>
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18 <div class="slide cover" id="Cover"><div>
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19 <section>
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20 <header>
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21 <h2>形式手法を広めるには</h2>
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22 <h3 id="author">河野真治 <br> 比嘉健太</h3>
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23 <h3 id="profile">琉球大学工学部情報工学科</h3>
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24 </header>
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25 </section>
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26 </div></div>
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27
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28 <!-- todo: add slide.classes to div -->
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29 <!-- todo: create slide id from header? like a slug in blogs? -->
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31 <div class="slide" id="2"><div>
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32 <section>
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33 <header>
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34 <h1 id="agenda">Agenda</h1>
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35 </header>
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36 <!-- === begin markdown block ===
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38 generated by markdown 1.1.1 on Ruby 2.2.0 (2014-12-25) [x86_64-darwin13]
53
65391f6321a8 Add description for Delta
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39 on 2015-01-22 10:48:46 +0900 with Markdown engine kramdown (1.4.2)
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40 using options {}
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41 -->
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42
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43 <!-- _S9SLIDE_ -->
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44
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45 <ul>
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46 <li>大学ではどんなことをやっているか(講義, イベント, 研究)</li>
51
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47 <li>講義などでつまづくポイント</li>
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48 <li>つまづきの解決策</li>
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49 <li>どのような講義をするべきか?</li>
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50 </ul>
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53
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54 </section>
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55 </div></div>
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56
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57 <div class="slide" id="3"><div>
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58 <section>
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59 <header>
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60 <h1 id="section">講義で使用している形式手法</h1>
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61 </header>
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62 <!-- _S9SLIDE_ -->
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63
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64 <ul>
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65 <li>仕様記述
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66 <ul>
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67 <li>UML</li>
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68 </ul>
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69 </li>
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70 <li>model checking 的なアプローチ
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71 <ul>
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72 <li>Java Path Finder</li>
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73 </ul>
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74 </li>
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75 <li>証明的なアプローチ
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76 <ul>
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77 <li>Haskell, Agda</li>
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78 </ul>
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79 </li>
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80 </ul>
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81
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83
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84 </section>
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85 </div></div>
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86
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87 <div class="slide" id="4"><div>
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88 <section>
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89 <header>
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90 <h1 id="section-1">仕様記述</h1>
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91 </header>
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92 <!-- _S9SLIDE_ -->
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93
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94 <ul>
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95 <li>モデリングと設計 の講義</li>
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96 <li>iOS Application を作成する</li>
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97 <li>ユースケース図やクラス図を使って仕様を考える</li>
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98 </ul>
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99
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100
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101
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102 </section>
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103 </div></div>
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104
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105 <div class="slide" id="5"><div>
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106 <section>
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107 <header>
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108 <h1 id="model-checking-">model checking 的なアプローチ</h1>
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109 </header>
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110 <!-- _S9SLIDE_ -->
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111
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112 <ul>
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113 <li><a href="http://www.ie.u-ryukyu.ac.jp/%7Ekono/lecture/os/index.html">Operationg System</a> の講義</li>
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114 <li>Process/Thread Scheduling を考えた時に</li>
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115 <li>Dead Lock を起こすような Scheduling を実際に書いて実行させる</li>
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116 <li>Java Path Finder で Thread の実行順序を網羅的に実行する</li>
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117 </ul>
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118
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119
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120
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121 </section>
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122 </div></div>
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123
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124 <div class="slide" id="6"><div>
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125 <section>
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126 <header>
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127 <h1 id="section-2">証明的なアプローチ</h1>
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128 </header>
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129 <!-- _S9SLIDE_ -->
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130
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131 <ul>
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132 <li><a href="http://www.ie.u-ryukyu.ac.jp/%7Ekono/lecture/software/index.html">ソフトウェア工学</a> の講義</li>
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133 <li>集合, 論理, 関数, 自然演繹による証明</li>
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134 <li>型システム, Curry-Howard Isomorphism を通して Haskell, Agda で証明</li>
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135 <li>Haskell : 自然演繹と lambda calculus</li>
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136 <li>Agda : Data type に対する証明 (Product, Sum, List, Functor, Monad …)</li>
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137 <li>Agda : SystemT を使った自然数に対する演算の証明</li>
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138 </ul>
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139
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140
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141
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142 </section>
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143 </div></div>
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144
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145 <div class="slide" id="7"><div>
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146 <section>
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147 <header>
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148 <h1 id="agda-">Agda による証明を解説した例</h1>
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149 </header>
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150 <!-- _S9SLIDE_ -->
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151
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152 <ul>
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153 <li>Open Source Conference</li>
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154 <li>ソフトウェア工学で学んだ Agda を <a href="http://ie.u-ryukyu.ac.jp/~e115763/slides/events/osc2014/slide.html">Agda 入門</a>として発表</li>
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155 <li>Agda で SystemT の Nat の加法の交換法則を解説</li>
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156 <li>定義の解説にほとんどの時間を取られてしまう</li>
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157 </ul>
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158
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159
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160
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161 </section>
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162 </div></div>
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163
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164 <div class="slide" id="8"><div>
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165 <section>
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166 <header>
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167 <h1 id="section-3">圏によるプログラムの形式化</h1>
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168 </header>
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169 <!-- _S9SLIDE_ -->
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170
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171 <ul>
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172 <li>プログラムの変更を Monad で表す</li>
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173 <li>プログラムの変更時に変更前のプログラムも残したまま変更する</li>
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174 <li>全てのバージョンのプログラムを同時に実行できる</li>
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175 <li>デバッグやテストと組み合せることでバグを見付けたい</li>
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176 <li>実行系と検証系を同時に走らせることもできる</li>
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177 </ul>
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178
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179
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180
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181 </section>
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182 </div></div>
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183
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184 <div class="slide" id="9"><div>
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185 <section>
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186 <header>
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187 <h1 id="section-4">学習コスト</h1>
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188 </header>
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189 <!-- _S9SLIDE_ -->
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190
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191 <ul>
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192 <li>論理, 自然演繹 -&gt; Haskell -&gt; Agda</li>
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193 <li>それぞれのステップに壁がある</li>
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194 <li>論理とプログラム間で変換できないなど</li>
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195 <li>自然演繹では解けるけれど lambda term で書き直す</li>
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196 <li>Haskell では定義できるけれど Agda で証明できない</li>
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197 </ul>
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198
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199
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200
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201 </section>
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202 </div></div>
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203
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204 <div class="slide" id="10"><div>
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205 <section>
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206 <header>
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207 <h1 id="section-5">つまづくポイント</h1>
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208 </header>
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209 <!-- _S9SLIDE_ -->
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210
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211 <ul>
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212 <li>Haskell -&gt; Agda の壁を考える</li>
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213 <li>コードを書いてる人なら型を合わせることは分かる</li>
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214 <li>型によって証明を書くことに繋げるには?
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215 <ul>
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216 <li>プログラムと論理の対応を把握してもらう必要がある</li>
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217 <li>どうしたら把握してもらえるか?</li>
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218 </ul>
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219 </li>
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220 </ul>
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221
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222
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223
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224 </section>
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225 </div></div>
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226
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227 <div class="slide" id="11"><div>
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228 <section>
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229 <header>
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230 <h1 id="section-6">つまづきをどう解決するか</h1>
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231 </header>
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232 <!-- _S9SLIDE_ -->
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233
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234 <ul>
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235 <li>書き続ける</li>
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236 <li>論理とプログラムの対応を見えるようにする
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237 <ul>
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238 <li>Agda は対話的に項を書き換えることができる</li>
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239 <li>どこでつまづいても情報が手に入るようにしたい
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240 <ul>
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241 <li>論理側でも、プログラム側でも、どのステップでも</li>
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242 </ul>
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243 </li>
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244 <li>対話的に情報を引き出す手段そのものを学ぶ</li>
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245 </ul>
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246 </li>
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247 </ul>
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248
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249
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250
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251 </section>
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252 </div></div>
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253
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254 <div class="slide" id="12"><div>
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255 <section>
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256 <header>
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257 <h1 id="section-7">他に講義に取りいれるもの?</h1>
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258 </header>
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259 <!-- _S9SLIDE_ -->
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260
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261 <ul>
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262 <li>仕様記述</li>
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263 <li>他の証明支援系
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264 <ul>
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265 <li>Coq, …</li>
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266 </ul>
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267 </li>
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268 <li>他の理論
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269 <ul>
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270 <li>Hoare Logic, Computational Tree Logic, …</li>
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271 </ul>
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272 </li>
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273 <li>どのようなカリキュラムが良いか?</li>
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274 </ul>
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275
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276
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277
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278 </section>
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279 </div></div>
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280
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281 <div class="slide" id="13"><div>
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282 <section>
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283 <header>
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284 <h1 id="delta-">データ構造 Delta の定義</h1>
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285 </header>
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286 <!-- _S9SLIDE_ -->
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287
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288 <ul>
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289 <li>Monad によってプログラムの変更を表す</li>
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290 <li>データ構造としては長さ1以上のリスト
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291 <ul>
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292 <li>nil に相当するものが元のプログラムの値</li>
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293 <li>プログラムの変更は変更した後の値を List に追加する</li>
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294 <li>全ての関数は Delta を返し、値は Delta によって定義する</li>
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295 </ul>
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296 </li>
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297 </ul>
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298
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299 <pre><code>data Delta a = Mono a | Delta a (Delta a)
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300 </code></pre>
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301
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302
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303
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304 </section>
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305 </div></div>
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306
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307 <div class="slide" id="14"><div>
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308 <section>
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309 <header>
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310 <h1 id="delta--monad--instance-">Delta に対する Monad の instance 定義</h1>
52
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311 </header>
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312 <!-- _S9SLIDE_ -->
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313
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314 <ul>
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315 <li>return はバージョンが無いプログラムをバージョン1とする</li>
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316 <li><code>&gt;&gt;=</code> は同じバージョンの値に対する計算を同時に行なう</li>
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317 </ul>
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318
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319 <pre><code>instance Monad Delta where
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320 return x = Mono x
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321 (Mono x) &gt;&gt;= f = f x
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322 (Delta x d) &gt;&gt;= f = Delta (headDelta (f x))
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323 (d &gt;&gt;= (tailDelta . f))
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324 </code></pre>
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325
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326
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327
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328 </section>
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329 </div></div>
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330
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331 <div class="slide" id="15"><div>
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332 <section>
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333 <header>
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334 <h1 id="section-8">元のプログラムとプログラムの変更</h1>
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335 </header>
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336 <!-- _S9SLIDE_ -->
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337
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338 <p><img src="pictures/original_program.svg" alt="original_program" /></p>
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339
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340
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341
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342 </section>
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343 </div></div>
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344
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345 <div class="slide" id="16"><div>
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346 <section>
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347 <header>
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348 <h1 id="delta--1">Delta によって記述されたプログラムの実行</h1>
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349 </header>
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350 <!-- _S9SLIDE_ -->
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351
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352 <p><img src="pictures/delta_program.svg" alt="delta_program" /></p>
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353
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354
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355
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356 </section>
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357 </div></div>
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358
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359 <div class="slide" id="17"><div>
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360 <section>
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361 <header>
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362 <h1 id="delta--2">Delta のメリット</h1>
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363 </header>
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364 <!-- _S9SLIDE_ -->
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365
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366 <ul>
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367 <li>全てのバージョンを同時に実行できる</li>
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368 <li>任意のバージョンの組み合せを同時に実行できる
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369 <ul>
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370 <li>デバッグに利用したり 通常系/検証系 として動かす</li>
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371 </ul>
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372 </li>
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373 <li>Monad なので Category との対応がある
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374 <ul>
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375 <li>2 つのバージョンを選ぶことは Delta が持つプログラムの product</li>
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376 <li>任意のバージョンを生成できる Colimit は Program の Repository</li>
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377 </ul>
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378 </li>
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379 </ul>
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380
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381 <style>
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382 .slide.cover H2 {
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383 margin-top:72px;
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384 font-size:72px;
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385 }
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386 .slide.cover H3#author {
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387 margin-top:72px;
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388 font-size:42px;
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389 }
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390 </style>
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391
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392 <!-- vim: set filetype=markdown.slide: -->
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393 <!-- === end markdown block === -->
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394
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395 </section>
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396 </div></div>
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397
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398
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399 <script src="scripts/script.js"></script>
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400 <!-- Copyright © 2010–2011 Vadim Makeev, http://pepelsbey.net/ -->
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401 </body>
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402 </html>