changeset 120:8a84cda440f3

Update slide
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Tue, 14 Feb 2017 11:31:08 +0900
parents 26563097333c
children 137aae675a94
files presentation/images/akashaPut.graffle presentation/images/akashaPut.pdf presentation/images/akashaPut.svg presentation/images/mcs.graffle presentation/images/mcs.pdf presentation/images/mcs.svg presentation/images/put.graffle presentation/images/put.pdf presentation/images/put.svg presentation/slide.html presentation/slide.md presentation/slide.pdf.html
diffstat 12 files changed, 447 insertions(+), 228 deletions(-) [+]
line wrap: on
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Binary file presentation/images/akashaPut.graffle has changed
Binary file presentation/images/akashaPut.pdf has changed
--- a/presentation/images/akashaPut.svg	Mon Feb 13 17:41:26 2017 +0900
+++ b/presentation/images/akashaPut.svg	Tue Feb 14 11:31:08 2017 +0900
@@ -21,54 +21,72 @@
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--- a/presentation/slide.html	Mon Feb 13 17:41:26 2017 +0900
+++ b/presentation/slide.html	Tue Feb 14 11:31:08 2017 +0900
@@ -86,7 +86,7 @@
 <!-- === begin markdown block ===
 
       generated by markdown/1.2.0 on Ruby 2.3.3 (2016-11-21) [x86_64-darwin16]
-                on 2017-02-13 17:40:39 +0900 with Markdown engine kramdown (1.13.0)
+                on 2017-02-14 11:30:47 +0900 with Markdown engine kramdown (1.13.0)
                   using options {}
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@@ -129,7 +129,22 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-2">モデル検査的アプローチについての流れ</h1>
+<h1 id="section-2">本発表ではモデル検査的アプローチについて中心に見ていきます</h1>
+<ul>
+  <li>修士論文の内部の比率は半分半分くらい</li>
+  <li>定理証明の方は説明する内容が多くて複雑</li>
+  <li>モデル検査的アプローチは過去論文を提出したもの
+    <ul>
+      <li>なのでそちらをメインで発表します</li>
+    </ul>
+  </li>
+</ul>
+
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
+<h1 id="section-3">モデル検査的アプローチについての流れ</h1>
 <ul>
   <li>Continuation based C (CbC) 言語について</li>
   <li>CbC における CodeSegment と DataSegment を用いたプログラミングスタイル</li>
@@ -159,16 +174,24 @@
 <ul>
   <li>CodeSegment とは
     <ul>
-      <li>処理の単位</li>
+      <li>処理の単位であり、入力と出力を持つ</li>
       <li>結合や分割が容易</li>
-      <li>入力と出力を持つ</li>
     </ul>
   </li>
-  <li>CodeSegment どうしを接続することによりプログラム全体を作る</li>
+  <li>CodeSegment どうしを接続することによりプログラム全体を作る
+    <ul>
+      <li>関数呼び出しと違って戻ってこない(goto)</li>
+    </ul>
+  </li>
 </ul>
 
 <p><img src="./images/cs.svg" alt="cs" width="50%" /></p>
 
+<pre><code>__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+</code></pre>
+
 
 </div>
 <div class='slide '>
@@ -186,11 +209,16 @@
 
 <p><img src="./images/ds.svg" alt="ds" width="50%" /></p>
 
+<pre><code>__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+</code></pre>
+
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-3">メタ計算</h1>
+<h1 id="section-4">メタ計算</h1>
 <ul>
   <li>とある計算を実現するための計算</li>
   <li>ネットワーク接続、例外処理、メモリ確保、並列処理など</li>
@@ -244,7 +272,7 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-4">赤黒木</h1>
+<h1 id="section-5">赤黒木</h1>
 <ul>
   <li>データの保存に用いる二分木</li>
   <li>特に赤黒木はノードが持つ赤か黒の色を使って木のバランスを取る
@@ -256,7 +284,7 @@
   </li>
 </ul>
 
-<p><img src="./images/rbtree.svg" alt="rbtree" width="50%" /></p>
+<p><img src="./images/rbtree.svg" alt="rbtree" width="35%" /></p>
 
 
 </div>
@@ -271,11 +299,14 @@
 
 <p><img src="./images/put.svg" alt="put" width="50%" /></p>
 
+<pre><code>goto meta(context, Put);
+</code></pre>
+
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-5">仕様の記述とその確認</h1>
+<h1 id="section-6">仕様の記述とその確認</h1>
 <ul>
   <li>「バランスが取れている」とは何かを表現できる必要がある
     <ul>
@@ -306,6 +337,9 @@
   </li>
 </ul>
 
+<pre><code>assert(x &lt; 10);
+</code></pre>
+
 
 </div>
 <div class='slide '>
@@ -326,36 +360,21 @@
   </li>
 </ul>
 
-
-</div>
-<div class='slide '>
-<!-- _S9SLIDE_ -->
-<h1 id="akasha">メタ計算ライブラリ akasha</h1>
-<ul>
-  <li>メタ計算としてプログラムの状態を数え上げる
-    <ul>
-      <li>goto された時に挿入される要素の組み合わせを全て列挙して実行する</li>
-      <li>その度に仕様の式は成り立つかをチェックする</li>
-    </ul>
-  </li>
-  <li>ノーマルレベルのコードを検証用に変更せず検証可能</li>
-</ul>
-
-<p><img src="./images/akashaPut.svg" alt="akashaPut" width="51%" /></p>
+<pre><code>assert(x &lt; 10);
+</code></pre>
 
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-6">チェックする仕様</h1>
+<h1 id="section-7">チェックする仕様</h1>
 <ul>
   <li>赤黒木の高さに関する仕様に以下のものがある
     <ul>
       <li>木をルートから辿った際に最も長い経路は最も短い経路の高々2倍に収まる</li>
     </ul>
   </li>
-  <li>以下のように assert を用いて CbC で定義できる</li>
-  <li>この仕様が満たされるかをチェックする</li>
+  <li>以下のような条件式を仕様として CbC で定義、検証できる</li>
 </ul>
 
 <pre><code>__code verifySpecificationFinish(struct Context* context) {
@@ -373,6 +392,27 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
+<h1 id="akasha">メタ計算ライブラリ akasha</h1>
+<ul>
+  <li>メタ計算としてプログラムの状態を数え上げる
+    <ul>
+      <li>goto された時に挿入される要素の組み合わせを全て列挙して実行する
+        <ul>
+          <li>赤黒木の状態の保存、挿入、チェック、次の状態の列挙、赤黒木の再現……</li>
+        </ul>
+      </li>
+      <li>その度に仕様の式は成り立つかをチェックする</li>
+    </ul>
+  </li>
+  <li>ノーマルレベルのコードを検証用に変更せず検証可能</li>
+</ul>
+
+<p><img src="./images/akashaPut.svg" alt="akashaPut" width="51%" /></p>
+
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
 <h1 id="akasha--cbmc-">akasha と CBMC の比較</h1>
 <ul>
   <li>akasha は有限の要素数の組み合わせをチェックする
@@ -395,18 +435,6 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-7">定理証明的なアプローチの流れ</h1>
-<ul>
-  <li>プログラムを証明するにはどうするのか</li>
-  <li>証明支援系 Agda における証明</li>
-  <li>Agda による CbC の定義</li>
-  <li>Agda を用いて CbC のコードを証明する</li>
-</ul>
-
-
-</div>
-<div class='slide '>
-<!-- _S9SLIDE_ -->
 <h1 id="continuation-based-c-">定理証明を Continuation based C へ適用するには</h1>
 <ul>
   <li>任意の回数だけ木の操作を行なっても大丈夫なことを保証したい</li>
@@ -475,7 +503,7 @@
   <li>部分型を使う
     <ul>
       <li>Java におけるインターフェース、Haskell における型クラス</li>
-      <li>「このデータにはこのフィールドさえあれば良い」</li>
+      <li>「このフィールドXがあればデータ型Tとみなして良い」</li>
     </ul>
   </li>
 </ul>
@@ -493,11 +521,16 @@
   </li>
 </ul>
 
+<pre><code>cs0 : CodeSegment ds0 ds1
+cs0 = cs (\d -&gt; goto cs1 (record {c = (ds0.a d) + (ds0.b d)}))
+</code></pre>
+
 <pre><code>main : ds1
 main = goto cs0 (record {a = 100 ; b = 50})
 </code></pre>
 <pre><code>main : Meta
-main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70}) ; c' = 0 ; next = (N.cs id)})
+main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70})
+                                 ; c' = 0 ; next = (N.cs id)})
 </code></pre>
 
 
@@ -553,6 +586,30 @@
   <li>赤黒木の挿入に関する性質を証明する</li>
 </ul>
 
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
+<h1 id="section-11">発表履歴</h1>
+<ul>
+  <li>Agda 入門.
+    <ul>
+      <li>オープンソースカンファレンス 2014 Okinawa, May 2014.</li>
+    </ul>
+  </li>
+  <li>形式手法を学び始めて思うことと、形式手法を広めるには(2p).
+    <ul>
+      <li>情報処理学会ソフトウェア工学研究会 (IPSJ SIGSE) ウィンターワークショップ 2015・ イン・宜野湾 (WWS2015), Jan 2015.</li>
+    </ul>
+  </li>
+  <li>Continuation based C を用いたプログラムの検証手法(6p).
+    <ul>
+      <li>2016 年並列/分散/協調処理に関する『松本』サマー・ワークショップ (SWoPP2016)</li>
+      <li>情報処理学会・プログラミング研究会 第 110 回プログラミング研究会 (PRO-2016-2) Aug 2016.</li>
+    </ul>
+  </li>
+</ul>
+
 <!-- vim: set filetype=markdown.slide: -->
 
 <!-- === end markdown block === -->
--- a/presentation/slide.md	Mon Feb 13 17:41:26 2017 +0900
+++ b/presentation/slide.md	Tue Feb 14 11:31:08 2017 +0900
@@ -21,6 +21,12 @@
     * 型システムを通して CbC の形式的な定義を得る
     * SingleLinkedStack の性質の証明
 
+# 本発表ではモデル検査的アプローチについて中心に見ていきます
+* 修士論文の内部の比率は半分半分くらい
+* 定理証明の方は説明する内容が多くて複雑
+* モデル検査的アプローチは過去論文を提出したもの
+    *  なのでそちらをメインで発表します
+
 # モデル検査的アプローチについての流れ
 * Continuation based C (CbC) 言語について
 * CbC における CodeSegment と DataSegment を用いたプログラミングスタイル
@@ -37,13 +43,19 @@
 
 # CodeSegment
 * CodeSegment とは
-    * 処理の単位
+    * 処理の単位であり、入力と出力を持つ
     * 結合や分割が容易
-    * 入力と出力を持つ
 * CodeSegment どうしを接続することによりプログラム全体を作る
+    * 関数呼び出しと違って戻ってこない(goto)
 
 ![cs](./images/cs.svg){:width="50%"}
 
+```
+__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+```
+
 
 # DataSegment
 * DataSegment とは
@@ -53,6 +65,12 @@
 
 ![ds](./images/ds.svg){:width="50%"}
 
+```
+__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+```
+
 # メタ計算
 * とある計算を実現するための計算
 * ネットワーク接続、例外処理、メモリ確保、並列処理など
@@ -87,15 +105,20 @@
     * 赤ノードは2つの黒ノードを子として持つ(よって赤ノードが続くことは無い)
     * ルートから最下位ノードへの経路に含まれる黒ノードの数はどの最下位ノードでも一定
 
-![rbtree](./images/rbtree.svg){:width="50%"}
+![rbtree](./images/rbtree.svg){:width="35%"}
 
 # GearsOS における赤黒木の利用例(ノードの挿入)
 * 挿入したい要素を DataSegment に格納して次の CodeSegment へ goto
 * goto する前に Meta CodeSegment が実行されて木に挿入する
 * GearsOS では木の実装のためにスタックを用いて経路情報を保持している
 
+
 ![put](./images/put.svg){:width="50%"}
 
+```
+goto meta(context, Put);
+```
+
 # 仕様の記述とその確認
 * 「バランスが取れている」とは何かを表現できる必要がある
     * 実行可能な CbC の式を使った assert になる
@@ -110,6 +133,10 @@
     * 仕様は bool になる式を用いた assert
     * デメリット: promela は C とは記述が異なる
 
+```
+assert(x < 10);
+```
+
 # 既存のモデル検査器 CBMC
 * CBMC
     * 検証対象のCソースを変更しないでも良い
@@ -118,19 +145,14 @@
     * 仕様は bool になる式を用いた assert
     * 有限ステップ検証する有界モデル検査器
 
-# メタ計算ライブラリ akasha
-* メタ計算としてプログラムの状態を数え上げる
-    * goto された時に挿入される要素の組み合わせを全て列挙して実行する
-    * その度に仕様の式は成り立つかをチェックする
-* ノーマルレベルのコードを検証用に変更せず検証可能
-
-![akashaPut](./images/akashaPut.svg){:width="51%"}
+```
+assert(x < 10);
+```
 
 # チェックする仕様
 * 赤黒木の高さに関する仕様に以下のものがある
     * 木をルートから辿った際に最も長い経路は最も短い経路の高々2倍に収まる
-* 以下のように assert を用いて CbC で定義できる
-* この仕様が満たされるかをチェックする
+* 以下のような条件式を仕様として CbC で定義、検証できる
 
 ```
 __code verifySpecificationFinish(struct Context* context) {
@@ -144,6 +166,15 @@
 }
 ```
 
+# メタ計算ライブラリ akasha
+* メタ計算としてプログラムの状態を数え上げる
+    * goto された時に挿入される要素の組み合わせを全て列挙して実行する
+        * 赤黒木の状態の保存、挿入、チェック、次の状態の列挙、赤黒木の再現……
+    * その度に仕様の式は成り立つかをチェックする
+* ノーマルレベルのコードを検証用に変更せず検証可能
+
+![akashaPut](./images/akashaPut.svg){:width="51%"}
+
 # akasha と CBMC の比較
 * akasha は有限の要素数の組み合わせをチェックする
     * 要素数が13個までならどの順で木に挿入しても良い
@@ -154,12 +185,6 @@
     * akasha は返した
 * 固定の要素数までの仕様検査で十分なのか?
 
-# 定理証明的なアプローチの流れ
-* プログラムを証明するにはどうするのか
-* 証明支援系 Agda における証明
-* Agda による CbC の定義
-* Agda を用いて CbC のコードを証明する
-
 # 定理証明を Continuation based C へ適用するには
 * 任意の回数だけ木の操作を行なっても大丈夫なことを保証したい
 * そのままプログラムの性質を保証してやる
@@ -206,19 +231,25 @@
 * メタレベルを使うための制約を満たしていれば良い、ということを表現できれば良い
 * 部分型を使う
     * Java におけるインターフェース、Haskell における型クラス
-    * 「このデータにはこのフィールドさえあれば良い」
+    * 「このフィールドXがあればデータ型Tとみなして良い」
 
 # Agda 上のメタ計算
 * ノーマルレベルの型を保持したままメタレベルの計算を利用できる
     * cs0 の定義はメタ計算用に変更しなくても良い
 
 ```
+cs0 : CodeSegment ds0 ds1
+cs0 = cs (\d -> goto cs1 (record {c = (ds0.a d) + (ds0.b d)}))
+```
+
+```
 main : ds1
 main = goto cs0 (record {a = 100 ; b = 50})
 ```
 ```
 main : Meta
-main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70}) ; c' = 0 ; next = (N.cs id)})
+main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70})
+                                 ; c' = 0 ; next = (N.cs id)})
 ```
 
 # Agda 上に CbC を記述した成果
@@ -244,5 +275,14 @@
 * 型情報から stub を自動生成すkる
 * 赤黒木の挿入に関する性質を証明する
 
+# 発表履歴
+* Agda 入門.
+    * オープンソースカンファレンス 2014 Okinawa, May 2014.
+* 形式手法を学び始めて思うことと、形式手法を広めるには(2p).
+    * 情報処理学会ソフトウェア工学研究会 (IPSJ SIGSE) ウィンターワークショップ 2015・ イン・宜野湾 (WWS2015), Jan 2015.
+* Continuation based C を用いたプログラムの検証手法(6p).
+    * 2016 年並列/分散/協調処理に関する『松本』サマー・ワークショップ (SWoPP2016)
+    * 情報処理学会・プログラミング研究会 第 110 回プログラミング研究会 (PRO-2016-2) Aug 2016.
+
 <!-- vim: set filetype=markdown.slide: -->
 
--- a/presentation/slide.pdf.html	Mon Feb 13 17:41:26 2017 +0900
+++ b/presentation/slide.pdf.html	Tue Feb 14 11:31:08 2017 +0900
@@ -70,7 +70,7 @@
 <!-- === begin markdown block ===
 
       generated by markdown/1.2.0 on Ruby 2.3.3 (2016-11-21) [x86_64-darwin16]
-                on 2017-02-13 17:40:39 +0900 with Markdown engine kramdown (1.13.0)
+                on 2017-02-14 11:30:47 +0900 with Markdown engine kramdown (1.13.0)
                   using options {}
   -->
 
@@ -113,7 +113,22 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-2">モデル検査的アプローチについての流れ</h1>
+<h1 id="section-2">本発表ではモデル検査的アプローチについて中心に見ていきます</h1>
+<ul>
+  <li>修士論文の内部の比率は半分半分くらい</li>
+  <li>定理証明の方は説明する内容が多くて複雑</li>
+  <li>モデル検査的アプローチは過去論文を提出したもの
+    <ul>
+      <li>なのでそちらをメインで発表します</li>
+    </ul>
+  </li>
+</ul>
+
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
+<h1 id="section-3">モデル検査的アプローチについての流れ</h1>
 <ul>
   <li>Continuation based C (CbC) 言語について</li>
   <li>CbC における CodeSegment と DataSegment を用いたプログラミングスタイル</li>
@@ -143,16 +158,24 @@
 <ul>
   <li>CodeSegment とは
     <ul>
-      <li>処理の単位</li>
+      <li>処理の単位であり、入力と出力を持つ</li>
       <li>結合や分割が容易</li>
-      <li>入力と出力を持つ</li>
     </ul>
   </li>
-  <li>CodeSegment どうしを接続することによりプログラム全体を作る</li>
+  <li>CodeSegment どうしを接続することによりプログラム全体を作る
+    <ul>
+      <li>関数呼び出しと違って戻ってこない(goto)</li>
+    </ul>
+  </li>
 </ul>
 
 <p><img src="./images/cs.svg" alt="cs" width="50%" /></p>
 
+<pre><code>__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+</code></pre>
+
 
 </div>
 <div class='slide '>
@@ -170,11 +193,16 @@
 
 <p><img src="./images/ds.svg" alt="ds" width="50%" /></p>
 
+<pre><code>__code cs0(int a, int b){
+  goto cs1(a+b);
+}
+</code></pre>
+
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-3">メタ計算</h1>
+<h1 id="section-4">メタ計算</h1>
 <ul>
   <li>とある計算を実現するための計算</li>
   <li>ネットワーク接続、例外処理、メモリ確保、並列処理など</li>
@@ -228,7 +256,7 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-4">赤黒木</h1>
+<h1 id="section-5">赤黒木</h1>
 <ul>
   <li>データの保存に用いる二分木</li>
   <li>特に赤黒木はノードが持つ赤か黒の色を使って木のバランスを取る
@@ -240,7 +268,7 @@
   </li>
 </ul>
 
-<p><img src="./images/rbtree.svg" alt="rbtree" width="50%" /></p>
+<p><img src="./images/rbtree.svg" alt="rbtree" width="35%" /></p>
 
 
 </div>
@@ -255,11 +283,14 @@
 
 <p><img src="./images/put.svg" alt="put" width="50%" /></p>
 
+<pre><code>goto meta(context, Put);
+</code></pre>
+
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-5">仕様の記述とその確認</h1>
+<h1 id="section-6">仕様の記述とその確認</h1>
 <ul>
   <li>「バランスが取れている」とは何かを表現できる必要がある
     <ul>
@@ -290,6 +321,9 @@
   </li>
 </ul>
 
+<pre><code>assert(x &lt; 10);
+</code></pre>
+
 
 </div>
 <div class='slide '>
@@ -310,36 +344,21 @@
   </li>
 </ul>
 
-
-</div>
-<div class='slide '>
-<!-- _S9SLIDE_ -->
-<h1 id="akasha">メタ計算ライブラリ akasha</h1>
-<ul>
-  <li>メタ計算としてプログラムの状態を数え上げる
-    <ul>
-      <li>goto された時に挿入される要素の組み合わせを全て列挙して実行する</li>
-      <li>その度に仕様の式は成り立つかをチェックする</li>
-    </ul>
-  </li>
-  <li>ノーマルレベルのコードを検証用に変更せず検証可能</li>
-</ul>
-
-<p><img src="./images/akashaPut.svg" alt="akashaPut" width="51%" /></p>
+<pre><code>assert(x &lt; 10);
+</code></pre>
 
 
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-6">チェックする仕様</h1>
+<h1 id="section-7">チェックする仕様</h1>
 <ul>
   <li>赤黒木の高さに関する仕様に以下のものがある
     <ul>
       <li>木をルートから辿った際に最も長い経路は最も短い経路の高々2倍に収まる</li>
     </ul>
   </li>
-  <li>以下のように assert を用いて CbC で定義できる</li>
-  <li>この仕様が満たされるかをチェックする</li>
+  <li>以下のような条件式を仕様として CbC で定義、検証できる</li>
 </ul>
 
 <pre><code>__code verifySpecificationFinish(struct Context* context) {
@@ -357,6 +376,27 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
+<h1 id="akasha">メタ計算ライブラリ akasha</h1>
+<ul>
+  <li>メタ計算としてプログラムの状態を数え上げる
+    <ul>
+      <li>goto された時に挿入される要素の組み合わせを全て列挙して実行する
+        <ul>
+          <li>赤黒木の状態の保存、挿入、チェック、次の状態の列挙、赤黒木の再現……</li>
+        </ul>
+      </li>
+      <li>その度に仕様の式は成り立つかをチェックする</li>
+    </ul>
+  </li>
+  <li>ノーマルレベルのコードを検証用に変更せず検証可能</li>
+</ul>
+
+<p><img src="./images/akashaPut.svg" alt="akashaPut" width="51%" /></p>
+
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
 <h1 id="akasha--cbmc-">akasha と CBMC の比較</h1>
 <ul>
   <li>akasha は有限の要素数の組み合わせをチェックする
@@ -379,18 +419,6 @@
 </div>
 <div class='slide '>
 <!-- _S9SLIDE_ -->
-<h1 id="section-7">定理証明的なアプローチの流れ</h1>
-<ul>
-  <li>プログラムを証明するにはどうするのか</li>
-  <li>証明支援系 Agda における証明</li>
-  <li>Agda による CbC の定義</li>
-  <li>Agda を用いて CbC のコードを証明する</li>
-</ul>
-
-
-</div>
-<div class='slide '>
-<!-- _S9SLIDE_ -->
 <h1 id="continuation-based-c-">定理証明を Continuation based C へ適用するには</h1>
 <ul>
   <li>任意の回数だけ木の操作を行なっても大丈夫なことを保証したい</li>
@@ -459,7 +487,7 @@
   <li>部分型を使う
     <ul>
       <li>Java におけるインターフェース、Haskell における型クラス</li>
-      <li>「このデータにはこのフィールドさえあれば良い」</li>
+      <li>「このフィールドXがあればデータ型Tとみなして良い」</li>
     </ul>
   </li>
 </ul>
@@ -477,11 +505,16 @@
   </li>
 </ul>
 
+<pre><code>cs0 : CodeSegment ds0 ds1
+cs0 = cs (\d -&gt; goto cs1 (record {c = (ds0.a d) + (ds0.b d)}))
+</code></pre>
+
 <pre><code>main : ds1
 main = goto cs0 (record {a = 100 ; b = 50})
 </code></pre>
 <pre><code>main : Meta
-main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70}) ; c' = 0 ; next = (N.cs id)})
+main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70})
+                                 ; c' = 0 ; next = (N.cs id)})
 </code></pre>
 
 
@@ -537,6 +570,30 @@
   <li>赤黒木の挿入に関する性質を証明する</li>
 </ul>
 
+
+</div>
+<div class='slide '>
+<!-- _S9SLIDE_ -->
+<h1 id="section-11">発表履歴</h1>
+<ul>
+  <li>Agda 入門.
+    <ul>
+      <li>オープンソースカンファレンス 2014 Okinawa, May 2014.</li>
+    </ul>
+  </li>
+  <li>形式手法を学び始めて思うことと、形式手法を広めるには(2p).
+    <ul>
+      <li>情報処理学会ソフトウェア工学研究会 (IPSJ SIGSE) ウィンターワークショップ 2015・ イン・宜野湾 (WWS2015), Jan 2015.</li>
+    </ul>
+  </li>
+  <li>Continuation based C を用いたプログラムの検証手法(6p).
+    <ul>
+      <li>2016 年並列/分散/協調処理に関する『松本』サマー・ワークショップ (SWoPP2016)</li>
+      <li>情報処理学会・プログラミング研究会 第 110 回プログラミング研究会 (PRO-2016-2) Aug 2016.</li>
+    </ul>
+  </li>
+</ul>
+
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