# HG changeset patch
# User e155702
# Date 1550130710 -32400
# Node ID 83f997abf3b52f095faa10a5fa06360bf9434365
first commit
diff -r 000000000000 -r 83f997abf3b5 final_main/Makefile
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/Makefile Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,89 @@
+# target and root file name
+TARGET = main
+
+# class files
+CLASS_FILE =
+
+# figure pass
+FIG_DIR = ./fig
+
+# ebb or extractbb
+EBB = extractbb
+
+# dependent document files
+TEX_FILES = \
+ chapter*.tex \
+ thanks.tex
+
+# dependent image files
+SVG_FILES =
+
+# use bibtex or not (yes|no)
+BIBTEX_ENABLED = yes
+
+# commands to compile document
+LATEX = platex
+BIBTEX = pbibtex
+DVIPDF = dvipdfmx
+DVIPS = dvips
+
+# generated files
+DVI_FILE = $(TARGET).dvi
+PDF_FILE = $(TARGET).pdf
+PS_FILE = $(TARGET).ps
+TEX_FILES += $(TARGET).tex
+EPS_FILES = $(SVG_FILES:%.svg=%.eps)
+AUX_FILES = $(TEX_FILES:%.tex=%.aux)
+GENERATED_FILE = \
+ $(EPS_FILES) \
+ $(DVI_FILE) \
+ $(PDF_FILE) \
+ $(AUX_FILES) \
+ $(TARGET).log \
+ $(TARGET).toc \
+ $(TARGET).bbl \
+ $(TARGET).blg \
+ $(TARGET).lof \
+ $(TARGET).lol \
+ texput.log
+
+.DEFAULT_GOAL = pdf
+
+.PHONY : pdf
+pdf : $(PDF_FILE)
+ open $(TARGET).pdf
+$(PDF_FILE) : $(DVI_FILE) $(TEX_FILES) $(EPS_FILES) $(CLASS_FILE)
+ $(DVIPDF) $(TARGET)
+
+.PHONY : ps
+ps : $(PS_FILE)
+$(PS_FILE) : $(DVI_FILE) $(TEX_FILES) $(EPS_FILES) $(CLASS_FILE)
+ $(DVIPS) $(TARGET)
+
+.PHONY : dvi
+dvi : $(DVI_FILE)
+$(DVI_FILE) : $(TEX_FILES) $(EPS_FILES) $(CLASS_FILE)
+ $(LATEX) -halt-on-error $(TARGET)
+ifeq ($(BIBTEX_ENABLED),yes)
+ $(BIBTEX) $(TARGET)
+endif
+ $(LATEX) -halt-on-error $(TARGET)
+ $(LATEX) -halt-on-error $(TARGET)
+
+%.eps : %.svg
+ inkscape --export-area-drawing --without-gui --file="$<" --export-eps="$@"
+
+.PHONY : clean
+clean:
+ rm -f $(GENERATED_FILE)
+
+.PHONY : help
+help:
+ @echo "make dvi"
+ @echo " Make DVI file from tex documents."
+ @echo "make pdf"
+ @echo " Make PDF file from DVI file."
+ @echo "make ps"
+ @echo " Make PS file from DVI file."
+ @echo "make clean"
+ @echo " Remove all generated files."
diff -r 000000000000 -r 83f997abf3b5 final_main/bibliography.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/bibliography.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,40 @@
+% 参考文献
+\def\line{−\hspace*{-.7zw}−}
+
+\begin{thebibliography}{99}
+%\bibitem{*}内の * は各自わかりやすい名前などをつけて、
+%論文中には \cite{*} のように使用する。
+%これをベースに書き換えた方が楽かも。
+%書籍、論文、URLによって若干書き方が異なる。
+%URLを載せる人は参考にした年月日を最後に記入すること。
+
+\bibitem{Verified}
+{比嘉健太, 河野真治}: メタ計算を用いた Continuation based C の検証手法
+, 琉球大学工学部情報工学科平成 29 年度学位論文(修士) (2017).
+
+\bibitem{CbC-meta}
+{宮城光希, 河野真治}: CbC 言語による OS 記述
+, 琉球大学工学部情報工学科平成 29 年度学位論文(学士) (2017).
+
+\bibitem{CbC-llvm}
+{徳森海斗, 河野真治}: LLVM Clang 上の Contimuation based C コンパイラの改良
+, 琉球大学工学部情報工学科平成 28 年度学位論文(修士) (2016).
+
+\bibitem{Agda}
+The Agda wiki \\\verb|http://wiki.portal.chalmers.se/agda/pmwiki.php|
+
+% \bibtem{Agda-Tutorial}
+% {Ulf Norell and James Chapman}: Dependently Typed Programming in Agda
+% \\\verb|http://www.cse.chalmers.se/~ulfn/papers/afp08/tutorial.pdf|
+
+% \bibitem{gears}
+% {伊波立樹, 東恩納琢偉, 河野真治}: Code Gear、Data Gear に基づく OS のプロトタイプ
+% , 情報処理学会システムソフトウェアとオペレーティング・システム研究会(OS) (2016).
+
+% \bibitem{llvm}
+% The LLVM Compiler Infrastructure. \\\verb|http://llvm.org|
+
+% \bibitem{llvm_ir}
+% LLVM Language Reference Manual. \\\verb|http://llvm.org/docs/LangRef.html|
+
+\end{thebibliography}
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter1.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter1.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,36 @@
+\chapter{画面配信ソフトウェアの活用}
+\label{chap:introduction}
+\pagenumbering{arabic}
+
+% 序論の目安としては1枚半ぐらい．
+% 英語発表者は，最終予稿の「はじめに」の英訳などを載せてもいいかも．
+
+
+
+ 現代の講義や発表、プレゼンなどは、用意された資料や PC 画面を見ながら進行することが多い。ゼミなどでは発表者を切り替えながら発表を行う場合もある。通常このような場面では、資料やスライドを表示するためにプロジェクタが使用されている。ゼミの際には発表者を切り替えるたびにプロジェクタにケーブルを差し替える必要がある。ケーブルの差し替えの際に発表者の PC によってはアダプターの種類や解像度の設定により、正常に PC 画面を表示できない場合がある。また、参加者もプロジェクタに集中を割く必要があり、手元の PC と交互に参照する場合、負担になる可能性がある。
+
+当研究室で開発している画面配信システム TreeVNC は、発表者の画面を参加者の PC に表示するソフトウェアである。そのため TreeVNC を使用することで、参加者は不自由なく手元の PC を使用しながら講義を受ける事が可能になる。更に発表者の切り替えの際も、ケーブルの差し替えを行わずに共有する画面の切替を可能としている。
+
+TreeVNC は VNC(Virtual Network Computing) を使用した画面配信を行っている。通常の VNC では配信側の PC に全ての参加者が接続するため、多人数が接続した際処理しきれず、最悪の場合ソフトウェアが落ちてしまう。TreeVNC ではネットワークに接続した参加者をバイナリツリー状に接続し、 配信コストをクライアントに分散させる仕組みをとっている。そのため、講義で発表者の画面を表示する際、多人数の生徒が参加しても処理性能が下がらない。また、ツリーのルートが参照している VNC サーバーを変更することで、共有する画面の切替が可能となっている。
+
+しかし、画面共有は送信するデータ量が多いため、現在の TreeVNC では無線 LAN 接続の場合、画面の配信に遅延が生じてしまう場合がある。そこで本研究では、multicast でのデータ通信の実装やデータの分割・圧縮方法の評価を行うことにより、無線 LAN での配信環境の向上を目指し、TreeVNC の有用性を評価することで講義やゼミを円滑に行えることを目標とする。
+
+
+
+%% TreeVNC を 有線・無線接続の両方で快適に使用できるようにしたい
+
+%% そのため当研究室では無線接続の際、multicast で通信を行う手法を提案する
+
+%% multicast 接続で、TreeVNC の実用性を向上させたい
+
+%%%
+% やってること、やりたいことは TreeVNC 上で multicast を実装し、無線接続でも問題なく使用できるようにすること
+%%%
+
+% なんで multicast で実装するの ?
+% 現在の TreeVNC は無線接続だと多人数での接続や動画配信を行なった際、画面共有が遅くなる場合があるので、multicast でデータの通信を行えば、クライアント側の負担が軽減され、通信速度の改善が見られやすいと考えるから
+
+
+%\section{論文の構成}
+
+%\section{Introduction}
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter2.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter2.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,87 @@
+\chapter{TreeVNC の基本概念}
+%% VNCとはなにか？どのようなものか？どのようにしてなりたっているか？
+
+ TreeVNC は当研究室で開発している画面配信ソフトウェアである。
+
+本章は TreeVNC の基本概念となっている技術について説明する。
+
+%% どういう概念？ どうしてそうするの？ どうやってつかうの？
+\section{ Virtual Network Computing }
+
+VNC(Virtual Network Computing) は、RFB プロトコルを用いて PC の遠隔操作を行うことを目的としたリモートデスクトップソフトウェアである。
+
+サーバー側とクライアント側に分かれており、起動したサーバーにクライアントが接続することで遠隔操作を可能にしている。
+
+
+\section{ RFB プロトコル}
+
+RFB(Remote Frame Buffer)プロトコルは、自身の画面をネットワークを通じて送信し他者の画面に表示するプロトコルである。
+
+ユーザがいる側と FrameBuffer への更新が行われる側に分かれ、それぞれを RFB クライアント、RFB サーバと呼ぶ。FrameBuffer は、メモリ上に置かれた画像データのことである。
+
+RFB プロトコルでは、始めにプロトコルバージョンの確認、認証を行う。その後クライアントに向けて FrameBuffer の大きさやデスクトップに付けられた名前などが含まれている初期メッセージが送信される。RFB サーバ側は FrameBuffer の更新が行われるたびに RFB クライアントに対して FrameBuffer の変更部分だけを送信する。更に、RFB クライアントの FramebufferUpdateRequest が来るとそれに答え返信する。変更部分だけを送信する理由は、更新がある度に全画面を送信していると、送信するデータ面、更新にかかる時間面において効率が悪いからである。
+
+RFB プロトコルには、描画データに使われるエンコードが多数用意されており、更に、独自のエンコードを実装することも可能である。
+
+
+%%ここより上を修正したい
+\section{ TreeVNC の基本構造}
+TreeVNC は TightVNC を元に作成されている
+
+
+\section{従来の VNC と TreeVNC の相違点}
+
+従来の VNC は画面配信を行う際、サーバー側に全てのクライアントが同時に接続してしまうため、多人数に配信を行う場合、クライアントに対する全ての処理をサーバー1つで負担することになり、サーバーの処理性能が落ちてしまう問題点が存在する。
+
+
+%%従来の VNC の接続方式の図
+%%従来の VNC 使用時のパフォーマンスの計測結果
+
+
+\section{}
+CbC で DataGear を扱う際、 Context と呼ばれる接続可能な CodeGear、 DataGear のリ
+スト、Temporal DataGear のためのメモリ空間等を持っている Meta DataGearである。
+CbC で必要な CodeGear 、 DataGear を参照する際は Context を通してアクセスする必
+要がある。
+
+\section{stub CodeGear}
+CodeGear が必要とする DataGear を取り出す際、 Context を通す必要がある。
+しかし、 Context を直接扱えるようにするのは信頼性を損なう。そのため CbC では
+Context を通して必要なデータを取り出して次の Code Gear に接続する stub CodeGear
+を定義している。CodeGear は stub CodeGear を介してのみ必要な DataGear へアクセス
+することができる。 stub CodeGear は CodeGear 毎に生成され、次の CodeGear へと接
+続される。
+stub CodeGear は CodeGear の Meta CodeGear に当たる。
+
+
+\section{CbCによる Interface の記述と継続}
+
+CodeGear は通常の関数と比べ、細かく分割されるためメタ計算をより柔軟に記述でき
+る。 CodeGear 、 DataGear にはそれぞれメタレベルとして、 Meta CodeGear
+、 Meta DataGear が存在する。
+
+CbC で実装していくうちに、stub CodeGear の記述が煩雑になることが分かった。
+そのため 既存の実装を モジュールとして扱うため Interface という仕組みを導入した。
+
+Interface は DataGear に対して何らかの操作(API)を行う CodeGear とその
+CodeGear で使われる DataGear の集合を抽象化した メタレベルの DataGear
+として定義されている。
+
+% interface は データ構造に record で interface 名を列挙し、実際の動作をする関数と紐付けている。使用する際は、$ DataName->InterfaceFunk $のように使用する。
+
+例として CbC による Stack Interface のソースコード\ref{src:interface-define},
+\ref{src:interface}がある。Stack への push 操作に注目して見ると、
+実態は SingleLinkedStack の push であることが\ref{src:interface}で分
+かる。実際の SingleLinkedStack の push では Stack を指定する必要があるが、
+Interface で実装した Stack では push 先の Stack が stackImpl として扱
+われている。この stackImpl は$ Stack->push $で呼ばれた時の Stack と同じになる。
+これにより、 ユーザーは実行時に Stack を指定する必要がなくなる。
+また、ユーザーが誤って異なる Stack を指定することを防ぐこともできる。
+
+このように Interface 記述をすることで CbC で通常記述する必要がある一定の部分を省略し呼び出
+しが容易になる。
+
+\lstinputlisting[label=src:interface-define, caption=CbCでのStack-Interfaceの定義] {src/interface.cbc}
+
+\lstinputlisting[label=src:interface, caption=CbCでのStack-Interfaceの実装] {src/singleLinkedStackInterface.cbc}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter3.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter3.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,487 @@
+\chapter{定理証明支援器 Agda での証明}
+
+型システムを用いて証明を行うことができる言語として Agda \cite{agda}が存在する。
+Agda は依存型という型システムを持つ。依存型とは型も第一級オブジェクトとする型シ
+ステムで、依存型を持っている言語では型を基本的な操作に制限なしに使用できる
+。
+型システムは Curry-Howard 同型対応により命題と型付きラムダ計算が一対一で対応する。
+
+
+本章では Agda で証明をするために必要な要素について説明し、Natural Deduction での証明とそれに対応して Agda 使って証明ができることを示す。
+% 型システムは Curry-Howard 同型対応により命題と型付きラムダ計算が一対一で対応する。
+% 依存型という表現力の高い型を持つ証明支援系 Agda を用いて型システムで証明が行える
+% ことを示す。
+
+%% ここではAgdaの文法に触るだけにとどめて Agdaと証明のchapを一つ追加。
+% 其処に自然証明とAgdaの証明とかCurry-Howard対応の話とかを入れるときれいになるか
+% も
+%% 依存型を持っている言語には Agda の他に ATS 、 Coq 、 F* 、 Idris 、 Shen など
+%% がある。
+
+\section{Agda の文法}
+
+
+Agda はインデントに意味を持つため、きちんと揃える必要がある。
+また、スペースの有無は厳格にチェックされる。
+なお、 \verb/--/ の後はコメントである。
+
+Agda のプログラムでは全てモジュール内部に記述されるため、まずはトップレベルにモ
+ジュールを定義する必要がある。トップレベルのモジュールはファイル名と同一になる。
+
+通常のモジュールをインポートする時は \verb/import/ キーワードを指定する。
+また、インポートを行なう際に名前を別名に変更することもでき、その際は \verb/as/ キーワードを用いる。
+モジュールから特定の関数のみをインポートする場合は \verb/using/ キーワードの後に
+関数名を、関数の名前を変える時は \verb/renaming/キーワードを、特定の関数のみを隠
+す場合は \verb/hiding/ キーワードを用いる。
+なお、モジュールに存在する関数をトップレベルで用いる場合は \verb/opestack に対する操作を定義しており、n/ キーワードを使うことで展開できる。
+モジュールをインポートする例をリスト~\ref{src:agda-import}に示す。
+
+\lstinputlisting[label=src:agda-import, caption=Agdaにおけるモジュールのインポート] {src/AgdaImport.agda}
+
+% また、モジュールには値を渡すことができる。
+% そのようなモジュールは Parameterized Module と呼ばれ、渡された値はそのモジュール内部で一貫して扱える。
+% 例えば、要素の型と比較する二項演算子を使って並べ替えをするモジュール\verb/Sort/ を考える。
+% そのモジュールは引数に型Aと二項演算子 \verb// を用いる。
+
+例えば引数が型 \verb/A/ で返り値が型 \verb/B/ の関数は \verb/A -> B/ のように書
+ける。
+また、複数の引数を取る関数の型は \verb/A -> A -> B/ のように書ける。この
+時の型は \verb/A -> (A -> B)/のように考えられる。
+Bool 変数 \verb/x/ を取って true を返す関数 \verb/f/はリスト~\ref{src:agda-function}のようになる。
+
+\lstinputlisting[label=src:agda-function, caption=Agda における関数定義] {src/AgdaFunction.agda}
+
+引数は変数名で受けることもでき、具体的なコンストラクタを指定することでそのコンストラクタが渡された時の挙動を定義できる。
+これはパターンマッチと呼ばれ、コンストラクタで case 文を行なっているようなもので
+例えば Bool 型の値を反転する \verb/not/ 関数を書くとリスト~\ref{src:agda-not}のようになる。
+
+\lstinputlisting[label=src:agda-not, caption=Agdaにおける関数 not の定義] {src/AgdaNot.agda}
+
+パターンマッチでは全てのコンストラクタのパターンを含まなくてはならない。
+例えば、Bool 型を受け取る関数で \verb/true/ の時の挙動のみを書くことはできない。
+なお、コンストラクタをいくつか指定した後に変数で受けると、変数が持ちうる値は指定した以外のコンストラクタとなる。
+例えばリスト~\ref{src:agda-pattern}の not は x には true しか入ることは無い。
+なお、マッチした値以外の挙動をまとめて書く際には \verb/_/ を用いることもできる。
+
+\lstinputlisting[label=src:agda-pattern, caption=Agdaにおけるパターンマッチ] {src/AgdaPattern.agda}
+
+Agda にはラムダ式が存在している。ラムダ式とは関数内で生成できる無名の関数であり、
+\verb/\arg1 arg2 -> function body/ のように書くことができる。
+例えば Bool 型の引数 \verb/b/ を取って not を適用する \verb/not-apply/ をラムダ式で書くとリスト~\ref{src:agda-lambda}のようになる。
+関数 \verb/not-apply/ をラムダ式を使わずに定義すると \verb/not-apply-2/ になるが、この二つの関数は同一の動作をする。
+
+\lstinputlisting[label=src:agda-lambda, caption=Agda におけるラムダ式] {src/AgdaLambda.agda}
+
+Agda では特定の関数内のみで利用できる関数を \verb/where/ 句で記述できる。
+スコープは \verb/where/句が存在する関数内部のみであるため、名前空間が汚染させることも無い。
+例えば自然数3つを取ってそれぞれ3倍して加算する関数 \verb/f/ を定義するとき、 \verb/where/ を使うとリスト~\ref{src:agda-where} のように書ける。
+これは \verb/f'/ と同様の動作をする。
+\verb/where/ 句は利用したい関数の末尾にインデント付きで \verb/where/ キーワードを記述し、改行の後インデントをして関数内部で利用する関数を定義する。
+
+\lstinputlisting[label=src:agda-where, caption=Agda における where 句] {src/AgdaWhere.agda}
+
+データ型のコンストラクタには自分自身の型を引数に取ることもできる(リスト~\ref{src:agda-nat})。
+自然数のコンストラクタは2つあり、片方は自然数ゼロ、片方は自然数を取って後続数を返すものである。
+例えば0 は \verb/zero/ であり、1 は \verb/suc zero/に、3は \verb/suc (suc (suc zero))/ に対応する。
+
+\lstinputlisting[label=src:agda-nat, caption=Agdaにおける自然数の定義] {src/AgdaNat.agda}
+
+自然数に対する演算は再帰関数として定義できる。
+例えば自然数どうしの加算は二項演算子\verb/+/としてリスト~\ref{src:agda-plus}のように書ける。
+
+この二項演算子は中置関数として振る舞う。
+前置や後置で定義できる部分を関数名に \verb/_/ として埋め込んでおくと、関数を呼ぶ
+時にあたかも前置や後置演算子のように振る舞うことができる。
+例えば \verb/!_/ を定義すると \verb/! true/ のように利用でき、\verb/_~/ を定義すると \verb/false ~/ のように利用できる。
+
+また、Agda は再帰関数が停止するかを判別できる。
+この加算の二項演算子は左側がゼロに対しては明らかに停止する。
+左側が1以上の時の再帰時には \verb/suc n/ から \verb/n/へと減っているため、再帰で繰り返し減らすことでいつかは停止する。
+もし \verb/suc n/ のまま自分自身へと再帰した場合、Agda は警告を出す。
+
+\lstinputlisting[label=src:agda-plus, caption=Agda における自然数の加算の定義] {src/AgdaPlus.agda}
+
+次に依存型について見ていく。
+依存型で最も基本的なものは関数型である。
+依存型を利用した関数は引数の型に依存して返す型を決定できる。
+なお、依存型の解決はモジュールのインポート時に行なわれる。
+
+Agda で \verb/(x : A) -> B/ と書くと関数は型 A を持つ x を受け取り、Bを返す。
+ここで B の中で x を扱っても良い。
+例えば任意の型に対する恒等関数はリスト~\ref{src:agda-id}のように書ける。
+
+\lstinputlisting[label=src:agda-id, caption=依存型を持つ関数の定義] {src/AgdaId.agda}
+
+この恒等関数 \verb/identitiy/ は任意の型に適用可能である。
+実際に関数 \verb/identitiy/ を Nat へ適用した例が \verb/identitiy-zero/ である。
+
+多相の恒等関数では型を明示的に指定せずとも \verb/zero/ に適用した場合の型は自明に \verb/Nat -> Nat/である。
+Agda はこのような推論をサポートしており、推論可能な引数は省略できる。
+推論によって解決される引数を暗黙的な引数(implicit arguments) と言い、変数を
+\verb/{}/ でくくることで表す。
+
+例えば、\verb/identitiy/ の対象とする型\verb/A/を暗黙的な引数として省略するとリスト~\ref{src:agda-implicit-id}のようになる。
+この恒等関数を利用する際は特定の型に属する値を渡すだけでその型が自動的に推論される。
+よって関数を利用する際は \verb/id-zero/ のように型を省略して良い。
+なお、関数の本体で暗黙的な引数を利用したい場合は \verb/{variableName}/ で束縛することもできる(\verb/id'/ 関数)。
+適用する場合も \verb/{}/でくくり、\verb/id-true/のように使用する。
+
+\lstinputlisting[label=src:agda-implicit-id, caption=Agdaにおける暗黙的な引数を持つ関数] {src/AgdaImplicitId.agda}
+
+Agda のデータには C における構造体に相当するレコード型も存在する。
+定義を行なう際は \verb/record/キーワードの後にレコード名、型、\verb/where/ の後に \verb/field/ キーワードを入れた後、フィールド名と型名を列挙する。
+例えば x と y の二つの自然数からなるレコード \verb/Point/ を定義するとリスト~\ref{src:agda-record}のようになる。
+レコードを構築する際は \verb/record/ キーワードの後の \verb/{}/ の内部に \verb/fieldName = value/ の形で値を列挙していく。
+複数の値を列挙する際は \verb/;/ で区切る。
+
+\lstinputlisting[label=src:agda-record, caption=Agdaにおけるレコード型の定義] {src/AgdaRecord.agda}
+
+構築されたレコードから値を取得する際には \verb/RecordName.fieldName/ という名前の関数を適用する(リスト~\ref{src:agda-record-proj} 内2行目) 。
+なお、レコードにもパターンマッチが利用できる(リスト~\ref{src:agda-record-proj} 内5行目)。
+レコード内の値は \verb/record oldRecord {field = value ; ... }/ という構文を利用し更新することができる。
+Point の中の x の値を5増やす関数 \verb/xPlus5/ はリスト~\ref{src:agda-record-proj}の 7,8行目のように書ける。
+
+\lstinputlisting[label=src:agda-record-proj, caption=Agda におけるレコードの射影、パターンマッチ、値の更新] {src/AgdaRecordProj.agda}
+
+% Agda における部分型のように振る舞う機能として Instance Arguments が存在する。
+% これはとあるデータ型が、ある型と名前を持つ関数を持つことを保証する機能であり、Haskell における型クラスや Java におけるインターフェースに相当する。
+% Agda における部分型の制約は、必要な関数を定義した record に相当し、その制約を保証するにはその record を instance として登録することになる。
+% 例えば、同じ型と比較することができる、という性質を表すとリスト~\ref{src:agda-type-class}のようになる。
+% 具体的にはとある型 A における中置関数 \verb/_==_/ を定義することに相当する。
+
+% \lstinputlisting[label=src:agda-type-class, caption=Agdaにおける部分型制約] {src/AgdaTypeClass.agda}
+
+% ある型 T がこの部分型制約を満たすことを示すには、型 T でこのレコードを作成できることを示し、それを instance 構文で登録する。
+% Nat 型が Eq の上位型であることを記述するとリスト~\ref{src:agda-instance}のようになる。
+
+% \lstinputlisting[label=src:agda-instance, caption=Agdaにおける部分型関係の構築] {src/AgdaInstance.agda}
+
+% これで \verb/Eq/ が要求される関数に対して Nat が適用できるようになる。
+% 例えば型 A の要素を持つ List A から要素を探してくる elem を定義する。
+% 部分型のインスタンスは \verb/{{}}/ 内部に名前と型名で記述する。
+% なお、名前部分は必須である。
+% 仮に変数として受けても利用しない場合は \verb/_/ で捨てると良い。
+% 部分型として登録した record は関数本体において \verb/{{variableName}}/ という構文で変数に束縛できる。
+
+% \lstinputlisting[label=src:agda-use-instance, caption=Agdaにおける部分型を使う関数の定義] {src/AgdaElem.agda}
+
+% この \verb/elem/ 関数はリスト~\ref{src:agda-elem-apply} のように利用できる。
+% Nat型の要素を持つリストの内部に4が含まれるか確認している。
+% この \verb/listHas4/ は \verb/true/ に評価される。
+
+% \lstinputlisting[label=src:agda-elem-apply, caption=部分型を持つ関数の適用] {src/AgdaElemApply.agda}
+
+\section{Natural Deduction}
+% Natural Deduction のお話。細かい規則は…書かなきゃいけないよね…
+% いらない規則は省略しようと、少なくとも3段論法を証明できるだけ置く。。。？
+% とりあえず証明に使えるやつは全部書いて必要あるやつを詳しく。
+
+Natural Deduction (自然演繹)は Gentzen によって作られた論理及びその証明システムである。
+% ~\cite{Girard:1989:PT:64805}。
+命題変数と記号を用いた論理式で論理を記述し、推論規則により変形することで求める論理式を導く。
+
+Natural Deduction では次のように
+
+\begin{eqnarray}
+ \vdots \\ \nonumber
+ A \\ \nonumber
+\end{eqnarray}
+
+と書いた時、命題Aを証明したことを意味する。証明は木構造で表わされ、葉の命題は仮
+定となる。
+
+\begin{eqnarray}
+ \label{exp:a_implies_b}
+ A \\ \nonumber
+ \vdots \\ \nonumber
+ B \\ \nonumber
+\end{eqnarray}
+
+式\ref{exp:a_implies_b}のように A を仮定して B を導いたとする。
+この時 A は alive な仮定であり、証明された B は A の仮定に依存していることを意味する。
+
+ここで、推論規則により記号 $ \Rightarrow $ を導入する。
+
+\begin{prooftree}
+ \AxiomC{[$ A $]}
+ \noLine
+ \UnaryInfC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ B $ }
+ \RightLabel{ $ \Rightarrow \mathcal{I} $}
+ \UnaryInfC{$ A \Rightarrow B $}
+\end{prooftree}
+
+$ \Rightarrow \mathcal{I} $ を適用することで仮定 A は dead となり、新たな命題 $ A \Rightarrow B $ を導くことができる。
+A という仮定に依存して B を導く証明から、「A が存在すれば B が存在する」という証明を導いたこととなる。
+このように、仮定から始めて最終的に全ての仮定を dead とすることで、仮定に依存しない証明を導ける。
+なお、dead な仮定は \verb/[A]/ のように \verb/[]/ で囲んで書く。
+
+alive な仮定を dead にすることができるのは $ \Rightarrow \mathcal{I} $ 規則のみである。
+それを踏まえ、 natural deduction には以下のような規則が存在する。
+
+\begin{itemize}
+ \item Hypothesis
+
+ 仮定。葉にある式が仮定となるため、論理式A を仮定する場合に以下のように書く。
+
+ $ A $
+
+ \item Introductions
+
+ 導入。証明された論理式に対して記号を導入することで新たな証明を導く。
+
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A $ }
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ B $ }
+ \RightLabel{ $ \land \mathcal{I} $}
+ \BinaryInfC{$ A \land B $}
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A $ }
+ \RightLabel{ $ \lor 1 \mathcal{I} $}
+ \UnaryInfC{$ A \lor B $}
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ B $ }
+ \RightLabel{ $ \lor 2 \mathcal{I} $}
+ \UnaryInfC{$ A \lor B $}
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{[$ A $]}
+ \noLine
+ \UnaryInfC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ B $ }
+ \RightLabel{ $ \Rightarrow \mathcal{I} $}
+ \UnaryInfC{$ A \Rightarrow B $}
+ \end{prooftree}
+
+\item Eliminations
+
+ 除去。ある論理記号で構成された証明から別の証明を導く。
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A \land B $ }
+ \RightLabel{ $ \land 1 \mathcal{E} $}
+ \UnaryInfC{$ A $}
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A \land B $ }
+ \RightLabel{ $ \land 2 \mathcal{E} $}
+ \UnaryInfC{$ B $}
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A \lor B $ }
+
+ \AxiomC{[$A$]}
+ \noLine
+ \UnaryInfC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ C $ }
+
+ \AxiomC{[$B$]}
+ \noLine
+ \UnaryInfC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ C $ }
+
+ \RightLabel{ $ \lor \mathcal{E} $}
+ \TrinaryInfC{ $ C $ }
+ \end{prooftree}
+
+\begin{prooftree}
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A $ }
+
+ \AxiomC{ $ \vdots $}
+ \noLine
+ \UnaryInfC{ $ A \Rightarrow B $ }
+
+ \RightLabel{ $ \Rightarrow \mathcal{E} $}
+ \BinaryInfC{$ B $}
+ \end{prooftree}
+
+\end{itemize}
+
+記号 $ \lor, \land, \Rightarrow $ の導入の除去規則について述べた。
+natural deduction には他にも $ \forall, \exists, \bot $ といった記号が存在するが、ここでは解説を省略する。
+
+それぞれの記号は以下のような意味を持つ
+\begin{itemize}
+ \item $ \land $
+ conjunction。2つの命題が成り立つことを示す。
+ $ A \land B $ と記述すると、 A かつ B と考えることができる。
+
+ \item $ \lor $
+ disjunction。2つの命題のうちどちらかが成り立つことを示す。
+ $ A \lor B $ と記述すると、 A または B と考えることができる。
+
+ \item $ \Rightarrow $
+ implication。左側の命題が成り立つ時、右側の命題が成り立つことを示す。
+ $ A \Rightarrow B $ と記述すると、 A ならば B と考えることができる。
+\end{itemize}
+
+Natural Deduction では、これまでで説明したような規則を使い証明を行うことができる。
+
+例として Natural Deduction で三段論法の証明を行う。
+このとき、「A は B であり、 B は C である。よって A は C である」 が証明するべき
+命題である。
+
+この命題では 「A は B であり」と 「B は C である」の二つの小さい命題に分けられる。
+この「A は B であり」から、AからBが導出できることが分かり、これは $ A \Rightarrow B $ と表せる。
+また、「B は C である」から、BからCが導出できることが分かる。これも「A は B であ
+り」の時と同様に $ B \Rightarrow C $ と表せる。
+
+
+\begin{prooftree}
+ \AxiomC{ $ [A] $ $_{(1)}$}
+ \AxiomC{ [$ (A \Rightarrow B) \land (B \Rightarrow C)$] $_{(2)}$ }
+ \RightLabel{ $ \land 1 \mathcal{E} $ }
+ \UnaryInfC{ $ (A \Rightarrow B) $ }
+ \RightLabel{ $ \Rightarrow \mathcal{E} $}
+ \BinaryInfC{ $ B $ }
+
+ \AxiomC{ [$ (A \Rightarrow B) \land (B \Rightarrow C)$] $_{(2)}$ }
+ \RightLabel{ $ \land 2 \mathcal{E} $ }
+ \UnaryInfC{ $ (B \Rightarrow C) $ }
+
+ \RightLabel{ $ \Rightarrow \mathcal{E} $}
+ \BinaryInfC{ $ C $ }
+ \RightLabel{ $ \Rightarrow \mathcal{I} _{(1)}$}
+ \UnaryInfC{ $ A \Rightarrow C $}
+ \RightLabel{ $ \Rightarrow \mathcal{I} _{(2)}$}
+ \UnaryInfC{ $ ((A \Rightarrow B) \land (B \Rightarrow C)) \Rightarrow (A \Rightarrow C) $}
+\end{prooftree}
+
+
+Natural Deductionでは次のような証明木になる。
+
+
+\begin{figure}[htpb]
+ \begin{center}
+ \includegraphics{pic/modus-ponens.pdf}
+ \end{center}
+ \caption{自然演繹での三段論法の証明}
+ \label{fig:modus-ponens}
+\end{figure}
+
+これにより自然演繹を使って三段論法が証明できた。
+%%%%%%%%%%%%%%%%%%%%%%
+
+
+\section{Natural Deduction と 型付き $ \lambda $ 計算}
+
+ここでは、 Natural Deduction と型付き$ \lambda $ 計算の対応を定義する。
+対応は以下の表\ref{table:curry-howard}のようになる。
+
+\begin{center}
+ \begin{table}[h]
+% \scalebox{0.75}{
+ \begin{tabular}{|c|c|} \hline
+ Natural Deduction & 型付き $ \lambda $ 計算 \\ \hline \hline
+ $ A $ & 型 A を持つ変数 x \\ \hline
+ $ A \Rightarrow B $ & 型 A を取り型 B の変数を返す関数 f \\ \hline
+ $ \Rightarrow \mathcal{I} $ & ラムダの抽象化 \\ \hline
+ $ \Rightarrow \mathcal{E} $ & 関数適用 \\ \hline
+ $ A \land B $ & 型 A と型 B の直積型 を持つ変数 x \\ \hline
+ $ \land \mathcal{I} $ & 型A,Bを持つ値から直積型へのコンストラクタ \\ \hline
+ $ \land 1 \mathcal{E} $ & 直積型からの型Aを取り出す射影fst \\ \hline
+ $ \land 2 \mathcal{E} $ & 直積型からの型Bを取り出す射影snd \\ \hline
+ \end{tabular}
+% }
+ \caption{natural deuction と 型付き $ \lambda $ 計算との対応(Curry-Howard Isomorphism)}
+ \label{table:curry-howard}
+ \end{table}
+\end{center}
+
+この対応をもとに Agda で型付き $\lambda$ 計算による証明を示す。
+% ここでは例として ((A ならば B) かつ (B ならば C)) ならば (A ならば C) が成り立つという三段論法を証明をする。
+ここでも先程 Natural Deduction で証明した三段論法を例とする。
+% この三段論法は自然演繹では\ref{fig:modus-ponens}のようになっていた。
+
+% \begin{figure}[htpb]
+% \begin{center}
+% \includegraphics{pic/modus-ponens.pdf}
+% \end{center}
+% \caption{自然演繹での三段論法の証明}
+% \label{fig:modus-ponens}
+% \end{figure}
+
+%McCこの証明木に対応するAgdaによる証明はリスト\ref{agda-moduse-ponens}のようになる。
+
+\begin{lstlisting}[frame=lrbt,label=agda-moduse-ponens,caption={\footnotesize Agda による
+ 三段論法の定義と証明}]
+data _×_ (A B : Set) : Set where
+ <_,_> : A → B → A × B
+
+fst : {A B : Set} → A × B → A
+fst < a , _ > = a
+
+snd : {A B : Set} → A × B → B
+snd < _ , b > = b
+
+
+f : {A B C : Set} → ((A → B) × (B → C)) → (A → C)
+f = λ p x → (snd p) ((fst p) x)
+\end{lstlisting}
+
+自然演繹での三段論法の証明は、1つの仮定から $ \land 1 \mathcal{E} $ と $ \land 2 \mathcal{E} $ を用いて仮定を二つ取り出し、それぞれに $ \Rightarrow \mathcal{E} $ を適用した後に仮定を $ \Rightarrow \mathcal{I}$ して導出していた。
+
+ここで $ \Rightarrow \mathcal{I}$ に対応するのは関数適用である。
+よってこの証明は「一つの変数から fst と snd を使って関数を二つ取り出し、それぞれを関数適用する」という形になる。
+これをラムダ式で書くとリスト~\ref{src:agda-modus-ponens}のようになる。
+仮定 $ (A \rightarrow B) \times (B \rightarrow C) $ と仮定 A から A $ \rightarrow $ C を導いている。
+
+仮定に相当する変数 p の型は$ (A \rightarrow B) \times (B \rightarrow C) $ であり、p からそれぞれの命題を取り出す操作が fst と snd に相当する。
+fst p の型は $ (A \rightarrow B) $ であり、snd p の型は $ (B \rightarrow C) $ である。
+もう一つの仮定xの型は A なので、fst p を関数適用することで B が導ける。
+得られた B を snd p に適用することで最終的に C が導ける。
+
+\lstinputlisting[label=src:agda-modus-ponens, caption=Agda における三段論法の証明] {src/AgdaModusPonens.agda}
+
+このように Agda でも自然演繹と同様に証明を記述できる。
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter4.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter4.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,199 @@
+%% Natural Deduction の説明をして、 Agda が命題を証明することができることを示す
+%% 章? 要る。。。かどうかは微妙な気がする。 「こういう話で Agda では証明ができます。」
+%% で勝手に証明して証明できたね！はありだけど読み手があんまり嬉しくないかも。
+%% ソレだとやっぱり自然演繹の話しして~同型対応でちゃんとつながってるね~じゃあ
+%% Agda で表現できるし証明できるねでいい感じかも
+
+\chapter{Agda における CbC の表現}
+
+% ツッコミどころさん
+% どうするのかは書けるけどなんでAgdaなの？みたいな話が飛んでくる
+
+前章では Agda の文法について説明した。
+本章では CbC と対応して CodeGear、 DataGear、 継続を Agda で表現する。
+また、 Agda で継続を記述することで得た知見を示す。
+
+\section{Agda での CodeGear 、 DataGear 、 継続の表現}
+
+%% 書くこと
+% CodeGearとDataGearのAgda上での定義
+
+DataGear はレコード型で表現できるため、 Agda のレコード型をそのまま利用して定義
+してく。
+記述は~\ref{src:agda-ds}のようになる。
+
+\lstinputlisting[label=src:agda-ds, caption=Agda における DataGear の定義]
+{src/DataSegment.agda.replaced}
+
+CodeGear は DataGear を受け取って DataGear を返すという定義であるため、
+$ I \rightarrow O $ を内包する CodeGear 型のデータ型(~\ref{src:agda-cs})を定義する。
+
+\lstinputlisting[label=src:agda-cs, caption= Agda における CodeGear 型の定義] {src/CodeSegment.agda.replaced}
+
+CodeGear 型を定義することで、 Agda での CodeGear の本体は Agda での関数そのもの
+と対応する。
+% しかし、そのままだと再帰呼び出しの点で CbC との対応が失われてしまう。
+% そのため、 Agda では \verb/goto/を利用できるのは関数の末尾のみという制約を設ける
+% 必要がある。
+% この制約さえ満たせば、
+
+CodeGear の実行は CodeGear 型から関数本体を取り出し、レコード型を持つ値を適用す
+ることに相当する。
+
+
+CbC での軽量継続は
+
+\begin{itemize}
+ \item 次に実行する CodeGear を指定する
+ \item CodeGear に渡す DataGear を指定する
+ \item 現在実行している CodeGear から制御を指定された CodeGear へと移す
+\end{itemize}
+
+の機能を持っている。
+
+この機能を満たす関数はソースコード\ref{src:agda-goto} として定義されている。
+
+\lstinputlisting[label=src:agda-goto, caption=Agdaにおける goto の定義] {src/Goto.agda.replaced}
+
+goto は CodeGear よりも一つ Level が上の Meta CodeGear にあたり、次に実行する
+CodeGear 型を受け取り、Input DataGear、 Output DataGear を返す。型になっている。
+
+
+\section{Agda での Stack、 Tree の実装}
+
+ここでは Agda での Stack 、 Tree の実装を示す。
+
+Stack の実装を以下のソースコード\ref{src:stack-impl}で示す。
+実装は SingleLinkedStack という名前で定義されている。
+定義されている API は push を例に残りは省略する。残りのの実装は付録に示す。 %~\
+
+\lstinputlisting[label=src:stack-impl, caption=Agdaにおける Stack の実装] {src/AgdaStackImpl.agda.replaced}
+
+Element は SingleLinkedStack で扱われる要素の定義で、現在のデータ datum と次のデー
+タを Maybe 型という値の存在が不確かな場合の型で包み、自身で再帰的に定義している。
+Maybe 型では値が存在する場合は Just 、 存在しない場合は Nothing を返す。
+
+SingleLinkedStack 型では、この Element の top 部分のみを定義している。
+
+Stack に対する push 操作では stack と push する element 型の datum を受け取り、 datum
+の next に現在の top を入れ、 stack の top を受け取った datum に切り替え、新しい
+stack を返すというような実装をしている。
+
+Tree の実装(以下のソースコード\ref{src:tree-impl})は RedBlackTree という名前で定義されている。
+定義されている API は put 以後省略する。残りのの実装は付録に示す。 %~\
+
+\lstinputlisting[label=src:tree-impl, caption=Agdaにおける Tree の実装] {src/AgdaTreeImpl.agda.replaced}
+
+Node 型は key と value 、 Color と Node の rihgt 、 left の情報を持っている。
+Tree を構成する末端の Node は leafNode 型で定義されている。
+
+RedBlackTree 型は root の Node 情報と Tree に関する計算をする際に、そこまでの
+Node の経路情報を保持するための nodeStack と 比較するための compare を持っている。
+
+Tree の put 操作では tree 、 put するノードのキーと値(k1、value)を引数として受け
+取り、Tree の root に Node が存在しているかどうかで場合分けしている。
+Nothing が返ってきたときは RedBlackTree 型の tree 内に定義されている root に受け
+取ったキーと値を新しいノードとして追加する。
+Just が返ってきたときは root が存在するので、経路情報を積むために nodeStack を初
+期化し、受け取ったキーと値で新たなノードを作成した後、ノードが追加されるべき位置
+までキーの値を比べて新しい Tree を返すというような実装になっている。
+
+\section{Agda における Interface の実装}
+
+%% 書くこと
+% stack の Interface部分と redBlackTree の Interface部分。
+% interfaceとは?->cbcのとこに突っ込んでこっちは同様に〜で済ませたい
+
+Agda 側でも CbC 側と同様に interface を実装した。
+interface は record で列挙し、ソースコード~\ref{src:agda-interface}のように紐付けることができる。
+CbC とは異なり、 Agda では型を明記する必要があるため record 内に型を記述している。
+
+例として Agda で実装した Stack 上の interface (ソースコード\ref{src:agda-interface})を見る。
+Stack の実装は SingleLinkedStack(ソースコード\ref{src:agda-single-linked-stack}) として書かれている。それを Stack 側から
+interface を通して呼び出している。
+
+ここでの interface の型は Stack の record 内にある pushStack や popStack などで、
+実際に使われる Stack の操作は StackMethods にある push や popである。この push
+や pop は SingleLinkedStack で実装されている。
+
+% \lstinputlisting[label=src:agda-single-linked-stack, caption=Agda における Stack
+% の実装] {src/AgdaSingleLinkedStack.agda.replaced}
+
+\lstinputlisting[label=src:agda-interface, caption=Agda における Interface の定義] {src/AgdaInterface.agda.replaced}
+
+interface を通すことで、実際には Stack の push では stackImpl と何らかのデータ a を取
+り、 stack を変更し、継続を返す型であったのが、 pushStack では 何らかのデータ a を取り stack を変更
+して継続を返す型に変わっている。
+
+また、 Tree でも interface を記述した。
+
+\lstinputlisting[label=src:agda-tree, caption=Tree Interface の定義]{src/AgdaTree.agda.replaced}
+
+interface を記述することによって、データを push する際に予め決まっている引数を省
+略することができた。
+また、 Agda で interface を記述することで CbC 側では意識していなかった型が、明確
+化された。
+
+% 元の push では 送り先の stack を関数に書く必要があり、異なる stack に push
+% する可能性があったが、 pushStack では紐付けた Stack に push することになり
+
+\section{継続を使った Agda における Test , Debug}
+
+Agda ではプログラムのコンパイルが通ると型の整合性が取れていることは保証できるが、必ず
+しも期待した動作をするとは限らない。そのため、本研究中に書いたプログラムが正しい動
+作をしているかを確認するために行なった手法を幾つか示す。
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+今回は実験中にソースコード\ref{src:agda-stack-test}のような Test を書いた。
+この Test では Stack をターゲットにしていて、 Stack に1、 2の二つの$ \mathbb{N} $型のデー
+タを push した後、 pop2 Interface を使って Stack に入っている 1、 2 が Stack の
+定義である First in Last out の通りに 2、 1 の順で取り出せるかを確認するために作成した。
+
+\lstinputlisting[label=src:agda-stack-test, caption=Agdaにおけるテスト]{src/AgdaStackTest.agda.replaced}
+
+上の Test では、02 が 2つのデータを push し、 03 で 二つのデータを pop する pop2
+を行っている。それらをまとめて記述したものが 04 で 2 回 push し、 2つのデータを pop する動
+作が正しく行われていれば 04 は True を返し、 05 で記述された型通りに互いに等しくなる
+ため 05 が refl でコンパイルが通るようになる。
+今回は、 pop2 で取れた値を確認するため 03 の後に 031、 032 の二つの作成した。
+032 では 03 で扱っている値が Maybe であるため、 031 のような比較をする前に値が確
+実に存在していることを示す補題である。 032 を通すことで 031 では 2つの値があり、
+かつ$\mathbb{N}$型である事がわかる。 031 では直接取れた値が 2、 1 の順番で入って
+いるかを確認している。
+
+この Test でエラーが出なかったことから、 Stack に1、2の二つのデータを pushする
+と、 push した値が Stack 上から消えることなく push した順番に取り出せることが分
+かる。
+
+
+また、継続を用いて記述することで関数の Test を書くことで計算途中のデータ内部をチェックするこ
+とができた。
+
+ここでの \$ は \( \) をまとめる糖衣構文で、 \$ が書かれた一行を\(\)でくくること
+ができる。
+% \ref{sintax}のようなコードを
+% \begin{lstlisting}[frame=lrbt,label=sintax,caption={\footnotesize 通常の継続の
+% コード}]
+
+% \end{lstlisting}
+
+% \begin{lstlisting}[frame=lrbt,label=sintax-sugar,caption={\footnotesize 糖衣構文
+% を用いた継続のコード}]
+
+% \end{lstlisting}
+
+ソースコード~\ref{src:agda-tree-debug}のように関数本体に記述してデータを返し、C-c C-n
+(Compute normal form) で関数を評価すると関数で扱っているデータを見ることができる。
+また、途中の計算で受ける変数名を変更し、 Return 時にその変更した変数名に変えるこ
+とで、計算途中のデータの中身を確認することができる。評価結果はソースコード内にコメントで記述した。
+
+ \lstinputlisting[label=src:agda-tree-debug, caption=Agdaにおけるテスト]{src/AgdaTreeDebug.agda.replaced}
+
+今回、この手法を用いることで複数の関数を組み合わせた findNode 関数内に異常があるこ
+とが分かった。
+
+
+%getRedBlackTree の関数に
+
+% \lstinputlisting[label=agda-Debug, caption=Agdaにおけるデバッグ]{src/AgdaTreeDebug.agda.replaced}
+% Tree全然載せてないけどどうしよ。。。どこに書こうかは考えておきましょう
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter5.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter5.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,139 @@
+\chapter{Agda による CbC の証明}
+
+前章では Agda で CodeGear や DataGear の定義を示した。また、 CbC のコード
+を Agda にマッピングし等価なコードを生成できることを示した。
+本章では前章で生成した Interface の Stack や Tree のコードを使い Agda で
+Interface を経由したコードでの証明が可能であることを示す。
+
+% Hoare Logic ベースで証明をすすめる〜みたいなとこをどっかにいれたい。
+% ↑ 上は Tree のコードが証明できないことを示して、その次の章に Hoare Logic でこ
+% んな感じにするとできるのでは？っていう感じにしよ
+
+\section{Agda による Interface 部分を含めた Stack の部分的な証明}
+\label{src:agda-interface-stack}
+
+% Stack の仕様記述
+ここでの証明とは Stack の処理が特定の性質を持つことを保証することである。
+
+Stack の処理として様々な性質が存在する。例えば、
+
+\begin{itemize}
+ \item Stack に push した値は存在する
+ \item Stack に push した値は取り出すことができる
+ \item Stack に push した値を pop した時、その値は Stack から消える
+ \item どのような状態の Stack に値を push しても中に入っているデータの順序は変わらない
+ \item どのような状態の Stack でも、値を push した後 pop した値は直前に入れた値と一致する
+\end{itemize}
+
+などの性質がある。
+
+本セクションでは「どのような状態の Stack でも、値を push した後 pop した値は直前
+に入れた値と一致する」という性質を証明する。
+
+
+% この証明では任意の Stack に2回 push したあと2回 pop すると push したものと同じ
+% ものが受け取れることを 証明している。
+
+まず始めに不定状態の Stack を定義する。ソースコード~\ref{src:agda-in-some-state}
+の stackInSomeState 型は中身の分からない抽象的な Stack を表現している。ソースコー
+ド~\ref{src:agda-in-some-state}の証明ではこのstackInSomeState に対して、 push を
+2回行い、 pop2 をして取れたデータは push したデータと同じものになることを証明してい
+る。
+
+ \lstinputlisting[label=src:agda-in-some-state, caption=抽象的なStackの定義とpush$->$push$->$pop2 の証明]{src/AgdaStackSomeState.agda.replaced}
+
+% Agda でも継続を使った書き方で Interface 部分の実装を示した。
+
+この証明では stackInSomeState 型の s が抽象的な Stack で、そこに x 、 y の２つのデー
+タを push している。また、 pop2 で取れたデータは y1 、 x1 となっていて両方が
+Just で返ってくるかつ、 x と x1 、 y と y1 がそれぞれ合同であることが仮定として
+型に書かれている。
+
+% この辺ちょっと怪しい感じ
+この関数本体で返ってくる値は$ x \equiv x1 と y \equiv y1$ のため record でまと
+めて refl で推論が通る。
+これにより、抽象化した Stack に対して push 、 pop を行うと push したものと同じも
+のを受け取れることが証明できた。
+
+
+% \lstinputlisting[label=src:agda-Test, caption=]{src/AgdaStackTest.agda.replaced}
+
+\section{Agda による Interface 部分を含めた Binary Tree の部分的な証明と課題}
+ここでは Binary Tree の性質の一部に対して証明を行う。
+Binary Tree の性質として挙げられるのは次のようなものである
+% 上の２つはデータ構造として最低限守られるべき部分ではあるがとりあえず書いてる
+
+\begin{itemize}
+ \item Tree に対して Node を Put することができる。
+ \item Tree に Put された Node は Delete されるまでなくならない。
+ \item Tree に 存在する Node とその子の関係は必ず「右の子 $>$ Node」かつ「Node $>$ 左の子」の関係になっている。
+ \item どのような状態の Tree に値を put しても Node と子の関係は保たれる
+ \item どのような状態の Tree でも値を Put した後、その値を Get すると値が取れる。
+\end{itemize}
+
+ここで証明する性質は
+
+${!!}$ と書かれているところはまだ記述できていない部分で $?$ としている部分である。
+
+\lstinputlisting[label=src:agda-tree-proof, caption=Tree Interface の証
+明]{src/AgdaTreeProof.agda.replaced}
+
+この Tree の証明では、不定状態の Tree を redBlackInSomeState で作成し、その状態の Tree
+に一つ Node を Put し、その Node を Get することができるかを証明しようとしたもの
+である。
+
+しかし、この証明は Node を取得する際に Put した Node が存在するか、 Get した
+Node が存在するのか、などの条件や、 Get した Node と Put した Node が合同なのか、
+key の値が等しい場合の eq は合同と同義であるのか等の様々な補題を証明する必要が
+あった。今回この証明では Put した Node と Get した
+Node が合同であることを記述しようとしていたがそれまでの計算が異なるため完全に合
+同であることを示すことが困難であった。
+
+今後の研究では\ref{hoare-logic} で説明する Hoare Logic を元に証明を
+行おうと考えている。
+
+\section{Hoare Logic}
+\label{hoare-logic}
+
+Hoare Logic \cite{Hoare1969AnAB} とは Tony Hoare によって提案されたプログラム正
+しさを推論する手法である。図\ref{fig:hoare}のように、 P を前状態(Pre Condition)
+、C を処理(Command) 、 Q を後状態(Post Condition) とし、$\{P\} \ C \ \{Q\}$ のように考えたとき、
+プログラムの処理を「前状態を満たした後、処理を行い状態が後状態に変化する」といった形で考える事ができる。
+
+\begin{figure}[htpb]
+ \begin{center}
+ \scalebox{0.6}[0.6]{\includegraphics{fig/hoare-logic.pdf}}
+ \end{center}
+ \caption{hoare logicの流れ}
+ \label{fig:hoare}
+\end{figure}
+
+
+このとき、後状態から前状態を推論することができればそのプログラムは部分的に正しい
+動きをすることを証明することができる。
+
+この Hoare Logic の前状態、処理、後状態を CodeGear、 input/output の DataGear が表
+\ref{fig:cbc-hoare} のように表せるのではないか考えている。
+
+\begin{figure}[htpb]
+ \begin{center}
+ \scalebox{0.8}[0.8]{\includegraphics{fig/cbc-hoare.pdf}}
+ \end{center}
+ \caption{cbc と hoare logic}
+ \label{fig:cbc-hoare}
+\end{figure}
+
+この状態を当研究室で提案している CodeGear、 DataGear の単位で考えると
+Pre Condition が CodeGear に入力として与えられる Input DataGear、Command が
+CodeGear、 Post Condition を Output DataGear として当てはめることができると考えて
+いる。
+
+今後の研究では CodeGear、 DataGear、継続の概念を Hoare Logic に当てはめ Agda に
+当てはめ、幾つかの実装を証明していく。
+
+% Hoare Logic ではプログラムの動作が部分的に正しいことが証明できる。
+% 最終的な Stack、Tree の証明は Hoare Logic ベースで行う。
+%%
+% 部分正当性がプログラムに関する構造機能法によって合成的に証明できるという考えを導
+% 入した。
+%%
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/chapter6.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/chapter6.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,16 @@
+\chapter{まとめ}
+
+本研究では CodeGear、 DataGear を用いたプログラミング手法を使い、Agda で
+Interface を用いたプログラムを実装し、証明を記述した。
+これにより、 CbC で記述した時には細かく分かっていなかった Interface の型が明確になった。
+また、 Hoare Logic を CodeGear 、 DataGear と対応させることで Hoare Logic ベース
+で証明が進められると考えている。
+今回の研究中に継続を利用することで得られた知見は、今後の研究で大いに役立つと
+考える。
+
+今後の課題としては、CbC 上での RedBlackTree の実装や、 Agda 上での RedBlackTree
+の実装と証明がある。また、 CodeGear、DataGear をベースにした Hoare Logic を Agda で実
+装する。
+Agda 定義した Hoare Logic を使い、いくつかの証明を実際に記述し、書き方を確立するなどが考えられる。
+他にも、タスクスケジューラの実装を Agda に移し、 SynchronizedQueue の同期、非同
+期の検証などが考えられる。
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+ float
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+ float
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+
+
+ PrintOnePage
+
+ ReadOnly
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+ Canvas 1
+ SmartAlignmentGuidesActive
+ YES
+ SmartDistanceGuidesActive
+ YES
+ UniqueID
+ 1
+ UseEntirePage
+
+ VPages
+ 1
+ WindowInfo
+
+ CurrentSheet
+ 0
+ Expanded_Canvases
+
+ Frame
+ {{252, -73}, {1263, 938}}
+ ShowInfo
+
+ ShowRuler
+
+ Sidebar
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+ SidebarWidth
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
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+ Text
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+%%Title: fig/ryukyu.pdf
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+%!PS-Adobe-3.0 EPSF-3.0
%%Creator: Adobe Illustrator(TM) 6.0
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%%DocumentProcessColors: Black
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%AI5_FileFormat 3
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%AI3_IncludePlacedImages
%%CMYKCustomColor: 1 0 0.55 0 (Aqua)
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%%+ 1 0.9 0.1 0 (Dark Blue)
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%%+ 0.05 0.2 0.95 0 (Gold)
%%+ 0.75 0.05 1 0 (Grass Green)
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%%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set)
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%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
userdict /Adobe_level2_AI5 25 dict dup begin
put
/packedarray where not
{
userdict begin
/packedarray
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array astore readonly
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/setpacking /pop load def
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end
0
} if
pop
userdict /defaultpacking currentpacking put true setpacking
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Adobe_level2_AI5 begin
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currentdict Adobe_level2_AI5 eq
{
end
} if
} bind def
mark
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0
6 packedarray
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/findrgbcustomcolor
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1
5 packedarray
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/setcustomcolor
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exch
aload pop
0 eq
{
pop
4
{
4 index mul
4 1 roll
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5 -1 roll pop
setcmykcolor
}
{
pop
3
{
1 exch sub
3 index mul
1 exch sub
3 1 roll
} repeat
4 -1 roll pop
setrgbcolor
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def
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/gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def
userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put
userdict /level2?
systemdict /languagelevel known dup
{
pop systemdict /languagelevel get 2 ge
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put
/level2ScreenFreq
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begin
60
HalftoneType 1 eq
{
pop Frequency
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HalftoneType 2 eq
{
pop GrayFrequency
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HalftoneType 5 eq
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pop Default level2ScreenFreq
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{
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/setoverprint where not
{
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makefont
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{
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setfont
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{
/cshow
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[
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cleartomark
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gsave
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grestore
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testColor anyColor?
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{
gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore
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{
1 0 0 0 testCMYKColorThrough
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0 0 1 0 testCMYKColorThrough
0 0 0 1 testCMYKColorThrough
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composite? not
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gsave
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userdict /Adobe_ColorImage_AI6 24 dict put
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Adobe_ColorImage_AI6 begin
Adobe_ColorImage_AI6
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dup type /arraytype eq
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dup xcheck
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bind
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pop pop
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currentdict /Adobe_ColorImage_AI6_Vars known not
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/Adobe_ColorImage_AI6_Vars 15 dict def
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/channelcount 0 def
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/plateindex -1 def
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/WalkRGBString null def
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/RGBToGrayImageProc null def
/StuffCMYKIntoGrayString null def
/CMYKToGrayImageProc null def
/ColorImageCompositeEmulator null def
/SeparateCMYKImageProc null def
/FourEqual null def
/TestPlateIndex null def
currentdict /_colorimage known not
{
/colorimage where
{
/colorimage get /_colorimage exch def
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{
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} if
/_currenttransfer systemdict /currenttransfer get def
/colorimage null def
/XI null def
/WalkRGBString
{
0 3 index
dup length 1 sub 0 3 3 -1 roll
{
3 getinterval { } forall
5 index exec
3 index
} for
5 { pop } repeat
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/WalkCMYKString
{
0 3 index
dup length 1 sub 0 4 3 -1 roll
{
4 getinterval { } forall
6 index exec
3 index
} for
5 { pop } repeat
} def
/StuffRGBIntoGrayString
{
.11 mul exch
.59 mul add exch
.3 mul add
cvi 3 copy put
pop 1 add
} def
/RGBToGrayImageProc
{
Adobe_ColorImage_AI6_Vars begin
sourcearray 0 get exec
dup length 3 idiv string
dup 3 1 roll
/StuffRGBIntoGrayString load exch
WalkRGBString
end
} def
/StuffCMYKIntoGrayString
{
exch .11 mul add
exch .59 mul add
exch .3 mul add
dup 255 gt { pop 255 } if
255 exch sub cvi 3 copy put
pop 1 add
} def
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{
Adobe_ColorImage_AI6_Vars begin
sourcearray 0 get exec
dup length 4 idiv string
dup 3 1 roll
/StuffCMYKIntoGrayString load exch
WalkCMYKString
end
} def
/ColorImageCompositeEmulator
{
pop true eq
{
Adobe_ColorImage_AI6_Vars /sourcecount get 5 add { pop } repeat
}
{
Adobe_ColorImage_AI6_Vars /channelcount get 1 ne
{
Adobe_ColorImage_AI6_Vars begin
sourcearray 0 3 -1 roll put
channelcount 3 eq
{
/RGBToGrayImageProc
}
{
/CMYKToGrayImageProc
} ifelse
load
end
} if
image
} ifelse
} def
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{
Adobe_ColorImage_AI6_Vars begin
sourcecount 0 ne
{
sourcearray plateindex get exec
}
{
sourcearray 0 get exec
dup length 4 idiv string
0 2 index
plateindex 4 2 index length 1 sub
{
get 255 exch sub
3 copy put pop 1 add
2 index
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pop pop exch pop
} ifelse
end
} def
/FourEqual
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4 index ne
{
pop pop pop false
}
{
4 index ne
{
pop pop false
}
{
4 index ne
{
pop false
}
{
4 index eq
} ifelse
} ifelse
} ifelse
} def
/TestPlateIndex
{
Adobe_ColorImage_AI6_Vars begin
/plateindex -1 def
/setcmykcolor where
{
pop
gsave
1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
grestore
1 0 0 0 FourEqual
{
/plateindex 0 def
}
{
0 1 0 0 FourEqual
{
/plateindex 1 def
}
{
0 0 1 0 FourEqual
{
/plateindex 2 def
}
{
0 0 0 1 FourEqual
{
/plateindex 3 def
}
{
0 0 0 0 FourEqual
{
/plateindex 5 def
} if
} ifelse
} ifelse
} ifelse
} ifelse
pop pop pop pop
} if
plateindex
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} def
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Adobe_ColorImage_AI6_Vars begin
/channelcount 1 index def
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4 sourcecount add index dup
8 eq exch 1 eq or not
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{
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{
_colorimage
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{
Adobe_ColorImage_AI6_Vars /sourcecount get
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{
dup 3 eq
TestPlateIndex
dup -1 eq exch 5 eq or or
{
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{
ColorImageCompositeEmulator
}
{
dup 1 eq
{
pop pop image
}
{
Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
{
gsave
0 _currenttransfer exec
1 _currenttransfer exec
eq
{ 0 _currenttransfer exec 0.5 lt }
{ 0 _currenttransfer exec 1 _currenttransfer exec gt } ifelse
{ { pop 0 } } { { pop 1 } } ifelse
systemdict /settransfer get exec
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_colorimage
Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
{
grestore
} if
} ifelse
} ifelse
}
{
dup 1 eq
{
pop pop
image
}
{
pop pop
Adobe_ColorImage_AI6_Vars begin
sourcecount -1 0
{
exch sourcearray 3 1 roll put
} for
/SeparateCMYKImageProc load
end
systemdict /image get exec
} ifelse
} ifelse
} ifelse
} def
/XG
{
pop pop
} def
/XF
{
13 {pop} repeat
} def
/Xh
{
Adobe_ColorImage_AI6_Vars begin
gsave
/XIMask exch 0 ne def
/XIImageHeight exch def
/XIImageWidth exch def
/XIImageMatrix exch def
0 0 moveto
XIImageMatrix concat
XIImageWidth XIImageHeight scale
XIMask
{
/_lp /null ddef
_fc
/_lp /imagemask ddef
}
if
/XIVersion 7 def
end
} def
/XH
{
Adobe_ColorImage_AI6_Vars begin
/XIVersion 6 def
grestore
end
} def
/XI
{
Adobe_ColorImage_AI6_Vars begin
gsave
/XIMask exch 0 ne def
/XIBinary exch 0 ne def
pop
pop
/XIChannelCount exch def
/XIBitsPerPixel exch def
/XIImageHeight exch def
/XIImageWidth exch def
pop pop pop pop
/XIImageMatrix exch def
XIBitsPerPixel 1 eq
{
XIImageWidth 8 div ceiling cvi
}
{
XIImageWidth XIChannelCount mul
} ifelse
/XIBuffer exch string def
XIBinary
{
/XIDataProc { currentfile XIBuffer readstring pop } def
XIVersion 6 le
{
currentfile 128 string readline pop pop
}
if
}
{
/XIDataProc { currentfile XIBuffer readhexstring pop } def
} ifelse
XIVersion 6 le
{
0 0 moveto
XIImageMatrix concat
XIImageWidth XIImageHeight scale
XIMask
{
/_lp /null ddef
_fc
/_lp /imagemask ddef
} if
} if
XIMask
{
XIImageWidth XIImageHeight
false
[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
/XIDataProc load
imagemask
}
{
XIImageWidth XIImageHeight
XIBitsPerPixel
[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
/XIDataProc load
XIChannelCount 1 eq
{
gsave
0 setgray
image
grestore
}
{
false
XIChannelCount
colorimage
} ifelse
} ifelse
grestore
end
} def
end
%%EndProcSet
%%BeginResource: procset Adobe_Illustrator_AI5 1.1 0
%%Title: (Adobe Illustrator (R) Version 5.0 Full Prolog)
%%Version: 1.1 0
%%CreationDate: (3/7/1994) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_Illustrator_AI5_vars 81 dict dup begin
put
/_eo false def
/_lp /none def
/_pf
{
} def
/_ps
{
} def
/_psf
{
} def
/_pss
{
} def
/_pjsf
{
} def
/_pjss
{
} def
/_pola 0 def
/_doClip 0 def
/cf currentflat def
/_tm matrix def
/_renderStart
[
/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0
] def
/_renderEnd
[
null null null null /i1 /i1 /i1 /i1
] def
/_render -1 def
/_rise 0 def
/_ax 0 def
/_ay 0 def
/_cx 0 def
/_cy 0 def
/_leading
[
0 0
] def
/_ctm matrix def
/_mtx matrix def
/_sp 16#020 def
/_hyphen (-) def
/_fScl 0 def
/_cnt 0 def
/_hs 1 def
/_nativeEncoding 0 def
/_useNativeEncoding 0 def
/_tempEncode 0 def
/_pntr 0 def
/_tDict 2 dict def
/_wv 0 def
/Tx
{
} def
/Tj
{
} def
/CRender
{
} def
/_AI3_savepage
{
} def
/_gf null def
/_cf 4 array def
/_if null def
/_of false def
/_fc
{
} def
/_gs null def
/_cs 4 array def
/_is null def
/_os false def
/_sc
{
} def
/_pd 1 dict def
/_ed 15 dict def
/_pm matrix def
/_fm null def
/_fd null def
/_fdd null def
/_sm null def
/_sd null def
/_sdd null def
/_i null def
/discardSave null def
/buffer 256 string def
/beginString null def
/endString null def
/endStringLength null def
/layerCnt 1 def
/layerCount 1 def
/perCent (%) 0 get def
/perCentSeen? false def
/newBuff null def
/newBuffButFirst null def
/newBuffLast null def
/clipForward? false def
end
userdict /Adobe_Illustrator_AI5 known not {
userdict /Adobe_Illustrator_AI5 91 dict put
} if
userdict /Adobe_Illustrator_AI5 get begin
/initialize
{
Adobe_Illustrator_AI5 dup begin
Adobe_Illustrator_AI5_vars begin
discardDict
{
bind pop pop
} forall
dup /nc get begin
{
dup xcheck 1 index type /operatortype ne and
{
bind
} if
pop pop
} forall
end
newpath
} def
/terminate
{
end
end
} def
/_
null def
/ddef
{
Adobe_Illustrator_AI5_vars 3 1 roll put
} def
/xput
{
dup load dup length exch maxlength eq
{
dup dup load dup
length 2 mul dict copy def
} if
load begin
def
end
} def
/npop
{
{
pop
} repeat
} def
/sw
{
dup length exch stringwidth
exch 5 -1 roll 3 index mul add
4 1 roll 3 1 roll mul add
} def
/swj
{
dup 4 1 roll
dup length exch stringwidth
exch 5 -1 roll 3 index mul add
4 1 roll 3 1 roll mul add
6 2 roll /_cnt 0 ddef
{
1 index eq
{
/_cnt _cnt 1 add ddef
} if
} forall
pop
exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop
} def
/ss
{
4 1 roll
{
2 npop
(0) exch 2 copy 0 exch put pop
gsave
false charpath currentpoint
4 index setmatrix
stroke
grestore
moveto
2 copy rmoveto
} exch cshow
3 npop
} def
/jss
{
4 1 roll
{
2 npop
(0) exch 2 copy 0 exch put
gsave
_sp eq
{
exch 6 index 6 index 6 index 5 -1 roll widthshow
currentpoint
}
{
false charpath currentpoint
4 index setmatrix stroke
} ifelse
grestore
moveto
2 copy rmoveto
} exch cshow
6 npop
} def
/sp
{
{
2 npop (0) exch
2 copy 0 exch put pop
false charpath
2 copy rmoveto
} exch cshow
2 npop
} def
/jsp
{
{
2 npop
(0) exch 2 copy 0 exch put
_sp eq
{
exch 5 index 5 index 5 index 5 -1 roll widthshow
}
{
false charpath
} ifelse
2 copy rmoveto
} exch cshow
5 npop
} def
/pl
{
transform
0.25 sub round 0.25 add exch
0.25 sub round 0.25 add exch
itransform
} def
/setstrokeadjust where
{
pop true setstrokeadjust
/c
{
curveto
} def
/C
/c load def
/v
{
currentpoint 6 2 roll curveto
} def
/V
/v load def
/y
{
2 copy curveto
} def
/Y
/y load def
/l
{
lineto
} def
/L
/l load def
/m
{
moveto
} def
}
{
/c
{
pl curveto
} def
/C
/c load def
/v
{
currentpoint 6 2 roll pl curveto
} def
/V
/v load def
/y
{
pl 2 copy curveto
} def
/Y
/y load def
/l
{
pl lineto
} def
/L
/l load def
/m
{
pl moveto
} def
} ifelse
/d
{
setdash
} def
/cf
{
} def
/i
{
dup 0 eq
{
pop cf
} if
setflat
} def
/j
{
setlinejoin
} def
/J
{
setlinecap
} def
/M
{
setmiterlimit
} def
/w
{
setlinewidth
} def
/XR
{
0 ne
/_eo exch ddef
} def
/H
{
} def
/h
{
closepath
} def
/N
{
_pola 0 eq
{
_doClip 1 eq
{
_eo {eoclip} {clip} ifelse /_doClip 0 ddef
} if
newpath
}
{
/CRender
{
N
} ddef
} ifelse
} def
/n
{
N
} def
/F
{
_pola 0 eq
{
_doClip 1 eq
{
gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc
/_doClip 0 ddef
}
{
_pf
} ifelse
}
{
/CRender
{
F
} ddef
} ifelse
} def
/f
{
closepath
F
} def
/S
{
_pola 0 eq
{
_doClip 1 eq
{
gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
/_doClip 0 ddef
}
{
_ps
} ifelse
}
{
/CRender
{
S
} ddef
} ifelse
} def
/s
{
closepath
S
} def
/B
{
_pola 0 eq
{
_doClip 1 eq
gsave F grestore
{
gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
/_doClip 0 ddef
}
{
S
} ifelse
}
{
/CRender
{
B
} ddef
} ifelse
} def
/b
{
closepath
B
} def
/W
{
/_doClip 1 ddef
} def
/*
{
count 0 ne
{
dup type /stringtype eq
{
pop
} if
} if
newpath
} def
/u
{
} def
/U
{
} def
/q
{
_pola 0 eq
{
gsave
} if
} def
/Q
{
_pola 0 eq
{
grestore
} if
} def
/*u
{
_pola 1 add /_pola exch ddef
} def
/*U
{
_pola 1 sub /_pola exch ddef
_pola 0 eq
{
CRender
} if
} def
/D
{
pop
} def
/*w
{
} def
/*W
{
} def
/`
{
/_i save ddef
clipForward?
{
nulldevice
} if
6 1 roll 4 npop
concat pop
userdict begin
/showpage
{
} def
0 setgray
0 setlinecap
1 setlinewidth
0 setlinejoin
10 setmiterlimit
[] 0 setdash
/setstrokeadjust where {pop false setstrokeadjust} if
newpath
0 setgray
false setoverprint
} def
/~
{
end
_i restore
} def
/O
{
0 ne
/_of exch ddef
/_lp /none ddef
} def
/R
{
0 ne
/_os exch ddef
/_lp /none ddef
} def
/g
{
/_gf exch ddef
/_fc
{
_lp /fill ne
{
_of setoverprint
_gf setgray
/_lp /fill ddef
} if
} ddef
/_pf
{
_fc
_eo {eofill} {fill} ifelse
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/G
{
/_gs exch ddef
/_sc
{
_lp /stroke ne
{
_os setoverprint
_gs setgray
/_lp /stroke ddef
} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/k
{
_cf astore pop
/_fc
{
_lp /fill ne
{
_of setoverprint
_cf aload pop setcmykcolor
/_lp /fill ddef
} if
} ddef
/_pf
{
_fc
_eo {eofill} {fill} ifelse
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/K
{
_cs astore pop
/_sc
{
_lp /stroke ne
{
_os setoverprint
_cs aload pop setcmykcolor
/_lp /stroke ddef
} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/x
{
/_gf exch ddef
findcmykcustomcolor
/_if exch ddef
/_fc
{
_lp /fill ne
{
_of setoverprint
_if _gf 1 exch sub setcustomcolor
/_lp /fill ddef
} if
} ddef
/_pf
{
_fc
_eo {eofill} {fill} ifelse
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/X
{
/_gs exch ddef
findcmykcustomcolor
/_is exch ddef
/_sc
{
_lp /stroke ne
{
_os setoverprint
_is _gs 1 exch sub setcustomcolor
/_lp /stroke ddef
} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/A
{
pop
} def
/annotatepage
{
userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse
} def
/XT {
pop pop
} def
/discard
{
save /discardSave exch store
discardDict begin
/endString exch store
gt38?
{
2 add
} if
load
stopped
pop
end
discardSave restore
} bind def
userdict /discardDict 7 dict dup begin
put
/pre38Initialize
{
/endStringLength endString length store
/newBuff buffer 0 endStringLength getinterval store
/newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store
/newBuffLast newBuff endStringLength 1 sub 1 getinterval store
} def
/shiftBuffer
{
newBuff 0 newBuffButFirst putinterval
newBuffLast 0
currentfile read not
{
stop
} if
put
} def
0
{
pre38Initialize
mark
currentfile newBuff readstring exch pop
{
{
newBuff endString eq
{
cleartomark stop
} if
shiftBuffer
} loop
}
{
stop
} ifelse
} def
1
{
pre38Initialize
/beginString exch store
mark
currentfile newBuff readstring exch pop
{
{
newBuff beginString eq
{
/layerCount dup load 1 add store
}
{
newBuff endString eq
{
/layerCount dup load 1 sub store
layerCount 0 eq
{
cleartomark stop
} if
} if
} ifelse
shiftBuffer
} loop
} if
} def
2
{
mark
{
currentfile buffer readline not
{
stop
} if
endString eq
{
cleartomark stop
} if
} loop
} def
3
{
/beginString exch store
/layerCnt 1 store
mark
{
currentfile buffer readline not
{
stop
} if
dup beginString eq
{
pop /layerCnt dup load 1 add store
}
{
endString eq
{
layerCnt 1 eq
{
cleartomark stop
}
{
/layerCnt dup load 1 sub store
} ifelse
} if
} ifelse
} loop
} def
end
userdict /clipRenderOff 15 dict dup begin
put
{
/n /N /s /S /f /F /b /B
}
{
{
_doClip 1 eq
{
/_doClip 0 ddef _eo {eoclip} {clip} ifelse
} if
newpath
} def
} forall
/Tr /pop load def
/Bb {} def
/BB /pop load def
/Bg {12 npop} def
/Bm {6 npop} def
/Bc /Bm load def
/Bh {4 npop} def
end
/Lb
{
4 npop
6 1 roll
pop
4 1 roll
pop pop pop
0 eq
{
0 eq
{
(%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard
}
{
/clipForward? true def
/Tx /pop load def
/Tj /pop load def
currentdict end clipRenderOff begin begin
} ifelse
}
{
0 eq
{
save /discardSave exch store
} if
} ifelse
} bind def
/LB
{
discardSave dup null ne
{
restore
}
{
pop
clipForward?
{
currentdict
end
end
begin
/clipForward? false ddef
} if
} ifelse
} bind def
/Pb
{
pop pop
0 (%AI5_EndPalette) discard
} bind def
/Np
{
0 (%AI5_End_NonPrinting--) discard
} bind def
/Ln /pop load def
/Ap
/pop load def
/Ar
{
72 exch div
0 dtransform dup mul exch dup mul add sqrt
dup 1 lt
{
pop 1
} if
setflat
} def
/Mb
{
q
} def
/Md
{
} def
/MB
{
Q
} def
/nc 3 dict def
nc begin
/setgray
{
pop
} bind def
/setcmykcolor
{
4 npop
} bind def
/setcustomcolor
{
2 npop
} bind def
currentdict readonly pop
end
end
setpacking
%%EndResource
%%EndProlog
%%BeginSetup
Adobe_level2_AI5 /initialize get exec
Adobe_ColorImage_AI6 /initialize get exec
Adobe_Illustrator_AI5 /initialize get exec
%AI5_Begin_NonPrinting
Np
%AI3_BeginPattern: (Arrow1.2.out/in)
(Arrow1.2.out/in) 1 1 39.4039 39.4039 [
%AI3_Tile
(0 O 0 R 0.75 0.75 0.375 0 k
0.75 0.75 0.375 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
1 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
33.9039 15.6187 m
39.4247 20.202 L
39.4247 20.202 L
33.8869 24.6252 L
S
39.2997 20.202 m
24.5706 20.202 l
20.4039 20.4792 20.4039 16.8125 v
20.4039 13.1458 20.4039 12.5625 y
S
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Arrow1.2.side)
(Arrow1.2.side) 1 1 39.404 39.4039 [
%AI3_Tile
(0 O 0 R 0.75 0.75 0.375 0 k
0.75 0.75 0.375 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
1 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
20.202 20.202 m
39.404 20.202 l
S
33.904 15.6187 m
39.4248 20.202 L
39.4248 20.202 L
33.887 24.6252 L
S
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Bricks)
(Bricks) 1.6 1.6 73.6 73.6 [
%AI3_Tile
(0 O 0 R 0.3 0.85 0.85 0 k
0.3 0.85 0.85 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 1.6 m
1.6 73.6 L
73.6 73.6 L
73.6 1.6 L
1.6 1.6 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R 1 g
1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 70.01 m
73.6 70.01 l
S
1.6 62.809 m
73.6 62.809 L
S
1.6 55.609 m
73.6 55.609 L
S
1.6 48.408 m
73.6 48.408 L
S
1.6 41.208 m
73.6 41.208 L
S
1.6 34.007 m
73.6 34.007 L
S
1.6 26.807 m
73.6 26.807 L
S
1.6 19.606 m
73.6 19.606 L
S
1.6 12.406 m
73.6 12.406 L
S
1.6 5.206 m
73.6 5.206 L
S
70.01 70.01 m
70.01 62.822 l
S
55.61 70.01 m
55.61 62.822 L
S
41.21 70.01 m
41.21 62.822 L
S
26.81 70.01 m
26.81 62.822 L
S
12.41 70.01 m
12.41 62.822 L
S
70.01 55.572 m
70.01 48.385 l
S
55.61 55.572 m
55.61 48.385 L
S
41.21 55.572 m
41.21 48.385 L
S
26.81 55.572 m
26.81 48.385 L
S
12.41 55.572 m
12.41 48.385 L
S
70.01 41.197 m
70.01 34.01 l
S
55.61 41.197 m
55.61 34.01 L
S
41.21 41.197 m
41.21 34.01 L
S
26.81 41.197 m
26.81 34.01 L
S
12.41 41.197 m
12.41 34.01 L
S
70.01 26.822 m
70.01 19.635 l
S
55.61 26.822 m
55.61 19.635 L
S
41.21 26.822 m
41.21 19.635 L
S
26.81 26.822 m
26.81 19.635 L
S
12.41 26.822 m
12.41 19.635 L
S
70.01 12.385 m
70.01 5.197 l
S
55.61 12.385 m
55.61 5.197 L
S
41.21 12.385 m
41.21 5.197 L
S
26.81 12.385 m
26.81 5.197 L
S
12.41 12.385 m
12.41 5.197 L
S
62.797 5.197 m
62.797 1.6 L
S
48.397 5.197 m
48.397 1.6 L
S
33.997 5.197 m
33.997 1.6 L
S
19.597 5.197 m
19.597 1.6 L
S
5.197 5.197 m
5.197 1.6 l
S
62.797 19.635 m
62.797 12.447 L
S
48.397 19.635 m
48.397 12.447 L
S
33.997 19.635 m
33.997 12.447 L
S
19.597 19.635 m
19.597 12.447 L
S
5.197 19.635 m
5.197 12.447 l
S
62.797 34.01 m
62.797 26.822 L
S
48.397 34.01 m
48.397 26.822 L
S
19.597 34.01 m
19.597 26.822 L
S
5.197 34.01 m
5.197 26.822 l
S
62.797 48.385 m
62.797 41.197 L
S
48.397 48.385 m
48.397 41.197 L
S
33.997 48.385 m
33.997 41.197 L
S
19.597 48.385 m
19.597 41.197 L
S
5.197 48.385 m
5.197 41.197 l
S
62.797 62.822 m
62.797 55.635 L
S
48.397 62.822 m
48.397 55.635 L
S
33.997 62.822 m
33.997 55.635 L
S
19.597 62.822 m
19.597 55.635 L
S
5.197 62.822 m
5.197 55.635 l
S
62.797 73.5589 m
62.797 70.072 L
S
48.397 73.5589 m
48.397 70.072 L
S
33.997 73.5589 m
33.997 70.072 L
S
19.597 73.5589 m
19.597 70.072 L
S
5.197 73.5589 m
5.197 70.072 l
S
33.997 34.01 m
33.997 26.822 L
S
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Checks)
(Checks) 1 1 31.3995 31.3995 [
%AI3_Tile
(0 O 0 R 0 0.9 1 0 k
0 0.9 1 0 K
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156.1001 180.3999 L
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89.6001 169.1001 88.8999 170 89.2002 170.3999 C
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94.5 174.7002 95.7002 175.7002 95.2998 177 C
96.3999 177.1001 94.8999 178.5 96.2002 178.6001 C
96.3999 179.8999 L
96.6001 179.6001 L
96.7002 181.1001 97.2998 181.7998 98 183.1001 C
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99.1001 182.5 98.8999 180.8999 98.8999 179.2998 C
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99.8999 173.5 100.5 174.2998 100.3999 175.2998 C
101.2998 175.8999 101.2002 177.6001 101.5 178.2998 C
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101.7998 179.3999 102.7002 180.7002 103.2002 181.3999 C
102.8999 182.3999 103.7998 182.5 103.7998 183.2002 C
103.7998 181.7002 104.7998 180.6001 103.7998 179.3999 C
104.1001 177.2998 103.2998 175.7002 104.2998 173.7998 C
104.6001 174 105 174.1001 104.8999 174.6001 C
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105.5 175.8999 L
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108.6001 181.7002 L
108.7998 181.3999 109 180.7002 109.3999 180.1001 C
108.7002 180 109.3999 179.2998 108.7998 179.2998 C
109 177.2998 107.6001 175.1001 108.7002 173.7998 C
108.3999 173.5 108.8999 173.2002 109.1001 173 C
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111 176.7002 111.7998 177.2002 111.7002 177.7998 C
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112.6001 179.5 L
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113.7002 172.5 114.2002 172.8999 113.8999 173.2998 C
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113.2998 165.8999 109 165.7002 105.5 165.7002 C
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65.2998 163.8999 58.5 157.2002 50.8999 154.7002 C
46.8999 153.7998 43.2998 151.8999 39.5 151.7998 C
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12.6001 138.1001 L
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24.3999 155.8999 L
25 155.6001 25.7998 153.1001 27 153.7002 C
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27.6001 158.5 L
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29 156.5 L
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31.3999 159.1001 L
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33.3999 158.2998 L
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41.7002 164.7002 40.5 165.5 40.6001 167 C
40.1001 167.2002 40.5 167.5 40.6001 167.7998 C
40 168.2002 40 169.2998 40.1001 169.8999 C
41.3999 170.3999 41 168.2002 41.8999 168.1001 C
42 167.2998 42.3999 166.7998 43 166.3999 C
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49.3999 167.2002 49.3999 165.3999 49.8999 166.1001 C
50.7002 165.1001 50.7998 163.2002 52.1001 162.7002 C
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55.3999 168.2998 55.2998 167.3999 55.7998 167.2998 C
55.8999 166.8999 56 166.1001 56.8999 166.1001 C
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57.5 173.3999 55.6001 175.2002 56.6001 177.1001 C
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58.2002 179.5 57.7002 177.1001 58.2998 176.2998 C
58.3999 176.3999 L
58.7002 175.8999 58.7998 175 59.2002 174.7998 C
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59.5 172.6001 60.7002 171.7998 60.5 171 C
60.8999 170.8999 60.7002 170.2002 61 169.8999 C
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62.2998 171.5 L
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62.8999 176.2002 61.7998 178.3999 62.2998 180.6001 C
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63.7002 179.3999 64.2002 178.2998 64.2998 176.6001 C
64.3999 176.7998 L
64.2002 175.6001 65.2002 174.2998 65.2998 172.8999 C
65.6001 172.8999 L
65.5 172.2998 65.7002 171.8999 65.8999 171.3999 C
66.2998 171.1001 67 171.6001 66.7002 172.1001 C
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67.3999 177.3999 67.2002 178.7998 67.1001 180.1001 C
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67.1001 180.5 67.8999 180.2998 67.7002 180.7998 C
67.7002 181.3999 L
67.8999 181.3999 68 181.7002 68.2002 181.7998 C
68.2002 182 67.6001 182.3999 68.2002 182.3999 C
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69.3999 177 70.1001 175.6001 70.2002 173.2002 C
70.2998 173.1001 70.3999 173.2002 70.3999 173.2998 C
70.2998 173.2998 70.6001 172.7998 70.8999 172.6001 C
71.7002 172.6001 71.1001 172.6001 71.6001 172.3999 C
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72.3999 174 L
72.6001 174.2002 L
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73.1001 178.2998 72.7998 179.1001 73.6001 180.2002 C
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74.2002 183.7998 L
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75.1001 182.2002 75.8999 180.2998 75.7002 178.3999 C
75.7002 178.6001 75.7998 178.7998 75.6001 178.8999 C
75 177.2002 76.1001 175.7002 76.1001 174 C
76.3999 173.7998 76.7002 173.6001 76.7998 173.2002 C
77.5 173.3999 77.2998 173.8999 77.5 174.6001 C
77.7002 174.6001 77.8999 174.5 78 174.7002 C
77.5 174.7998 77.8999 175.6001 78.1001 175.8999 C
77.8999 176 77.8999 176.2998 78.1001 176.3999 C
78.3999 177.3999 78.6001 178.2998 78.5 179.3999 C
78.6001 179.2998 L
79.2998 180.7002 79 181.7002 79.7998 182.7998 C
80 183.6001 80.7002 184.2998 80.7998 184.8999 C
81.1001 181 80.6001 176.7002 81 172.8999 C
81.1001 173 81.1001 173.1001 81.2002 173 C
81.1001 172.6001 81.2002 172.5 81.2002 172 C
81.1001 172.1001 81 172.1001 V
80.5 171.7002 81.3999 171.7002 81.2002 171.3999 C
81.1001 170.8999 81.3999 170.3999 81.5 169.8999 C
81.7998 169.7998 L
81.3999 169.6001 L
82.2002 168.7002 L
82 168.5 L
82.1001 168.3999 82.1001 168.2002 82.2998 168.2002 C
83.1001 168.6001 82.2998 169 82.8999 169.2998 C
83.2002 170.7998 83.3999 171.3999 83.5 172.6001 C
83.7998 173.6001 84.1001 174.3999 84.1001 175.3999 C
83.7002 176.1001 84.8999 176.5 84.5 177.3999 C
84.7998 178.7998 85.7998 180 85.7002 181.3999 C
85.7998 181.2998 L
86.1001 181.7002 86.2002 182.3999 86.2998 182.7998 C
86.5 183.3999 87.2998 184.1001 87.1001 185.2998 C
87.3999 184.8999 L
87.7002 185.2998 L
f
106.2002 162.7002 m
106.2998 159.5 105.3999 156.8999 106.7998 154.2998 C
108.5 153.1001 107.7002 155.6001 108.3999 156 C
108 156 L
108.3999 156.5 L
108.7002 157.2002 107.5 158.2002 108.2002 159 C
107.8999 160.7998 108.1001 161.7998 109.6001 162.7998 C
109.8999 159.7002 110.3999 158 110.5 154.7002 C
110.7998 154.7002 L
110.7002 154.1001 110.7002 153.2002 111.2002 152.8999 C
111.7998 152.7002 111.1001 151.8999 111.7998 151.8999 C
112.2002 152.2998 L
112 152.2998 112.1001 152.5 112.1001 152.6001 C
112.2002 152.5 L
112.2998 152.7998 113.1001 153.1001 112.3999 153.5 C
112.7998 153.5 L
112.7002 155.2002 113.5 157 113.2998 158.7998 C
113.7998 160.6001 L
113.3999 160.6001 L
114 161.2002 L
114.3999 160.3999 115.2998 160.7002 115.3999 160 C
115.7998 159.5 116.2998 158.7002 116.2998 158 C
116 156.7002 117 155.2002 116.2002 154 C
115.8999 150.7002 116.7998 148.8999 116 146 C
111.1001 148.7998 106 147.3999 101.2998 145.1001 C
96.2002 143.1001 92.1001 139.5 86.8999 140.3999 C
84.3999 140.2002 82.6001 141.8999 80.6001 143.2002 C
79.6001 144.3999 78.2998 146.7002 76.2002 146 C
72.1001 145.3999 70.6001 141.3999 67.6001 139.3999 C
67.3999 139 L
65.7998 136.8999 62.7998 135.2998 60.7002 134.2002 C
60.6001 134.2998 L
58.7002 133.2002 55.6001 132.1001 53.2998 131 C
52.6001 130.2998 50.2998 129.6001 49.6001 128.2998 C
47.8999 126.7002 46.7002 123.7998 47.3999 121.6001 C
46.5 119.6001 48.7002 118.8999 47.2998 117.2002 C
45.7002 113.7002 40.8999 112 38.2998 109.7002 C
36.1001 108.7998 34.7998 107.2998 33.7002 105.7002 C
33.8999 106.7002 32.7998 107.7002 33.7002 108.3999 C
33.7002 109 L
33.7998 109 34 109 34.1001 108.7998 C
33.7998 110.7998 36.3999 109.3999 35.7998 111.5 C
35.8999 111.5 L
35.8999 112.8999 L
36.8999 113.2002 38 113.1001 37.6001 114.3999 C
36.7002 114.6001 37.2998 115.8999 36.3999 116 C
36.2002 116.5 36.7002 116.6001 36.7998 116.8999 C
37.6001 117.2998 39.1001 115.7002 39.1001 117.2002 C
40 117.5 38.8999 118 39.1001 118.8999 C
38.7998 120.1001 L
39 119.8999 L
39.1001 120.5 L
40.1001 120.2998 40.7002 118.2998 41.6001 119.3999 C
41.3999 120 L
41.8999 120.1001 41.5 120.3999 41.7998 120.6001 C
40.8999 121 41.5 123.2998 40.8999 124.1001 C
40.7002 124.1001 L
40.7002 123.8999 41.3999 124.2998 41.2002 124.7002 C
41.8999 124.6001 42.6001 122.6001 43.6001 122.7998 C
42.7998 122.7998 44 124.3999 43.1001 124.7998 C
43 125 43.2002 125 43.2998 125.2002 C
43.2002 125.3999 43 125.2002 42.7998 125.2998 C
43.2002 126.7002 42.1001 127.2998 42.7998 128.6001 C
43.1001 128.6001 43.2998 128.7002 43.3999 128.8999 C
43.7002 128.6001 L
43.8999 129.1001 43.8999 128.7002 44.2998 128.6001 C
44.6001 128 44.2998 127.1001 45.2002 126.7998 C
45.1001 126.2998 45.7002 126.2002 46 126.1001 C
46.6001 126.1001 46.2998 126.7998 46.7002 127.1001 C
46.6001 127.5 45.7998 127.7002 46.3999 128 C
46.1001 129 46 130.6001 45.6001 131.3999 C
46.1001 131.6001 L
45.7002 131.8999 45.7002 132.7002 46.1001 133 C
46.7998 133.2998 47.6001 132.1001 48.2002 133.1001 C
48.1001 133.7002 48.3999 134.3999 48.5 134.8999 C
48.5 135.1001 48.3999 134.6001 48.6001 134.6001 C
48.6001 135.2002 49 136 48.3999 136.2998 C
48.5 136.2002 48.6001 136.2002 V
48.7002 136.2998 48.7002 136.3999 48.7002 136.6001 C
49.7002 136.2002 50.2002 135.1001 50.7998 134 C
51.2002 134.2002 L
51.2002 134 51.2998 134 51.3999 133.8999 C
51.8999 134.2002 51.7998 135.1001 52.1001 135.6001 C
51.6001 136.5 52.3999 136.8999 51.5 137.3999 C
52 138.7002 51.5 139.3999 51.5 140.6001 C
52.2002 140.7002 52.7998 140 52.7998 139.2998 C
53.2002 139.3999 L
53.1001 139.1001 53.3999 138.8999 53.2998 138.6001 C
53.6001 138 54.1001 138.7998 54.5 138.3999 C
55.2998 140.2998 54.5 140.7002 54.1001 142.3999 C
54.6001 142.5 54.1001 143.3999 54.7998 143.2998 C
54.7002 143.2002 L
55.5 142.2002 56.2998 141 56.7998 140 C
57.1001 140.2998 57.6001 139.2998 58 140 C
58 141.7002 57.8999 141.2998 58.1001 142.7002 C
58.2002 142.7002 L
57.7998 143.1001 58.5 143.8999 57.7998 144.3999 C
57.8999 144 58.7002 145.3999 58.1001 145.6001 C
58.1001 146 58.7998 145.7998 59 145.7002 C
59.1001 144.7002 60.1001 144.5 60 143.5 C
60.6001 143.2998 60.1001 141.2002 61.3999 142.2998 C
61.8999 143.6001 61.2998 144.7998 61.7002 146.3999 C
61.6001 146.3999 L
61.8999 147.3999 61.7002 148.2998 61.7998 149.7998 C
63.5 148.6001 63.2002 147.2998 64.3999 145.7998 C
65.2002 145.8999 64.8999 146.7002 65.2998 147.1001 C
65.2998 147.5 64.6001 148.2998 65 148.7002 C
64.6001 149 65 149.2998 65.2002 149.6001 C
65.2002 151.2998 L
65.2998 151.2998 65.3999 151.5 65.5 151.6001 C
65.6001 151.7002 65.3999 151.7998 65.2998 151.8999 C
65.5 152.2002 L
65.8999 151.3999 67.2998 150.7998 67 149.6001 C
67.6001 148.8999 67.7002 147.5 68.5 146.6001 C
68.7002 146.6001 68.8999 146.2002 69.1001 146.5 C
69.1001 146.7998 L
69.5 146.5 68.8999 145.8999 69.6001 146.2002 C
69.7002 146.6001 L
69.7998 146.5 L
69.7002 147.5 70.8999 147.8999 70.3999 148.8999 C
70 149.6001 L
70.1001 149.7998 70.6001 149.7002 70.3999 150.1001 C
70 149.6001 70.2998 150.6001 70.1001 150.7002 C
70.2002 150.6001 L
70.2998 150.7002 70.2998 150.7002 70.2998 150.7998 C
69.3999 151.2002 69.8999 152.8999 70.1001 153.7998 C
70.2002 154.1001 70.3999 154.2998 70.2998 154.7002 C
71.3999 154.7002 70.7998 153 71.7998 153 C
72.1001 152 72 150 73.2998 149.5 C
74.1001 150.1001 73.2998 151.2998 74 151.8999 C
73.7002 151.8999 L
74.5 152.5 74 153.7002 74.2002 154.7002 C
74.2998 154.6001 74.3999 154.7998 74.5 154.8999 C
74.5 155.2002 74.2002 155.1001 74.2002 155.3999 C
74.2002 155.7998 74.5 156 74.7998 156.3999 C
76 154.3999 75.2002 152.8999 76.7998 151.2002 C
77.7002 151.6001 77.5 151.8999 78 152.5 C
77.7998 154 77.6001 155.2998 78.2002 157 C
78.3999 156.7998 L
78.6001 157.2002 78.2998 157.6001 78.5 158 C
78.6001 157.2998 79.1001 157.1001 79.2002 156.5 C
79.6001 154.7998 79.6001 152.5 79.8999 150.7002 C
80 150.7998 L
80.7002 150.3999 79.7002 149.3999 80.8999 149.2998 C
81.3999 149.7002 81.2998 150.8999 81.2002 151.2002 C
81.3999 151.2002 81.6001 151.1001 81.7002 151.2998 C
81.3999 151.8999 L
82.2002 151.7002 81.7002 152.7002 81.7998 153.1001 C
82 153.1001 L
81.5 154.2998 82.5 154.8999 82.3999 156.2002 C
82.7002 155.7002 83.8999 154.8999 83.6001 153.6001 C
84.1001 153.1001 L
84.1001 149.5 L
84.5 149.5 L
84.7002 148.7002 84.2002 147.8999 85.1001 147.6001 C
85.2002 147.8999 85.7998 147.8999 85.6001 148.3999 C
85.8999 148.3999 L
86.2998 150.7998 85.6001 153.1001 86.5 155.2998 C
86.3999 155.3999 L
86.6001 155.6001 L
87.2998 154.7002 87.1001 153.7002 87.7998 153.1001 C
87.7998 151.2002 88.5 151.1001 88.3999 149.2998 C
89.2002 149.2998 88.8999 146.6001 90.1001 148.2998 C
90.1001 148.7002 L
90.3999 148.7002 L
90.7998 149.5 90 150.8999 90.7002 151.6001 C
90.5 151.7998 L
90.2998 151.7002 90.3999 151.6001 90.3999 151.3999 C
90 151.8999 90.7002 152.2002 90.7998 152.6001 C
90.5 153.8999 91.2998 155 91.6001 155.8999 C
92.2002 154.6001 92.2998 153.3999 92.3999 152 C
92.5 150.6001 93.1001 149.7002 93.5 148.2998 C
93.6001 148.3999 L
94.1001 147.6001 L
95.1001 148.2002 94.5 148.7002 94.7998 149.5 C
94.6001 150.2998 94.8999 151 94.7002 151.7998 C
94.7998 152.3999 95.3999 151.5 95.2998 152.2998 C
94.7002 152.5 95.3999 152.7998 95.2998 153.1001 C
95.6001 154.3999 96 155.7998 96.3999 157.2002 C
97 155.2002 97.3999 153.2002 97.8999 151.3999 C
98.1001 151.2002 98.5 151.2998 98.7998 151.2998 C
98.7998 152.2002 100.1001 153 99.5 154 C
99.5 155 L
99.6001 154.8999 L
99.6001 156 100.2998 157.2998 100.1001 158.6001 C
100.8999 159.1001 100.2998 159.7002 101 160.2998 C
101 160.3999 101.1001 160.5 101.2002 160.6001 C
102 159.7002 101.3999 158.2998 102.1001 157.3999 C
101.6001 157.1001 101.7998 156.3999 101.7998 155.7998 C
101.7998 155.6001 102 155.6001 102.1001 155.6001 C
102.1001 155.2002 102.2002 154.7998 102.5 154.3999 C
103 154.7998 103.3999 154.6001 103.7002 155.2998 C
103.3999 155.5 L
103.7002 155.5 L
103.7002 157.6001 L
103.7002 157.3999 103.8999 157.3999 104 157.3999 C
103.5 159 104.3999 160.1001 104.5 161.7998 C
104.7002 161.7002 104.8999 161.7998 104.8999 162 C
104.8999 162.3999 L
104.8999 162.2998 105 162.2002 105.1001 162.2002 C
104.6001 163 105.8999 162.7998 106.2002 162.7002 C
f
172 159.6001 m
172.2998 159.7998 L
172.2998 159.7002 L
172.7998 159.7002 173.3999 159.7998 173.7998 159.3999 C
174.1001 159.3999 175.1001 159.7002 175.7002 159.6001 C
176.2998 159.7998 178.2998 160.2998 178 159 C
178.3999 158.7002 178.5 158.2998 178.3999 157.7998 C
178.7998 157.7998 L
179.5 154 179.5 150.3999 179.2998 146.2998 C
178.7998 145.2998 178.7002 143.5 179.2998 142.7002 C
179.5 142.7002 179 142.6001 178.8999 142.3999 C
178.8999 142.1001 179.5 141.6001 178.8999 141.5 C
179.5 140.2002 179.7002 138.6001 178.7998 137.3999 C
177.7002 136.2998 L
173.2002 136.8999 169.6001 135.7998 165.2002 136.2998 C
164.6001 136.6001 163.7998 138.6001 163.7002 139.7002 C
164.8999 141.2998 167.5 141.2998 170.2002 141.2002 C
171.3999 141 172.2998 141.1001 173.5 141.6001 C
173.8999 141.2998 174.2998 141.7998 174.6001 142.1001 C
174.6001 142.2002 L
174.7998 142.2002 L
174.7002 143.2998 175.7002 144.7998 174.1001 145.3999 C
171 146.2002 167.3999 144.7998 164.3999 146.3999 C
164.6001 146.5 164.5 146.7002 164.5 146.8999 C
163.7998 147.2002 164.3999 148.7002 164.2998 149.3999 C
164.7998 149.1001 164.7998 150 165.3999 149.8999 C
165.2002 150 L
167.8999 151.7998 171.2998 149.6001 174.3999 150.5 C
175.5 151 174.5 151.8999 175.6001 152.3999 C
175.2002 152.3999 L
175.5 152.7002 175.5 153.5 175 153.7002 C
172.3999 155.7998 167.7002 153.7002 165.2002 155.5 C
164.7002 156.2998 164.2998 157.3999 164.2002 158.5 C
164.5 158.2998 164.7002 159.2002 165 158.7998 C
166.3999 160.2998 169.2998 159.7002 171.1001 160 C
172 159.6001 L
f
135.7002 157.1001 m
135.1001 153.6001 129.7998 154.8999 127.1001 154 C
126.2998 153.7998 124.2998 154 124.7002 152.5 C
123.8999 151.7002 125.1001 151.2998 125 150.3999 C
128.1001 149.2002 131.5 151.2002 133.8999 149.5 C
134.1001 149.2002 136.1001 148.2998 135.2002 147.1001 C
134.6001 147 134.6001 145.8999 133.6001 145.6001 C
130.7002 144.3999 127 146.6001 124.7998 143.5 C
124.2002 142.5 125.3999 141.7002 126 141.3999 C
127 141.2002 127.8999 140.6001 129 141 C
129 140.8999 L
130.6001 140.6001 133.2998 141 134.7998 140 C
134.5 139.3999 135.2998 139.7002 135.3999 139.2998 C
137 137 133.6001 136.7998 132.3999 136 C
129.6001 135.3999 126.2002 135.8999 123 136.1001 C
121.7998 135.8999 120.8999 137.1001 120.6001 138.2002 C
120.6001 139.3999 120.7002 140.5 120.1001 141.7002 C
120 141.6001 L
120.1001 143.7998 119.7998 144.8999 119.7998 147.6001 C
120.2002 147.5 L
120.2002 149.5 L
119.8999 148.8999 L
119.8999 150.3999 120.1001 152.2998 119.8999 153.7998 C
120.5 154.1001 120 154.8999 119.8999 155.3999 C
120.7002 155.2002 119.6001 156.1001 120.5 155.7998 C
119.8999 156.3999 120.7998 157.2998 121.1001 158.3999 C
121.2998 158.2002 L
121.3999 158.5 121.6001 158.7002 121.6001 159.1001 C
121.7002 159 L
122 159.6001 L
126.6001 157.5 132.1001 161 135.7002 157.1001 C
f
49.8999 150.5 m
49.7998 150.6001 L
49.6001 148.6001 46.7998 147.1001 45.6001 145.6001 C
44 146.1001 41.7998 146.1001 40.2998 145.1001 C
40 144.1001 41.6001 144.7002 41.8999 144.2002 C
42.7998 143.8999 43.6001 143.5 44 142.7002 C
43.3999 142.2998 42.2002 142.2998 41.8999 141.7002 C
41.6001 142 L
39 140.8999 L
39.5 139.6001 42 140 41.3999 138.7002 C
40.2998 137.7998 38.8999 137.2998 38 136.2002 C
38.7002 135.7002 39.5 134.8999 39.3999 133.8999 C
39.3999 134 L
38.1001 133.2002 36.7002 132.7998 35.2002 131.7998 C
35.2998 130.8999 36.3999 131 36.6001 130.2002 C
36.2998 128.6001 32.5 128.1001 34.7998 126 C
34.2002 125.7998 34.6001 124.8999 33.7998 124.8999 C
34 124.7998 L
33.2002 123.7998 31.6001 123.6001 32.3999 121.7002 C
32.8999 121.3999 L
32.6001 121.1001 32.5 121.6001 32.2998 121.2002 C
30.6001 120.3999 30.6001 117.7002 30.5 115.8999 C
30 115.2998 30 114.6001 29.5 114 C
29.7998 112.5 28.3999 111.3999 28.8999 110.2002 C
27.8999 111.2998 28.3999 113.5 28.2002 115.3999 C
28 115.3999 28 115.6001 27.7998 115.7002 C
28.2002 115.7002 L
27.8999 116.3999 28 116.5 27.7998 117.2002 C
28 117.1001 L
28.2002 117.6001 28.3999 119.2002 28.2998 120.6001 C
28.6001 120.6001 L
28.6001 121.1001 L
28.2998 121.1001 L
28.6001 121.8999 L
28.7002 121.7998 L
28.8999 123.1001 28.7998 124.1001 28.7998 124.8999 C
29 124.8999 L
29.3999 125.2998 28.6001 125.5 29.2998 125.6001 C
29.7002 126.5 28.7998 127.7002 29.8999 128.2002 C
29.5 128.5 L
29.6001 128.3999 L
30.2002 129.1001 29.7998 130 30.5 130.7002 C
30.1001 131.2002 L
30.6001 131.2002 30.2998 131.8999 30.3999 132.2002 C
30.6001 132.2002 30.7002 132.3999 31 132.6001 C
30.6001 133.5 31.5 134.5 31.6001 135.5 C
31.8999 136.5 31.8999 136.3999 32 137.6001 C
33 137.3999 32.2002 138.7998 32.6001 139.1001 C
31.7998 140 33.7998 140.1001 33.1001 141 C
33.3999 141.2002 33.2998 142.3999 34.2002 142.6001 C
34.2002 143.2998 L
34.2998 143.2002 L
34.7998 143.5 34.3999 144.7998 35.3999 145.1001 C
34.8999 145.3999 35.3999 145.7998 35.3999 146.2002 C
35.5 146.1001 35.5 146 35.6001 146 C
35.5 147.3999 36.7998 148.5 38 149.5 C
38.7002 148.8999 39 150.1001 39.6001 149.3999 C
39.8999 149.5 40.8999 149.1001 41.3999 149.2998 C
44.2998 149.5 47.6001 150.1001 50 151.3999 C
50 151.1001 49.6001 150.7998 49.8999 150.5 C
f
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159.5 158.2998 m
159.8999 155.5 151.6001 151.8999 158.2002 150.6001 C
158.7998 150.5 158.8999 149.7998 159.3999 149.5 C
160.1001 149.2002 159.8999 147.3999 159.7998 146.6001 C
159.1001 145.2002 155.6001 144.7998 156.1001 142.2998 C
157 141.7002 158.6001 141.1001 159 139.7002 C
159.6001 139.6001 L
159.6001 138.2002 159.2998 137.2002 158 136.2998 C
155.5 137.1001 152.8999 138.3999 150.6001 139.7998 C
146.2998 140.7998 145.1001 134.8999 140.8999 136.7002 C
140.6001 137.2002 140.3999 137.7002 139.8999 137.8999 C
139.5 140 142.2998 141.2002 143.7998 142.3999 C
143.6001 144 141.7002 144.7002 140.7998 145.8999 C
140.2998 146.5 140 147.6001 140.2002 148.3999 C
140.2998 148.2998 L
140.5 148.3999 140.6001 148.7998 140.3999 148.8999 C
139.8999 149 140.5 149.2998 140.5 149.5 C
140.7998 149.7002 141.1001 149.3999 141 150 C
141.7998 149.7002 141.7998 150.8999 142.2998 151 C
142.6001 151.5 144 152.2998 143.7998 153 C
142.2002 154.6001 139.5 155.5 140.2002 158 C
143 159.7998 145.6001 157 147.7002 156.2002 C
148.1001 155.8999 148.8999 155.5 149.7998 155.5 C
151 156.1001 152.2998 156.3999 153.5 157.3999 C
153.3999 157.6001 L
154.3999 157.6001 154.7998 158.8999 156.3999 158.8999 C
156.8999 159.2998 157.7998 159.1001 158.3999 158.8999 C
158.7998 158.2998 158.7998 158.5 159.5 158.2998 C
f
1 D
149 149.3999 m
147.6001 149.2002 147.7002 148.7002 146.7998 148 C
146.8999 147.1001 147.8999 146.7002 148.6001 146.5 C
149.8999 145.7002 151.2998 146.6001 152.7998 146.6001 C
152.6001 147 153 147.7002 152.8999 147.6001 C
152.7998 148.1001 152.7002 148.7002 152.2002 148.7998 C
151.2998 148.8999 150 149.7002 149 149.3999 C
f
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184.3999 145 m
184.8999 144.6001 185.2002 143.6001 185.7998 142.8999 C
186.7998 139.8999 189.1001 137.3999 189.2002 134.5 C
189.7002 133.7998 190.2998 132.6001 190.3999 131.5 C
190.7002 131.5 L
190.6001 129.8999 191.5 129.1001 191.5 127.2998 C
192.1001 125.7002 192.2998 123.2998 193 121.7998 C
193 119.5 194.1001 117.3999 193.7002 115.1001 C
194.2002 113.7998 194.1001 112.7998 194.2998 111.5 C
194.5 111.5 L
194.2002 105.2002 195.3999 100.2002 194.2002 93.7998 C
193.8999 90.6001 193.7002 88 193.3999 85 C
192.6001 84 193.2002 82.7998 192.7002 81.7998 C
192.3999 78.3999 191 74.5 190.2002 71 C
189.6001 70.7002 189.7998 69.7998 189.6001 69.5 C
188.8999 67.1001 187.6001 64.8999 187 62.2998 C
186 62.2002 186.7998 60.8999 186 60.7998 C
186.1001 60.5 185.8999 60.1001 185.6001 60.1001 C
184.2998 56.3999 182.2998 53.5 180.1001 50.2998 C
180.2002 49.7998 L
179.7002 49.7998 179.6001 49.2002 179.5 48.7998 C
178.1001 46.8999 176.5 44.8999 175.2002 43 C
175.2998 42.7998 L
173.2002 40.5 171.6001 38.5 169.3999 36 C
162.1001 28.2002 154.2998 21.5 144.6001 16.1001 C
129.8999 8.2998 113.3999 3.8999 97.1001 4.3999 C
96.7998 3.7998 96.5 4.7998 96.2002 4.3999 C
87.8999 3.7002 79.8999 6.7998 71.6001 8.7998 C
71.3999 8.5 L
69.6001 9.6001 67.2998 10 65.5 10.3999 C
55.7002 13.7002 45.5 19.1001 37.2998 26 C
37.2998 26.6001 36.3999 26.6001 36.3999 27.1001 C
33 29 31.2998 32.2998 28.7002 34.7998 C
28.8999 35.7002 28 34.8999 28.2998 35.6001 C
32.7998 32.2002 38.5 27.3999 43.7002 24.7998 C
47.2002 22.7002 51.1001 21 54.5 18.5 C
56.5 17.5 58.3999 15.2998 60.3999 13.8999 C
60.7998 13.3999 61.7002 14.2002 61.2998 14.6001 C
62.7998 15.7002 63.5 14.7998 64.7002 14 C
65.3999 13.2998 66.3999 11.2998 67.7998 11.7998 C
68.3999 13.3999 L
71.5 13.8999 72.3999 10.6001 74.5 9.6001 C
75 10.3999 74.2998 11.5 74.8999 12.1001 C
76.7998 11.7002 77.6001 10.7998 78.6001 9.1001 C
79.2998 9.6001 79.8999 10.1001 79.7998 10.8999 C
81.1001 10.7002 83.2002 9.7998 84 8.8999 C
84.5 9.5 84.6001 10 84.7002 10.7998 C
86.7002 10.6001 88.1001 8.3999 89.6001 8.3999 C
90.1001 10.7998 L
90.5 10.5 91.6001 9.8999 92.2002 10 C
93.6001 8.7998 94 7.2002 96.2002 7 C
97 8.7998 94.2002 9.6001 96.1001 11.2002 C
97.5 10.6001 98.5 9.6001 99.6001 8.6001 C
100.5 8.7998 100.1001 9.8999 100.1001 10.2998 C
99.7998 10.6001 99.2998 10.8999 99.6001 11.3999 C
101.2002 12 102.7002 10.1001 104.2998 8.8999 C
104.8999 8.7002 105.7002 8.5 106 9.2002 C
106 10.6001 104.7002 10.3999 104.2002 10.8999 C
104.2002 12.2002 105.2998 11.7998 106.1001 12.2002 C
106.5 11.7998 107.2002 11.6001 107.6001 11.5 C
108.7002 10.6001 L
109 10.8999 109.2002 10.2002 109.6001 10.2002 C
110.1001 9.7002 111.7002 8.2002 113 8.7998 C
112.3999 10.2002 111.3999 10.7002 110.5 11.8999 C
110.6001 12 L
110.2002 12.6001 L
111.5 12.6001 112.3999 13 113.7998 12 C
114.6001 11.7998 115.7002 11.6001 116.7998 11 C
117.2002 11.7998 116.6001 12.3999 116.2998 13.1001 C
115.7998 13.1001 L
115.8999 13.3999 115.6001 13.8999 115.2002 14 C
116.2002 14.2998 117.6001 14.6001 118.2998 13.8999 C
119.7998 13.7998 119.6001 13.8999 120.6001 13.2002 C
121.1001 13.2002 122 12.7002 122.6001 13.2002 C
121.8999 13.8999 121 14.7998 121 15.3999 C
121.2998 16.6001 123.1001 15.6001 124 15.7002 C
125.6001 15.1001 126.8999 13.3999 128.3999 14 C
127.7998 15.5 126.6001 16.2998 125.5 17.2998 C
127.5 18.1001 129.6001 16.8999 131 16 C
132.6001 16.2002 L
132.7002 18.1001 127.8999 19.1001 130.8999 20.6001 C
131.5 20.1001 132.7002 20.2002 133.3999 19.2998 C
134.6001 18.7998 136.1001 18 137.5 17.2002 C
137.7002 17.3999 138.1001 17.2002 138.2002 17.5 C
137.7998 19.3999 135.8999 20.2002 134.5 21.2002 C
134.6001 21.3999 L
134.6001 21.8999 133.8999 21.5 134.2002 22.2002 C
134.2002 22.1001 L
137.2002 22.1001 139.6001 19.7998 142.8999 20 C
142.6001 20.3999 L
142.7002 20.3999 142.8999 20.3999 142.8999 20.5 C
141.7002 22 139.5 22.7998 138.3999 24.7998 C
139.7998 25 L
139.7998 25.2002 L
141.7002 24.7998 143.7998 23 145.7002 23 C
146.1001 24.6001 143.7002 25.2998 142.8999 26.2002 C
142.6001 26.5 142.2002 26.7002 142.6001 27.2002 C
143.2998 27.5 L
145 26.7998 147.7002 26.3999 149.2998 25.8999 C
149.5 25.8999 150.2002 26.2998 149.7998 26.6001 C
148.2002 27.7002 146.2002 28.2002 145.7998 30 C
147.8999 29.7002 150.6001 28.7002 152.6001 28.6001 C
152.7998 28.7002 L
151.7002 30.7002 149.2998 30.5 148 31.8999 C
148.7998 32.6001 148.8999 32.2998 150 32.8999 C
150.5 32.7002 151.3999 32.2002 152.2002 32 C
154 32.3999 156.2002 30.8999 158.2998 31.8999 C
158.2998 32.1001 158.1001 32.2002 158 32.2998 C
157.7002 32.2002 L
157.8999 32.3999 L
156.2998 34.2002 152.2998 34.2002 151.7002 36.1001 C
152.7998 36 154.7998 35.8999 156 35.7998 C
157.6001 35.6001 159.2998 35 161 35.6001 C
161.2998 36.2998 160.6001 36 160.2998 36.3999 C
160 36.3999 L
160 36.7002 L
158.2002 37.3999 156.5 38.3999 155.2002 39.3999 C
158.6001 39.1001 162.1001 38.7998 165 38.7998 C
165.2002 39.6001 164.1001 39.8999 163.3999 40.1001 C
161.7002 40.7998 159.7002 41.2002 158.2998 42.3999 C
159.1001 42.7002 161 42.1001 161.5 42.7998 C
162.2002 42.3999 162.8999 42.3999 163.6001 42.7998 C
165.3999 42.5 167.2998 42.7002 169.1001 42.5 C
169.2998 42.7002 169.2002 43 169.2002 43.2998 C
168.7002 43.5 167.7998 44.5 166.6001 44.5 C
165.2002 45.1001 163.3999 45.2002 162 46.1001 C
161.7002 46.6001 162.2998 46.7002 161.7998 47.2002 C
163.8999 48 166.1001 46.5 168.2002 47 C
168.8999 46.6001 169.6001 47 170.3999 47.3999 C
168.8999 49.2998 166.5 48.3999 164.7998 50.2002 C
165.8999 50.6001 168.1001 51.1001 169.8999 50.5 C
170.2002 50.7002 170.3999 50.7998 170.6001 50.5 C
172.2998 50.2002 174.2998 50.3999 175.7998 50.2998 C
176.3999 50.6001 L
175.8999 51.3999 174.7002 52.1001 173.8999 51.7998 C
171.8999 53.1001 170 53.1001 167.6001 53.8999 C
167.2002 54.3999 167.7998 54.7002 168.1001 55.1001 C
171 55.5 174.1001 55.3999 177.2002 55.3999 C
177.8999 55.8999 177 56.5 176.7998 56.6001 C
175.2998 57.3999 172 56.8999 171 58.3999 C
170.3999 58.2998 170.5 59 170 59.2002 C
172.2998 60.2998 175 59.2998 177.3999 60.1001 C
177.2002 60.2002 L
177.7998 60.2002 178.2002 60.7002 178.7002 61 C
177 62.8999 174 61.3999 172.2002 63.3999 C
172.3999 63.8999 173.7998 63.6001 174.3999 63.7998 C
176.6001 64.2998 179.2998 64.1001 181.6001 65.2002 C
181.6001 66.1001 180.2002 66.2002 179.6001 66.3999 C
177.8999 66.7002 175.2998 66.2002 173.8999 66.7002 C
173.8999 67.1001 L
175.2998 67.2998 176.7998 68 177.7998 68 C
178 68.3999 178.8999 68.2998 179.3999 68.7998 C
180.8999 69 182.7002 69.1001 184.2002 69.6001 C
184.3999 70 L
182.7002 70.7998 181.3999 70.7998 179.3999 71.2998 C
178.2998 71.7998 177 71.2002 175.8999 71.3999 C
176.7998 73.7998 179.5 72.8999 181.2998 73.7998 C
182.3999 73.7998 183.1001 74.1001 183.6001 75 C
181.7998 77.1001 178.8999 74.5 177.2002 75.7998 C
176.7998 78.3999 181 77.2002 181.7998 78.6001 C
183.5 78.7998 185.2998 79.2998 186.7002 79.7998 C
187 80.2998 L
184.7002 81.1001 181.2002 81 178.7002 81 C
178.6001 81.6001 179.1001 82.2998 179.6001 82.7002 C
180.2002 82.7002 180.3999 83.1001 180.7998 83.2998 C
182.6001 84.2002 183.2002 83.7998 184.8999 85.1001 C
183.5 87.2002 181.2998 85.5 179.3999 85.3999 C
179.1001 86.3999 179.5 87.3999 180 88.2002 C
180.7002 88.2002 180.7002 88.7002 181.1001 89 C
183.7002 90.5 185.7998 91 188.5 92.2002 C
188.8999 92.7998 L
185.8999 94.7998 183.3999 91.3999 179.8999 92.3999 C
180.6001 92.7998 179.7998 93.5 180.2002 94.2002 C
181.6001 94.7998 183.2002 95.2998 184.2002 96.2002 C
184.8999 96.2998 185.7998 97.2002 186.6001 97.2998 C
188 97.5 189 98.6001 190.2998 99.1001 C
187.2002 100.7002 184.2998 97.7002 181 98 C
180.2998 99.5 180.7002 100.3999 182.2002 101 C
183.7002 101.7998 185.2002 102.6001 186.5 103.7002 C
186.5 103.6001 L
186.8999 103.2998 186.8999 103.8999 187.2002 104 C
187.2002 103.8999 L
188.1001 104.1001 188.2002 105.2998 189.6001 105.3999 C
189.7002 106 L
188.8999 106.2002 L
186 105.3999 183.3999 104.2998 180.5 103.8999 C
180.7998 104.6001 181.3999 105.3999 181.7998 105.5 C
182.3999 106.3999 183.6001 107.3999 185 107.5 C
185 108.1001 186 107.8999 186.3999 108.7998 C
185.7998 109.5 184.3999 108.8999 183.7002 109.7998 C
183.5 110.2998 184.6001 110.3999 184.2002 111.2002 C
184.7998 111.3999 184.8999 112.5 185.6001 112.6001 C
185.2002 112.8999 187.2002 114 185.3999 114.1001 C
184.1001 113.5 L
183.7998 114.7998 183.6001 116.1001 184.2002 117.3999 C
184.2998 117.2002 L
184.7998 117.8999 185.7002 117.7998 186.3999 118.7998 C
185.7998 119.3999 L
185.2998 119.2998 184.6001 119.1001 184.1001 119.2002 C
184.2998 121.5 184 123.3999 184.2998 125.8999 C
184 126.6001 184.5 127.6001 183.7998 128.2002 C
184.6001 128.7002 183.7002 129.2002 183.7998 129.7998 C
183.7002 129.7002 L
183.7998 130.7002 183.6001 132.1001 183.5 133.2998 C
183.2002 133.2998 L
183.5 133.8999 183.2002 134.6001 183.5 135 C
183.1001 135.2998 183.5 135.3999 183.2002 135.7002 C
183.5 136 L
183 136 L
183.2998 136.8999 182.8999 139.2002 183.2002 140.5 C
183.5 140.7998 L
182.8999 141.6001 183.6001 142.2998 183.1001 143.3999 C
183.7002 143.3999 183.5 144.7002 183.7002 145.1001 C
183 145.3999 183.7998 146.2002 183.6001 146.8999 C
183.7002 145.8999 184.2998 145.8999 184.3999 145 C
f
131.8999 132.7998 m
132.8999 132.5 134.2002 132.7002 135.3999 132.7998 C
135.3999 132.7002 L
138.8999 132.2002 141.7998 132.7002 145.1001 132.5 C
145.6001 132.6001 L
145.6001 132.5 L
146.2998 132.5 147.8999 132.7002 149 132.3999 C
150 133.2998 151 132 151.8999 132.6001 C
154.7002 132.7998 157 132.2002 160 132.6001 C
160 132.5 L
165.2998 132.2002 172.7002 132.5 178 132.2002 C
178.2998 131.6001 179.2002 131.2002 179.5 130.6001 C
179.2998 126 179.8999 120.5 179 116.2998 C
179.2002 115.2998 179.2998 114.2998 179.3999 113.5 C
178.7002 112 180.5 109.7998 177.7998 109.2002 C
176.7998 109 176 109.3999 175.2002 109.8999 C
175.1001 110.7998 174.8999 112.1001 175 113.2002 C
175 114 174.3999 116.6001 175.1001 118 C
175.3999 119.7998 174.2002 120.8999 175 122.6001 C
173.8999 122.7998 174.6001 124 174.6001 124.6001 C
174.6001 125.8999 173.7998 127.1001 173.2998 128.5 C
171.1001 129.3999 169.6001 128.2002 167.5 128.6001 C
165.2998 129 162.2998 129.1001 160 128.5 C
150.3999 128.3999 142.1001 127.7998 132.2002 128 C
132 127.7998 L
130.3999 127.8999 127.5 128.1001 126.2002 127.2002 C
125.8999 126.2002 125.7998 125.7002 125.5 124.8999 C
125.7002 123.8999 125.2998 122.7998 125.7998 121.8999 C
125.5 121.6001 L
126 121.3999 L
125.7002 120.2002 126.1001 118.6001 125.6001 117.5 C
126 116.7998 L
125.7998 116.7998 125.7998 116.6001 125.6001 116.5 C
125.7002 114.7002 125.5 113.1001 125.3999 111.3999 C
124.5 110.7002 125.7998 108.1001 123.7998 108.6001 C
122.6001 108.3999 121.2998 108.8999 120.6001 109.7998 C
120.7002 110.7002 120.3999 111.7998 120.6001 112.7998 C
119.8999 113.1001 121 113.2998 120.6001 113.7998 C
120.3999 115.5 120.5 117.6001 120.5 119.5 C
120.7002 119.5 L
120.2002 119.7998 120.7002 120.2998 121 120.7002 C
120.6001 120.7998 121 121.3999 120.7002 121.7002 C
120.2998 121.3999 121.5 122.1001 120.7002 122.2998 C
120.7998 122.2002 120.8999 122.2998 121 122.3999 C
120.7002 122.6001 L
120.8999 122.6001 121 122.7998 121.1001 122.8999 C
120.6001 122.7998 121 123.7998 120.7002 124.1001 C
120.7998 124.1001 L
121 125.5 120.7998 125.7998 120.7998 127.7002 C
120.6001 128.2998 120.7002 128.2998 120.7998 129.1001 C
121 129.1001 L
120.7002 130.2002 L
121 130.2002 L
120.1001 130.5 121.6001 131.2002 121.1001 131.6001 C
121.8999 132.1001 122.3999 132.1001 V
122.6001 131.8999 L
123.2002 132.3999 124 131.7998 124.2998 132.6001 C
130.2002 132.7998 L
130.2002 132.7002 L
131.8999 133 L
131.8999 132.7998 L
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135.3999 123 m
135.7002 122.7998 L
135.2002 122.3999 L
135.6001 121.8999 L
135.5 122 L
135.2998 121.8999 135.3999 121.7002 135.3999 121.6001 C
135.3999 121.3999 135.6001 121.3999 135.7002 121.3999 C
135 119.3999 135.5 117.6001 135.2002 115.2998 C
135.2002 114.3999 135.7998 114 136.1001 113.3999 C
136.2002 113.5 L
137.3999 111.7002 140.8999 112.8999 142.8999 112.7002 C
144 112.6001 144.7002 113.3999 145.8999 112.7998 C
146.5 113.3999 148.2002 113 147.5 114.2002 C
145.2998 117.2002 141.2002 113.2002 139.7998 117.2002 C
139.5 118.2002 139.3999 119.1001 139.3999 120.2002 C
139.3999 120.1001 L
139.7998 119.7998 139.6001 120.5 139.7998 120.6001 C
139.3999 120.6001 L
140.3999 120.8999 139.6001 121.8999 140.2002 122.5 C
140.1001 122.3999 140.2002 122.2998 140.2998 122.2998 C
140.3999 122.2998 L
139.8999 122.7998 140.8999 123.1001 140.3999 123.6001 C
140.8999 123.3999 L
140.7998 123.8999 141 124.7998 141.6001 124.8999 C
147.6001 124.8999 152.7998 124.5 158.8999 124.7002 C
159.6001 123.6001 160.3999 122.7002 160.1001 121.1001 C
160.2002 120.7998 160.3999 120.2998 160.3999 120.1001 C
160.3999 120.2002 L
159.7002 118.6001 160.7998 115.8999 157.7002 115.6001 C
155.8999 115.2002 154 115.5 152.8999 114.1001 C
152.8999 112.7998 154.5 113.3999 154.8999 112.6001 C
157.6001 112.3999 161 112.3999 164.2002 112.6001 C
165.2998 113.6001 164.5 115.2998 165.2002 116.2002 C
164.7998 116.7998 165.3999 117.1001 165 118.1001 C
164.7998 118 164.7998 118.2002 164.6001 118.2998 C
164.7002 119.2002 165 121.1001 165.2002 121.8999 C
164.8999 122.2998 L
165.8999 122.7002 164.2998 124 165.7998 124.2002 C
165.7002 124.7998 166.7002 125.5 167.2002 125.7998 C
167.6001 125.7998 L
167.7998 125.3999 168.3999 125.2998 168.7998 124.8999 C
169.7002 123.7998 L
169.8999 121.3999 169.6001 118.1001 169.8999 115.2998 C
169.7002 115.1001 L
169.7002 109.1001 L
164 107.7998 158.8999 108.6001 153.2002 107.8999 C
151.8999 106.2002 152.5 103.5 150.5 102.3999 C
149.3999 102.2998 148.2998 102.7998 147.6001 103.3999 C
146.8999 104.3999 148.1001 105.3999 146.8999 106.2002 C
147 106.7002 147.1001 107.1001 146.8999 107.6001 C
145.3999 108.3999 L
141 108.6001 136.3999 107.8999 131.5 108.3999 C
130.7998 110.1001 131 111.2002 130.3999 112.7998 C
129.8999 113.2002 131 113.8999 130.2002 114.2002 C
130.2998 116.3999 129.7998 119 130.7002 120.7998 C
129.6001 120.7002 131.3999 121.5 130.3999 121.8999 C
130.1001 122.3999 131 122.2002 130.6001 122.6001 C
130 124 130.8999 125 132.1001 125.7998 C
132.7002 125.7002 133.6001 126.2002 134 125.5 C
134.5 124.7998 135.3999 124.2998 135.3999 123 C
f
1 D
148.6001 121.1001 m
147 120.8999 145.2998 122.2002 144.1001 120.2002 C
143.6001 119.5 144.5 119.7002 144.7002 119.2002 C
147.7998 118.3999 152.1001 119 155.2998 119.2002 C
155.5 119.7998 L
155.2998 119.7998 L
155.2002 120.5 154.3999 120.6001 154.1001 121 C
152.2002 121.2002 150.6001 121.6001 148.6001 121.1001 C
f
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162.6001 105.7998 m
162.7998 105.1001 164 105.3999 164.2998 105.1001 C
165.7998 104 168.1001 102.1001 169.2998 100.6001 C
169.3999 99.8999 169.7002 98.7998 169.1001 98.7998 C
165.7002 100.3999 162.5 102.3999 159.7002 105 C
159.7002 105.1001 158.7998 105.1001 159.1001 105.5 C
160 105.7002 160.7002 105.6001 161.7998 105.6001 C
161.8999 106 L
162.2002 105.7998 162.2002 105.5 162.6001 105.7998 C
f
144.3999 104.5 m
144.5 102.7002 145.6001 100.2998 147.2002 99.3999 C
147.7002 99 148.2998 99.2002 148.6001 98.5 C
150.2998 99.5 151.8999 98.7998 153.1001 97.7998 C
153.7002 96.3999 156.1001 95.1001 157.2998 94.6001 C
157.5 94.2998 157.3999 94 157.3999 93.7002 C
157.6001 93.6001 158.5 92.7002 158.5 91.7998 C
158.8999 91.8999 159.2002 91.2998 159.2002 91 C
159.3999 91.1001 L
162.2002 87.6001 165.1001 84.7998 165.7998 80.2002 C
165.3999 79.7002 165.6001 78.7002 165.3999 77.8999 C
163.8999 78.2002 164 80 162.7998 80.8999 C
160.5 84 157.6001 87 154.3999 89.7998 C
153.6001 90.7998 152 92.2002 150.7998 93.1001 C
150.6001 92.7998 150.1001 92.5 150.5 92.2002 C
150.3999 92 150.6001 91.8999 150.7002 91.7998 C
151 92 L
151.5 90.7998 152.2998 89.6001 153.1001 88.6001 C
155.3999 85 L
155.5 85.1001 L
156.8999 83.6001 157.8999 81.1001 159 79.8999 C
159.1001 78.1001 161 77.8999 160.8999 76.1001 C
161.2002 76.1001 L
161.5 75.2002 161.6001 74.1001 162.2002 73.3999 C
162.2998 72.3999 163 72.1001 163 71 C
163 70 162.2998 69.7998 161.8999 69.1001 C
159.3999 72.6001 L
159.5 72.7002 L
154.2002 80.7002 148.7998 87.7002 141.5 94 C
141 94 L
140.8999 94.2998 140.2002 94.8999 139.7002 95.2002 C
139.2998 96 138.1001 95.5 138.1001 96.6001 C
137.8999 96.6001 L
137.7998 100.3999 L
138.3999 101 L
138 101.2998 L
138.3999 101.2998 L
138.3999 102.3999 138.2002 103.1001 139 103.8999 C
138.7002 104.7002 140.2998 104.7002 141.1001 105 C
144.3999 104.5 L
f
158.2998 101.2998 m
158.5 100.1001 159.7002 100.2002 160.3999 99.2002 C
163.2998 96.5 165.5 94.1001 168.1001 90.3999 C
167.7002 89.5 169 88 167.5 87.2002 C
166.6001 88.3999 164.7998 89.5 164.2002 90.7002 C
163.2002 91 162.7002 92.3999 161.6001 93 C
160.6001 93.6001 159.7002 95.2002 158.7998 95.8999 C
157.3999 97.5 155.2002 98.7998 154.2998 100.7002 C
155.2002 101.7998 L
155.1001 102 155.7002 102.6001 155.6001 103.2002 C
156.2998 102.7002 157.5 101.7998 158.2998 101.2998 C
f
136.7998 93.7002 m
136.8999 93.8999 137.5 93.2998 138 93.5 C
138.5 92.7998 139.6001 93.2002 140.2002 92.3999 C
142.1001 91.2998 142.6001 90 144.7002 88.3999 C
144.7998 88.6001 L
145.2998 87.7998 L
145.3999 88 L
145.8999 87.3999 146.7998 86.3999 147.2002 85.7002 C
148.1001 85.8999 147.3999 83.8999 148.7998 84 C
148.6001 83.6001 149.1001 83 149.2998 83.2998 C
150 81.5 151.2998 81 151.7998 79.1001 C
152 79.1001 L
151.6001 78.6001 152.3999 78.7998 152.2002 78.2002 C
152.6001 78.2998 152.5 77.6001 152.8999 77.2002 C
153 77.2998 L
153.2998 75.7998 154.7002 74.2002 154.8999 72.6001 C
155.2002 72.6001 L
155.5 70 157.2002 67.7002 157.3999 65.6001 C
157.8999 65.2998 158.2002 64.7002 158 64.1001 C
158.3999 64.2002 L
159.5 62.3999 157.8999 60.8999 157.2998 59.7998 C
157.2002 59.7998 157.1001 60.1001 157 60 C
156.7002 59.7998 L
156.3999 60.6001 156.1001 61.5 155.6001 62.2002 C
155.1001 63.5 154.8999 66.1001 153.5 67.1001 C
152.1001 69.7998 151 72.2002 149 74.5 C
149.2002 74.5 149.2002 74.6001 149.2998 74.6001 C
147.6001 76.7002 146.5 79 145 80.2998 C
144.3999 79.6001 L
145 77.7998 146.2002 76 147 74.2998 C
146.7998 73 147.8999 72.7002 148.2002 71.2002 C
148.5 70.8999 148.1001 69.7998 148.7002 70 C
149.2002 68.1001 150 65.8999 150.7002 63.6001 C
151 63.6001 L
150.7002 62.1001 151.8999 61.5 151.7998 60.1001 C
152.8999 57.7998 152.3999 57 153.7002 54.7002 C
153.5 54.7002 152.2998 53.2998 151.7998 52.7002 C
150.8999 52.8999 151.7002 54.1001 150.7998 54.2002 C
151 54.2002 L
151 54.3999 150.7002 54.7998 150.6001 55 C
150.3999 55.6001 150.1001 57.1001 149.3999 57.7002 C
149.5 57.7002 L
149.2002 58.6001 148.5 59.7998 148.1001 60.6001 C
148.2998 61 147.7002 61.5 147.7998 61.8999 C
147.5 61.8999 L
147.7998 63 147 63.2002 146.7998 64.2998 C
146.5 64.2998 L
146.2998 65.2002 146 65.5 145.7998 66.6001 C
145.6001 67.1001 L
145.3999 67 145.3999 66.7998 145.3999 66.7002 C
145.2002 68.2998 143.8999 68.6001 143.5 70.2002 C
143 70.2002 L
142.7998 69.6001 142.8999 68.8999 142.8999 68.2998 C
143.2998 68.3999 L
143.7998 66.7998 143.6001 65 144.5 64 C
144.5 62.7998 144.8999 62.2002 145.1001 61 C
145.5 60.7998 145.2998 59.2002 146 58.8999 C
145.7998 58.3999 146.5 58.1001 146 57.5 C
147 54.8999 147.3999 50.8999 148.3999 48.2002 C
146.5 46.2998 L
145.3999 48.7998 144.5 51.3999 143.7998 53.6001 C
143.3999 54.7998 142.6001 55.7998 142.2998 57.3999 C
142.1001 57.3999 L
142.2002 57.6001 142.2998 58.1001 142.2002 58.2998 C
140.8999 58.6001 142.2002 60 141.1001 60.2002 C
141.2002 60.8999 140.5 61.7998 140.2998 62 C
140.5 62.2998 L
139.7998 62.5 140.3999 62.7998 139.7998 63.2002 C
139.6001 63.7002 139.2998 64.2002 138.7998 64.6001 C
138.7002 64.3999 L
138.7002 64.2998 138.7998 64.8999 138.6001 65 C
137.2998 65 138.3999 64.2002 138.1001 63.5 C
138.3999 63.2002 L
138.5 63.2998 138.5 63.5 138.5 63.6001 C
138.2998 62.7998 138.7002 62.6001 138.6001 61.7998 C
139.2998 61.5 139.2002 60.6001 139.1001 59.8999 C
139.7998 59.8999 139.6001 58 140 57.6001 C
140.2998 56.3999 140 55.2998 140.7998 54.3999 C
140.7002 52.2998 141.3999 51.1001 141.2002 49.2002 C
141.8999 47.2002 141.7998 44.7002 142.2002 42.6001 C
142.2002 42.2998 142.2998 41.6001 141.7002 41.3999 C
141.1001 41.2998 L
141.2002 41.5 141 41.6001 140.8999 41.7998 C
141 41.7998 L
140.7002 43.5 140.2002 44.7002 139.3999 46.2998 C
139.1001 46.7998 139.7998 47.7002 138.7998 47.8999 C
139.3999 49.1001 138.1001 50 138.1001 51.2002 C
137.7998 52.6001 L
137.6001 52.3999 L
137 54.5 135.8999 57.3999 135 59.2002 C
135.3999 59.8999 134.2002 60.1001 134.2998 60.7998 C
134.2002 60.7002 L
133.8999 61.2002 134.2002 61.7002 133.3999 61.7998 C
132.5 60.2998 134.2002 58.6001 133.7998 56.7998 C
134.2002 55.2002 134.7998 52.6001 135.1001 50.7998 C
135.5 50.5 135.1001 49.2002 135.7002 48.7998 C
135.6001 48.7998 L
136.1001 48 135.6001 46.5 136.2998 46 C
136.2002 46 L
136.7002 44.2002 136.2002 42 136.7002 40.7002 C
136.8999 40.7002 L
136.6001 39.7998 136.6001 40.1001 136.3999 39 C
136.3999 38.1001 136.1001 37.2998 135.3999 36.7002 C
134.2998 37.2002 134.8999 39.7002 134.2998 39.7002 C
134.3999 39.7002 L
134.1001 41.2998 133.6001 42.2998 133.3999 44.2998 C
133.1001 44.5 L
133.5 44.8999 132.7998 45.8999 133 46.3999 C
132.5 46.8999 132.8999 47 132.5 47.2998 C
132.7002 47.5 L
131.5 49.6001 131.2002 52.7002 129.7002 54.7002 C
128.5 52.7002 130.2998 48.8999 130.2998 46.6001 C
130.5 42.2998 131.5 38.7998 131 34.6001 C
130.8999 34.3999 130.7002 34.2998 130.7002 34.1001 C
130.7998 34 L
129.5 32.8999 L
129 33.7002 129.1001 34.7998 128.7998 35.3999 C
129.2002 36.1001 127.8999 37.2998 128.5 37.8999 C
128 38.6001 128 40.7002 128 41.3999 C
127.6001 41.6001 L
128.2998 42.1001 127.2002 42.2002 127.6001 42.7002 C
127.6001 43.3999 127.6001 44.2002 127.1001 44.5 C
127 45.1001 127.2998 45.8999 126.7998 46.2998 C
127.3999 46.7998 126.2002 47.2002 126.5 47.8999 C
126.7002 49.3999 125.7002 50.1001 125.5 51.5 C
125.3999 51.3999 125.3999 51.2002 125.3999 51.1001 C
125 51.7002 L
124.2002 51.7002 124.7002 51.1001 124.6001 50.5 C
124.6001 50.3999 124.7998 50.3999 124.8999 50.3999 C
124.6001 45.3999 126 39.2998 125.5 34.7998 C
124.8999 33.8999 125.2998 32.6001 124.7002 31.7002 C
124.6001 30.7998 124.1001 30.3999 123.7998 29.6001 C
123 31.1001 123.5 32.5 123 33.7998 C
123.1001 33.7998 L
122.3999 35.2002 123.5 36.7002 122.2998 38.2998 C
123.1001 39.2002 121.7002 40.2998 122.2002 41.6001 C
121.7002 42.1001 L
121.7998 42.1001 L
121.7998 42.2998 121.8999 42.7998 121.3999 42.7998 C
121.7002 42.7998 L
121.8999 43.2002 121.7002 43.7002 121.2998 43.7998 C
121.6001 43.7998 L
121.6001 44.2998 L
121.1001 44.2998 L
121.5 45.7998 120.3999 46.7998 120.1001 48.2002 C
119.7998 48 L
119.7998 48.1001 119.7998 48.2998 119.6001 48.3999 C
118.2998 45.7002 119.3999 42.2998 119.2998 39.7998 C
119.3999 39.7998 119.3999 39.7998 Y
119.2002 39.6001 L
119.7998 39.3999 119.2998 38.2002 119.6001 37.8999 C
119.5 37.8999 L
118.7002 35.6001 119.2998 32.7998 118.7998 30.2002 C
119 30.2002 L
118.3999 29.5 118.5 27.5 117 27.5 C
116.7998 27.2002 L
117 28.6001 115.8999 29.7002 116.2998 31.7002 C
116 31.8999 L
116.2002 33 116.2002 33.8999 116 35 C
116.2998 35.2998 L
115.7998 35.6001 L
116.2002 35.7998 L
116.3999 36.6001 116.2998 38.2002 116.2002 39.3999 C
116.2998 39.2002 L
116.1001 41.5 115.7998 43.2998 115.1001 45.3999 C
115.2998 46.1001 115.2002 46.7002 115.1001 47.5 C
113.8999 47.8999 115.2998 49.2998 114.3999 49.8999 C
115.1001 50.2998 113.7998 50.7002 114.6001 51.1001 C
114.5 51.3999 114.2998 50.8999 114.3999 51.3999 C
114.5 51.5 L
114.1001 51.5 L
114.1001 52.6001 L
114.2002 52.6001 L
114.1001 53.1001 114 53.3999 114.6001 53.8999 C
114.2002 54.1001 L
115.1001 54.6001 113.8999 54.8999 114.5 55.3999 C
115.1001 55.8999 115.6001 57 116.2998 57.5 C
116.3999 57.7002 117.1001 58.6001 117.3999 58 C
117.6001 58.2998 117.6001 58.3999 117.2002 58.7002 C
118.6001 60.2998 119.7998 61.2002 120.7002 62.8999 C
120.7998 62.7998 L
121.1001 63.1001 122.2998 64.3999 122.3999 65.2002 C
122.5 65 L
122.3999 65.8999 123.7002 65.7002 123.2002 66.6001 C
124 66.7002 124.2002 67.8999 124.3999 68.7998 C
125.7002 68.7998 124.8999 70 126 70.2998 C
125.5 71.3999 127.1001 71.2002 126.5 72.1001 C
126.7002 72.5 128 72.7002 127.7002 73.7998 C
128.7998 74 128 75.2002 128.7998 75.6001 C
129 76 129.3999 76.2998 129.2002 76.8999 C
129.3999 76.8999 129.3999 76.8999 129.5 76.7998 C
129.8999 76.8999 129.1001 77.3999 129.7002 77.2998 C
130.2002 77.7002 129.2998 78.2002 130.1001 78.5 C
130.1001 78.3999 130 78.2002 130.2002 78.1001 C
130.3999 78.3999 130.2998 78.8999 130.2998 79.2998 C
130.6001 79.1001 L
131 80.3999 L
131.2998 80.2002 L
131.6001 80.6001 131.2002 81.7002 131.6001 81.7002 C
131.8999 81.5 L
132 82.6001 L
132.2002 82.6001 132.2002 82.2998 132.3999 82.6001 C
132.6001 83.6001 L
132.7002 83.6001 132.7002 83.5 132.7998 83.5 C
132.7998 84.1001 L
133 84.1001 L
133.1001 85.1001 L
133.6001 85.1001 L
132.8999 86.2998 134.7998 86.2998 134.2002 87.6001 C
134.7002 88 135 88.7002 135.1001 89.2002 C
135.2002 90 L
136 90.5 135.7998 90.7998 136.1001 91.6001 C
136.6001 92 136.7002 93 136.7998 93.7998 C
136.7998 93.7002 L
f
0 J 0 w 4 M
177 105 m
173 105 L
172.5 55 135.373 20.021 91.479 20.021 c
47.5845 20.021 7.5 55.5 12 114.5 C
1.626 108.4907 L
1.4585 106.2656 1.3735 104.0176 1.3735 101.75 c
1.3735 52.8184 41.0415 13.1499 89.9731 13.1499 c
138.9048 13.1499 178 52 177 105 C
f
0.2 w
116.5 186.75 m
92.75 194.25 67 187.5 v
34.3887 178.9517 20.75 155.75 y
38.5 178.25 67.75 185.5 v
96.1782 192.5464 116.25 183.75 y
116.5 186.75 l
f
0 w
77.25 162 m
75 164.5 l
42.25 149.5 32.5 113.75 v
43 144.75 77.25 162 v
f
111 51.8335 m
109.937 52.9429 109.1665 52 108.1665 51.6665 c
107.1665 51.3335 102.1665 48.1665 98.1665 46.8335 c
94.1665 45.5 93.8335 45.1665 91.1665 45 c
88.5 44.8335 85.8335 44.1665 84 43.6665 c
82.1665 43.1665 80.3335 43.5 78.3335 44 c
76.3335 44.5 70.5 46.3335 67.3335 45.6665 c
64.1665 45 63.6665 43.1665 61.5 42.5 c
59.3335 41.8335 56.3335 41.6665 52.8335 43.3335 c
49.3335 45 47.0103 46.1846 45 47.3335 c
43.8335 48 42.9429 48.8501 42 50.5 c
41.3335 51.6665 38.4165 53.8335 35.5 55.8335 c
31.7988 58.3711 24.3335 63.6665 22.8335 65.5 c
27 57 28.5 55.3335 v
30 53.6665 30 52.3335 32.6665 52.3335 c
35.3335 52.3335 36.6665 51.8335 37.5 51 c
38 50.5 37.1665 50 35.8335 50.1665 c
34.9902 50.272 33.2739 50.1968 34.1665 48.6665 c
34.9165 48.75 35.5835 48.6665 v
36.25 48.5835 37.5 48.75 38.25 48.6665 c
39 48.5835 40.3335 48.1665 40.8335 47.4165 c
40.3335 46.75 39.3335 46.5 v
38.3335 46.25 37.1665 45.8335 37.75 45.3335 c
38.3335 44.8335 39.5835 44.3335 40.9165 44.5835 c
42.25 44.8335 44 45.25 44.6665 44.8335 c
45.3335 44.4165 44.8335 43.5835 43 43 c
41.1665 42.4165 40.9165 41.75 41.8335 41.4165 c
42.75 41.0835 44.5835 41.3335 45.5835 41.9165 c
46.5835 42.5 47 42.3335 47.4165 42.1665 c
47.8335 42 47.9165 41.4165 46.75 40.9165 c
45.5835 40.4165 44.5835 39.5 45.25 39.1665 c
45.9165 38.8335 48.3335 39.4165 49.1665 39.6665 c
50 39.9165 51.4165 40.25 52 39.8335 c
52.5835 39.4165 52.75 39 51.25 38.0835 c
49.75 37.1665 48.75 36.1665 49.3335 35.6665 c
49.9165 35.1665 51.3335 35.8335 52.0835 36.3335 c
52.8335 36.8335 55.4165 38.9165 56.25 38.3335 c
57.0835 37.75 55.9165 35.5 55.0835 34.5835 c
54.25 33.6665 53.8335 32.5 54.9165 32.0835 c
56 31.6665 56.6665 33 57.3335 33.75 c
58 34.5 63.4165 41.3335 64.4165 41 c
65.4165 40.6665 63.3335 36.5835 62.5 35.3335 c
61.6665 34.0835 59.25 29.9165 60.25 29.3335 c
61.25 28.75 64.0835 31.75 64.9165 33.25 c
65.75 34.75 67.9165 38.5835 68.75 38.25 c
69.5835 37.9165 69.5 36.0835 68.25 33.75 c
67 31.4165 64.9165 27.9165 66 27.25 c
67.0835 26.5835 69.3335 29.75 70.5835 32 c
71.8335 34.25 73.8335 38.25 74.9165 37.9165 c
76 37.5835 75.1665 35.25 74.0835 32.4165 c
73 29.5835 71.4165 25.8335 72.5835 25.5 c
73.75 25.1665 76.0835 27.6665 76.9165 29.9165 c
77.75 32.1665 80 37 81.25 36.6665 c
82.5 36.3335 81.8335 34.3335 81.4165 32.8335 c
81 31.3335 80.1665 28.0835 79.4165 26.6665 c
78.6665 25.25 78.8335 24.1665 79.4165 24.1665 c
80 24.1665 83.3335 28.5835 84.5 31.6665 c
85.6665 34.75 86.6665 37.8335 87.4165 38.1665 c
88.1665 38.5 88.1665 38.5 88.0835 37.8335 c
88 37.1665 88.0835 35.6665 87.9165 33.5835 c
87.75 31.5 87.25 28.4165 86.6665 27.1665 c
86.0835 25.9165 85.9165 23 86.75 23.0835 c
87.5835 23.1665 87.4165 24.5 88.25 25.25 c
89.0835 26 90.1665 28 90.5835 30.3335 c
91.75 31.9165 91.9165 33.3335 v
92.0835 34.75 92.5835 35.1665 92.8335 36.1665 c
93.0835 37.1665 93.3335 38.75 93.8335 38.5835 c
94.3335 38.4165 94.25 37.5835 94.3335 36.6665 c
94.4165 35.75 94.75 35 94.5 34.0835 c
94.25 33.1665 94.5 32.5835 94.3335 31.9165 c
94.1665 31.25 93.5835 29.8335 93.4165 28.5 c
93.25 27.1665 93.4165 25.9165 93.25 25.1665 c
93.0835 24.4165 93 23.0835 93.8335 23.6665 c
94.6665 24.25 95.5645 25.6519 95.75 28.25 c
95.8335 29.4165 96.9165 30.5 y
97.3335 30.75 97.4165 31.75 v
97.5 32.75 98.4165 37.3335 99.0835 37.25 c
99.75 37.1665 99.5835 36.6665 99.5835 35.6665 c
99.5835 34.6665 99.9165 32 99.5 30.25 c
99.0835 28.5 98.1665 24.25 98.6665 24.0835 c
99.1665 23.9165 100.8335 24.8335 101.1665 27.5835 c
101.5 30.3335 102.3335 31.75 102.4165 33.75 c
102.5 35.75 103.6665 38.5 104.3335 38.25 c
105 38 105 37.0835 105 36.25 c
105 35.4165 106 31.8335 105.5835 30.6665 c
105.1665 29.5 104.9165 27.0835 105 26.4165 c
105.0835 25.75 105.3335 24.75 105.8335 25.1665 c
106.3335 25.5835 106.9092 27.4375 107.25 30.25 c
107.5835 33 107.6665 34.9165 107.9165 35.8335 c
108.1665 36.75 107.9165 38.0835 108.25 38.5835 c
108.5835 39.0835 108.5835 39.4165 109.0835 38.5835 c
109.5835 37.75 110.25 36.5835 110.25 35.3335 c
110.25 34.0835 110.4165 30.1665 110 28.5 c
109.5835 26.8335 109.9165 26.0835 110.75 26.1665 c
111.7207 26.2637 112.5 28.1665 112.8335 31.3335 c
113.2173 34.9834 113.3335 41.6665 113 44.5835 c
112.6665 47.5 112.9165 49.8335 111 51.8335 c
f
LB
%AI5_EndLayer--
%%PageTrailer
gsave annotatepage grestore showpage
%%Trailer
Adobe_Illustrator_AI5 /terminate get exec
Adobe_ColorImage_AI6 /terminate get exec
Adobe_level2_AI5 /terminate get exec
%%EOF
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/main.pdf
Binary file final_main/main.pdf has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/main.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/main.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,130 @@
+\documentclass[a4j,12pt]{jreport}
+\usepackage[dvipdfmx]{graphicx}
+\usepackage{mythesis}
+\usepackage{bussproofs}
+\usepackage{multirow}
+\usepackage{here}
+\usepackage{listings}
+\usepackage{url}
+\usepackage{cite}
+\usepackage{listings}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage[utf8]{inputenc}
+
+\lstset{
+ basicstyle={\ttfamily},
+ breaklines=true,
+ columns=[l]{fullflexible},
+ commentstyle={\ttfamily},
+ escapechar={@},
+ frame=single,
+ framerule=.5pt,
+ identifierstyle={\ttfamily},
+ keepspaces=true,
+ keywordstyle={\ttfamily},
+ language={},
+ lineskip=-0.1zw,
+ numbers=left,
+ numbersep=1em,
+ numberstyle={\scriptsize},
+ stepnumber=1,
+ stringstyle={\ttfamily},
+ tabsize=4,
+ xleftmargin=0zw,
+ xrightmargin=0zw,
+}
+
+% \lstset{
+% language={C},
+% basicstyle={\footnotesize\ttfamily},
+% identifierstyle={\footnotesize},
+% commentstyle={\footnotesize\itshape},
+% keywordstyle={\footnotesize\bfseries},
+% ndkeywordstyle={\footnotesize},
+% stringstyle={\footnotesize\ttfamily},
+% frame={tb},
+% breaklines=true,
+% columns=[l]{fullflexible},
+% numbers=left,
+% xrightmargin=0zw,
+% xleftmargin=3zw,
+% numberstyle={\scriptsize},
+% stepnumber=1,
+% numbersep=1zw,
+% lineskip=-0.5ex
+% }
+\def\lstlistingname{ソースコード}
+\def\lstlistlistingname{ソースコード目次}
+\setlength{\itemsep}{-1zh}
+\title{画面共有システム TreeVNC の拡張}
+\icon{
+ \includegraphics[width=80mm,bb=0 0 595 642]{fig/ryukyu.pdf} %%元は 642じゃなくて842
+}
+\year{平成31年度 卒業論文}
+\belongto{琉球大学工学部情報工学科}
+\author{155702F 大城 由也 \\ 指導教員 {河野 真治} }
+%%
+%% プリアンブルに記述
+%% Figure 環境中で Table 環境の見出しを表示・カウンタの操作に必要
+%%
+\makeatletter
+\newcommand{\figcaption}[1]{\def\@captype{figure}\caption{#1}}
+\newcommand{\tblcaption}[1]{\def\@captype{table}\caption{#1}}
+\newcommand{\coderef}[1]{ソースコード \ref{code:#1}}
+\makeatother
+\setlength\abovecaptionskip{0pt}
+
+\begin{document}
+
+% タイトル
+\maketitle
+\baselineskip 17pt plus 1pt minus 1pt
+
+\pagenumbering{roman}
+\setcounter{page}{0}
+
+\tableofcontents % 目次
+\listoffigures % 図目次
+%\listoftables % 表目次
+\lstlistoflistings
+
+%以下のように、章ごとに個別の tex ファイルを作成して、
+% main.tex をコンパイルして確認する。
+%章分けは個人で違うので下のフォーマットを参考にして下さい。
+
+% はじめに
+\input{chapter1.tex}
+
+% 基礎概念
+\input{chapter2.tex}
+
+% 実験
+\input{chapter3.tex}
+
+% 実装
+\input{chapter4.tex}
+
+% 評価
+\input{chapter5.tex}
+
+% 結論
+\input{chapter6.tex}
+
+% 参考文献
+%% こっちで書きたいよね
+
+\nocite{*}
+\bibliographystyle{junsrt}
+\bibliography{reference}
+
+% \input{bibliography.tex}
+
+% 謝辞
+\input{thanks.tex}
+
+\appendix
+% 付録
+%\input{appendix.tex}
+
+\end{document}
diff -r 000000000000 -r 83f997abf3b5 final_main/mythesis.sty
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/mythesis.sty Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,156 @@
+%
+% 卒業論文スタイルファイル(mythesis.sty)
+% version 1.0e
+%
+% ver 1.0e 02/07/2000 since
+% usage:
+
+%\documentclass[a4j]{jreport}
+%\usepackage{master_paper}
+%
+%
+%\title{卒論タイトル \\ 長い}
+%\etitle{\pLaTeX2e style test file for Teri's thesis }
+%\year{平成11年度}
+%\belongto{琉球大学大学工学部\\ 情報工学科}
+%\author{豊平 絵梨}
+%
+%\begin{document}
+%
+%\maketitle
+%
+%%要旨
+%\input{abstract.tex}
+%
+%%目次
+%\tableofcontents
+%
+%%図目次
+%\listoffigures
+%
+%%表目次
+%\listoftables
+%
+%%第一章
+%\input{chapter1.tex}
+%%chapter1.texの\chapter{}の後ろに次のコマンドを追加してください。
+%%ページカウントがリセットされ、ページ数がアラビア文字になります。
+%% \pagenumbering{arabic}
+%%第二章
+%\input{chapter2.tex}
+%%第三章
+%\input{chapter3.tex}
+%
+%%付録
+%\input{appendix.tex}
+%
+%%謝辞
+%%\input{thanx.tex}
+%
+%%参考文献
+%\input{biblography.tex}
+%
+%\end{document}
+
+
+%長さ設定
+%\setlength{\topmargin}{-30mm}
+%\addtolength{\oddsidemargin}{-15mm}
+%\addtolength{\textwidth}{60mm}
+
+\topmargin -1in \addtolength{\topmargin}{35mm}
+\headheight 0mm
+\headsep 0mm
+\oddsidemargin -1in \addtolength{\oddsidemargin}{30mm}
+%\evensidemargin -1in \addtolength{\evensidemargin}{8mm}
+\textwidth 160mm
+\textheight 230mm
+%\footheight 0mm
+%\footskip 0mm
+%\pagestyle{empty}
+
+
+%年度
+\def\@year{}
+\def\year#1{\gdef\@year{#1}}
+%英文タイトル
+\def\@etitle{}
+\def\etitle#1{\gdef\@etitle{#1}}
+%アイコン
+\def\@icon{}
+\def\icon#1{\gdef\@icon{#1}}
+%所属
+\def\@belongto{}
+\def\belongto#1{\gdef\@belongto{#1}}
+
+%表紙
+\renewcommand{\maketitle}{%
+\newpage\null
+\thispagestyle{empty}
+\vskip 0cm%
+\begin{center}%
+\let\footnote\thanks
+ {\huge \@year \par}%
+ \vskip 3em%
+ {\Huge \@title \par}%
+ \vskip 1em%
+ {\huge \@etitle \par}%
+ \vskip 8em%
+ {\huge \@icon \par}%
+ \vskip 0.5em%
+ {\huge \@belongto \par}%
+ \vskip 1.0em%
+ {\huge \@author \par}%
+
+\end{center}%
+\par\vskip 1.5em
+}
+
+
+%abstract
+\renewenvironment{abstract}{%
+ \titlepage
+ \thispagestyle{empty}
+ \null\vfil
+ \@beginparpenalty\@lowpenalty
+ {\Huge \bfseries \abstractname}%
+ \begin{center}%
+ \@endparpenalty\@M
+ \end{center}
+}%
+
+
+%目次
+\renewcommand{\tableofcontents}{%
+ \pagestyle{plain}
+ \if@twocolumn\@restonecoltrue\onecolumn
+ \else\@restonecolfalse\fi
+ \chapter*{\contentsname
+ \@mkboth{\contentsname}{\contentsname}%
+ } \pagenumbering{roman}\@starttoc{toc}%
+ \if@restonecol\twocolumn\fi
+}
+
+%章
+\renewcommand{\chapter}{%
+ \pagestyle{plain}
+ \if@openright\cleardoublepage\else\clearpage\fi
+ \thispagestyle{jpl@in}%
+ \global\@topnum\z@
+ \@afterindentfalse
+ \secdef\@chapter\@schapter}
+
+
+\renewcommand{\prepartname}{} %\renewcommand{\prepartname}{第}
+\renewcommand{\postpartname}{部}
+\renewcommand{\prechaptername}{第}%\renewcommand{\prechaptername}{第}
+\renewcommand{\postchaptername}{章}
+\renewcommand{\contentsname}{目 次}
+\renewcommand{\listfigurename}{図 目 次}
+\renewcommand{\listtablename}{表 目 次}
+\renewcommand{\bibname}{参考文献}
+\renewcommand{\indexname}{索 引}
+\renewcommand{\figurename}{図}
+\renewcommand{\tablename}{表}
+\renewcommand{\appendixname}{付 録}
+\renewcommand{\abstractname}{要 旨}
diff -r 000000000000 -r 83f997abf3b5 final_main/pic/modus-ponens.pdf
Binary file final_main/pic/modus-ponens.pdf has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/pic/modus-ponens.xbb
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/pic/modus-ponens.xbb Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+%%Title: modus-ponens.pdf
+%%Creator: extractbb 20160307
+%%BoundingBox: 96 684 500 799
+%%HiResBoundingBox: 96.082030 683.554700 499.886700 799.296900
+%%PDFVersion: 1.3
+%%Pages: 1
+%%CreationDate: Mon Jan 29 15:58:01 2018
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaBasics.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaBasics.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,1 @@
+module AgdaBasics where
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaBasics.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaBasics.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,1 @@
+module AgdaBasics where
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaBool.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaBool.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+data Bool : Set where
+ true : Bool
+ false : Bool
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaDebug.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaDebug.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,32 @@
+open import Level renaming (suc to succ ; zero to Zero )
+
+module AgdaDebug where
+
+open import stack
+
+open import Relation.Binary.PropositionalEquality
+open import Relation.Binary.Core
+open import Data.Nat
+open import Function
+
+
+open SingleLinkedStack
+open Stack
+
+testStack07 : {m : Level } -> Maybe (Element ℕ)
+testStack07 = pushSingleLinkedStack emptySingleLinkedStack 1 (\s -> pushSingleLinkedStack s 2 (\s -> top s))
+
+testStack08 = pushSingleLinkedStack emptySingleLinkedStack 1
+ $ \s -> pushSingleLinkedStack s 2
+ $ \s -> pushSingleLinkedStack s 3
+ $ \s -> pushSingleLinkedStack s 4
+ $ \s -> pushSingleLinkedStack s 5
+ $ \s -> top s
+
+
+testStack10 = pushStack emptySingleLinkedStack 1
+ $ \s -> pushStack 2
+ $ \s -> pushStack 3
+ $ \s -> pushStack 4
+ $ \s -> pushStack 5
+ $ \s -> top s
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaDebug.agdai
Binary file final_main/src/AgdaDebug.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaElem.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaElem.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+elem : {A : Set} {{eqA : Eq A}} → A → List A → Bool
+elem {{eqA}} x (y ∷ xs) = (Eq._==_ eqA x y) || (elem {{eqA}} x xs)
+elem x [] = false
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaElemApply.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaElemApply.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+listHas4 : Bool
+listHas4 = elem 4 (3 ∷ 2 ∷ 5 ∷ 4 ∷ []) -- true
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaFunction.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaFunction.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,2 @@
+f : Bool -> Bool
+f x = true
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaId.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaId.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,5 @@
+identity : (A : Set) -> A -> A
+identity A x = x
+
+identity-zero : Nat
+identity-zero = identity Nat zero
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaImplicitId.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaImplicitId.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,11 @@
+id : {A : Set} -> A -> A
+id x = x
+
+id-zero : Nat
+id-zero = id zero
+
+id' : {A : Set} -> A -> A
+id' {A} x = x
+
+id-true : Bool
+id-true = id {Bool} true
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaImport.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaImport.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,6 @@
+import Data.Nat -- import module
+import Data.Bool as B -- renamed module
+import Data.List using (head) -- import Data.head function
+import Level renaming (suc to S) -- import module with rename suc to S
+import Data.String hiding (_++_) -- import module without _++_
+open import Data.List -- import and expand Data.List
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaInstance.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaInstance.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,9 @@
+_==Nat_ : Nat -> Nat -> Bool
+zero ==Nat zero = true
+(suc n) ==Nat zero = false
+zero ==Nat (suc m) = false
+(suc n) ==Nat (suc m) = n ==Nat m
+
+instance
+ natHas== : Eq Nat
+ natHas== = record { _==_ = _==Nat_}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaInterface.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaInterface.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,35 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module AgdaInterface where
+
+data Maybe {n : Level } (a : Set n) : Set n where
+ Nothing : Maybe a
+ Just : a -> Maybe a
+
+record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ push : stackImpl -> a -> (stackImpl -> t) -> t
+ pop : stackImpl -> (stackImpl -> Maybe a -> t) -> t
+ pop2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
+ get : stackImpl -> (stackImpl -> Maybe a -> t) -> t
+ get2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
+ clear : stackImpl -> (stackImpl -> t) -> t
+open StackMethods
+
+record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.⊔ n) where
+ field
+ stack : si
+ stackMethods : StackMethods {n} {m} a {t} si
+ pushStack : a -> (Stack a si -> t) -> t
+ pushStack d next = push (stackMethods ) (stack ) d (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
+ popStack : (Stack a si -> Maybe a -> t) -> t
+ popStack next = pop (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ pop2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
+ pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ getStack : (Stack a si -> Maybe a -> t) -> t
+ getStack next = get (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ get2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
+ get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ clearStack : (Stack a si -> t) -> t
+ clearStack next = clear (stackMethods ) (stack ) (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
+
+open Stack
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaInterface.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaInterface.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,35 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module AgdaInterface where
+
+data Maybe {n : Level } (a : Set n) : Set n where
+ Nothing : Maybe a
+ Just : a @$\rightarrow$@ Maybe a
+
+record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ push : stackImpl @$\rightarrow$@ a @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ clear : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+open StackMethods
+
+record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ stack : si
+ stackMethods : StackMethods {n} {m} a {t} si
+ pushStack : a @$\rightarrow$@ (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
+ pushStack d next = push (stackMethods ) (stack ) d (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
+ popStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ popStack next = pop (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ pop2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ getStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getStack next = get (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ get2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ clearStack : (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
+ clearStack next = clear (stackMethods ) (stack ) (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
+
+open Stack
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaInterface.agdai
Binary file final_main/src/AgdaInterface.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaLambda.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaLambda.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,5 @@
+not-apply : Bool -> Bool
+not-apply = (\b -> not b) -- use lambda
+
+not-apply : Bool -> Bool
+not-appy b = not b -- not use lambda
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaModusPonens.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaModusPonens.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,2 @@
+f : {A B C : Set} -> ((A -> B) × (B -> C)) -> (A -> C)
+f = \p x -> (snd p) ((fst p) x)
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaNPushNPop.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaNPushNPop.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,13 @@
+n-push : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
+n-push {{mm}} (zero) = M.cs {{mm}} {{mm}} id
+n-push {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-push {m} {{mm}} n) (pushOnce m))
+
+n-pop : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
+n-pop {{mm}} (zero) = M.cs {{mm}} {{mm}} id
+n-pop {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-pop {m} {{mm}} n) (popOnce m))
+
+pop-n-push-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
+pop-n-push-type n cn ce s = M.exec (M.csComp {meta} (M.cs popOnce) (n-push {meta} (suc n))) meta
+ ≡ M.exec (n-push {meta} n) meta
+ where
+ meta = id-meta cn ce s
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaNPushNPopProof.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaNPushNPopProof.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,58 @@
+pop-n-push-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
+pop-n-push-type n cn ce s = M.exec (M.csComp (M.cs popOnce) (n-push (suc n))) meta
+ ≡ M.exec (n-push n) meta
+ where
+ meta = id-meta cn ce s
+
+pop-n-push : (n cn ce : ℕ) -> (s : SingleLinkedStack ℕ) -> pop-n-push-type n cn ce s
+pop-n-push zero cn ce s = refl
+pop-n-push (suc n) cn ce s = begin
+ M.exec (M.csComp (M.cs popOnce) (n-push (suc (suc n)))) (id-meta cn ce s)
+ ≡⟨ refl ⟩
+ M.exec (M.csComp (M.cs popOnce) (M.csComp (n-push (suc n)) (M.cs pushOnce))) (id-meta cn ce s)
+ ≡⟨ exec-comp (M.cs popOnce) (M.csComp (n-push (suc n)) (M.cs pushOnce)) (id-meta cn ce s) ⟩
+ M.exec (M.cs popOnce) (M.exec (M.csComp (n-push (suc n)) (M.cs pushOnce)) (id-meta cn ce s))
+ ≡⟨ cong (\x -> M.exec (M.cs popOnce) x) (exec-comp (n-push (suc n)) (M.cs pushOnce) (id-meta cn ce s)) ⟩
+ M.exec (M.cs popOnce) (M.exec (n-push (suc n))(M.exec (M.cs pushOnce) (id-meta cn ce s)))
+ ≡⟨ refl ⟩
+ M.exec (M.cs popOnce) (M.exec (n-push (suc n)) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})))
+ ≡⟨ sym (exec-comp (M.cs popOnce) (n-push (suc n)) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))) ⟩
+ M.exec (M.csComp (M.cs popOnce) (n-push (suc n))) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))
+ ≡⟨ pop-n-push n cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}) ⟩
+ M.exec (n-push n) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))
+ ≡⟨ refl ⟩
+ M.exec (n-push n) (pushOnce (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-push n) (M.exec (M.cs pushOnce) (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-push (suc n)) (id-meta cn ce s)
+ ∎
+
+
+
+n-push-pop-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
+n-push-pop-type n cn ce st = M.exec (M.csComp (n-pop n) (n-push n)) meta ≡ meta
+ where
+ meta = id-meta cn ce st
+
+n-push-pop : (n cn ce : ℕ) -> (s : SingleLinkedStack ℕ) -> n-push-pop-type n cn ce s
+n-push-pop zero cn ce s = refl
+n-push-pop (suc n) cn ce s = begin
+ M.exec (M.csComp (n-pop (suc n)) (n-push (suc n))) (id-meta cn ce s)
+ ≡⟨ refl ⟩
+ M.exec (M.csComp (M.cs (\m -> M.exec (n-pop n) (popOnce m))) (n-push (suc n))) (id-meta cn ce s)
+ ≡⟨ exec-comp (M.cs (\m -> M.exec (n-pop n) (popOnce m))) (n-push (suc n)) (id-meta cn ce s) ⟩
+ M.exec (M.cs (\m -> M.exec (n-pop n) (popOnce m))) (M.exec (n-push (suc n)) (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-pop n) (popOnce (M.exec (n-push (suc n)) (id-meta cn ce s)))
+ ≡⟨ refl ⟩
+ M.exec (n-pop n) (M.exec (M.cs popOnce) (M.exec (n-push (suc n)) (id-meta cn ce s)))
+ ≡⟨ cong (\x -> M.exec (n-pop n) x) (sym (exec-comp (M.cs popOnce) (n-push (suc n)) (id-meta cn ce s))) ⟩
+ M.exec (n-pop n) (M.exec (M.csComp (M.cs popOnce) (n-push (suc n))) (id-meta cn ce s))
+ ≡⟨ cong (\x -> M.exec (n-pop n) x) (pop-n-push n cn ce s) ⟩
+ M.exec (n-pop n) (M.exec (n-push n) (id-meta cn ce s))
+ ≡⟨ sym (exec-comp (n-pop n) (n-push n) (id-meta cn ce s)) ⟩
+ M.exec (M.csComp (n-pop n) (n-push n)) (id-meta cn ce s)
+ ≡⟨ n-push-pop n cn ce s ⟩
+ id-meta cn ce s
+ ∎
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaNat.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaNat.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+data Nat : Set where
+ zero : Nat
+ suc : Nat -> Nat
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaNot.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaNot.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+not : Bool -> Bool
+not true = false
+not false = true
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaParameterizedModule.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaParameterizedModule.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+module Sort (A : Set) (_<_ : A -> A -> Bool) where
+sort : List A -> List A
+sort = -- 実装は省略 ...
+
+-- Parameterized Module により N.sort や B.sort が可能
+open import Sort Nat Nat._<_ as N
+open import Sort Bool Bool._<_ as B
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaPattern.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaPattern.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+not : Bool -> Bool
+not false = true
+not x = false
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaPlus.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaPlus.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+_+_ : Nat -> Nat -> Nat
+zero + m = m
+suc n + m = suc (n + m)
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaProduct.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaProduct.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+data _×_ (A B : Set) : Set where
+ <_,_> : A -> B -> A × B
+
+fst : {A B : Set} -> A × B -> A
+fst < a , _ > = a
+
+snd : {A B : Set} -> A × B -> B
+snd < _ , b > = b
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaProp.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaProp.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,2 @@
+prop : Bool
+prop = true
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaPushPop.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaPushPop.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,28 @@
+pushSingleLinkedStack : Meta -> Meta
+pushSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (push s e) })
+ where
+ n = Meta.nextCS m
+ s = Meta.stack m
+ e = Context.element (Meta.context m)
+ push : SingleLinkedStack A -> Maybe A -> SingleLinkedStack A
+ push s nothing = s
+ push s (just x) = record {top = just (cons x (top s))}
+
+popSingleLinkedStack : Meta -> Meta
+popSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (st m) ; context = record con {element = (elem m)}})
+ where
+ n = Meta.nextCS m
+ con = Meta.context m
+ elem : Meta -> Maybe A
+ elem record {stack = record { top = (just (cons x _)) }} = just x
+ elem record {stack = record { top = nothing }} = nothing
+ st : Meta -> SingleLinkedStack A
+ st record {stack = record { top = (just (cons _ s)) }} = record {top = s}
+ st record {stack = record { top = nothing }} = record {top = nothing}
+
+
+pushSingleLinkedStackCS : M.CodeSegment Meta Meta
+pushSingleLinkedStackCS = M.cs pushSingleLinkedStack
+
+popSingleLinkedStackCS : M.CodeSegment Meta Meta
+popSingleLinkedStackCS = M.cs popSingleLinkedStack
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaPushPopProof.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaPushPopProof.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,11 @@
+id-meta : ℕ -> ℕ -> SingleLinkedStack ℕ -> Meta
+id-meta n e s = record { context = record {n = n ; element = just e}
+ ; nextCS = (N.cs id) ; stack = s}
+
+push-pop-type : ℕ -> ℕ -> ℕ -> Element ℕ -> Set₁
+push-pop-type n e x s = M.exec (M.csComp {meta} (M.cs popOnce) (M.cs pushOnce)) meta ≡ meta
+ where
+ meta = id-meta n e record {top = just (cons x (just s))}
+
+push-pop : (n e x : ℕ) -> (s : Element ℕ) -> push-pop-type n e x s
+push-pop n e x s = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaRecord.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaRecord.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+record Point : Set where
+ field
+ x : Nat
+ y : Nat
+
+makePoint : Nat -> Nat -> Point
+makePoint a b = record { x = a ; y = b }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaRecordProj.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaRecordProj.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+getX : Point -> Nat
+getX p = Point.x p
+
+getY : Point -> Nat
+getY record { x = a ; y = b} = b
+
+xPlus5 : Point -> Point
+xPlus5 p = record p { x = (Point.x p) + 5}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaSingleLinkedStack.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaSingleLinkedStack.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,63 @@
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} -> StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+push = pushSingleLinkedStack
+; pop = popSingleLinkedStack
+; pop2 = pop2SingleLinkedStack
+; get = getSingleLinkedStack
+; get2 = get2SingleLinkedStack
+; clear = clearSingleLinkedStack
+}
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+stack = emptySingleLinkedStack ;
+stackMethods = singleLinkedStackSpec
+}
+
+-- Implementation
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+
+popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
+popSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack1 (Just data1)
+ where
+ data1 = datum d
+ stack1 = record { top = (next d) }
+
+pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = pop2SingleLinkedStack' {n} {m} stack cs
+ where
+ pop2SingleLinkedStack' : {n m : Level } {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+ pop2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs (record {top = (next d1)}) (Just (datum d)) (Just (datum d1))
+
+
+getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
+getSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack (Just data1)
+ where
+ data1 = datum d
+
+get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = get2SingleLinkedStack' {n} {m} stack cs
+ where
+ get2SingleLinkedStack' : {n m : Level} {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+ get2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs stack (Just (datum d)) (Just (datum d1))
+
+clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (SingleLinkedStack a -> t) -> t
+clearSingleLinkedStack stack next = next (record {top = Nothing})
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaSingleLinkedStack.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaSingleLinkedStack.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,63 @@
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+push = pushSingleLinkedStack
+; pop = popSingleLinkedStack
+; pop2 = pop2SingleLinkedStack
+; get = getSingleLinkedStack
+; get2 = get2SingleLinkedStack
+; clear = clearSingleLinkedStack
+}
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+stack = emptySingleLinkedStack ;
+stackMethods = singleLinkedStackSpec
+}
+
+-- Implementation
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} @$\rightarrow$@ SingleLinkedStack Data @$\rightarrow$@ Data @$\rightarrow$@ (Code : SingleLinkedStack Data @$\rightarrow$@ t) @$\rightarrow$@ t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+
+popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+popSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack1 (Just data1)
+ where
+ data1 = datum d
+ stack1 = record { top = (next d) }
+
+pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = pop2SingleLinkedStack' {n} {m} stack cs
+ where
+ pop2SingleLinkedStack' : {n m : Level } {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs (record {top = (next d1)}) (Just (datum d)) (Just (datum d1))
+
+
+getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+getSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack (Just data1)
+ where
+ data1 = datum d
+
+get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = get2SingleLinkedStack' {n} {m} stack cs
+ where
+ get2SingleLinkedStack' : {n m : Level} {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs stack (Just (datum d)) (Just (datum d1))
+
+clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (SingleLinkedStack a @$\rightarrow$@ t) @$\rightarrow$@ t
+clearSingleLinkedStack stack next = next (record {top = Nothing})
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStack.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStack.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,13 @@
+data Element (a : Set) : Set where
+ cons : a -> Maybe (Element a) -> Element a
+
+datum : {a : Set} -> Element a -> a
+datum (cons a _) = a
+
+next : {a : Set} -> Element a -> Maybe (Element a)
+next (cons _ n) = n
+
+record SingleLinkedStack (a : Set) : Set where
+ field
+ top : Maybe (Element a)
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackDS.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackDS.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,17 @@
+record Context : Set where
+ field
+ -- fields for stack
+ element : Maybe A
+
+
+open import subtype Context as N
+
+record Meta : Set₁ where
+ field
+ -- context as set of data segments
+ context : Context
+ stack : SingleLinkedStack A
+ nextCS : N.CodeSegment Context Context
+
+open import subtype Meta as M
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackImpl.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackImpl.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,28 @@
+record SingleLinkedStack {n : Level } (a : Set n) : Set n where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+-- Basic stack implementations are specifications of a Stack
+
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} -> StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+ push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ ; pop2 = pop2SingleLinkedStack
+ ; get = getSingleLinkedStack
+ ; get2 = get2SingleLinkedStack
+ ; clear = clearSingleLinkedStack
+ }
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+ stack = emptySingleLinkedStack ;
+ stackMethods = singleLinkedStackSpec
+ }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackImpl.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackImpl.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,28 @@
+record SingleLinkedStack {n : Level } (a : Set n) : Set n where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} @$\rightarrow$@ SingleLinkedStack Data @$\rightarrow$@ Data @$\rightarrow$@ (Code : SingleLinkedStack Data @$\rightarrow$@ t) @$\rightarrow$@ t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+-- Basic stack implementations are specifications of a Stack
+
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+ push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ ; pop2 = pop2SingleLinkedStack
+ ; get = getSingleLinkedStack
+ ; get2 = get2SingleLinkedStack
+ ; clear = clearSingleLinkedStack
+ }
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+ stack = emptySingleLinkedStack ;
+ stackMethods = singleLinkedStackSpec
+ }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackSomeState.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackSomeState.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,6 @@
+stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) -> Stack {l} {m} D {t} ( SingleLinkedStack D )
+stackInSomeState s = record { stack = s ; stackMethods = singleLinkedStackSpec }
+
+push->push->pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) ->
+pushStack ( stackInSomeState s ) x ( \s1 -> pushStack s1 y ( \s2 -> pop2Stack s2 ( \s3 y1 x1 -> (Just x ≡ x1 ) ∧ (Just y ≡ y1 ) ) ))
+push->push->pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackSomeState.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackSomeState.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,6 @@
+stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) @$\rightarrow$@ Stack {l} {m} D {t} ( SingleLinkedStack D )
+stackInSomeState s = record { stack = s ; stackMethods = singleLinkedStackSpec }
+
+push@$\rightarrow$@push@$\rightarrow$@pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) @$\rightarrow$@ pushStack (stackInSomeState s) x (\s1 @$\rightarrow$@ pushStack s1 y (\s2 @$\rightarrow$@ pop2Stack s2 (\s3 y1 x1 @$\rightarrow$@
+ (Just x @$\equiv$@ x1) ∧ (Just y @$\equiv$@ y1))))
+push@$\rightarrow$@push@$\rightarrow$@pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackTest.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackTest.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,37 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module AgdaStackTest where
+
+open import stack
+
+open import Relation.Binary.PropositionalEquality
+open import Relation.Binary.Core
+open import Data.Nat
+open import Function
+
+
+open SingleLinkedStack
+open Stack
+
+
+-- after push 1 and 2, pop2 get 1 and 2
+
+testStack02 : {m : Level } -> ( Stack ℕ (SingleLinkedStack ℕ) -> Bool {m} ) -> Bool {m}
+testStack02 cs = pushStack createSingleLinkedStack 1 (\s -> pushStack s 2 cs)
+
+
+testStack031 : (d1 d2 : ℕ ) -> Bool {Zero}
+testStack031 2 1 = True
+testStack031 _ _ = False
+
+testStack032 : (d1 d2 : Maybe ℕ) -> Bool {Zero}
+testStack032 (Just d1) (Just d2) = testStack031 d1 d2
+testStack032 _ _ = False
+
+testStack03 : {m : Level } -> Stack ℕ (SingleLinkedStack ℕ) -> ((Maybe ℕ) -> (Maybe ℕ) -> Bool {m} ) -> Bool {m}
+testStack03 s cs = pop2Stack s (\s d1 d2 -> cs d1 d2 )
+
+testStack04 : Bool
+testStack04 = testStack02 (\s -> testStack03 s testStack032)
+
+testStack05 : testStack04 ≡ True
+testStack05 = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackTest.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaStackTest.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,22 @@
+-- after push 1 and 2, pop2 get 1 and 2
+
+testStack02 : {m : Level } @$\rightarrow$@ ( Stack @$\mathbb{N}$@ (SingleLinkedStack @$\mathbb{N}$@) @$\rightarrow$@ Bool {m} ) @$\rightarrow$@ Bool {m}
+testStack02 cs = pushStack createSingleLinkedStack 1 (\s @$\rightarrow$@ pushStack s 2 cs)
+
+
+testStack031 : (d1 d2 : $\mathbb{N}$ ) @$\rightarrow$@ Bool {Zero}
+testStack031 2 1 = True
+testStack031 _ _ = False
+
+testStack032 : (d1 d2 : Maybe @$\mathbb{N}$@) @$\rightarrow$@ Bool {Zero}
+testStack032 (Just d1) (Just d2) = testStack031 d1 d2
+testStack032 _ _ = False
+
+testStack03 : {m : Level } @$\rightarrow$@ Stack @$\mathbb{N}$@ (SingleLinkedStack @$\mathbb{N}$@) @$\rightarrow$@ ((Maybe @$\mathbb{N}$@) @$\rightarrow$@ (Maybe @$\mathbb{N}$@) @$\rightarrow$@ Bool {m} ) @$\rightarrow$@ Bool {m}
+testStack03 s cs = pop2Stack s (\s d1 d2 @$\rightarrow$@ cs d1 d2 )
+
+testStack04 : Bool
+testStack04 = testStack02 (\s @$\rightarrow$@ testStack03 s testStack032)
+
+testStack05 : testStack04 @$\equiv$@ True
+testStack05 = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaStackTest.agdai
Binary file final_main/src/AgdaStackTest.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTree.Agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTree.Agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,17 @@
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ putImpl : treeImpl -> a -> (treeImpl -> t) -> t
+ getImpl : treeImpl -> (treeImpl -> Maybe a -> t) -> t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a -> (Tree treeImpl -> t) -> t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 -> next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl -> Maybe a -> t) -> t
+ getTree next = getImpl (treeMethods ) tree (\t1 d -> next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+
+open Tree
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTree.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTree.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,17 @@
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ putImpl : treeImpl @$\rightarrow$@ a @$\rightarrow$@ (treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ getImpl : treeImpl @$\rightarrow$@ (treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a @$\rightarrow$@ (Tree treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getTree next = getImpl (treeMethods ) tree (\t1 d @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+
+open Tree
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeDebug.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeDebug.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,15 @@
+test31 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ ) 1 1
+ $ \t -> putTree1 t 2 2
+ $ \t -> putTree1 t 3 3
+ $ \t -> putTree1 t 4 4
+ $ \t -> getRedBlackTree t 4
+ $ \t x -> x
+
+-- Just
+-- (record
+-- { key = 4
+-- ; value = 4
+-- ; right = Nothing
+-- ; left = Nothing
+-- ; color = Red
+-- })
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeDebug.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeDebug.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,15 @@
+test31 = putTree1 {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} (createEmptyRedBlackTree@$\mathbb{N}$@ @$\mathbb{N}$@ ) 1 1
+ $ \t @$\rightarrow$@ putTree1 t 2 2
+ $ \t @$\rightarrow$@ putTree1 t 3 3
+ $ \t @$\rightarrow$@ putTree1 t 4 4
+ $ \t @$\rightarrow$@ getRedBlackTree t 4
+ $ \t x @$\rightarrow$@ x
+
+-- Just
+-- (record
+-- { key = 4
+-- ; value = 4
+-- ; right = Nothing
+-- ; left = Nothing
+-- ; color = Red
+-- })
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeDebugReturnNode4.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeDebugReturnNode4.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,16 @@
+test31 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ ) 1 1
+$ \t -> putTree1 t 2 2
+$ \t -> putTree1 t 3 3
+$ \t -> putTree1 t 4 4
+$ \t -> getRedBlackTree t 4
+$ \t x -> x
+
+-- C-c C-n test31 return
+ -- Just
+ -- (record
+ -- { key = 4
+ -- ; value = 4
+ -- ; right = Nothing
+ -- ; left = Nothing
+ -- ; color = Red
+ -- })
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeImpl.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeImpl.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,33 @@
+record Node {n : Level } (a k : Set n) : Set n where
+ inductive
+ field
+ key : k
+ value : a
+ right : Maybe (Node a k)
+ left : Maybe (Node a k)
+ color : Color {n}
+open Node
+
+leafNode : {n : Level } {a k : Set n} -> k -> a -> Node a k
+leafNode k1 value = record {
+ key = k1 ;
+ value = value ;
+ right = Nothing ;
+ left = Nothing ;
+ color = Red
+ }
+open leafNode
+
+record RedBlackTree {n m : Level } {t : Set m} (a k : Set n) : Set (m Level.⊔ n) where
+ field
+ root : Maybe (Node a k)
+ nodeStack : SingleLinkedStack (Node a k)
+ compare : k -> k -> CompareResult {n}
+open RedBlackTree
+
+putRedBlackTree : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> k -> a -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+putRedBlackTree {n} {m} {a} {k} {t} tree k1 value next with (root tree)
+... | Nothing = next (record tree {root = Just (leafNode k1 value) })
+... | Just n2 = clearSingleLinkedStack (nodeStack tree) (\ s -> findNode tree s (leafNode k1 value) n2 (\ tree1 s n1 -> insertNode tree1 s n1 next))
+
+-- 以下省略
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeImpl.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeImpl.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,47 @@
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ putImpl : treeImpl @$\rightarrow$@ a @$\rightarrow$@ (treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ getImpl : treeImpl @$\rightarrow$@ (treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a @$\rightarrow$@ (Tree treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getTree next = getImpl (treeMethods ) tree (\t1 d @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+open Tree
+
+record Node {n : Level } (a k : Set n) : Set n where
+ inductive
+ field
+ key : k
+ value : a
+ right : Maybe (Node a k)
+ left : Maybe (Node a k)
+ color : Color {n}
+open Node
+
+leafNode : {n : Level } {a k : Set n} @$\rightarrow$@ k @$\rightarrow$@ a @$\rightarrow$@ Node a k
+leafNode k1 value = record {
+ key = k1 ;
+ value = value ;
+ right = Nothing ;
+ left = Nothing ;
+ color = Red
+ }
+record RedBlackTree {n m : Level } {t : Set m} (a k : Set n) : Set (m Level.@$\sqcup$@ n) where
+ field
+ root : Maybe (Node a k)
+ nodeStack : SingleLinkedStack (Node a k)
+ compare : k @$\rightarrow$@ k @$\rightarrow$@ CompareResult {n}
+open RedBlackTree
+
+putRedBlackTree : {n m : Level } {a k : Set n} {t : Set m} @$\rightarrow$@ RedBlackTree {n} {m} {t} a k @$\rightarrow$@ k @$\rightarrow$@ a @$\rightarrow$@ (RedBlackTree {n} {m} {t} a k @$\rightarrow$@ t) @$\rightarrow$@ t
+putRedBlackTree {n} {m} {a} {k} {t} tree k1 value next with (root tree)
+... | Nothing = next (record tree {root = Just (leafNode k1 value) })
+... | Just n2 = clearSingleLinkedStack (nodeStack tree) (\ s @$\rightarrow$@ findNode tree s (leafNode k1 value) n2 (\ tree1 s n1 @$\rightarrow$@ insertNode tree1 s n1 next))
+
+-- 以下省略
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeProof.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeProof.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,34 @@
+redBlackInSomeState : { m : Level } (a : Set Level.zero) (n : Maybe (Node a ℕ)) {t : Set m} -> RedBlackTree {Level.zero} {m} {t} a ℕ
+redBlackInSomeState {m} a n {t} = record { root = n ; nodeStack = emptySingleLinkedStack ; compare = compare2 }
+
+putTest1 :{ m : Level } (n : Maybe (Node ℕ ℕ))
+ -> (k : ℕ) (x : ℕ)
+ -> putTree1 {_} {_} {ℕ} {ℕ} (redBlackInSomeState {_} ℕ n {Set Level.zero}) k x
+ (\ t -> getRedBlackTree t k (\ t x1 -> check2 x1 x ≡ True))
+putTest1 n k x with n
+... | Just n1 = lemma2 ( record { top = Nothing } )
+ where
+ lemma2 : (s : SingleLinkedStack (Node ℕ ℕ) ) -> putTree1 (record { root = Just n1 ; nodeStack = s ; compare = compare2 }) k x (λ t →
+ GetRedBlackTree.checkNode t k (λ t₁ x1 → check2 x1 x ≡ True) (root t))
+ lemma2 s with compare2 k (key n1)
+ ... | EQ = lemma3 {!!}
+ where
+ lemma3 : compare2 k (key n1) ≡ EQ -> getRedBlackTree {_} {_} {ℕ} {ℕ} {Set Level.zero} ( record { root = Just ( record {
+ key = key n1 ; value = x ; right = right n1 ; left = left n1 ; color = Black
+ } ) ; nodeStack = s ; compare = λ x₁ y → compare2 x₁ y } ) k ( \ t x1 -> check2 x1 x ≡ True)
+ lemma3 eq with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl with compare2 k (key n1) | eq
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
+ ... | GT = {!!}
+ ... | LT = {!!}
+
+... | Nothing = lemma1
+ where
+ lemma1 : getRedBlackTree {_} {_} {ℕ} {ℕ} {Set Level.zero} ( record { root = Just ( record {
+ key = k ; value = x ; right = Nothing ; left = Nothing ; color = Red
+ } ) ; nodeStack = record { top = Nothing } ; compare = λ x₁ y → compare2 x₁ y } ) k
+ ( \ t x1 -> check2 x1 x ≡ True)
+ lemma1 with compare2 k k | putTest1Lemma2 k
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeProof.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeProof.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,34 @@
+redBlackInSomeState : { m : Level } (a : Set Level.zero) (n : Maybe (Node a @$\mathbb{N}$@)) {t : Set m} @$\rightarrow$@ RedBlackTree {Level.zero} {m} {t} a @$\mathbb{N}$@
+redBlackInSomeState {m} a n {t} = record { root = n ; nodeStack = emptySingleLinkedStack ; compare = compare2 }
+
+putTest1 :{ m : Level } (n : Maybe (Node @$\mathbb{N}$@ @$\mathbb{N}$@))
+ @$\rightarrow$@ (k : @$\mathbb{N}$@) (x : @$\mathbb{N}$@)
+ @$\rightarrow$@ putTree1 {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} (redBlackInSomeState {_} @$\mathbb{N}$@ n {Set Level.zero}) k x
+ (\ t @$\rightarrow$@ getRedBlackTree t k (\ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True))
+putTest1 n k x with n
+... | Just n1 = lemma2 ( record { top = Nothing } )
+ where
+ lemma2 : (s : SingleLinkedStack (Node @$\mathbb{N}$@ @$\mathbb{N}$@) ) @$\rightarrow$@ putTree1 (record { root = Just n1 ; nodeStack = s ; compare = compare2 }) k x (λ t →
+ GetRedBlackTree.checkNode t k (λ t@$\text{1}$@ x1 → check2 x1 x @$\equiv$@ True) (root t))
+ lemma2 s with compare2 k (key n1)
+ ... | EQ = lemma3 {!!}
+ where
+ lemma3 : compare2 k (key n1) @$\equiv$@ EQ @$\rightarrow$@ getRedBlackTree {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} {Set Level.zero} ( record { root = Just ( record {
+ key = key n1 ; value = x ; right = right n1 ; left = left n1 ; color = Black
+ } ) ; nodeStack = s ; compare = λ x@$\text{1}$@ y → compare2 x@$\text{1}$@ y } ) k ( \ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True)
+ lemma3 eq with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl with compare2 k (key n1) | eq
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
+ ... | GT = {!!}
+ ... | LT = {!!}
+
+... | Nothing = lemma1
+ where
+ lemma1 : getRedBlackTree {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} {Set Level.zero} ( record { root = Just ( record {
+ key = k ; value = x ; right = Nothing ; left = Nothing ; color = Red
+ } ) ; nodeStack = record { top = Nothing } ; compare = λ x@$\text{1}$@ y → compare2 x@$\text{1}$@ y } ) k
+ ( \ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True)
+ lemma1 with compare2 k k | putTest1Lemma2 k
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTreeTest.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTreeTest.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,6 @@
+test31 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ ) 1 1
+$ \t -> putTree1 t 2 2
+$ \t -> putTree1 t 3 3
+$ \t -> putTree1 t 4 4
+$ \t -> getRedBlackTree t 4
+$ \t x -> x
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaTypeClass.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaTypeClass.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+record Eq (A : Set) : Set where
+ field
+ _==_ : A -> A -> Bool
diff -r 000000000000 -r 83f997abf3b5 final_main/src/AgdaWhere.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/AgdaWhere.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+f : Int -> Int -> Int
+f a b c = (t a) + (t b) + (t c)
+ where
+ t x = x + x + x
+
+f' : Int -> Int -> Int
+f' a b c = (a + a + a) + (b + b + b) + (c + c + c)
diff -r 000000000000 -r 83f997abf3b5 final_main/src/CodeSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/CodeSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,2 @@
+data CodeSegment {l1 l2 : Level} (I : Set l1) (O : Set l2) : Set (l ⊔ l1 ⊔ l2) where
+ cs : (I -> O) -> CodeSegment I O
diff -r 000000000000 -r 83f997abf3b5 final_main/src/CodeSegment.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/CodeSegment.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,2 @@
+data CodeSegment {l1 l2 : Level} (I : Set l1) (O : Set l2) : Set (l @$\sqcup$@ l1 @$\sqcup$@ l2) where
+ cs : (I @$\rightarrow$@ O) @$\rightarrow$@ CodeSegment I O
diff -r 000000000000 -r 83f997abf3b5 final_main/src/CodeSegments.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/CodeSegments.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,12 @@
+cs2 : CodeSegment ds1 ds1
+cs2 = cs id
+
+cs1 : CodeSegment ds1 ds1
+cs1 = cs (\d -> goto cs2 d)
+
+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})
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/DataSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/DataSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+record ds0 : Set where
+ field
+ a : Int
+ b : Int
+
+record ds1 : Set where
+ field
+ c : Int
diff -r 000000000000 -r 83f997abf3b5 final_main/src/DataSegment.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/DataSegment.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+record ds0 : Set where
+ field
+ a : Int
+ b : Int
+
+record ds1 : Set where
+ field
+ c : Int
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Eq.Agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Eq.Agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,30 @@
+module Eq where
+open import Data.Nat
+open import Data.Bool
+open import Data.List
+
+record Eq (A : Set) : Set where
+ field
+ _==_ : A -> A -> Bool
+
+_==Nat_ : ℕ -> ℕ -> Bool
+zero ==Nat zero = true
+(suc n) ==Nat zero = false
+zero ==Nat (suc m) = false
+(suc n) ==Nat (suc m) = n ==Nat m
+
+
+instance
+ _ : Eq ℕ
+ _ = record { _==_ = _==Nat_}
+
+_||_ : Bool -> Bool -> Bool
+true || _ = true
+false || x = x
+
+elem : {A : Set} {{eqA : Eq A}} → A → List A → Bool
+elem {{eqA}} x (y ∷ xs) = (Eq._==_ eqA x y) || (elem {{eqA}} x xs)
+elem x [] = false
+
+listHas4 : Bool
+listHas4 = elem 4 (3 ∷ 2 ∷ 5 ∷ 4 ∷ []) -- true
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Equiv.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Equiv.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,1 @@
+data _≡_ {a} {A : Set a} (x : A) : A → Set a where
refl : x ≡ x
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Exec.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Exec.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,5 @@
+exec : {l1 l2 : Level} {I : Set l1} {O : Set l2}
+ {{_ : DataSegment I}} {{_ : DataSegment O}}
+ -> CodeSegment I O -> Context -> Context
+exec {l} {{i}} {{o}} (cs b) c = set o c (b (get i c))
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Goto.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Goto.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,4 @@
+goto : {l1 l2 : Level} {I : Set l1} {O : Set l2}
+ -> CodeSegment I O -> I -> O
+goto (cs b) i = b i
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Goto.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Goto.agda.replaced Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,4 @@
+goto : {l1 l2 : Level} {I : Set l1} {O : Set l2}
+ @$\rightarrow$@ CodeSegment I O @$\rightarrow$@ I @$\rightarrow$@ O
+goto (cs b) i = b i
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Maybe.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Maybe.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,3 @@
+data Maybe {a} (A : Set a) : Set a where
+ just : (x : A) -> Maybe A
+ nothing : Maybe A
diff -r 000000000000 -r 83f997abf3b5 final_main/src/MetaCodeSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/MetaCodeSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,4 @@
+data CodeSegment {l1 l2 : Level} (A : Set l1) (B : Set l2) : Set (l ⊔ l1 ⊔ l2) where
+ cs : {{_ : DataSegment A}} {{_ : DataSegment B}}
+ -> (A -> B) -> CodeSegment A B
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/MetaDataSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/MetaDataSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+module subtype {l : Level} (Context : Set l) where
+
+record DataSegment {ll : Level} (A : Set ll) : Set (l ⊔ ll) where
+ field
+ get : Context -> A
+ set : Context -> A -> Context
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/MetaMetaCodeSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/MetaMetaCodeSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,29 @@
+-- meta level
+liftContext : {X Y : Set} {{_ : N.DataSegment X}} {{_ : N.DataSegment Y}} -> N.CodeSegment X Y -> N.CodeSegment Context Context
+liftContext {{x}} {{y}} (N.cs f) = N.cs (\c -> N.DataSegment.set y c (f (N.DataSegment.get x c)))
+
+liftMeta : {X Y : Set} {{_ : M.DataSegment X}} {{_ : M.DataSegment Y}} -> N.CodeSegment X Y -> M.CodeSegment X Y
+liftMeta (N.cs f) = M.cs f
+
+gotoMeta : {I O : Set} {{_ : N.DataSegment I}} {{_ : N.DataSegment O}} -> M.CodeSegment Meta Meta -> N.CodeSegment I O -> Meta -> Meta
+gotoMeta mCode code m = M.exec mCode (record m {next = (liftContext code)})
+
+push : M.CodeSegment Meta Meta
+push = M.cs (\m -> M.exec (liftMeta (Meta.next m)) (record m {c' = Context.c (Meta.context m)}))
+
+-- normal level
+
+cs2 : N.CodeSegment ds1 ds1
+cs2 = N.cs id
+
+cs1 : N.CodeSegment ds1 ds1
+cs1 = N.cs (\d -> N.goto cs2 d)
+
+cs0 : N.CodeSegment ds0 ds1
+cs0 = N.cs (\d -> N.goto cs1 (record {c = (ds0.a d) + (ds0.b d)}))
+
+-- meta level (with extended normal)
+main : Meta
+main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70}) ; c' = 0 ; next = (N.cs id)})
+-- record {context = record {a = 100 ; b = 50 ; c = 150} ; c' = 70 ; next = (N.cs id)}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/MetaMetaDataSegment.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/MetaMetaDataSegment.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,12 @@
+-- 上で各 DataSegement の定義を行なっているとする
+open import subtype Context as N -- Meta Datasegment を定義
+
+-- Meta DataSegment を持つ Meta Meta DataSegment を定義できる
+record Meta : Set where
+ field
+ context : Context
+ c' : Int
+ next : N.CodeSegment Context Context
+
+open import subtype Meta as M
+-- 以下よりメタメタレベルのプログラムを記述できる
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Nat.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Nat.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,5 @@
+module nat where
+
+data Nat : Set where
+ O : Nat
+ S : Nat -> Nat
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/src/NatAdd.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/NatAdd.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,6 @@
+open import nat
+module nat_add where
+
+_+_ : Nat -> Nat -> Nat
+O + m = m
+(S n) + m = S (n + m)
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/src/NatAddSym.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/NatAddSym.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,12 @@
+open import Relation.Binary.PropositionalEquality
+open import nat
+open import nat_add
+open ≡-Reasoning
+
+module nat_add_sym where
+
+addSym : (n m : Nat) -> n + m ≡ m + n
+addSym O O = refl
+addSym O (S m) = cong S (addSym O m)
+addSym (S n) O = cong S (addSym n O)
+addSym (S n) (S m) = {!!} -- 後述
diff -r 000000000000 -r 83f997abf3b5 final_main/src/PushPopType.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/PushPopType.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,9 @@
+pushOnce : Meta -> Meta
+pushOnce m = M.exec pushSingleLinkedStackCS m
+
+popOnce : Meta -> Meta
+popOnce m = M.exec popSingleLinkedStackCS m
+
+push-pop-type : Meta -> Set₁
+push-pop-type meta =
+ M.exec (M.csComp (M.cs popOnce) (M.cs pushOnce)) meta ≡ meta
diff -r 000000000000 -r 83f997abf3b5 final_main/src/Reasoning.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/Reasoning.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,21 @@
+open import Relation.Binary.PropositionalEquality
+open import nat
+open import nat_add
+open ≡-Reasoning
+
+module nat_add_sym_reasoning where
+
+addToRight : (n m : Nat) -> S (n + m) ≡ n + (S m)
+addToRight O m = refl
+addToRight (S n) m = cong S (addToRight n m)
+
+addSym : (n m : Nat) -> n + m ≡ m + n
+addSym O O = refl
+addSym O (S m) = cong S (addSym O m)
+addSym (S n) O = cong S (addSym n O)
+addSym (S n) (S m) = begin
+ (S n) + (S m) ≡⟨ refl ⟩
+ S (n + S m) ≡⟨ cong S (addSym n (S m)) ⟩
+ S ((S m) + n) ≡⟨ addToRight (S m) n ⟩
+ S (m + S n) ≡⟨ refl ⟩
+ (S m) + (S n) ∎
diff -r 000000000000 -r 83f997abf3b5 final_main/src/RedBlackTree.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/RedBlackTree.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,231 @@
+module RedBlackTree where
+
+open import stack
+open import Level hiding (zero)
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ putImpl : treeImpl -> a -> (treeImpl -> t) -> t
+ getImpl : treeImpl -> (treeImpl -> Maybe a -> t) -> t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a -> (Tree treeImpl -> t) -> t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 -> next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl -> Maybe a -> t) -> t
+ getTree next = getImpl (treeMethods ) tree (\t1 d -> next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+
+open Tree
+
+data Color {n : Level } : Set n where
+ Red : Color
+ Black : Color
+
+data CompareResult {n : Level } : Set n where
+ LT : CompareResult
+ GT : CompareResult
+ EQ : CompareResult
+
+record Node {n : Level } (a k : Set n) : Set n where
+ inductive
+ field
+ key : k
+ value : a
+ right : Maybe (Node a k)
+ left : Maybe (Node a k)
+ color : Color {n}
+open Node
+
+record RedBlackTree {n m : Level } {t : Set m} (a k : Set n) : Set (m Level.⊔ n) where
+ field
+ root : Maybe (Node a k)
+ nodeStack : SingleLinkedStack (Node a k)
+ compare : k -> k -> CompareResult {n}
+
+open RedBlackTree
+
+open SingleLinkedStack
+
+--
+-- put new node at parent node, and rebuild tree to the top
+--
+{-# TERMINATING #-} -- https://agda.readthedocs.io/en/v2.5.3/language/termination-checking.html
+replaceNode : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+replaceNode {n} {m} {t} {a} {k} tree s n0 next = popSingleLinkedStack s (
+ \s parent -> replaceNode1 s parent)
+ where
+ replaceNode1 : SingleLinkedStack (Node a k) -> Maybe ( Node a k ) -> t
+ replaceNode1 s Nothing = next ( record tree { root = Just (record n0 { color = Black}) } )
+ replaceNode1 s (Just n1) with compare tree (key n1) (key n0)
+ ... | EQ = replaceNode tree s ( record n1 { value = value n0 ; left = left n0 ; right = right n0 } ) next
+ ... | GT = replaceNode tree s ( record n1 { left = Just n0 } ) next
+ ... | LT = replaceNode tree s ( record n1 { right = Just n0 } ) next
+
+
+rotateRight : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) ->
+ (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> t) -> t
+rotateRight {n} {m} {t} {a} {k} tree s n0 parent rotateNext = getSingleLinkedStack s (\ s n0 -> rotateRight1 tree s n0 parent rotateNext)
+ where
+ rotateRight1 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) ->
+ (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> t) -> t
+ rotateRight1 {n} {m} {t} {a} {k} tree s n0 parent rotateNext with n0
+ ... | Nothing = rotateNext tree s Nothing n0
+ ... | Just n1 with parent
+ ... | Nothing = rotateNext tree s (Just n1 ) n0
+ ... | Just parent1 with left parent1
+ ... | Nothing = rotateNext tree s (Just n1) Nothing
+ ... | Just leftParent with compare tree (key n1) (key leftParent)
+ ... | EQ = rotateNext tree s (Just n1) parent
+ ... | _ = rotateNext tree s (Just n1) parent
+
+
+rotateLeft : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) ->
+ (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> t) -> t
+rotateLeft {n} {m} {t} {a} {k} tree s n0 parent rotateNext = getSingleLinkedStack s (\ s n0 -> rotateLeft1 tree s n0 parent rotateNext)
+ where
+ rotateLeft1 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) ->
+ (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> t) -> t
+ rotateLeft1 {n} {m} {t} {a} {k} tree s n0 parent rotateNext with n0
+ ... | Nothing = rotateNext tree s Nothing n0
+ ... | Just n1 with parent
+ ... | Nothing = rotateNext tree s (Just n1) Nothing
+ ... | Just parent1 with right parent1
+ ... | Nothing = rotateNext tree s (Just n1) Nothing
+ ... | Just rightParent with compare tree (key n1) (key rightParent)
+ ... | EQ = rotateNext tree s (Just n1) parent
+ ... | _ = rotateNext tree s (Just n1) parent
+
+{-# TERMINATING #-}
+insertCase5 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Node a k -> Node a k -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+insertCase5 {n} {m} {t} {a} {k} tree s n0 parent grandParent next = pop2SingleLinkedStack s (\ s parent grandParent -> insertCase51 tree s n0 parent grandParent next)
+ where
+ insertCase51 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+ insertCase51 {n} {m} {t} {a} {k} tree s n0 parent grandParent next with n0
+ ... | Nothing = next tree
+ ... | Just n1 with parent | grandParent
+ ... | Nothing | _ = next tree
+ ... | _ | Nothing = next tree
+ ... | Just parent1 | Just grandParent1 with left parent1 | left grandParent1
+ ... | Nothing | _ = next tree
+ ... | _ | Nothing = next tree
+ ... | Just leftParent1 | Just leftGrandParent1
+ with compare tree (key n1) (key leftParent1) | compare tree (key leftParent1) (key leftGrandParent1)
+ ... | EQ | EQ = rotateRight tree s n0 parent
+ (\ tree s n0 parent -> insertCase5 tree s n0 parent1 grandParent1 next)
+ ... | _ | _ = rotateLeft tree s n0 parent
+ (\ tree s n0 parent -> insertCase5 tree s n0 parent1 grandParent1 next)
+
+insertCase4 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> Node a k -> Node a k -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+insertCase4 {n} {m} {t} {a} {k} tree s n0 parent grandParent next
+ with (right parent) | (left grandParent)
+... | Nothing | _ = insertCase5 tree s (Just n0) parent grandParent next
+... | _ | Nothing = insertCase5 tree s (Just n0) parent grandParent next
+... | Just rightParent | Just leftGrandParent with compare tree (key n0) (key rightParent) | compare tree (key parent) (key leftGrandParent)
+... | EQ | EQ = popSingleLinkedStack s (\ s n1 -> rotateLeft tree s (left n0) (Just grandParent)
+ (\ tree s n0 parent -> insertCase5 tree s n0 rightParent grandParent next))
+... | _ | _ = insertCase41 tree s n0 parent grandParent next
+ where
+ insertCase41 : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> Node a k -> Node a k -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+ insertCase41 {n} {m} {t} {a} {k} tree s n0 parent grandParent next
+ with (left parent) | (right grandParent)
+ ... | Nothing | _ = insertCase5 tree s (Just n0) parent grandParent next
+ ... | _ | Nothing = insertCase5 tree s (Just n0) parent grandParent next
+ ... | Just leftParent | Just rightGrandParent with compare tree (key n0) (key leftParent) | compare tree (key parent) (key rightGrandParent)
+ ... | EQ | EQ = popSingleLinkedStack s (\ s n1 -> rotateRight tree s (right n0) (Just grandParent)
+ (\ tree s n0 parent -> insertCase5 tree s n0 leftParent grandParent next))
+ ... | _ | _ = insertCase5 tree s (Just n0) parent grandParent next
+
+colorNode : {n : Level } {a k : Set n} -> Node a k -> Color -> Node a k
+colorNode old c = record old { color = c }
+
+{-# TERMINATING #-}
+insertNode : {n m : Level } {t : Set m } {a k : Set n} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+insertNode {n} {m} {t} {a} {k} tree s n0 next = get2SingleLinkedStack s (insertCase1 n0)
+ where
+ insertCase1 : Node a k -> SingleLinkedStack (Node a k) -> Maybe (Node a k) -> Maybe (Node a k) -> t -- placed here to allow mutual recursion
+ -- http://agda.readthedocs.io/en/v2.5.2/language/mutual-recursion.html
+ insertCase3 : SingleLinkedStack (Node a k) -> Node a k -> Node a k -> Node a k -> t
+ insertCase3 s n0 parent grandParent with left grandParent | right grandParent
+ ... | Nothing | Nothing = insertCase4 tree s n0 parent grandParent next
+ ... | Nothing | Just uncle = insertCase4 tree s n0 parent grandParent next
+ ... | Just uncle | _ with compare tree ( key uncle ) ( key parent )
+ ... | EQ = insertCase4 tree s n0 parent grandParent next
+ ... | _ with color uncle
+ ... | Red = pop2SingleLinkedStack s ( \s p0 p1 -> insertCase1 (
+ record grandParent { color = Red ; left = Just ( record parent { color = Black } ) ; right = Just ( record uncle { color = Black } ) }) s p0 p1 )
+ ... | Black = insertCase4 tree s n0 parent grandParent next
+ insertCase2 : SingleLinkedStack (Node a k) -> Node a k -> Node a k -> Node a k -> t
+ insertCase2 s n0 parent grandParent with color parent
+ ... | Black = replaceNode tree s n0 next
+ ... | Red = insertCase3 s n0 parent grandParent
+ insertCase1 n0 s Nothing Nothing = next tree
+ insertCase1 n0 s Nothing (Just grandParent) = next tree
+ insertCase1 n0 s (Just parent) Nothing = replaceNode tree s (colorNode n0 Black) next
+ insertCase1 n0 s (Just parent) (Just grandParent) = insertCase2 s n0 parent grandParent
+
+----
+-- find node potition to insert or to delete, the path will be in the stack
+--
+findNode : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> (Node a k) -> (Node a k) -> (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> t) -> t
+findNode {n} {m} {a} {k} {t} tree s n0 n1 next = pushSingleLinkedStack s n1 (\ s -> findNode1 s n1)
+ where
+ findNode2 : SingleLinkedStack (Node a k) -> (Maybe (Node a k)) -> t
+ findNode2 s Nothing = next tree s n0
+ findNode2 s (Just n) = findNode tree s n0 n next
+ findNode1 : SingleLinkedStack (Node a k) -> (Node a k) -> t
+ findNode1 s n1 with (compare tree (key n0) (key n1))
+ ... | EQ = popSingleLinkedStack s ( \s _ -> next tree s (record n1 { key = key n1 ; value = value n0 } ) )
+ ... | GT = findNode2 s (right n1)
+ ... | LT = findNode2 s (left n1)
+
+
+leafNode : {n : Level } {a k : Set n} -> k -> a -> Node a k
+leafNode k1 value = record {
+ key = k1 ;
+ value = value ;
+ right = Nothing ;
+ left = Nothing ;
+ color = Red
+ }
+
+putRedBlackTree : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> k -> a -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+putRedBlackTree {n} {m} {a} {k} {t} tree k1 value next with (root tree)
+... | Nothing = next (record tree {root = Just (leafNode k1 value) })
+... | Just n2 = clearSingleLinkedStack (nodeStack tree) (\ s -> findNode tree s (leafNode k1 value) n2 (\ tree1 s n1 -> insertNode tree1 s n1 next))
+
+getRedBlackTree : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> k -> (RedBlackTree {n} {m} {t} a k -> (Maybe (Node a k)) -> t) -> t
+getRedBlackTree {_} {_} {a} {k} {t} tree k1 cs = checkNode (root tree)
+ module GetRedBlackTree where -- http://agda.readthedocs.io/en/v2.5.2/language/let-and-where.html
+ search : Node a k -> t
+ checkNode : Maybe (Node a k) -> t
+ checkNode Nothing = cs tree Nothing
+ checkNode (Just n) = search n
+ search n with compare tree k1 (key n)
+ search n | LT = checkNode (left n)
+ search n | GT = checkNode (right n)
+ search n | EQ = cs tree (Just n)
+
+open import Data.Nat hiding (compare)
+
+compareℕ : ℕ → ℕ → CompareResult {Level.zero}
+compareℕ x y with Data.Nat.compare x y
+... | less _ _ = LT
+... | equal _ = EQ
+... | greater _ _ = GT
+
+compare2 : (x y : ℕ ) -> CompareResult {Level.zero}
+compare2 zero zero = EQ
+compare2 (suc _) zero = GT
+compare2 zero (suc _) = LT
+compare2 (suc x) (suc y) = compare2 x y
+
+
+createEmptyRedBlackTreeℕ : { m : Level } (a : Set Level.zero) {t : Set m} -> RedBlackTree {Level.zero} {m} {t} a ℕ
+createEmptyRedBlackTreeℕ {m} a {t} = record {
+ root = Nothing
+ ; nodeStack = emptySingleLinkedStack
+ ; compare = compare2
+ }
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/RedBlackTree.agdai
Binary file final_main/src/RedBlackTree.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/SingleLinkedStack.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/SingleLinkedStack.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,110 @@
+#include "../context.h"
+#include "../origin_cs.h"
+#include
+
+// typedef struct SingleLinkedStack {
+// struct Element* top;
+// } SingleLinkedStack;
+
+Stack* createSingleLinkedStack(struct Context* context) {
+ struct Stack* stack = new Stack();
+ struct SingleLinkedStack* singleLinkedStack = new SingleLinkedStack();
+ stack->stack = (union Data*)singleLinkedStack;
+ singleLinkedStack->top = NULL;
+ stack->push = C_pushSingleLinkedStack;
+ stack->pop = C_popSingleLinkedStack;
+ stack->pop2 = C_pop2SingleLinkedStack;
+ stack->get = C_getSingleLinkedStack;
+ stack->get2 = C_get2SingleLinkedStack;
+ stack->isEmpty = C_isEmptySingleLinkedStack;
+ stack->clear = C_clearSingleLinkedStack;
+ return stack;
+}
+
+void printStack1(union Data* data) {
+ struct Node* node = &data->Element.data->Node;
+ if (node == NULL) {
+ printf("NULL");
+ } else {
+ printf("key = %d ,", node->key);
+ printStack1((union Data*)data->Element.next);
+ }
+}
+
+void printStack(union Data* data) {
+ printStack1(data);
+ printf("\n");
+}
+
+__code clearSingleLinkedStack(struct SingleLinkedStack* stack,__code next(...)) {
+ stack->top = NULL;
+ goto next(...);
+}
+
+__code pushSingleLinkedStack(struct SingleLinkedStack* stack,union Data* data, __code next(...)) {
+ Element* element = new Element();
+ element->next = stack->top;
+ element->data = data;
+ stack->top = element;
+ goto next(...);
+}
+
+__code popSingleLinkedStack(struct SingleLinkedStack* stack, __code next(union Data* data, ...)) {
+ if (stack->top) {
+ data = stack->top->data;
+ stack->top = stack->top->next;
+ } else {
+ data = NULL;
+ }
+ goto next(data, ...);
+}
+
+__code pop2SingleLinkedStack(struct SingleLinkedStack* stack, __code next(union Data* data, union Data* data1, ...)) {
+ if (stack->top) {
+ data = stack->top->data;
+ stack->top = stack->top->next;
+ } else {
+ data = NULL;
+ }
+ if (stack->top) {
+ data1 = stack->top->data;
+ stack->top = stack->top->next;
+ } else {
+ data1 = NULL;
+ }
+ goto next(data, data1, ...);
+}
+
+
+__code getSingleLinkedStack(struct SingleLinkedStack* stack, __code next(union Data* data, ...)) {
+ if (stack->top)
+ data = stack->top->data;
+ else
+ data = NULL;
+ goto next(data, ...);
+}
+
+__code get2SingleLinkedStack(struct SingleLinkedStack* stack, __code next(union Data* data, union Data* data1, ...)) {
+ if (stack->top) {
+ data = stack->top->data;
+ if (stack->top->next) {
+ data1 = stack->top->next->data;
+ } else {
+ data1 = NULL;
+ }
+ } else {
+ data = NULL;
+ data1 = NULL;
+ }
+ goto next(data, data1, ...);
+}
+
+__code isEmptySingleLinkedStack(struct SingleLinkedStack* stack, __code next(...), __code whenEmpty(...)) {
+ if (stack->top)
+ goto next(...);
+ else
+ goto whenEmpty(...);
+}
+
+
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/ThreePlusOne.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/ThreePlusOne.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+open import Relation.Binary.PropositionalEquality
+open import nat
+open import nat_add
+
+module three_plus_one where
+
+3+1 : (S (S (S O))) + (S O) ≡ (S (S (S (S O))))
+3+1 = refl
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/src/akashaContext.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/akashaContext.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,31 @@
+// Data Segment
+union Data {
+ struct Tree { /* ... 赤黒木の定義と同様 */ } tree;
+ struct Node { /* ... 赤黒木の定義と同様 */ } node;
+
+ /* for verification */
+ struct IterElem {
+ unsigned int val;
+ struct IterElem* next;
+ } iterElem;
+ struct Iterator {
+ struct Tree* tree;
+ struct Iterator* previousDepth;
+ struct IterElem* head;
+ struct IterElem* last;
+ unsigned int iteratedValue;
+ unsigned long iteratedPointDataNum;
+ void* iteratedPointHeap;
+ } iterator;
+ struct AkashaInfo {
+ unsigned int minHeight;
+ unsigned int maxHeight;
+ struct AkashaNode* akashaNode;
+ } akashaInfo;
+ struct AkashaNode {
+ unsigned int height;
+ struct Node* node;
+ struct AkashaNode* nextAkashaNode;
+ } akashaNode;
+};
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/akashaMeta.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/akashaMeta.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,31 @@
+__code meta(struct Context* context, enum Code next) {
+ struct Iterator* iter = &context->data[Iter]->iterator;
+
+ switch (context->prev) {
+ case GoToPreviousDepth:
+ if (iter->iteratedPointDataNum == 0) break;
+ if (iter->iteratedPointHeap == NULL) break;
+
+ unsigned int diff =(unsigned long)context->heap - (unsigned long)iter->iteratedPointHeap;
+ memset(iter->iteratedPointHeap, 0, diff);
+ context->dataNum = iter->iteratedPointDataNum;
+ context->heap = iter->iteratedPointHeap;
+ break;
+ default:
+ break;
+ }
+ switch (next) {
+ case PutAndGoToNextDepth: // with assert check
+ if (context->prev == GoToPreviousDepth) break;
+ if (iter->previousDepth == NULL) break;
+ iter->previousDepth->iteratedPointDataNum = context->dataNum;
+ iter->previousDepth->iteratedPointHeap = context->heap;
+ break;
+ default:
+ break;
+ }
+
+ context->prev = next;
+ goto (context->code[next])(context);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/assert.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/assert.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+__code verifySpecificationFinish(struct Context* context) {
+ if (context->data[AkashaInfo]->akashaInfo.maxHeight > 2*context->data[AkashaInfo]->akashaInfo.minHeight) {
+ context->next = Exit;
+ goto meta(context, ShowTrace);
+ }
+ goto meta(context, DuplicateIterator);
+}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/atton-master-meta-sample.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/atton-master-meta-sample.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,77 @@
+module atton-master-meta-sample where
+
+open import Data.Nat
+open import Data.Unit
+open import Function
+Int = ℕ
+
+record Context : Set where
+ field
+ a : Int
+ b : Int
+ c : Int
+
+open import subtype Context as N
+
+record Meta : Set where
+ field
+ context : Context
+ c' : Int
+ next : N.CodeSegment Context Context
+
+open import subtype Meta as M
+
+instance
+ _ : N.DataSegment Context
+ _ = record { get = id ; set = (\_ c -> c) }
+ _ : M.DataSegment Context
+ _ = record { get = (\m -> Meta.context m) ;
+ set = (\m c -> record m {context = c}) }
+ _ : M.DataSegment Meta
+ _ = record { get = id ; set = (\_ m -> m) }
+
+
+liftContext : {X Y : Set} {{_ : N.DataSegment X}} {{_ : N.DataSegment Y}} -> N.CodeSegment X Y -> N.CodeSegment Context Context
+liftContext {{x}} {{y}} (N.cs f) = N.cs (\c -> N.DataSegment.set y c (f (N.DataSegment.get x c)))
+
+liftMeta : {X Y : Set} {{_ : M.DataSegment X}} {{_ : M.DataSegment Y}} -> N.CodeSegment X Y -> M.CodeSegment X Y
+liftMeta (N.cs f) = M.cs f
+
+
+gotoMeta : {I O : Set} {{_ : N.DataSegment I}} {{_ : N.DataSegment O}} -> M.CodeSegment Meta Meta -> N.CodeSegment I O -> Meta -> Meta
+gotoMeta mCode code m = M.exec mCode (record m {next = (liftContext code)})
+
+push : M.CodeSegment Meta Meta
+push = M.cs (\m -> M.exec (liftMeta (Meta.next m)) (record m {c' = Context.c (Meta.context m)}))
+
+
+record ds0 : Set where
+ field
+ a : Int
+ b : Int
+
+record ds1 : Set where
+ field
+ c : Int
+
+instance
+ _ : N.DataSegment ds0
+ _ = record { set = (\c d -> record c {a = (ds0.a d) ; b = (ds0.b d)})
+ ; get = (\c -> record { a = (Context.a c) ; b = (Context.b c)})}
+ _ : N.DataSegment ds1
+ _ = record { set = (\c d -> record c {c = (ds1.c d)})
+ ; get = (\c -> record { c = (Context.c c)})}
+
+cs2 : N.CodeSegment ds1 ds1
+cs2 = N.cs id
+
+cs1 : N.CodeSegment ds1 ds1
+cs1 = N.cs (\d -> N.goto cs2 d)
+
+cs0 : N.CodeSegment ds0 ds1
+cs0 = N.cs (\d -> N.goto cs1 (record {c = (ds0.a d) + (ds0.b d)}))
+
+
+main : Meta
+main = gotoMeta push cs0 (record {context = (record {a = 100 ; b = 50 ; c = 70}) ; c' = 0 ; next = (N.cs id)})
+-- record {context = record {a = 100 ; b = 50 ; c = 150} ; c' = 70 ; next = (N.cs id)}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/atton-master-sample.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/atton-master-sample.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,46 @@
+module atton-master-sample where
+
+open import Data.Nat
+open import Data.Unit
+open import Function
+Int = ℕ
+
+record Context : Set where
+ field
+ a : Int
+ b : Int
+ c : Int
+
+
+open import subtype Context
+
+
+
+record ds0 : Set where
+ field
+ a : Int
+ b : Int
+
+record ds1 : Set where
+ field
+ c : Int
+
+instance
+ _ : DataSegment ds0
+ _ = record { set = (\c d -> record c {a = (ds0.a d) ; b = (ds0.b d)})
+ ; get = (\c -> record { a = (Context.a c) ; b = (Context.b c)})}
+ _ : DataSegment ds1
+ _ = record { set = (\c d -> record c {c = (ds1.c d)})
+ ; get = (\c -> record { c = (Context.c c)})}
+
+cs2 : CodeSegment ds1 ds1
+cs2 = cs id
+
+cs1 : CodeSegment ds1 ds1
+cs1 = cs (\d -> goto cs2 d)
+
+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})
diff -r 000000000000 -r 83f997abf3b5 final_main/src/cbmc-assert.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/cbmc-assert.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+void verifySpecification(struct Context* context,
+ struct Tree* tree) {
+ assert(!(maxHeight(tree->root, 1) >
+ 2*minHeight(tree->root, 1)));
+ return meta(context, EnumerateInputs);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/context.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/context.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,47 @@
+/* Context definition */
+
+#define ALLOCATE_SIZE 1024
+
+enum Code {
+ Code1,
+ Code2,
+ Allocator,
+};
+
+enum UniqueData {
+ Allocate,
+ Tree,
+};
+
+struct Context {
+ int codeNum;
+ __code (**code) (struct Context *);
+ void* heap_start;
+ void* heap;
+ long dataSize;
+ int dataNum;
+ union Data **data;
+};
+
+union Data {
+ struct Tree {
+ union Data* root;
+ union Data* current;
+ union Data* prev;
+ int result;
+ } tree;
+ struct Node {
+ int key;
+ int value;
+ enum Color {
+ Red,
+ Black,
+ } color;
+ union Data* left;
+ union Data* right;
+ } node;
+ struct Allocate {
+ long size;
+ enum Code next;
+ } allocate;
+};
diff -r 000000000000 -r 83f997abf3b5 final_main/src/enumerate-inputs.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/enumerate-inputs.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,13 @@
+void enumerateInputs(struct Context* context,
+ struct Node* node) {
+ if (context->loopCount > LIMIT_OF_VERIFICATION_SIZE) {
+ return meta(context, Exit);
+ }
+
+ node->key = nondet_int();
+ node->value = node->key;
+ context->next = VerifySpecification;
+ context->loopCount++;
+
+ return meta(context, Put);
+}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/escape_agda.rb
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/escape_agda.rb Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,28 @@
+#!/usr/bin/env ruby
+# coding: utf-8
+
+Suffix = '.agda.replaced'
+EscapeChar = '@'
+FileName = ARGV.first
+
+ReplaceTable = {
+ '->' => 'rightarrow',
+ '⊔' => 'sqcup',
+ '∷' => 'text{::}',
+ '∙' => 'circ',
+ '≡' => 'equiv',
+ '×' => 'times',
+ '⟨' => 'langle',
+ '⟩' => 'rangle',
+ '₁' => 'text{1}',
+ 'ℕ' => 'mathbb{N}',
+ '∎' => 'blacksquare'
+}
+
+code = File.read(FileName)
+ReplaceTable.each do |k, v|
+ escaped_str = EscapeChar + "$\\#{v}$" + EscapeChar
+ code = code.gsub(k, escaped_str)
+end
+
+File.write(FileName.sub(/.agda$/, Suffix), code)
diff -r 000000000000 -r 83f997abf3b5 final_main/src/expr-term.txt
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/expr-term.txt Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,8 @@
+t ::=
+ true
+ false
+ if t then t else t
+ 0
+ succ t
+ pred t
+ iszero t
diff -r 000000000000 -r 83f997abf3b5 final_main/src/factrial.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/factrial.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,29 @@
+__code print_factorial(int prod)
+{
+ printf("factorial = %d\n", prod);
+ exit(0);
+}
+
+__code factorial0(int prod, int x)
+{
+ if (x >= 1) {
+ goto factorial0(prod*x, x-1);
+ } else {
+ goto print_factorial(prod);
+ }
+
+}
+
+__code factorial(int x)
+{
+ goto factorial0(1, x);
+}
+
+int main(int argc, char **argv)
+{
+ int i;
+ i = atoi(argv[1]);
+
+ goto factorial(i);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/getMinHeight.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/getMinHeight.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,51 @@
+__code getMinHeight_stub(struct Context* context) {
+ goto getMinHeight(context, &context->data[Allocate]->allocate, &context->data[AkashaInfo]->akashaInfo);
+}
+
+__code getMinHeight(struct Context* context, struct Allocate* allocate, struct AkashaInfo* akashaInfo) {
+ const struct AkashaNode* akashaNode = akashaInfo->akashaNode;
+
+ if (akashaNode == NULL) {
+ allocate->size = sizeof(struct AkashaNode);
+ allocator(context);
+ akashaInfo->akashaNode = (struct AkashaNode*)context->data[context->dataNum];
+
+ akashaInfo->akashaNode->height = 1;
+ akashaInfo->akashaNode->node = context->data[Tree]->tree.root;
+
+ goto getMaxHeight_stub(context);
+ }
+
+ const struct Node* node = akashaInfo->akashaNode->node;
+ if (node->left == NULL && node->right == NULL) {
+ if (akashaInfo->minHeight > akashaNode->height) {
+ akashaInfo->minHeight = akashaNode->height;
+ akashaInfo->akashaNode = akashaNode->nextAkashaNode;
+ goto getMinHeight_stub(context);
+ }
+ }
+
+ akashaInfo->akashaNode = akashaInfo->akashaNode->nextAkashaNode;
+
+ if (node->left != NULL) {
+ allocate->size = sizeof(struct AkashaNode);
+ allocator(context);
+ struct AkashaNode* left = (struct AkashaNode*)context->data[context->dataNum];
+ left->height = akashaNode->height+1;
+ left->node = node->left;
+ left->nextAkashaNode = akashaInfo->akashaNode;
+ akashaInfo->akashaNode = left;
+ }
+
+ if (node->right != NULL) {
+ allocate->size = sizeof(struct AkashaNode);
+ allocator(context);
+ struct AkashaNode* right = (struct AkashaNode*)context->data[context->dataNum];
+ right->height = akashaNode->height+1;
+ right->node = node->right;
+ right->nextAkashaNode = akashaInfo->akashaNode;
+ akashaInfo->akashaNode = right;
+ }
+
+ goto getMinHeight_stub(context);
+}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/goto.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/goto.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+__code cs0(int a, int b){
+ goto cs1(a+b);
+}
+
+__code cs1(int c){
+ goto cs2(c);
+}
diff -r 000000000000 -r 83f997abf3b5 final_main/src/initLLRBContext.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/initLLRBContext.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,53 @@
+__code initLLRBContext(struct Context* context, int num) {
+ context->heapLimit = sizeof(union Data)*ALLOCATE_SIZE;
+ context->code = malloc(sizeof(__code*)*ALLOCATE_SIZE);
+ context->data = malloc(sizeof(union Data*)*ALLOCATE_SIZE);
+ context->heapStart = malloc(context->heapLimit);
+
+ context->codeNum = Exit;
+
+ context->code[Code1] = code1_stub;
+ context->code[Code2] = code2_stub;
+ context->code[Code3] = code3_stub;
+ context->code[Code4] = code4;
+ context->code[Code5] = code5;
+ context->code[Find] = find;
+ context->code[Not_find] = not_find;
+ context->code[Code6] = code6;
+ context->code[Put] = put_stub;
+ context->code[Replace] = replaceNode_stub;
+ context->code[Insert] = insertNode_stub;
+ context->code[RotateL] = rotateLeft_stub;
+ context->code[RotateR] = rotateRight_stub;
+ context->code[InsertCase1] = insert1_stub;
+ context->code[InsertCase2] = insert2_stub;
+ context->code[InsertCase3] = insert3_stub;
+ context->code[InsertCase4] = insert4_stub;
+ context->code[InsertCase4_1] = insert4_1_stub;
+ context->code[InsertCase4_2] = insert4_2_stub;
+ context->code[InsertCase5] = insert5_stub;
+ context->code[StackClear] = stackClear_stub;
+ context->code[Exit] = exit_code;
+
+ context->heap = context->heapStart;
+
+ context->data[Allocate] = context->heap;
+ context->heap += sizeof(struct Allocate);
+
+ context->data[Tree] = context->heap;
+ context->heap += sizeof(struct Tree);
+
+ context->data[Node] = context->heap;
+ context->heap += sizeof(struct Node);
+
+ context->dataNum = Node;
+
+ struct Tree* tree = &context->data[Tree]->tree;
+ tree->root = 0;
+ tree->current = 0;
+ tree->deleted = 0;
+
+ context->node_stack = stack_init(sizeof(struct Node*), 100);
+ context->code_stack = stack_init(sizeof(enum Code), 100);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/insertCase2.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/insertCase2.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,17 @@
+__code insertCase2(struct Context* context, struct Node* current) {
+ struct Node* parent;
+ stack_pop(context->node_stack, &parent);
+
+ if (parent->color == Black) {
+ stack_pop(context->code_stack, &context->next);
+ goto meta(context, context->next);
+ }
+
+ stack_push(context->node_stack, &parent);
+ goto meta(context, InsertCase3);
+}
+
+__code insert2_stub(struct Context* context) {
+ goto insertCase2(context, context->data[Tree]->tree.current);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/interface.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/interface.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,15 @@
+typedef struct Stack{
+ union Data* stack;
+ union Data* data;
+ union Data* data1;
+
+ __code whenEmpty(...);
+ __code clear(Impl* stack,__code next(...));
+ __code push(Impl* stack,Type* data, __code next(...));
+ __code pop(Impl* stack, __code next(Type* data, ...));
+ __code pop2(Impl* stack, __code next(Type* data, Type* data1, ...));
+ __code isEmpty(Impl* stack, __code next(...), __code whenEmpty(...));
+ __code get(Impl* stack, __code next(Type* data, ...));
+ __code get2(Impl* stack, __code next(Type* data, Type* data1, ...));
+ __code next(...);
+} Stack;
diff -r 000000000000 -r 83f997abf3b5 final_main/src/meta.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/meta.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,4 @@
+__code meta(struct Context* context, enum Code next) {
+ goto (context->code[next])(context);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/rbtreeContext.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/rbtreeContext.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,50 @@
+// DataSegments for Red-Black Tree
+union Data {
+ struct Comparable { // interface
+ enum Code compare;
+ union Data* data;
+ } compare;
+ struct Count {
+ enum Code next;
+ long i;
+ } count;
+ struct Tree {
+ enum Code next;
+ struct Node* root;
+ struct Node* current;
+ struct Node* deleted;
+ int result;
+ } tree;
+ struct Node {
+ // need to tree
+ enum Code next;
+ int key; // comparable data segment
+ int value;
+ struct Node* left;
+ struct Node* right;
+ // need to balancing
+ enum Color {
+ Red,
+ Black,
+ } color;
+ } node;
+ struct Allocate {
+ enum Code next;
+ long size;
+ } allocate;
+};
+
+
+// Meta DataSegment
+struct Context {
+ enum Code next;
+ int codeNum;
+ __code (**code) (struct Context*);
+ void* heapStart;
+ void* heap;
+ long heapLimit;
+ int dataNum;
+ stack_ptr code_stack;
+ stack_ptr node_stack;
+ union Data **data;
+};
diff -r 000000000000 -r 83f997abf3b5 final_main/src/redBlackTreeTest.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/redBlackTreeTest.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,196 @@
+module redBlackTreeTest where
+
+open import RedBlackTree
+open import stack
+open import Level hiding (zero)
+
+open import Data.Nat
+
+open Tree
+open Node
+open RedBlackTree.RedBlackTree
+open Stack
+
+-- tests
+
+putTree1 : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> k -> a -> (RedBlackTree {n} {m} {t} a k -> t) -> t
+putTree1 {n} {m} {a} {k} {t} tree k1 value next with (root tree)
+... | Nothing = next (record tree {root = Just (leafNode k1 value) })
+... | Just n2 = clearSingleLinkedStack (nodeStack tree) (\ s -> findNode tree s (leafNode k1 value) n2 (\ tree1 s n1 -> replaceNode tree1 s n1 next))
+
+open import Relation.Binary.PropositionalEquality
+open import Relation.Binary.Core
+open import Function
+
+
+check1 : {m : Level } (n : Maybe (Node ℕ ℕ)) -> ℕ -> Bool {m}
+check1 Nothing _ = False
+check1 (Just n) x with Data.Nat.compare (value n) x
+... | equal _ = True
+... | _ = False
+
+check2 : {m : Level } (n : Maybe (Node ℕ ℕ)) -> ℕ -> Bool {m}
+check2 Nothing _ = False
+check2 (Just n) x with compare2 (value n) x
+... | EQ = True
+... | _ = False
+
+test1 : putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero} ) 1 1 ( \t -> getRedBlackTree t 1 ( \t x -> check2 x 1 ≡ True ))
+test1 = refl
+
+test2 : putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero} ) 1 1 (
+ \t -> putTree1 t 2 2 (
+ \t -> getRedBlackTree t 1 (
+ \t x -> check2 x 1 ≡ True )))
+test2 = refl
+
+open ≡-Reasoning
+test3 : putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero}) 1 1
+ $ \t -> putTree1 t 2 2
+ $ \t -> putTree1 t 3 3
+ $ \t -> putTree1 t 4 4
+ $ \t -> getRedBlackTree t 1
+ $ \t x -> check2 x 1 ≡ True
+test3 = begin
+ check2 (Just (record {key = 1 ; value = 1 ; color = Black ; left = Nothing ; right = Just (leafNode 2 2)})) 1
+ ≡⟨ refl ⟩
+ True
+ ∎
+
+test31 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ ) 1 1
+ $ \t -> putTree1 t 2 2
+ $ \t -> putTree1 t 3 3
+ $ \t -> putTree1 t 4 4
+ $ \t -> getRedBlackTree t 4
+ $ \t x -> x
+
+-- test5 : Maybe (Node ℕ ℕ)
+test5 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ ) 4 4
+ $ \t -> putTree1 t 6 6
+ $ \t0 -> clearSingleLinkedStack (nodeStack t0)
+ $ \s -> findNode1 t0 s (leafNode 3 3) ( root t0 )
+ $ \t1 s n1 -> replaceNode t1 s n1
+ $ \t -> getRedBlackTree t 3
+ -- $ \t x -> SingleLinkedStack.top (stack s)
+ -- $ \t x -> n1
+ $ \t x -> root t
+ where
+ findNode1 : {n m : Level } {a k : Set n} {t : Set m} -> RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> (Node a k) -> (Maybe (Node a k)) -> (RedBlackTree {n} {m} {t} a k -> SingleLinkedStack (Node a k) -> Node a k -> t) -> t
+ findNode1 t s n1 Nothing next = next t s n1
+ findNode1 t s n1 ( Just n2 ) next = findNode t s n1 n2 next
+
+-- test51 : putTree1 {_} {_} {ℕ} {ℕ} {_} {Maybe (Node ℕ ℕ)} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero} ) 1 1 $ \t ->
+-- putTree1 t 2 2 $ \t -> putTree1 t 3 3 $ \t -> root t ≡ Just (record { key = 1; value = 1; left = Just (record { key = 2 ; value = 2 } ); right = Nothing} )
+-- test51 = refl
+
+test6 : Maybe (Node ℕ ℕ)
+test6 = root (createEmptyRedBlackTreeℕ {_} ℕ {Maybe (Node ℕ ℕ)})
+
+
+test7 : Maybe (Node ℕ ℕ)
+test7 = clearSingleLinkedStack (nodeStack tree2) (\ s -> replaceNode tree2 s n2 (\ t -> root t))
+ where
+ tree2 = createEmptyRedBlackTreeℕ {_} ℕ {Maybe (Node ℕ ℕ)}
+ k1 = 1
+ n2 = leafNode 0 0
+ value1 = 1
+
+test8 : Maybe (Node ℕ ℕ)
+test8 = putTree1 {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ) 1 1
+ $ \t -> putTree1 t 2 2 (\ t -> root t)
+
+
+test9 : putRedBlackTree {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero} ) 1 1 ( \t -> getRedBlackTree t 1 ( \t x -> check2 x 1 ≡ True ))
+test9 = refl
+
+test10 : putRedBlackTree {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ {Set Level.zero} ) 1 1 (
+ \t -> putRedBlackTree t 2 2 (
+ \t -> getRedBlackTree t 1 (
+ \t x -> check2 x 1 ≡ True )))
+test10 = refl
+
+test11 = putRedBlackTree {_} {_} {ℕ} {ℕ} (createEmptyRedBlackTreeℕ ℕ) 1 1
+ $ \t -> putRedBlackTree t 2 2
+ $ \t -> putRedBlackTree t 3 3
+ $ \t -> getRedBlackTree t 2
+ $ \t x -> root t
+
+
+redBlackInSomeState : { m : Level } (a : Set Level.zero) (n : Maybe (Node a ℕ)) {t : Set m} -> RedBlackTree {Level.zero} {m} {t} a ℕ
+redBlackInSomeState {m} a n {t} = record { root = n ; nodeStack = emptySingleLinkedStack ; compare = compare2 }
+
+-- compare2 : (x y : ℕ ) -> compareresult
+-- compare2 zero zero = eq
+-- compare2 (suc _) zero = gt
+-- compare2 zero (suc _) = lt
+-- compare2 (suc x) (suc y) = compare2 x y
+
+putTest1Lemma2 : (k : ℕ) -> compare2 k k ≡ EQ
+putTest1Lemma2 zero = refl
+putTest1Lemma2 (suc k) = putTest1Lemma2 k
+
+putTest1Lemma1 : (x y : ℕ) -> compareℕ x y ≡ compare2 x y
+putTest1Lemma1 zero zero = refl
+putTest1Lemma1 (suc m) zero = refl
+putTest1Lemma1 zero (suc n) = refl
+putTest1Lemma1 (suc m) (suc n) with Data.Nat.compare m n
+putTest1Lemma1 (suc .m) (suc .(Data.Nat.suc m + k)) | less m k = lemma1 m
+ where
+ lemma1 : (m : ℕ) -> LT ≡ compare2 m (ℕ.suc (m + k))
+ lemma1 zero = refl
+ lemma1 (suc y) = lemma1 y
+putTest1Lemma1 (suc .m) (suc .m) | equal m = lemma1 m
+ where
+ lemma1 : (m : ℕ) -> EQ ≡ compare2 m m
+ lemma1 zero = refl
+ lemma1 (suc y) = lemma1 y
+putTest1Lemma1 (suc .(Data.Nat.suc m + k)) (suc .m) | greater m k = lemma1 m
+ where
+ lemma1 : (m : ℕ) -> GT ≡ compare2 (ℕ.suc (m + k)) m
+ lemma1 zero = refl
+ lemma1 (suc y) = lemma1 y
+
+putTest1Lemma3 : (k : ℕ) -> compareℕ k k ≡ EQ
+putTest1Lemma3 k = trans (putTest1Lemma1 k k) ( putTest1Lemma2 k )
+
+compareLemma1 : {x y : ℕ} -> compare2 x y ≡ EQ -> x ≡ y
+compareLemma1 {zero} {zero} refl = refl
+compareLemma1 {zero} {suc _} ()
+compareLemma1 {suc _} {zero} ()
+compareLemma1 {suc x} {suc y} eq = cong ( \z -> ℕ.suc z ) ( compareLemma1 ( trans lemma2 eq ) )
+ where
+ lemma2 : compare2 (ℕ.suc x) (ℕ.suc y) ≡ compare2 x y
+ lemma2 = refl
+
+
+putTest1 :{ m : Level } (n : Maybe (Node ℕ ℕ))
+ -> (k : ℕ) (x : ℕ)
+ -> putTree1 {_} {_} {ℕ} {ℕ} (redBlackInSomeState {_} ℕ n {Set Level.zero}) k x
+ (\ t -> getRedBlackTree t k (\ t x1 -> check2 x1 x ≡ True))
+putTest1 n k x with n
+... | Just n1 = lemma2 ( record { top = Nothing } )
+ where
+ lemma2 : (s : SingleLinkedStack (Node ℕ ℕ) ) -> putTree1 (record { root = Just n1 ; nodeStack = s ; compare = compare2 }) k x (λ t →
+ GetRedBlackTree.checkNode t k (λ t₁ x1 → check2 x1 x ≡ True) (root t))
+ lemma2 s with compare2 k (key n1)
+ ... | EQ = lemma3 {!!}
+ where
+ lemma3 : compare2 k (key n1) ≡ EQ -> getRedBlackTree {_} {_} {ℕ} {ℕ} {Set Level.zero} ( record { root = Just ( record {
+ key = key n1 ; value = x ; right = right n1 ; left = left n1 ; color = Black
+ } ) ; nodeStack = s ; compare = λ x₁ y → compare2 x₁ y } ) k ( \ t x1 -> check2 x1 x ≡ True)
+ lemma3 eq with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl with compare2 k (key n1) | eq
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
+ ... | GT = {!!}
+ ... | LT = {!!}
+
+... | Nothing = lemma1
+ where
+ lemma1 : getRedBlackTree {_} {_} {ℕ} {ℕ} {Set Level.zero} ( record { root = Just ( record {
+ key = k ; value = x ; right = Nothing ; left = Nothing ; color = Red
+ } ) ; nodeStack = record { top = Nothing } ; compare = λ x₁ y → compare2 x₁ y } ) k
+ ( \ t x1 -> check2 x1 x ≡ True)
+ lemma1 with compare2 k k | putTest1Lemma2 k
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/singleLinkedStack.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/singleLinkedStack.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,18 @@
+__code pushSingleLinkedStack(struct SingleLinkedStack* stack,union Data* data, __code next(...)) {
+ Element* element = new Element();
+ element->next = stack->top;
+ element->data = data;
+ stack->top = element;
+ goto next(...);
+}
+
+__code popSingleLinkedStack(struct SingleLinkedStack* stack, __code next(union Data* data, ...)) {
+ if (stack->top) {
+ data = stack->top->data;
+ stack->top = stack->top->next;
+ } else {
+ data = NULL;
+ }
+ goto next(data, ...);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/singleLinkedStackInterface.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/singleLinkedStackInterface.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,14 @@
+Stack* createSingleLinkedStack(struct Context* context) {
+ struct Stack* stack = new Stack();
+ struct SingleLinkedStack* singleLinkedStack = new SingleLinkedStack();
+ stack->stack = (union Data*)singleLinkedStack;
+ singleLinkedStack->top = NULL;
+ stack->push = C_pushSingleLinkedStack;
+ stack->pop = C_popSingleLinkedStack;
+ stack->pop2 = C_pop2SingleLinkedStack;
+ stack->get = C_getSingleLinkedStack;
+ stack->get2 = C_get2SingleLinkedStack;
+ stack->isEmpty = C_isEmptySingleLinkedStack;
+ stack->clear = C_clearSingleLinkedStack;
+ return stack;
+}
\ No newline at end of file
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack-product.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stack-product.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,158 @@
+module stack-product where
+
+open import product
+open import Data.Product
+open import Data.Nat
+open import Function using (id)
+open import Relation.Binary.PropositionalEquality
+
+-- definition based from Gears(209:5708390a9d88) src/parallel_execution
+goto = executeCS
+
+data Bool : Set where
+ True : Bool
+ False : Bool
+
+data Maybe (a : Set) : Set where
+ Nothing : Maybe a
+ Just : a -> Maybe a
+
+
+record Stack {a t : Set} (stackImpl : Set) : Set where
+ field
+ stack : stackImpl
+ push : CodeSegment (stackImpl × a × (CodeSegment stackImpl t)) t
+ pop : CodeSegment (stackImpl × (CodeSegment (stackImpl × Maybe a) t)) t
+
+
+data Element (a : Set) : Set where
+ cons : a -> Maybe (Element a) -> Element a
+
+datum : {a : Set} -> Element a -> a
+datum (cons a _) = a
+
+next : {a : Set} -> Element a -> Maybe (Element a)
+next (cons _ n) = n
+
+record SingleLinkedStack (a : Set) : Set where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+emptySingleLinkedStack : {a : Set} -> SingleLinkedStack a
+emptySingleLinkedStack = record {top = Nothing}
+
+
+
+
+pushSingleLinkedStack : {a t : Set} -> CodeSegment ((SingleLinkedStack a) × a × (CodeSegment (SingleLinkedStack a) t)) t
+pushSingleLinkedStack = cs push
+ where
+ push : {a t : Set} -> ((SingleLinkedStack a) × a × (CodeSegment (SingleLinkedStack a) t)) -> t
+ push (stack , datum , next) = goto next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+popSingleLinkedStack : {a t : Set} -> CodeSegment (SingleLinkedStack a × (CodeSegment (SingleLinkedStack a × Maybe a) t)) t
+popSingleLinkedStack = cs pop
+ where
+ pop : {a t : Set} -> (SingleLinkedStack a × (CodeSegment (SingleLinkedStack a × Maybe a) t)) -> t
+ pop (record { top = Nothing } , nextCS) = goto nextCS (emptySingleLinkedStack , Nothing)
+ pop (record { top = Just x } , nextCS) = goto nextCS (stack1 , (Just datum1))
+ where
+ datum1 = datum x
+ stack1 = record { top = (next x) }
+
+
+
+
+
+createSingleLinkedStack : {a b : Set} -> Stack {a} {b} (SingleLinkedStack a)
+createSingleLinkedStack = record { stack = emptySingleLinkedStack
+ ; push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ }
+
+
+
+
+test01 : {a : Set} -> CodeSegment (SingleLinkedStack a × Maybe a) Bool
+test01 = cs test01'
+ where
+ test01' : {a : Set} -> (SingleLinkedStack a × Maybe a) -> Bool
+ test01' (record { top = Nothing } , _) = False
+ test01' (record { top = Just x } , _) = True
+
+
+test02 : {a : Set} -> CodeSegment (SingleLinkedStack a) (SingleLinkedStack a × Maybe a)
+test02 = cs test02'
+ where
+ test02' : {a : Set} -> SingleLinkedStack a -> (SingleLinkedStack a × Maybe a)
+ test02' stack = goto popSingleLinkedStack (stack , (cs id))
+
+
+test03 : {a : Set} -> CodeSegment a (SingleLinkedStack a)
+test03 = cs test03'
+ where
+ test03' : {a : Set} -> a -> SingleLinkedStack a
+ test03' a = goto pushSingleLinkedStack (emptySingleLinkedStack , a , (cs id))
+
+
+lemma : {A : Set} {a : A} -> goto (test03 ◎ test02 ◎ test01) a ≡ False
+lemma = refl
+
+
+n-push : {A : Set} {a : A} -> CodeSegment (ℕ × SingleLinkedStack A) (ℕ × SingleLinkedStack A)
+n-push {A} {a} = cs (push {A} {a})
+ where
+ push : {A : Set} {a : A} -> (ℕ × SingleLinkedStack A) -> (ℕ × SingleLinkedStack A)
+ push {A} {a} (zero , s) = (zero , s)
+ push {A} {a} (suc n , s) = goto pushSingleLinkedStack (s , a , {!!} {- n-push -}) -- needs subtype
+
+
+{-
+
+n-push : {A : Set} {a : A} -> Nat -> SingleLinkedStack A -> SingleLinkedStack A
+n-push zero s = s
+n-push {A} {a} (suc n) s = pushSingleLinkedStack (n-push {A} {a} n s) a (\s -> s)
+
+n-pop : {A : Set} {a : A} -> Nat -> SingleLinkedStack A -> SingleLinkedStack A
+n-pop zero s = s
+n-pop {A} {a} (suc n) s = popSingleLinkedStack (n-pop {A} {a} n s) (\s _ -> s)
+
+open ≡-Reasoning
+
+push-pop-equiv : {A : Set} {a : A} (s : SingleLinkedStack A) -> popSingleLinkedStack (pushSingleLinkedStack s a (\s -> s)) (\s _ -> s) ≡ s
+push-pop-equiv s = refl
+
+push-and-n-pop : {A : Set} {a : A} (n : Nat) (s : SingleLinkedStack A) -> n-pop {A} {a} (suc n) (pushSingleLinkedStack s a id) ≡ n-pop {A} {a} n s
+push-and-n-pop zero s = refl
+push-and-n-pop {A} {a} (suc n) s = begin
+ n-pop (suc (suc n)) (pushSingleLinkedStack s a id)
+ ≡⟨ refl ⟩
+ popSingleLinkedStack (n-pop (suc n) (pushSingleLinkedStack s a id)) (\s _ -> s)
+ ≡⟨ cong (\s -> popSingleLinkedStack s (\s _ -> s)) (push-and-n-pop n s) ⟩
+ popSingleLinkedStack (n-pop n s) (\s _ -> s)
+ ≡⟨ refl ⟩
+ n-pop (suc n) s
+ ∎
+
+
+n-push-pop-equiv : {A : Set} {a : A} (n : Nat) (s : SingleLinkedStack A) -> (n-pop {A} {a} n (n-push {A} {a} n s)) ≡ s
+n-push-pop-equiv zero s = refl
+n-push-pop-equiv {A} {a} (suc n) s = begin
+ n-pop (suc n) (n-push (suc n) s)
+ ≡⟨ refl ⟩
+ n-pop (suc n) (pushSingleLinkedStack (n-push n s) a (\s -> s))
+ ≡⟨ push-and-n-pop n (n-push n s) ⟩
+ n-pop n (n-push n s)
+ ≡⟨ n-push-pop-equiv n s ⟩
+ s
+ ∎
+
+
+n-push-pop-equiv-empty : {A : Set} {a : A} -> (n : Nat) -> n-pop {A} {a} n (n-push {A} {a} n emptySingleLinkedStack) ≡ emptySingleLinkedStack
+n-push-pop-equiv-empty n = n-push-pop-equiv n emptySingleLinkedStack
+-}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack-subtype-sample.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stack-subtype-sample.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,212 @@
+module stack-subtype-sample where
+
+open import Level renaming (suc to S ; zero to O)
+open import Function
+open import Data.Nat
+open import Data.Maybe
+open import Relation.Binary.PropositionalEquality
+
+open import stack-subtype ℕ
+open import subtype Context as N
+open import subtype Meta as M
+
+
+record Num : Set where
+ field
+ num : ℕ
+
+instance
+ NumIsNormalDataSegment : N.DataSegment Num
+ NumIsNormalDataSegment = record { get = (\c -> record { num = Context.n c})
+ ; set = (\c n -> record c {n = Num.num n})}
+ NumIsMetaDataSegment : M.DataSegment Num
+ NumIsMetaDataSegment = record { get = (\m -> record {num = Context.n (Meta.context m)})
+ ; set = (\m n -> record m {context = record (Meta.context m) {n = Num.num n}})}
+
+
+plus3 : Num -> Num
+plus3 record { num = n } = record {num = n + 3}
+
+plus3CS : N.CodeSegment Num Num
+plus3CS = N.cs plus3
+
+
+
+plus5AndPushWithPlus3 : {mc : Meta} {{_ : N.DataSegment Num}}
+ -> M.CodeSegment Num (Meta)
+plus5AndPushWithPlus3 {mc} {{nn}} = M.cs (\n -> record {context = con n ; nextCS = (liftContext {{nn}} {{nn}} plus3CS) ; stack = st} )
+ where
+ co = Meta.context mc
+ con : Num -> Context
+ con record { num = num } = N.DataSegment.set nn co record {num = num + 5}
+ st = Meta.stack mc
+
+
+
+
+push-sample : {{_ : N.DataSegment Num}} {{_ : M.DataSegment Num}} -> Meta
+push-sample {{nd}} {{md}} = M.exec {{md}} (plus5AndPushWithPlus3 {mc} {{nd}}) mc
+ where
+ con = record { n = 4 ; element = just 0}
+ code = N.cs (\c -> c)
+ mc = record {context = con ; stack = emptySingleLinkedStack ; nextCS = code}
+
+
+push-sample-equiv : push-sample ≡ record { nextCS = liftContext plus3CS
+ ; stack = record { top = nothing}
+ ; context = record { n = 9} }
+push-sample-equiv = refl
+
+
+pushed-sample : {m : Meta} {{_ : N.DataSegment Num}} {{_ : M.DataSegment Num}} -> Meta
+pushed-sample {m} {{nd}} {{md}} = M.exec {{md}} (M.csComp {m} {{md}} pushSingleLinkedStackCS (plus5AndPushWithPlus3 {mc} {{nd}})) mc
+ where
+ con = record { n = 4 ; element = just 0}
+ code = N.cs (\c -> c)
+ mc = record {context = con ; stack = emptySingleLinkedStack ; nextCS = code}
+
+
+
+pushed-sample-equiv : {m : Meta} ->
+ pushed-sample {m} ≡ record { nextCS = liftContext plus3CS
+ ; stack = record { top = just (cons 0 nothing) }
+ ; context = record { n = 12} }
+pushed-sample-equiv = refl
+
+
+
+pushNum : N.CodeSegment Context Context
+pushNum = N.cs pn
+ where
+ pn : Context -> Context
+ pn record { n = n } = record { n = pred n ; element = just n}
+
+
+pushOnce : Meta -> Meta
+pushOnce m = M.exec pushSingleLinkedStackCS m
+
+n-push : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
+n-push {{mm}} (zero) = M.cs {{mm}} {{mm}} id
+n-push {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-push {m} {{mm}} n) (pushOnce m))
+
+popOnce : Meta -> Meta
+popOnce m = M.exec popSingleLinkedStackCS m
+
+n-pop : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
+n-pop {{mm}} (zero) = M.cs {{mm}} {{mm}} id
+n-pop {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-pop {m} {{mm}} n) (popOnce m))
+
+
+
+initMeta : ℕ -> Maybe ℕ -> N.CodeSegment Context Context -> Meta
+initMeta n mn code = record { context = record { n = n ; element = mn}
+ ; stack = emptySingleLinkedStack
+ ; nextCS = code
+ }
+
+n-push-cs-exec = M.exec (n-push {meta} 3) meta
+ where
+ meta = (initMeta 5 (just 9) pushNum)
+
+
+n-push-cs-exec-equiv : n-push-cs-exec ≡ record { nextCS = pushNum
+ ; context = record {n = 2 ; element = just 3}
+ ; stack = record {top = just (cons 4 (just (cons 5 (just (cons 9 nothing)))))}}
+n-push-cs-exec-equiv = refl
+
+
+n-pop-cs-exec = M.exec (n-pop {meta} 4) meta
+ where
+ meta = record { nextCS = N.cs id
+ ; context = record { n = 0 ; element = nothing}
+ ; stack = record {top = just (cons 9 (just (cons 8 (just (cons 7 (just (cons 6 (just (cons 5 nothing)))))))))}
+ }
+
+n-pop-cs-exec-equiv : n-pop-cs-exec ≡ record { nextCS = N.cs id
+ ; context = record { n = 0 ; element = just 6}
+ ; stack = record { top = just (cons 5 nothing)}
+ }
+
+n-pop-cs-exec-equiv = refl
+
+
+open ≡-Reasoning
+
+id-meta : ℕ -> ℕ -> SingleLinkedStack ℕ -> Meta
+id-meta n e s = record { context = record {n = n ; element = just e}
+ ; nextCS = (N.cs id) ; stack = s}
+
+exec-comp : (f g : M.CodeSegment Meta Meta) (m : Meta) -> M.exec (M.csComp {m} f g) m ≡ M.exec f (M.exec g m)
+exec-comp (M.cs x) (M.cs _) m = refl
+
+
+push-pop-type : ℕ -> ℕ -> ℕ -> Element ℕ -> Set₁
+push-pop-type n e x s = M.exec (M.csComp {meta} (M.cs popOnce) (M.cs pushOnce)) meta ≡ meta
+ where
+ meta = id-meta n e record {top = just (cons x (just s))}
+
+push-pop : (n e x : ℕ) -> (s : Element ℕ) -> push-pop-type n e x s
+push-pop n e x s = refl
+
+
+
+pop-n-push-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
+pop-n-push-type n cn ce s = M.exec (M.csComp {meta} (M.cs popOnce) (n-push {meta} (suc n))) meta
+ ≡ M.exec (n-push {meta} n) meta
+ where
+ meta = id-meta cn ce s
+
+pop-n-push : (n cn ce : ℕ) -> (s : SingleLinkedStack ℕ) -> pop-n-push-type n cn ce s
+
+pop-n-push zero cn ce s = refl
+pop-n-push (suc n) cn ce s = begin
+ M.exec (M.csComp {id-meta cn ce s} (M.cs popOnce) (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc (suc n)))) (id-meta cn ce s)
+ ≡⟨ refl ⟩
+ M.exec (M.csComp {id-meta cn ce s} (M.cs popOnce) (M.csComp {id-meta cn ce s} (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (M.cs pushOnce))) (id-meta cn ce s)
+ ≡⟨ exec-comp (M.cs popOnce) (M.csComp {id-meta cn ce s} (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (M.cs pushOnce)) (id-meta cn ce s) ⟩
+ M.exec (M.cs popOnce) (M.exec (M.csComp {id-meta cn ce s} (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (M.cs pushOnce)) (id-meta cn ce s))
+ ≡⟨ cong (\x -> M.exec (M.cs popOnce) x) (exec-comp (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (M.cs pushOnce) (id-meta cn ce s)) ⟩
+ M.exec (M.cs popOnce) (M.exec (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n))(M.exec (M.cs pushOnce) (id-meta cn ce s)))
+ ≡⟨ refl ⟩
+ M.exec (M.cs popOnce) (M.exec (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})))
+ ≡⟨ sym (exec-comp (M.cs popOnce) (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n)) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))) ⟩
+ M.exec (M.csComp {id-meta cn ce s} (M.cs popOnce) (n-push {id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))})} (suc n))) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))
+ ≡⟨ pop-n-push n cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}) ⟩
+ M.exec (n-push n) (id-meta cn ce (record {top = just (cons ce (SingleLinkedStack.top s))}))
+ ≡⟨ refl ⟩
+ M.exec (n-push n) (pushOnce (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-push n) (M.exec (M.cs pushOnce) (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s)
+ ∎
+
+
+
+n-push-pop-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
+n-push-pop-type n cn ce st = M.exec (M.csComp {meta} (n-pop {meta} n) (n-push {meta} n)) meta ≡ meta
+ where
+ meta = id-meta cn ce st
+
+n-push-pop : (n cn ce : ℕ) -> (s : SingleLinkedStack ℕ) -> n-push-pop-type n cn ce s
+n-push-pop zero cn ce s = refl
+n-push-pop (suc n) cn ce s = begin
+ M.exec (M.csComp {id-meta cn ce s} (n-pop {id-meta cn ce s} (suc n)) (n-push {id-meta cn ce s} (suc n))) (id-meta cn ce s)
+ ≡⟨ refl ⟩
+ M.exec (M.csComp {id-meta cn ce s} (M.cs (\m -> M.exec (n-pop {id-meta cn ce s} n) (popOnce m))) (n-push {id-meta cn ce s} (suc n))) (id-meta cn ce s)
+ ≡⟨ exec-comp (M.cs (\m -> M.exec (n-pop n) (popOnce m))) (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s) ⟩
+ M.exec (M.cs (\m -> M.exec (n-pop {id-meta cn ce s} n) (popOnce m))) (M.exec (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s))
+ ≡⟨ refl ⟩
+ M.exec (n-pop n) (popOnce (M.exec (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s)))
+ ≡⟨ refl ⟩
+ M.exec (n-pop n) (M.exec (M.cs popOnce) (M.exec (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s)))
+ ≡⟨ cong (\x -> M.exec (n-pop {id-meta cn ce s} n) x) (sym (exec-comp (M.cs popOnce) (n-push {id-meta cn ce s} (suc n)) (id-meta cn ce s))) ⟩
+ M.exec (n-pop n) (M.exec (M.csComp {id-meta cn ce s} (M.cs popOnce) (n-push {id-meta cn ce s} (suc n))) (id-meta cn ce s))
+ ≡⟨ cong (\x -> M.exec (n-pop {id-meta cn ce s} n) x) (pop-n-push n cn ce s) ⟩
+ M.exec (n-pop n) (M.exec (n-push n) (id-meta cn ce s))
+ ≡⟨ sym (exec-comp (n-pop n) (n-push n) (id-meta cn ce s)) ⟩
+ M.exec (M.csComp (n-pop n) (n-push n)) (id-meta cn ce s)
+ ≡⟨ n-push-pop n cn ce s ⟩
+ id-meta cn ce s
+ ∎
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack-subtype.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stack-subtype.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,123 @@
+open import Level hiding (lift)
+open import Data.Maybe
+open import Data.Product
+open import Data.Nat hiding (suc)
+open import Function
+
+module stack-subtype (A : Set) where
+
+-- data definitions
+
+data Element (a : Set) : Set where
+ cons : a -> Maybe (Element a) -> Element a
+
+datum : {a : Set} -> Element a -> a
+datum (cons a _) = a
+
+next : {a : Set} -> Element a -> Maybe (Element a)
+next (cons _ n) = n
+
+record SingleLinkedStack (a : Set) : Set where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+record Context : Set where
+ field
+ -- fields for concrete data segments
+ n : ℕ
+ -- fields for stack
+ element : Maybe A
+
+
+
+
+
+open import subtype Context as N
+
+instance
+ ContextIsDataSegment : N.DataSegment Context
+ ContextIsDataSegment = record {get = (\c -> c) ; set = (\_ c -> c)}
+
+
+record Meta : Set₁ where
+ field
+ -- context as set of data segments
+ context : Context
+ stack : SingleLinkedStack A
+ nextCS : N.CodeSegment Context Context
+
+
+
+
+open import subtype Meta as M
+
+instance
+ MetaIncludeContext : M.DataSegment Context
+ MetaIncludeContext = record { get = Meta.context
+ ; set = (\m c -> record m {context = c}) }
+
+ MetaIsMetaDataSegment : M.DataSegment Meta
+ MetaIsMetaDataSegment = record { get = (\m -> m) ; set = (\_ m -> m) }
+
+
+liftMeta : {X Y : Set} {{_ : M.DataSegment X}} {{_ : M.DataSegment Y}} -> N.CodeSegment X Y -> M.CodeSegment X Y
+liftMeta (N.cs f) = M.cs f
+
+liftContext : {X Y : Set} {{_ : N.DataSegment X}} {{_ : N.DataSegment Y}} -> N.CodeSegment X Y -> N.CodeSegment Context Context
+liftContext {{x}} {{y}} (N.cs f) = N.cs (\c -> N.DataSegment.set y c (f (N.DataSegment.get x c)))
+
+-- definition based from Gears(209:5708390a9d88) src/parallel_execution
+
+emptySingleLinkedStack : SingleLinkedStack A
+emptySingleLinkedStack = record {top = nothing}
+
+
+pushSingleLinkedStack : Meta -> Meta
+pushSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (push s e) })
+ where
+ n = Meta.nextCS m
+ s = Meta.stack m
+ e = Context.element (Meta.context m)
+ push : SingleLinkedStack A -> Maybe A -> SingleLinkedStack A
+ push s nothing = s
+ push s (just x) = record {top = just (cons x (top s))}
+
+
+
+popSingleLinkedStack : Meta -> Meta
+popSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (st m) ; context = record con {element = (elem m)}})
+ where
+ n = Meta.nextCS m
+ con = Meta.context m
+ elem : Meta -> Maybe A
+ elem record {stack = record { top = (just (cons x _)) }} = just x
+ elem record {stack = record { top = nothing }} = nothing
+ st : Meta -> SingleLinkedStack A
+ st record {stack = record { top = (just (cons _ s)) }} = record {top = s}
+ st record {stack = record { top = nothing }} = record {top = nothing}
+
+
+
+
+pushSingleLinkedStackCS : M.CodeSegment Meta Meta
+pushSingleLinkedStackCS = M.cs pushSingleLinkedStack
+
+popSingleLinkedStackCS : M.CodeSegment Meta Meta
+popSingleLinkedStackCS = M.cs popSingleLinkedStack
+
+
+-- for sample
+
+firstContext : Context
+firstContext = record {element = nothing ; n = 0}
+
+
+firstMeta : Meta
+firstMeta = record { context = firstContext
+ ; stack = emptySingleLinkedStack
+ ; nextCS = (N.cs (\m -> m))
+ }
+
+
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stack.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,149 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module stack where
+
+open import Relation.Binary.PropositionalEquality
+open import Relation.Binary.Core
+open import Data.Nat
+
+ex : 1 + 2 ≡ 3
+ex = refl
+
+data Bool {n : Level } : Set n where
+ True : Bool
+ False : Bool
+
+record _∧_ {n : Level } (a : Set n) (b : Set n): Set n where
+ field
+ pi1 : a
+ pi2 : b
+
+data Maybe {n : Level } (a : Set n) : Set n where
+ Nothing : Maybe a
+ Just : a -> Maybe a
+
+record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.⊔ n) where
+ field
+ push : stackImpl -> a -> (stackImpl -> t) -> t
+ pop : stackImpl -> (stackImpl -> Maybe a -> t) -> t
+ pop2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
+ get : stackImpl -> (stackImpl -> Maybe a -> t) -> t
+ get2 : stackImpl -> (stackImpl -> Maybe a -> Maybe a -> t) -> t
+ clear : stackImpl -> (stackImpl -> t) -> t
+open StackMethods
+
+record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.⊔ n) where
+ field
+ stack : si
+ stackMethods : StackMethods {n} {m} a {t} si
+ pushStack : a -> (Stack a si -> t) -> t
+ pushStack d next = push (stackMethods ) (stack ) d (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
+ popStack : (Stack a si -> Maybe a -> t) -> t
+ popStack next = pop (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ pop2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
+ pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ getStack : (Stack a si -> Maybe a -> t) -> t
+ getStack next = get (stackMethods ) (stack ) (\s1 d1 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ get2Stack : (Stack a si -> Maybe a -> Maybe a -> t) -> t
+ get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 -> next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ clearStack : (Stack a si -> t) -> t
+ clearStack next = clear (stackMethods ) (stack ) (\s1 -> next (record {stack = s1 ; stackMethods = stackMethods } ))
+
+open Stack
+
+{--
+data Element {n : Level } (a : Set n) : Set n where
+ cons : a -> Maybe (Element a) -> Element a
+
+
+datum : {n : Level } {a : Set n} -> Element a -> a
+datum (cons a _) = a
+
+next : {n : Level } {a : Set n} -> Element a -> Maybe (Element a)
+next (cons _ n) = n
+--}
+
+
+-- cannot define recrusive record definition. so use linked list with maybe.
+record Element {l : Level} (a : Set l) : Set l where
+ inductive
+ constructor cons
+ field
+ datum : a -- `data` is reserved by Agda.
+ next : Maybe (Element a)
+
+open Element
+
+
+record SingleLinkedStack {n : Level } (a : Set n) : Set n where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+
+popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
+popSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack1 (Just data1)
+ where
+ data1 = datum d
+ stack1 = record { top = (next d) }
+
+pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = pop2SingleLinkedStack' {n} {m} stack cs
+ where
+ pop2SingleLinkedStack' : {n m : Level } {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+ pop2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs (record {top = (next d1)}) (Just (datum d)) (Just (datum d1))
+
+
+getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
+getSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack (Just data1)
+ where
+ data1 = datum d
+
+get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = get2SingleLinkedStack' {n} {m} stack cs
+ where
+ get2SingleLinkedStack' : {n m : Level} {t : Set m } -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> (Maybe a) -> t) -> t
+ get2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs stack (Just (datum d)) (Just (datum d1))
+
+clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (SingleLinkedStack a -> t) -> t
+clearSingleLinkedStack stack next = next (record {top = Nothing})
+
+
+emptySingleLinkedStack : {n : Level } {a : Set n} -> SingleLinkedStack a
+emptySingleLinkedStack = record {top = Nothing}
+
+-----
+-- Basic stack implementations are specifications of a Stack
+--
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} -> StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+ push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ ; pop2 = pop2SingleLinkedStack
+ ; get = getSingleLinkedStack
+ ; get2 = get2SingleLinkedStack
+ ; clear = clearSingleLinkedStack
+ }
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+ stack = emptySingleLinkedStack ;
+ stackMethods = singleLinkedStackSpec
+ }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack.agdai
Binary file final_main/src/stack.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stack.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stack.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,7 @@
+struct SingleLinkedStack {
+ struct Element* top;
+} SingleLinkedStack;
+struct Element {
+ union Data* data;
+ struct Element* next;
+} Element;
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stackImpl.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stackImpl.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,38 @@
+record Element {l : Level} (a : Set l) : Set l where
+ inductive
+ constructor cons
+ field
+ datum : a -- `data` is reserved by Agda.
+ next : Maybe (Element a)
+open Element
+
+record SingleLinkedStack {n : Level } (a : Set n) : Set n where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> SingleLinkedStack Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+-- push 以下は省略
+
+-- Basic stack implementations are specifications of a Stack
+
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} -> StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+ push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ ; pop2 = pop2SingleLinkedStack
+ ; get = getSingleLinkedStack
+ ; get2 = get2SingleLinkedStack
+ ; clear = clearSingleLinkedStack
+ }
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+ stack = emptySingleLinkedStack ;
+ stackMethods = singleLinkedStackSpec
+ }
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stackTest.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stackTest.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,144 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module stackTest where
+
+open import stack
+
+open import Relation.Binary.PropositionalEquality
+open import Relation.Binary.Core
+open import Data.Nat
+open import Function
+
+
+open SingleLinkedStack
+open Stack
+
+----
+--
+-- proof of properties ( concrete cases )
+--
+
+test01 : {n : Level } {a : Set n} -> SingleLinkedStack a -> Maybe a -> Bool {n}
+test01 stack _ with (top stack)
+... | (Just _) = True
+... | Nothing = False
+
+
+test02 : {n : Level } {a : Set n} -> SingleLinkedStack a -> Bool
+test02 stack = popSingleLinkedStack stack test01
+
+test03 : {n : Level } {a : Set n} -> a -> Bool
+test03 v = pushSingleLinkedStack emptySingleLinkedStack v test02
+
+-- after a push and a pop, the stack is empty
+lemma : {n : Level} {A : Set n} {a : A} -> test03 a ≡ False
+lemma = refl
+
+testStack01 : {n m : Level } {a : Set n} -> a -> Bool {m}
+testStack01 v = pushStack createSingleLinkedStack v (
+ \s -> popStack s (\s1 d1 -> True))
+
+-- after push 1 and 2, pop2 get 1 and 2
+
+testStack02 : {m : Level } -> ( Stack ℕ (SingleLinkedStack ℕ) -> Bool {m} ) -> Bool {m}
+testStack02 cs = pushStack createSingleLinkedStack 1 (
+ \s -> pushStack s 2 cs)
+
+
+testStack031 : (d1 d2 : ℕ ) -> Bool {Zero}
+testStack031 2 1 = True
+testStack031 _ _ = False
+
+testStack032 : (d1 d2 : Maybe ℕ) -> Bool {Zero}
+testStack032 (Just d1) (Just d2) = testStack031 d1 d2
+testStack032 _ _ = False
+
+testStack03 : {m : Level } -> Stack ℕ (SingleLinkedStack ℕ) -> ((Maybe ℕ) -> (Maybe ℕ) -> Bool {m} ) -> Bool {m}
+testStack03 s cs = pop2Stack s (
+ \s d1 d2 -> cs d1 d2 )
+
+testStack04 : Bool
+testStack04 = testStack02 (\s -> testStack03 s testStack032)
+
+testStack05 : testStack04 ≡ True
+testStack05 = refl
+
+testStack06 : {m : Level } -> Maybe (Element ℕ)
+testStack06 = pushStack createSingleLinkedStack 1 (
+ \s -> pushStack s 2 (\s -> top (stack s)))
+
+testStack07 : {m : Level } -> Maybe (Element ℕ)
+testStack07 = pushSingleLinkedStack emptySingleLinkedStack 1 (
+ \s -> pushSingleLinkedStack s 2 (\s -> top s))
+
+testStack08 = pushSingleLinkedStack emptySingleLinkedStack 1
+ $ \s -> pushSingleLinkedStack s 2
+ $ \s -> pushSingleLinkedStack s 3
+ $ \s -> pushSingleLinkedStack s 4
+ $ \s -> pushSingleLinkedStack s 5
+ $ \s -> top s
+
+------
+--
+-- proof of properties with indefinite state of stack
+--
+-- this should be proved by properties of the stack inteface, not only by the implementation,
+-- and the implementation have to provides the properties.
+--
+-- we cannot write "s ≡ s3", since level of the Set does not fit , but use stack s ≡ stack s3 is ok.
+-- anyway some implementations may result s != s3
+--
+
+stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) -> Stack {l} {m} D {t} ( SingleLinkedStack D )
+stackInSomeState s = record { stack = s ; stackMethods = singleLinkedStackSpec }
+
+push->push->pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) ->
+ pushStack ( stackInSomeState s ) x ( \s1 -> pushStack s1 y ( \s2 -> pop2Stack s2 ( \s3 y1 x1 -> (Just x ≡ x1 ) ∧ (Just y ≡ y1 ) ) ))
+push->push->pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl }
+
+
+-- id : {n : Level} {A : Set n} -> A -> A
+-- id a = a
+
+-- push a, n times
+
+n-push : {n : Level} {A : Set n} {a : A} -> ℕ -> SingleLinkedStack A -> SingleLinkedStack A
+n-push zero s = s
+n-push {l} {A} {a} (suc n) s = pushSingleLinkedStack (n-push {l} {A} {a} n s) a (\s -> s )
+
+n-pop : {n : Level}{A : Set n} {a : A} -> ℕ -> SingleLinkedStack A -> SingleLinkedStack A
+n-pop zero s = s
+n-pop {_} {A} {a} (suc n) s = popSingleLinkedStack (n-pop {_} {A} {a} n s) (\s _ -> s )
+
+open ≡-Reasoning
+
+push-pop-equiv : {n : Level} {A : Set n} {a : A} (s : SingleLinkedStack A) -> (popSingleLinkedStack (pushSingleLinkedStack s a (\s -> s)) (\s _ -> s) ) ≡ s
+push-pop-equiv s = refl
+
+push-and-n-pop : {n : Level} {A : Set n} {a : A} (n : ℕ) (s : SingleLinkedStack A) -> n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack s a id) ≡ n-pop {_} {A} {a} n s
+push-and-n-pop zero s = refl
+push-and-n-pop {_} {A} {a} (suc n) s = begin
+ n-pop {_} {A} {a} (suc (suc n)) (pushSingleLinkedStack s a id)
+ ≡⟨ refl ⟩
+ popSingleLinkedStack (n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack s a id)) (\s _ -> s)
+ ≡⟨ cong (\s -> popSingleLinkedStack s (\s _ -> s )) (push-and-n-pop n s) ⟩
+ popSingleLinkedStack (n-pop {_} {A} {a} n s) (\s _ -> s)
+ ≡⟨ refl ⟩
+ n-pop {_} {A} {a} (suc n) s
+ ∎
+
+
+n-push-pop-equiv : {n : Level} {A : Set n} {a : A} (n : ℕ) (s : SingleLinkedStack A) -> (n-pop {_} {A} {a} n (n-push {_} {A} {a} n s)) ≡ s
+n-push-pop-equiv zero s = refl
+n-push-pop-equiv {_} {A} {a} (suc n) s = begin
+ n-pop {_} {A} {a} (suc n) (n-push (suc n) s)
+ ≡⟨ refl ⟩
+ n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack (n-push n s) a (\s -> s))
+ ≡⟨ push-and-n-pop n (n-push n s) ⟩
+ n-pop {_} {A} {a} n (n-push n s)
+ ≡⟨ n-push-pop-equiv n s ⟩
+ s
+ ∎
+
+
+n-push-pop-equiv-empty : {n : Level} {A : Set n} {a : A} -> (n : ℕ) -> n-pop {_} {A} {a} n (n-push {_} {A} {a} n emptySingleLinkedStack) ≡ emptySingleLinkedStack
+n-push-pop-equiv-empty n = n-push-pop-equiv n emptySingleLinkedStack
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stackTest.agdai
Binary file final_main/src/stackTest.agdai has changed
diff -r 000000000000 -r 83f997abf3b5 final_main/src/struct-init.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/struct-init.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,1 @@
+struct Point p = {100 , 200};
diff -r 000000000000 -r 83f997abf3b5 final_main/src/struct.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/struct.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,4 @@
+struct Point {
+ int x;
+ int y;
+};
diff -r 000000000000 -r 83f997abf3b5 final_main/src/stub.cbc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/stub.cbc Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,17 @@
+__code put(struct Context* context,
+ struct Tree* tree,
+ struct Node* root,
+ struct Allocate* allocate)
+{
+ /* 実装コードは省略 */
+}
+
+__code put_stub(struct Context* context)
+{
+ goto put(context,
+ &context->data[Tree]->tree,
+ context->data[Tree]->tree.root,
+ &context->data[Allocate]->allocate);
+}
+
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/subtype.agda
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/subtype.agda Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,44 @@
+open import Level
+open import Relation.Binary.PropositionalEquality
+
+module subtype {l : Level} (Context : Set l) where
+
+
+record DataSegment {ll : Level} (A : Set ll) : Set (l ⊔ ll) where
+ field
+ get : Context -> A
+ set : Context -> A -> Context
+open DataSegment
+
+data CodeSegment {l1 l2 : Level} (A : Set l1) (B : Set l2) : Set (l ⊔ l1 ⊔ l2) where
+ cs : {{_ : DataSegment A}} {{_ : DataSegment B}} -> (A -> B) -> CodeSegment A B
+
+goto : {l1 l2 : Level} {I : Set l1} {O : Set l2} -> CodeSegment I O -> I -> O
+goto (cs b) i = b i
+
+exec : {l1 l2 : Level} {I : Set l1} {O : Set l2} {{_ : DataSegment I}} {{_ : DataSegment O}}
+ -> CodeSegment I O -> Context -> Context
+exec {l} {{i}} {{o}} (cs b) c = set o c (b (get i c))
+
+
+comp : {con : Context} -> {l1 l2 l3 l4 : Level}
+ {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
+ {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
+ -> (C -> D) -> (A -> B) -> A -> D
+comp {con} {{i}} {{io}} {{oi}} {{o}} g f x = g (get oi (set io con (f x)))
+
+csComp : {con : Context} -> {l1 l2 l3 l4 : Level}
+ {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
+ {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
+ -> CodeSegment C D -> CodeSegment A B -> CodeSegment A D
+csComp {con} {A} {B} {C} {D} {{da}} {{db}} {{dc}} {{dd}} (cs g) (cs f)
+ = cs {{da}} {{dd}} (comp {con} {{da}} {{db}} {{dc}} {{dd}} g f)
+
+
+
+comp-associative : {A B C D E F : Set l} {con : Context}
+ {{da : DataSegment A}} {{db : DataSegment B}} {{dc : DataSegment C}}
+ {{dd : DataSegment D}} {{de : DataSegment E}} {{df : DataSegment F}}
+ -> (a : CodeSegment A B) (b : CodeSegment C D) (c : CodeSegment E F)
+ -> csComp {con} c (csComp {con} b a) ≡ csComp {con} (csComp {con} c b) a
+comp-associative (cs _) (cs _) (cs _) = refl
diff -r 000000000000 -r 83f997abf3b5 final_main/src/type-cs.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/type-cs.c Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,9 @@
+__code getMinHeight_stub(struct Context* context) {
+ goto getMinHeight(context, &context->data[Allocate]->allocate, &context->data[AkashaInfo]->akashaInfo);
+}
+
+__code getMinHeight(struct Context* context, struct Allocate* allocate, struct AkashaInfo* akashaInfo) {
+ /* ... */
+ goto getMinHeight_stub(context);
+}
+
diff -r 000000000000 -r 83f997abf3b5 final_main/src/type-ds.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/type-ds.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,5 @@
+struct AkashaInfo {
+ unsigned int minHeight;
+ unsigned int maxHeight;
+ struct AkashaNode* akashaNode;
+};
diff -r 000000000000 -r 83f997abf3b5 final_main/src/type-mds.h
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/src/type-mds.h Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,15 @@
+struct Data { /* data segments as types */
+ struct Tree { /* ... */ } tree;
+ struct Node { /* ... */ } node;
+
+ struct IterElem { /* ... */ } iterElem;
+ struct Iterator { /* ... */ } iterator;
+ struct AkashaInfo { /* ... */} akashaInfo;
+ struct AkashaNode { /* ... */} akashaNode;
+};
+
+
+struct Context { /* meta data segment as subtype */
+ /* ... fields for meta computations ... */
+ struct Data **data; /* data segments */
+};
diff -r 000000000000 -r 83f997abf3b5 final_main/thanks.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/final_main/thanks.tex Thu Feb 14 16:51:50 2019 +0900
@@ -0,0 +1,18 @@
+\chapter*{謝辞}
+\thispagestyle{empty}
+
+%基本的な内容は以下の通り．参考にしてみて下さい．
+%厳密な決まりは無いので，個々人の文体でも構わない．
+%GISゼミや英語ゼミに参加した人はその分も入れておく．
+%順番は重要なので気を付けるように．(提出前に周りの人に確認してもらう．)
+
+\hspace{1zw}本研究の遂行，また本論文の作成にあたり、御多忙にも関わらず終始懇切なる御指導と御教授を賜わりました河野真治准教授に深く感謝したします。
+また、一年間共に研究を行い、暖かな気遣いと励ましをもって支えてくれた並列信頼研究室のみなさんに感謝致します。
+
+最後に、有意義な時間を共に過ごした情報工学科の学友、並びに物心両面で支えてくれた両親に深く感謝致します。
+
+\begin{flushright}
+ 2018年 3月 \\ 外間政尊
+\end{flushright}
+
+