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changeset 22:b37e4cd69468

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author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 05 Feb 2023 16:35:38 +0900
parents 19f19ec356f5
children 016e82a71407
files Paper/master_paper.aux Paper/master_paper.bbl Paper/master_paper.blg Paper/master_paper.dvi Paper/master_paper.fdb_latexmk Paper/master_paper.fls Paper/master_paper.lof Paper/master_paper.log Paper/master_paper.lol Paper/master_paper.pdf Paper/master_paper.synctex.gz Paper/master_paper.toc Paper/tex/spin_dpp.tex Paper/tex/tree_desc.tex Paper/tex/while_loop.tex slide/DPP.jpg slide/logo.svg slide/memo.md slide/meta-cg-dg.jpg slide/meta_cg_dg.svg slide/slide.md slide/slide.pdf
diffstat 22 files changed, 3650 insertions(+), 13 deletions(-) [+]
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+++ b/Paper/master_paper.aux	Sun Feb 05 16:35:38 2023 +0900
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+++ b/Paper/master_paper.bbl	Sun Feb 05 16:35:38 2023 +0900
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+\begin{thebibliography}{10}
+
+\bibitem{cbc-gcc}
+cbc-gcc - 並列信頼研 mercurial repository.
+\newblock \url{http://www.cr.ie.u-ryukyu.ac.jp/hg/CbC/CbC_gcc/}.
+\newblock Accessed: 2020/2/9(Sun).
+
+\bibitem{agda}
+Ulf Norell.
+\newblock Dependently typed programming in agda.
+\newblock In {\em Proceedings of the 4th International Workshop on Types in
+  Language Design and Implementation}, TLDI '09, pp. 1--2, New York, NY, USA,
+  2009. ACM.
+
+\bibitem{ryokka-sigos}
+政尊外間, 真治河野.
+\newblock Gearsosのagdaによる記述と検証.
+\newblock Technical Report~5, 琉球大学大学院理工学研究科情報工学専攻,
+  琉球大学工学部情報工学科, may 2018.
+
+\bibitem{EdmundM}
+{Edmund M. Clarke, Jr}.
+\newblock In {\em {Model Checking, Second Edition}}, 2018.
+
+\bibitem{ikkun-master}
+東恩納琢偉.
+\newblock Gears os でモデル検査を実現する方法について.
+\newblock Master's thesis, 琉球大学 大学院理工学研究科 情報工学専攻, 2021.
+
+\bibitem{kaito-lola}
+Tokumori Kaito and Kono Shinji.
+\newblock Implementing continuation based language in llvm and clang.
+\newblock {\em LOLA 2015, Kyoto}, July 2015.
+
+\bibitem{agda-wiki}
+The agda wiki.
+\newblock \url{http://wiki.portal.chalmers.se/agda/pmwiki.php}.
+
+\bibitem{Stump:2016:VFP:2841316}
+Aaron Stump.
+\newblock {\em Verified Functional Programming in Agda}.
+\newblock Association for Computing Machinery and Morgan \&\#38; Claypool, New
+  York, NY, USA, 2016.
+
+\bibitem{agda-stdlib}
+agda-stdlib.
+\newblock \url{https://github.com/agda/agda-stdlib }.
+\newblock Accessed: 2023/2/1(Wed).
+
+\bibitem{atton-master}
+比嘉健太.
+\newblock メタ計算を用いた continuation based c の検証手法.
+\newblock Master's thesis, 琉球大学 大学院理工学研究科 情報工学専攻, 2017.
+
+\bibitem{agda2-hoare}
+Hoare logic in agda2.
+\newblock \url{https://github.com/IKEGAMIDaisuke/HoareLogic}.
+\newblock Accessed: 2020/2/9(Sun).
+
+\bibitem{cr-ryukyu}
+Hoare logic - 並列信頼研 mercurial repository.
+\newblock \url{http://www.cr.ie.u-ryukyu.ac.jp/hg/Members/ryokka/HoareLogic/}.
+\newblock Accessed: 2020/2/9(Sun).
+
+\bibitem{hoare}
+C.~A.~R. Hoare.
+\newblock An axiomatic basis for computer programming.
+\newblock {\em Commun. ACM}, Vol.~12, No.~10, p. 576^^e2^^80^^93580, October
+  1969.
+
+\bibitem{rbtree}
+渡邉.
+\newblock データ構造と基本アルゴリズム, 2000.
+
+\bibitem{parusu-master}
+伊波立樹.
+\newblock Gears os の並列処理.
+\newblock Master's thesis, 琉球大学 大学院理工学研究科 情報工学専攻, 2018.
+
+\bibitem{spin}
+Spin - formal verification.
+\newblock \url{http://spinroot.com/}.
+\newblock Accessed: 2023/2/1(Wed).
+
+\bibitem{mitsuki-prosym}
+宮城光希, 河野真治.
+\newblock Codegear と datagear を持つ gears os の設計.
+\newblock  第59回プログラミング・シンポジウム予稿集, 第2018巻, pp. 197--206,
+  jan 2018.
+
+\bibitem{model}
+広瀬健.
+\newblock コンピュータ基礎理論ハンドブック 形式的モデルと意味論, 1994.
+
+\end{thebibliography}
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+
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+] (./master_paper.lol [4
+
+])
+\tf@lol=\write7
+\openout7 = `master_paper.lol'.
+
+ (./tex/intro.tex [5]
+第 1 章(6ページ)
+) (./tex/cbc.tex [6
+
+]
+第 2 章(7ページ)
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+File: ts1cmtt.fd 2019/12/16 v2.5j Standard LaTeX font definitions
+) [8]) (./src/cbc/cbc.txt) [9]
+File: fig/cbc_codegear.pdf Graphic file (type pdf)
+<fig/cbc_codegear.pdf>
+) (./tex/agda.tex [10]
+第 3 章(11ページ)
+LaTeX Font Info:    Font shape `JT2/hmc/m/n' will be
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+ [14] (./src/cong.agda.replaced) (./src/agda-term3.agda.replaced) [15]) (./tex/cbc_agda.tex [16]
+第 4 章(17ページ)
+(./src/agda/cbc-agda.agda.replaced
+consecutive:
+) (./src/agda/cbc-agda.agda.replaced
+consecutive:
+) [17
+
+] (./src/agda/cbc-agda.agda.replaced
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+ []
+
+[18]) (./tex/hoare.tex [19]
+第 5 章(20ページ)
+[20
+
+]) (./tex/while_loop.tex (./src/while_loop_impl/while_loop_dg.agda.replaced) (./src/while_loop_impl/init_cg.agda.replaced) (./src/while_loop_impl/while_loop.agda.replaced) [21] (./src/while_loop_impl/while_loop_c.agda.replaced) (./src/while_loop_verif/init_cg.agda.replaced) (./src/while_loop_verif/conversion.agda.replaced) [22] (./src/while_loop_verif/while_loop.agda.replaced) (./src/while_loop_verif/verif_term.agda.replaced) [23] (./src/while_loop_verif/verif_loop.agda.replaced) (./src/while_loop_verif/verif.agda.replaced)) (./tex/tree_desc.tex [24]
+File: fig/rbt-stack.pdf Graphic file (type pdf)
+<fig/rbt-stack.pdf>
+ (./src/bt_impl/bt_env.agda.replaced) [25] (./src/bt_impl/find.agda.replaced
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+第 6 章(29ページ)
+File: fig/Dining.pdf Graphic file (type pdf)
+<fig/Dining.pdf>
+[29
+
+] (./src/dpp-verif/spin.pml [30])
+File: fig/dpp-model.pdf Graphic file (type pdf)
+<fig/dpp-model.pdf>
+) (./tex/dpp_impl.tex [31] [32] (./src/agda-dpp-impl.agda.replaced) (./src/agda-dpp-impl.agda.replaced
+consecutive:
+) (./src/agda-dpp-impl.agda.replaced
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+) (./src/agda-dpp-impl.agda.replaced
+consecutive:
+) (./src/agda-dpp-impl.agda.replaced
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+第 7 章(41ページ)
+) (./tex/thanks.tex [41
+
+]) (./master_paper.bbl [42
+
+]
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+Output written on master_paper.dvi (49 pages, 322416 bytes).
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/master_paper.lol	Sun Feb 05 16:35:38 2023 +0900
@@ -0,0 +1,43 @@
+\contentsline {lstlisting}{\numberline {2.1}C言語で記述した フィボナッチ数列の n 番目を求めるコード}{7}{lstlisting.2.1}%
+\contentsline {lstlisting}{\numberline {2.2}CbCで記述した フィボナッチ数列の n 番目を求めるコード}{8}{lstlisting.2.2}%
+\contentsline {lstlisting}{\numberline {2.3}cで記述した際の fib 関数のアセンブラ}{8}{lstlisting.2.3}%
+\contentsline {lstlisting}{\numberline {2.4}cbcで記述した際の fib 関数のアセンブラ}{9}{lstlisting.2.4}%
+\contentsline {lstlisting}{\numberline {3.1}plusの実装}{11}{lstlisting.3.1}%
+\contentsline {lstlisting}{\numberline {3.2}二項演算子を用いたplusの実装}{12}{lstlisting.3.2}%
+\contentsline {lstlisting}{\numberline {3.3}Natural の定義}{12}{lstlisting.3.3}%
+\contentsline {lstlisting}{\numberline {3.4}Andの記述}{13}{lstlisting.3.4}%
+\contentsline {lstlisting}{\numberline {3.5}syllogism の記述}{13}{lstlisting.3.5}%
+\contentsline {lstlisting}{\numberline {3.6}入力を省略する Agda コードの例}{14}{lstlisting.3.6}%
+\contentsline {lstlisting}{\numberline {3.7}自然数に0を足しても値が等しいことを証明するAgda}{14}{lstlisting.3.7}%
+\contentsline {lstlisting}{\numberline {3.8}congの定義}{15}{lstlisting.3.8}%
+\contentsline {lstlisting}{\numberline {3.9}加算の交換法則を証明するAgda}{15}{lstlisting.3.9}%
+\contentsline {lstlisting}{\numberline {4.1}Agdaでの DataGear の定義}{17}{lstlisting.4.1}%
+\contentsline {lstlisting}{\numberline {4.2}Agdaでの CodeGear の定義}{17}{lstlisting.4.2}%
+\contentsline {lstlisting}{\numberline {4.3}Agdaでの 停止性が示せない CodeGear の例}{18}{lstlisting.4.3}%
+\contentsline {lstlisting}{\numberline {4.4}Agdaでの CodeGear の初期化}{18}{lstlisting.4.4}%
+\contentsline {lstlisting}{\numberline {5.1}DataGearの定義}{21}{lstlisting.5.1}%
+\contentsline {lstlisting}{\numberline {5.2}DataGear の定義を行う CodeGear}{21}{lstlisting.5.2}%
+\contentsline {lstlisting}{\numberline {5.3}Loop の部分を担う CodeGears}{21}{lstlisting.5.3}%
+\contentsline {lstlisting}{\numberline {5.4}While Loop を行う CodeGear}{22}{lstlisting.5.4}%
+\contentsline {lstlisting}{\numberline {5.5}While Loop を行う CodeGear}{22}{lstlisting.5.5}%
+\contentsline {lstlisting}{\numberline {5.6}init時の Pre Condition を Post Condition に変換する CodeGear}{22}{lstlisting.5.6}%
+\contentsline {lstlisting}{\numberline {5.7}停止性以外の Loop の検証も行う CodeGear}{23}{lstlisting.5.7}%
+\contentsline {lstlisting}{\numberline {5.8}停止性以外の While Loop の検証を行う CodeGear}{23}{lstlisting.5.8}%
+\contentsline {lstlisting}{\numberline {5.9}停止性の検証も行う Loop 部分の CodeGear}{24}{lstlisting.5.9}%
+\contentsline {lstlisting}{\numberline {5.10}停止性の検証も行う While Loop の CodeGear}{24}{lstlisting.5.10}%
+\contentsline {lstlisting}{\numberline {5.11}Binary Tree の DataGear}{25}{lstlisting.5.11}%
+\contentsline {lstlisting}{\numberline {5.12}root から目的のnodeまで辿る CodeGear}{26}{lstlisting.5.12}%
+\contentsline {lstlisting}{\numberline {5.13}Stack から tree を再構築する CodeGear}{26}{lstlisting.5.13}%
+\contentsline {lstlisting}{\numberline {5.14}Binary Tree の Invariant}{27}{lstlisting.5.14}%
+\contentsline {lstlisting}{\numberline {5.15}Binary Tree の検証}{28}{lstlisting.5.15}%
+\contentsline {lstlisting}{\numberline {6.1}SPINにてDPPをモデル検査する際のコードの一部}{30}{lstlisting.6.1}%
+\contentsline {lstlisting}{\numberline {6.2}Gears Agdaでの DPP の 哲学者の状態}{33}{lstlisting.6.2}%
+\contentsline {lstlisting}{\numberline {6.3}Gears Agdaでの DPP の プロセス}{33}{lstlisting.6.3}%
+\contentsline {lstlisting}{\numberline {6.4}Gears Agdaでの DPP の DataGear}{33}{lstlisting.6.4}%
+\contentsline {lstlisting}{\numberline {6.5}Gears Agdaでの DPP の DataGear のinit}{34}{lstlisting.6.5}%
+\contentsline {lstlisting}{\numberline {6.6}Gears Agdaでの DPP の step 実行}{34}{lstlisting.6.6}%
+\contentsline {lstlisting}{\numberline {6.7}Gears Agdaでの DPP の左のフォークを取る記述}{34}{lstlisting.6.7}%
+\contentsline {lstlisting}{\numberline {6.8}Gears Agda で DPP のモデル検査を行うための Meta DataGear}{35}{lstlisting.6.8}%
+\contentsline {lstlisting}{\numberline {6.9}状態の分岐数をカウントする Meta DataGear の定義}{36}{lstlisting.6.9}%
+\contentsline {lstlisting}{\numberline {6.10}DPP での dead lock を検知する Meta CodeGear}{37}{lstlisting.6.10}%
+\contentsline {lstlisting}{\numberline {6.11}重複しているstateを除外する Meta CodeGear}{38}{lstlisting.6.11}%
Binary file Paper/master_paper.pdf has changed
Binary file Paper/master_paper.synctex.gz has changed
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/master_paper.toc	Sun Feb 05 16:35:38 2023 +0900
@@ -0,0 +1,42 @@
+\contentsline {chapter}{研究関連論文業績}{iv}{chapter*.3}%
+\contentsline {chapter}{\numberline {第1章}Gears Agda でのプログラムの検証}{6}{chapter.1}%
+\contentsline {chapter}{\numberline {第2章}Continuation based C}{7}{chapter.2}%
+\contentsline {section}{\numberline {2.1}CodeGear / DataGear}{7}{section.2.1}%
+\contentsline {section}{\numberline {2.2}CbC と C言語の違い}{7}{section.2.2}%
+\contentsline {section}{\numberline {2.3}Meta CodeGear / Meta DataGear}{10}{section.2.3}%
+\contentsline {chapter}{\numberline {第3章}定理証明支援系言語 Agda}{11}{chapter.3}%
+\contentsline {section}{\numberline {3.1}Agdaの基本}{11}{section.3.1}%
+\contentsline {subsection}{\numberline {3.1.1}関数の実装}{11}{subsection.3.1.1}%
+\contentsline {subsection}{\numberline {3.1.2}二項演算子の実装}{12}{subsection.3.1.2}%
+\contentsline {subsection}{\numberline {3.1.3}Data 型の実装}{12}{subsection.3.1.3}%
+\contentsline {subsection}{\numberline {3.1.4}Record 型の実装}{13}{subsection.3.1.4}%
+\contentsline {section}{\numberline {3.2}本論で使用する Agda の記法}{13}{section.3.2}%
+\contentsline {subsection}{\numberline {3.2.1}Agdaの省略記法}{13}{subsection.3.2.1}%
+\contentsline {section}{\numberline {3.3}Agdaによる定理証明}{14}{section.3.3}%
+\contentsline {subsection}{\numberline {3.3.1}自然数に0を足しても値が等しいことを証明するAgda}{14}{subsection.3.3.1}%
+\contentsline {subsection}{\numberline {3.3.2}加算の交換法則を証明するAgda}{15}{subsection.3.3.2}%
+\contentsline {chapter}{\numberline {第4章}GearsAgda 形式で書く Agda}{17}{chapter.4}%
+\contentsline {section}{\numberline {4.1}Gears Agda での Meta Gears}{18}{section.4.1}%
+\contentsline {chapter}{\numberline {第5章}Gears Agda による定理証明}{20}{chapter.5}%
+\contentsline {section}{\numberline {5.1}Hoare Logic}{20}{section.5.1}%
+\contentsline {section}{\numberline {5.2}Invariant を用いた Hoare Logic による検証の方法 }{20}{section.5.2}%
+\contentsline {section}{\numberline {5.3}Gears Agda にて Hoare Logic を用いた検証の例}{21}{section.5.3}%
+\contentsline {subsection}{\numberline {5.3.1}While Loop の実装}{21}{subsection.5.3.1}%
+\contentsline {subsection}{\numberline {5.3.2}While Loop の検証}{22}{subsection.5.3.2}%
+\contentsline {section}{\numberline {5.4}Gears Agda における Binary Tree の検証}{24}{section.5.4}%
+\contentsline {subsection}{\numberline {5.4.1}Gears Agda における木構造の設計}{24}{subsection.5.4.1}%
+\contentsline {subsection}{\numberline {5.4.2}Gears Agda における Binary Tree の実装}{25}{subsection.5.4.2}%
+\contentsline {subsection}{\numberline {5.4.3}Gears Agda における Binary Tree の検証}{27}{subsection.5.4.3}%
+\contentsline {chapter}{\numberline {第6章}Gears Agda によるモデル検査}{29}{chapter.6}%
+\contentsline {section}{\numberline {6.1}モデル検査とは}{29}{section.6.1}%
+\contentsline {section}{\numberline {6.2}Dining Philosophers Problem}{29}{section.6.2}%
+\contentsline {section}{\numberline {6.3}SPINによるモデル検査}{30}{section.6.3}%
+\contentsline {section}{\numberline {6.4}Gears Agdaによるモデル検査の流れ}{31}{section.6.4}%
+\contentsline {section}{\numberline {6.5}Gears Agda によるDPPの実装}{33}{section.6.5}%
+\contentsline {section}{\numberline {6.6}Gears Agda によるDPPの検証}{35}{section.6.6}%
+\contentsline {section}{\numberline {6.7}Gears Agda による live lockの検証方法について}{39}{section.6.7}%
+\contentsline {section}{\numberline {6.8}Gears Agda でのモデル検査の評価}{39}{section.6.8}%
+\contentsline {chapter}{\numberline {第7章}まとめと今後の展望}{41}{chapter.7}%
+\contentsline {section}{\numberline {7.1}今後の課題}{41}{section.7.1}%
+\contentsline {chapter}{謝辞}{42}{chapter*.7}%
+\contentsline {chapter}{参考文献}{43}{chapter*.8}%
--- a/Paper/tex/spin_dpp.tex	Fri Feb 03 19:06:13 2023 +0900
+++ b/Paper/tex/spin_dpp.tex	Sun Feb 05 16:35:38 2023 +0900
@@ -67,7 +67,7 @@
 
 \begin{figure}[htpb]
     \begin{center}
-     \scalebox{0.6}{\includegraphics{fig/dpp-model.pdf}}
+     \scalebox{0.5}{\includegraphics{fig/dpp-model.pdf}}
     \end{center}
     \caption{SPINにて作成した状態遷移図}
     \label{fig:DPP-model}
--- a/Paper/tex/tree_desc.tex	Fri Feb 03 19:06:13 2023 +0900
+++ b/Paper/tex/tree_desc.tex	Sun Feb 05 16:35:38 2023 +0900
@@ -87,10 +87,10 @@
 条件としている。
 
 これを先ほど実装した CodeGear に対して加えることで検証していく。
-先ほど実装した \coderef{bt_find_impl} に対して加えると \coderef{bt_invariant} のようになる。
+先ほど実装した \coderef{bt_find_impl} に対して加えると \coderef{bt_invariant2} のようになる。
 
 
-\lstinputlisting[label=code:bt_invariant, caption=Binary Tree の検証] {src/bt_verif/find.agda.replaced}
+\lstinputlisting[label=code:bt_invariant2, caption=Binary Tree の検証] {src/bt_verif/find.agda.replaced}
 
 現時点では条件を満たしていることの証明まで行っていないが
 コード中の {!!} に記述を行い、前述した While Loop と同じように中身を記述することで検証を行える。
--- a/Paper/tex/while_loop.tex	Fri Feb 03 19:06:13 2023 +0900
+++ b/Paper/tex/while_loop.tex	Sun Feb 05 16:35:38 2023 +0900
@@ -23,9 +23,9 @@
 \{-$\#$ TERMINATING $\#$-\} のタグを付けると
 停止しないプログラムをコンパイルすることができる
 
-これらの CodeGear を繋げることで、 While Loop を行う \coderef{while-loop} を実装することができる。
+これらの CodeGear を繋げることで、 While Loop を行う \coderef{while-loop2} を実装することができる。
 
-\lstinputlisting[label=code:while-loop, caption=While Loop を行う CodeGear] {src/while_loop_impl/while_loop_c.agda.replaced}
+\lstinputlisting[label=code:while-loop2, caption=While Loop を行う CodeGear] {src/while_loop_impl/while_loop_c.agda.replaced}
 
 \subsection{While Loop の検証}
 
@@ -55,21 +55,21 @@
 ここで変換されて作成された Post Condition はプログラム実行中の Invariant となるため、
 停止するまでこの Pre / Post Condition を用いる。
 
-以下の \coderef{loop_verif_cg} は停止性の検証を行っていないが、 Wile Loop の Loop 部分の検証を行う CodeGear となる。
+以下の \coderef{loop_verif_cg1} は停止性の検証を行っていないが、 Wile Loop の Loop 部分の検証を行う CodeGear となる。
 
-\lstinputlisting[label=code:loop_verif_cg, caption=停止性以外の Loop の検証も行う CodeGear] {src/while_loop_verif/while_loop.agda.replaced}
+\lstinputlisting[label=code:loop_verif_cg1, caption=停止性以外の Loop の検証も行う CodeGear] {src/while_loop_verif/while_loop.agda.replaced}
 
 Loop が停止することを示していないため、関数定義の直前に \{-\# TERMINATING \#-\} が記述されている。
 こちらも Loop の実装以外に、Pre / Post Condition を満たしているか検証を行い、次の CodeGear に渡している。
 
 ここまでで定義した Pre / Post Consition が付いている CodeGear を繋げることで、
-停止性以外の While Loop の検証を行う CodeGear を実装できる。
+停止性以外の While Loop の検証を行う CodeGear を実装できる。\coderef{loop_verif_cg2}のようになる。
 
-\lstinputlisting[label=loop_verif_cg, caption=停止性以外の While Loop の検証を行う CodeGear] {src/while_loop_verif/verif_term.agda.replaced}
+\lstinputlisting[label=code:loop_verif_cg2, caption=停止性以外の While Loop の検証を行う CodeGear] {src/while_loop_verif/verif_term.agda.replaced}
 
-停止性の検証も行う While Loop の検証を行う CodeGear を実装する
+\coderef{loop_verif_cg3} 停止性の検証も行う While Loop の検証を行う CodeGear を実装する
 
-\lstinputlisting[label=loop_verif_cg, caption=停止性の検証も行う Loop 部分の CodeGear] {src/while_loop_verif/verif_loop.agda.replaced}
+\lstinputlisting[label=code:loop_verif_cg3, caption=停止性の検証も行う Loop 部分の CodeGear] {src/while_loop_verif/verif_loop.agda.replaced}
 
 停止することを Agda が理解できるように記述する。
 そのため引数に減少する変数 reduce を追加し、
@@ -78,9 +78,9 @@
 loop には先ほど実装した loop の部分を担う CodeGear が次の関数遷移先を引数に受け取れるようにした
 whileLoopSeg を使用する。
 
-そしてこれらを繋げて While Loop の検証を行える\coderef{loop_verif_cg} を実装できた。
+そしてこれらを繋げて While Loop の検証を行える\coderef{loop_verif_cg4} を実装できた。
 
-\lstinputlisting[label=code:loop_verif_cg, caption=停止性の検証も行う While Loop の CodeGear] {src/while_loop_verif/verif.agda.replaced}
+\lstinputlisting[label=code:loop_verif_cg4, caption=停止性の検証も行う While Loop の CodeGear] {src/while_loop_verif/verif.agda.replaced}
 
 
 
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/slide/memo.md	Sun Feb 05 16:35:38 2023 +0900
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+# 
+
+# 目的
+
+
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+      <font-face-src>
+        <font-face-name name="Helvetica"/>
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+    </font-face>
+    <font-face font-family="Helvetica Neue" font-size="12" panose-1="2 0 5 3 0 0 0 2 0 4" units-per-em="1000" underline-position="-100" underline-thickness="50" slope="0" x-height="517" cap-height="714" ascent="951.9958" descent="-212.99744" font-weight="400">
+      <font-face-src>
+        <font-face-name name="HelveticaNeue"/>
+      </font-face-src>
+    </font-face>
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+    <title>Canvas 1</title>
+    <rect fill="white" x="17.5" y="287.5" width="585.3511" height="421.08984"/>
+    <g id="Canvas_1_Layer_1">
+      <title>Layer 1</title>
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+          <tspan font-family="Helvetica" font-size="9" font-weight="400" fill="#945200" x="0" y="9">  </tspan>
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+        </g>
+        <g id="Graphic_95">
+          <text transform="translate(38.798856 392)" fill="#c25800">
+            <tspan font-family="Helvetica Neue" font-size="12" font-weight="400" fill="#c25800" x=".6286934" y="11">Meta Data Gear</tspan>
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+        </g>
+      </g>
+      <g id="Group_91">
+        <g id="Graphic_93">
+          <rect x="472.17553" y="378" width="130.17553" height="90" fill="white"/>
+          <path d="M 472.17553 378 L 602.3511 378 L 602.3511 468 L 472.17553 468 Z" stroke="#ff9300" stroke-linecap="round" stroke-linejoin="round" stroke-dasharray="4.0,4.0" stroke-width="1"/>
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+            <tspan font-family="Helvetica Neue" font-size="12" font-weight="400" fill="#c25800" x=".6286934" y="11">Meta Data Gear</tspan>
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+      <g id="Graphic_121">
+        <ellipse cx="310.17553" cy="436.5" rx="45.8794865380515" ry="22.5000359527927" fill="white"/>
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+        <text transform="translate(278.472 429.5)" fill="black">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="black" x="2.353922" y="11">Code Gear</tspan>
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+        <text transform="translate(50.65788 429.5)" fill="black">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="black" x="5.07914" y="11">Data Gear</tspan>
+        </text>
+      </g>
+      <g id="Line_118">
+        <line x1="121.67553" y1="436.5" x2="254.3961" y2="436.5" marker-end="url(#FilledArrow_Marker)" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1"/>
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+        <text transform="translate(504.17553 429.5)" fill="black">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="black" x="5.07914" y="11">Data Gear</tspan>
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+        <text transform="translate(387.0822 422.5)" fill="#c25800">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="#c25800" x="18.01593" y="11">Meta </tspan>
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="#c25800" x="2.005188" y="25">Code Gear</tspan>
+        </text>
+      </g>
+      <g id="Graphic_103">
+        <ellipse cx="310.17553" cy="310.5" rx="44.2896033411883" ry="22.5000359527927" fill="white"/>
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+        <text transform="translate(279.7439 303.5)" fill="black">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="black" x="1.082016" y="11">Code Gear</tspan>
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+        <rect x="45.65788" y="288" width="75.51765" height="45" stroke="black" stroke-linecap="round" stroke-linejoin="round" stroke-width="1"/>
+        <text transform="translate(50.65788 303.5)" fill="black">
+          <tspan font-family="Helvetica" font-size="12" font-weight="400" fill="black" x="5.07914" y="11">Data Gear</tspan>
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+        <text transform="translate(504.17553 303.5)" fill="black">
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/slide/slide.md	Sun Feb 05 16:35:38 2023 +0900
@@ -0,0 +1,345 @@
+---
+marp: true
+title: Gears Agda での形式手法を用いたプログラムの検証
+paginate: true
+
+theme: default
+size: 16:9
+style: |
+  section {
+    background-color: #FFFFFF;
+    font-size: 28px;
+    color: #4b4b4b;
+    font-family: "Droid Sans Mono", "Hiragino Maru Gothic ProN";
+    background-image: url("logo.svg");
+    background-position: right 3% bottom 2%;
+    background-repeat: no-repeat;
+    background-attachment: 5%;
+    background-size: 20% auto;
+  }
+  
+    section.title h1 {
+      color: #808db5;
+      text-align: center;
+      }
+    
+    section.title p {
+        bottom: 25%;
+        width: 100%;
+        position: absolute;
+        font-size: 25px;
+        color: #4b4b4b;
+        background: linear-gradient(transparent 90%, #ffcc00 0%);
+    }
+
+  section.slide h1 {
+      width: 95%;
+      color: white;
+      background-color: #808db5;
+      position: absolute;
+      left: 50px; 
+      top: 35px;
+  }
+
+  section.fig_cg p {
+     top: 300px;
+     text-align: center;
+  }
+
+---
+<!-- headingDivider: 1 -->
+
+# Gears Agda での形式手法を用いたプログラムの検証
+<!-- class: title -->
+
+Uechi Yuto, 琉球大学
+
+# 証明を用いてプログラムの信頼性の向上を目指す
+<!-- class: slide -->
+
+<!-- 研究目的 -->
+- プログラムの信頼性を高めることは重要な課題である
+  - 信頼性を高める手法として「モデル検査」や「定理証明」など
+  - 欠点として、実装コストが高い点が挙げられる
+- プログラムの検証に適した Gears Agda を用いる
+    - これは Agda に CbC の継続の概念を取り入れたもの
+    <!-- Agda は Curru-Howard 対応に基づく関数型言語 -->
+- Continuation based C (CbC)という言語を当研究室で開発している
+  - C言語からループ構造とサブルーチンを取り除き、継続を導入したC言語の下位言語となる
+- 本研究では Gears Agda にて定理証明を用いた検証と、モデル検査による検証をする
+
+# CbC について
+- CbCとは当研究室で開発しているC言語の下位言語
+    - 継続呼び出しは引数付き goto 文で表現される
+      - 関数呼び出し時のスタックの操作を行わずjmp命令で次の処理に移動する
+    - 処理の単位を Code Gear, データの単位を Data Gear として記述するプログラミング言語
+- CbC のプログラミングでは Data Gear を Code Gear で変更し、その変更を次の Code Gear に渡して処理を行う
+
+
+# Agda の基本 
+- Agdaとは定理証明支援器であり、関数型言語
+- Agdaでの関数は、最初に型について定義した後に、関数を定義する事で記述する
+- 型の定義部分で、入力と出力の型を定義できる
+  -  input → output のようになる
+- 関数の定義は = を用いて行う
+  - 関数名を定義した行よりも後ろの行で実装する
+  - = の前で受け取る引数を記述、= の後ろで実装を記述する
+
+
+```
+sample : (A : Set ) → (B : Set ) → Set
+sample a b = b
+```
+
+
+# Agda の基本 record
+オブジェクトあるいは構造体
+```
+record Env  : Set where
+  field
+    varn : N
+    vari : N
+open Env
+```
+
+型に対応する値の導入(intro)
+```
+record {varn = zero ; vari = suc zero}
+```
+record の値のアクセス(elim)
+```
+(env : Env) → varn env
+```
+
+
+
+# Gears Agda の記法
+<!-- Gears Agdaの説明が必要かも -->
+Gears Agda では CbC と対応させるためにすべてLoopで記述する
+loopは`→ t`の形式で表現する
+末尾再帰以外の再帰呼び出しは使わない(構文的には禁止していないので注意が必要)
+```
+{-# TERMINATING #-}
+whileLoop : {l : Level} {t : Set l} → Env → (Code : Env → t) → t
+whileLoop env next with lt 0 (varn env)
+whileLoop env next | false = next env
+whileLoop env next | true = whileLoop (record {varn = (varn env) - 1 ; vari = (vari env) + 1}) next
+```
+- tを返すことで継続を表す(tは呼び出し時に任意に指定してもよい. testに使える)
+- tail call により light weight continuation を定義している
+
+
+# Gears Agda と Gears CbC の対応
+Gears Agda
+- 証明向きの記述
+- Hoare Condition を含む
+
+Gears CbC
+- 実行向きの記述
+- メモリ管理, 並列実行を含む
+
+Context
+- processに相当する
+- Code Gear 単位で並列実行
+
+
+# Normal level と Meta Level を用いた信頼性の向上
+Normal Level 
+- 軽量継続
+- Code Gear 単位で関数型プログラミングとなる
+- atomic(Code Gear 自体の実行は割り込まれない)
+- ポインタの操作は含まれない
+
+Meta Level 
+- メモリやCPUなどの資源管理, ポインタ操作
+- Hoare Condition と証明
+- Contextによる並列実行
+- monadに相当するData構造
+
+# Normal level と Meta Level の対応
+![height:400px](meta-cg-dg.jpg)
+
+# Gears Agda と Hoare Logic
+<!-- class: slide -->
+C.A.R Hoare, R.W Floyd が考案
+- Pre Condition → Command → Post Condition
+
+Gears Agda による Command の例
+```
+{-# TERMINATING #-}
+whileLoop : {l : Level} {t : Set l} → Env → (Code : Env → t) → t
+whileLoop env next with lt 0 (varn env)
+whileLoop env next | false = next env
+whileLoop env next | true = whileLoop (record {varn = (varn env) - 1 ; vari = (vari env) + 1}) next
+```
+- `{-# TERMINATING #-}`
+- with 文
+
+# Gears Agda の Pre Condition / Post Condition
+```
+whileLoopSeg : {l : Level} {t : Set l} → {c10 :  N } → (env : Env) → (varn env + vari env ≡ c10)
+   → (next : (e1 : Env )→ varn e1 + vari e1 ≡ c10 → varn e1 < varn env → t) 
+   → (exit : (e1 : Env )→ vari e1 ≡ c10 → t) → t
+```
+- `{-# TERMINATING #-}`を避けるためにloopを分割
+- `varn env + vari env ≡ c10` が Pre Condition
+- `varn e1 + vari e1 ≡ c10` が Post Condition
+- `varn e1 < varn env` が停止を保証する減少列
+
+これは命題なので証明を与えて Pre Condition から Post Condition を導出する必要がある。証明は値として次の CodeGear に渡される
+
+# Loop の接続
+分割したloopを接続するMeta Code Gearを作成する
+```
+TerminatingLoopS : {l : Level} {t : Set l} ( Index : Set ) 
+  → {Invraiant : Index → Set } → ( reduce : Index → N) 
+  → (loop : (r : Index) → Invraiant r 
+    → (next : (r1 : Index) → Invraiant r1 → reduce r1 < reduce r → t ) → t) 
+  → (r : Index) → (p : Invraiant r) → t
+```
+- IndexはLoop変数
+- Invariantはloop変数の不変条件
+- loopに接続するCode Gearを与える
+- reduceは停止性を保証する減少列
+
+これを証明することで検証ができる
+
+# 実際のloopの接続
+証明したい性質を以下のように記述する
+```
+whileTestSpec1 : (c10 : N) →  (e1 : Env ) → vari e1 ≡ c10 → ⊤
+whileTestSpec1 _ _ x = tt
+```
+loopをTerminatingLoopSで接続して仕様記述に繋げる
+```
+proofGearsTermS : {c10 :  N} → ⊤
+proofGearsTermS {c10} = whileTest' {_} {_}  {c10} (λ n p →  conversion1 n p (λ n1 p1 →
+    TerminatingLoopS Env (λ env → varn env)(λ n2 p2 loop → whileLoopSeg {_} {_} {c10} n2 p2 loop 
+    (λ ne pe → whileTestSpec1 c10 ne pe)) n1 p1 )) 
+```
+- conversion1はPre Condition をPost Conditionに変換する
+- ⊤
+
+# test との違い
+- test では実数を与えた際の出力が仕様に沿ったものであるかを検証する
+    - コーナーケースを人力で完全に考慮し、testする必要がある
+- 今回の定理証明を用いた証明では実数を必要としない
+    - そのため、入力の型の範囲全てに対して仕様を満たしているか検証できる
+
+# モデル検査と定理証明の違い
+- モデル検査では全ての状態を網羅し、それが仕様を満たしているか検証する
+- 無限にある状態を検証することはできないため、定理証明と比べると完全な検証にならないこともある
+- 定理証明に比べて実装コストが低い<!-- 計算コストは高い -->
+
+# Dining Philosophers Problem
+
+||哲学者の遷移|
+|---|---|
+|![height:450px](DPP.jpg)|1. 哲学者は思考をしている  <br> 2. 食事をするために右のフォークを取る <br> 3. 次に左のフォークを取る <br> 4. 両方のフォークが取れたら食事をする <br> 5. 思考に戻るために左のフォークを置く <br> 6. 次に右のフォークを置く |
+
+# Dining Philosophers Problem の実装
+- DPPはマルチプロセスの同期問題である
+  - しかし、Agdaでは並列実行をサポートしていないため、step実行毎に一つずつ処理することで並列実行を表現している
+- 加えて、哲学者が思考を止めて食事をしようとするのか、食事中に思考に戻ろうとするのかで分岐が発生する
+  - 今回はその状態に対して網羅することでモデル検査を行っている
+
+# Dining Philosophers Problem の実装
+Gears Agdaで使用する Data Gear を以下のように定義した
+```
+record Phi : Set where
+  field
+    pid : ℕ
+    right-hand : Bool
+    left-hand : Bool
+    next-code : Code
+open Phi
+```
+```
+record Env : Set where
+  field
+    table : List ℕ
+    ph : List Phi
+open Env
+```
+
+# Dining Philosophers Problem の実装
+```
+data Code : Set  where
+   C_putdown_rfork : Code
+   C_putdown_lfork : Code
+   C_thinking : Code
+   C_pickup_rfork : Code
+   C_pickup_lfork : Code
+   C_eating : Code
+```
+
+```
+code_table : {n : Level} {t : Set n} → Code → ℕ → Phi → Env → (Env → t) → t
+code_table C_putdown_rfork = putdown-rfork-c
+code_table C_putdown_lfork = putdown-lfork-c
+code_table C_thinking = thinking-c
+code_table C_pickup_rfork = pickup-rfork-c
+code_table C_pickup_lfork = pickup-lfork-c
+code_table C_eating = eating-c
+```
+
+# Dining Philosophers Problem の実装
+以下が哲学者の動作の実装の一つ
+```
+pickup-lfork-c : {n : Level} {t : Set n} → ℕ → Phi → Env → (Env → t) → t
+pickup-lfork-c ind p env exit = pickup-lfork-p (suc ind) [] (table env) p env exit where
+  pickup-lfork-p : {n : Level} {t : Set n} → ℕ → (f b : List ℕ) → Phi → Env → (Env → t) → t
+  pickup-lfork-p zero f [] p env exit with table env
+  ... | [] = exit env
+  ... | 0 ∷ ts = exit record env{ph = ((ph env) ++ (record p{left-hand = true ;
+         next-code = C_eating} ∷ [])); table = ((pid p) ∷ ts)}
+  ... | (suc x) ∷ ts = exit record env{ph = ((ph env) ++ p ∷ [])}
+  pickup-lfork-p zero f (0 ∷ ts) p env exit = exit record env{
+    ph = ((ph env) ++ (record p{left-hand = true ;
+         next-code = C_eating} ∷ [])); table = (f ++ ((pid p) ∷ ts))}
+```
+
+# モデル検査でのデッドロック検知
+- 今回Gears Agdaでのデッドロックの定義として、以下2つを設定した
+  - その状態から分岐が作れない
+  - 実行時に状態が一切変化しない
+- これでプログラムが dead Lock しているのか検知するところまではできた
+
+# モデル検査でのデッドロック検知
+網羅には以下の Meta CodeGear を実装した(一部抜粋)
+```
+brute-force-search : {n : Level} {t : Set n} 
+  → Env → (exit : List Env → t) → t
+brute-force-search env exit = make-state-list 
+  1 [] (ph env) env (env ∷ []) exit where
+  make-state-list : {n : Level} {t : Set n} 
+    → ℕ → List Bool → List Phi 
+    → Env → (List Env) → (exit : List Env → t) → t
+  make-state-list redu state (x ∷ pl) env envl exit with next-code x
+  ... | C_thinking = make-state-list (redu + redu) 
+    (state ++ (false ∷ [])) pl env envl exit
+  ... | C_eating = make-state-list (redu + redu)
+    (state ++ (false ∷ [])) pl env envl exit
+  ... | _ = make-state-list redu state pl env envl exit
+  make-state-list redu state [] env envl exit = 
+    bit-force-search redu [] state env envl exit where
+```
+
+# 今後の研究方針
+- モデル検査
+    - 有向グラフからなる有限オートマトンの遷移を全自動探索する
+    - live lock の検出や LTTL も用いたアサーションなどの検証
+    - State List のデータ構造を blanced tree にする
+    - モデル検査に定理証明を組み込む
+- 定理証明
+    - Red Black Tree の検証を行う
+- Gears Agda
+    - Gears Agda を CbC に自動変換できるようにする
+
+
+# まとめ
+- 定理証明について、Invariant によるプログラムの検証を行うことができるようになった
+
+- Gears Agda によるモデル検査により、並列動作の検証を行えるようになった
+
+<!-- 英語版も欲しい-->
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