Mercurial > hg > Papers > 2013 > kono-prosym

changeset 12:5b51dffd2b19 default tip

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add fig
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sat, 11 Jan 2014 09:48:32 +0900
parents 0a2454365e55
children
files presen/agda-prog.ind presen/fig/Kleisli.graffle presen/fig/Kleisli.svg presen/fig/Monad.graffle presen/fig/Monad.svg presen/fig/arrow.graffle presen/fig/arrow.svg presen/fig/assoc-monad.png presen/fig/flatten.graffle presen/fig/flatten.svg presen/fig/join.graffle presen/fig/join.svg presen/fig/nat.graffle presen/fig/nat.svg
diffstat 14 files changed, 5374 insertions(+), 11 deletions(-) [+]
line wrap: on
line diff
--- a/presen/agda-prog.ind	Sat Jan 11 00:52:00 2014 +0900
+++ b/presen/agda-prog.ind	Sat Jan 11 09:48:32 2014 +0900
@@ -1,6 +1,6 @@
 -title:  Agda での Programming 技術
 
--author: 河野真治
+-author: 　
 
 --なんで、今、証明支援系なのか?
 
@@ -8,8 +8,17 @@
 
 Haskell が流行ってるようだが…
 
+     Haskell はMonad使いまくり
+
      Monadって何?
 
+--この発表は...
+
+Agdaをさんざん触って面白かった
+
+  1部　Monad って何?
+  2部　Agda って何?
+
 --Monadって何?
 
 Monad を解説しているサイトは多いが、多くは皮相的
@@ -18,7 +27,7 @@
 
 →　だったら、Monad を証明支援系を使って理解すれば良いんじゃないの?
 
-とりあえず、目標は Monad の合成則
+とりあえず、目標は Monad の合成則の証明
 
 --圏
 
@@ -37,7 +46,12 @@
 
 これだけ。(あとは、Functor, Natural Transformation, Adjunction, Monad ... )
 
---圏と関数型プログラミング
+--射と合成則
+
+<center><img src="fig/arrow.jpg"></center>
+
+
+--圏と関数型プログラミングとの関係
 
 射が関数 ( = 関数型プログラミングのプログラム)
 
@@ -53,19 +67,26 @@
 
 型は圏でもある。
 
+   Int → List
+
 --Functor
 
-Functor F とは、Category C から D への写像
-対象AをDの対象B対応させる写像をFObjとする。
+Functor F とは、Category C から D への射
+
+Cの対象aをDの対象a'に対応させる写像をFObjとする。
+Cの射fをDの射f'に対応させる写像をFMapとする。
+
 射の対応が、以下を満たす時に、F はFunctor と言う。
 
-    (1) C の射 f:A->B を Dの射 F(f):F(A)->F(B) に割り当てる (FMap)
-    (2) id(F(A)) = F(id(A))
-    (3) f: A->B, g: B->C に対して、
-        F(g) ○ F(f) : F(g○f)
+    (1) C の射 f:a->b を Dの射 F(f):F(a)->F(b) に割り当てる (FMap)
+    (2) id(F(a)) = F(id(a))
+    (3) f: a->b, g: b->c に対して、
+        F(g) ○ F(f) : F(g○f)   分配法則
 
 Functor は対象の写像FObjと、射の写像FMapの二つを持つ。
 
+Functor の数学記法は polymorphic
+
 --Constructor としての Functor
 
 Integer と List はどちらも圏であり、
@@ -81,10 +102,11 @@
        |       Leaf a
 
 List や Node を Functor のFObj(対象の射)として考えることができる。
+(Leaf や :: は　constructor )
 
 --FMap
 
-Functor は射の写像も持っている必要があり、fmap として(自分で)定義する。
+Functor の射の写像は、fmap として(自分で)定義する。
 
      class Functor f where
         fmap :: (a->b) -> f a -> f b
@@ -177,8 +199,24 @@
 
 <center><img src="fig/join.jpg"></center>
 
-合成則の証明は煩雑
+合成則の証明は
+<a href="fig/monad-assoc.png">煩雑 </a>
+
+--Haskell 使うのに圏論とか必要なのか?
+
+知らなくても困らない
+
+Monad とか用語は理解できる
 
+Functor と map はわかる
+
+煩雑な証明を自分でやって理解する
+
+そもそも証明自体が圏論( Curry Howard 対応)
+
+Curry Howard 対応な証明支援系である Agda を使えば?
+
+(これで1部終わり。長かった...)
 
 --Curry Howard 対応
 
@@ -461,9 +499,28 @@
 
 --結局、Monad は役に立つのか?
 
+メタプログラミング(IOや並列処理)として便利
+
+構文やややうざい。C のプログラミングみたい。
+
+結合則や Functor(fmapを持つ) は必須ではない
+
+Monad の合成はさらに煩雑 (Beck Law)
+
+Monad Transform も「一度Monadを分解して再合成」
+
+圏論知らなくても使えるが、勉強すれば用語は納得できる
 
 --結局、証明 は役に立つのか?
 
+Monad に関しては役に立たない
+
+圏論を理解するのは役に立つ
+
+教科書は「道標のみ」
+
+自分で山を登らないと。山を登るためのツール。
+
 --Agda は面白い
 
 詰将棋みたいなもの
@@ -472,7 +529,16 @@
 
 Agda は Coq よりもマイナー
 
+Agda の情報が少ないので面白い
 
+みんな Agda を使おう!
 
+--おまけ
+
+Agda は Emacs で使うもの
+
+Vimmer にはつらすぎる (手がつる)
+
+vim emulator を使うと幸せになれます
 
  
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+++ b/presen/fig/Kleisli.graffle	Sat Jan 11 09:48:32 2014 +0900
@@ -0,0 +1,373 @@
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/presen/fig/Monad.graffle	Sat Jan 11 09:48:32 2014 +0900
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+		<dict>
+			<key>Bounds</key>
+			<string>{{66.92783267006098, 101.34005200862885}, {26, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>22</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>14</integer>
+				<key>Offset</key>
+				<real>-18.072183609008789</real>
+				<key>Position</key>
+				<real>0.44984209537506104</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;\f1\fnil\fcharset128 HiraKakuProN-W3;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \uc0\u951 
+\f1 T}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{121.40782934427261, 56.49031922083347}, {25, 24}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>21</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>13</integer>
+				<key>Offset</key>
+				<real>11.509682655334473</real>
+				<key>Position</key>
+				<real>0.45582613348960876</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 T\uc0\u951 }</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>20</integer>
+			<key>Points</key>
+			<array>
+				<string>{383.00000314968503, 87}</string>
+				<string>{383.00000314968503, 150}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>19</integer>
+			<key>Points</key>
+			<array>
+				<string>{298, 157}</string>
+				<string>{379, 157}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+			<key>ID</key>
+			<integer>18</integer>
+			<key>Points</key>
+			<array>
+				<string>{290.49999684968503, 87}</string>
+				<string>{290.49999684968503, 150}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+			<key>ID</key>
+			<integer>17</integer>
+			<key>Points</key>
+			<array>
+				<string>{301.5, 80.000002255839377}</string>
+				<string>{375.5, 80.000002255839377}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>7</integer>
+			</dict>
+			<key>ID</key>
+			<integer>16</integer>
+			<key>Points</key>
+			<array>
+				<string>{179.50000314968182, 87}</string>
+				<string>{179.50000314968182, 150}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>5</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>7</integer>
+			</dict>
+			<key>ID</key>
+			<integer>15</integer>
+			<key>Points</key>
+			<array>
+				<string>{105.5, 157.0000060489256}</string>
+				<string>{172, 157.0000060489256}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>6</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>6</integer>
+			</dict>
+			<key>ID</key>
+			<integer>14</integer>
+			<key>Points</key>
+			<array>
+				<string>{98.000016279069769, 87}</string>
+				<string>{98.000016279069769, 150}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>4</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>5</integer>
+			</dict>
+			<key>ID</key>
+			<integer>13</integer>
+			<key>Points</key>
+			<array>
+				<string>{102, 80.000001876167943}</string>
+				<string>{172, 80.000001876167943}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>4</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{379, 150}, {8, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>11</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
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+{\colortbl;\red255\green255\blue255;}
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+
+\f0\fs24 \cf0 T}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{283, 150}, {15, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>10</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
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+
+\f0\fs24 \cf0 TT}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{375.5, 73}, {15, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>9</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
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+
+\f0\fs24 \cf0 TT}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{279.5, 73}, {22, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>8</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
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+{\colortbl;\red255\green255\blue255;}
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+
+\f0\fs24 \cf0 TTT}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{172, 150}, {15, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>Vertical</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>7</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg65001\cocoartf1187\cocoasubrtf390
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+{\colortbl;\red255\green255\blue255;}
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+
+\f0\fs24 \cf0 T}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{90.5, 150}, {15, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>6</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
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+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>25</integer>
+			<key>Points</key>
+			<array>
+				<string>{113.50001433129972, 169.02882937555302}</string>
+				<string>{184.49999793412184, 169.01886099019171}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>3</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{244.45394313335419, 251.4567037820816}, {80, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>24</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>23</integer>
+				<key>Position</key>
+				<real>0.5107157826423645</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
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+
+\f0\fs24 \cf0 \'8e\'cbh
+\f1 (gf)=(hg)f}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>15</integer>
+			</dict>
+			<key>ID</key>
+			<integer>23</integer>
+			<key>Points</key>
+			<array>
+				<string>{95.361123446700233, 187.76154404254115}</string>
+				<string>{147, 266}</string>
+				<string>{400, 265}</string>
+				<string>{471.14714856626586, 186.49281094083884}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>3</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{328.84354731440544, 209.60164687037468}, {36, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>22</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>21</integer>
+				<key>Position</key>
+				<real>0.48014342784881592</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'8e\'cb
+\f1 hg}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>15</integer>
+			</dict>
+			<key>ID</key>
+			<integer>21</integer>
+			<key>Points</key>
+			<array>
+				<string>{237.97990233040034, 182.44568753374489}</string>
+				<string>{309, 224}</string>
+				<string>{404, 223}</string>
+				<string>{465.11057558541853, 183.24132069569202}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{198.18465663454145, 104.52632015943527}, {33, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>20</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>19</integer>
+				<key>Position</key>
+				<real>0.50266808271408081</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
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+
+\f0\fs24 \cf0 \'8e\'cb
+\f1 gf}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>12</integer>
+			</dict>
+			<key>ID</key>
+			<integer>19</integer>
+			<key>Points</key>
+			<array>
+				<string>{104.82973196495688, 154.75055840610796}</string>
+				<string>{161, 118}</string>
+				<string>{263.00000070706716, 119}</string>
+				<string>{324.19161901737732, 155.42358263415986}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>3</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{398.04929663372951, 155.00257346135098}, {29, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>17</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>16</integer>
+				<key>Position</key>
+				<real>0.44366195797920227</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'8e\'cb
+\f1 h}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>15</integer>
+			</dict>
+			<key>ID</key>
+			<integer>16</integer>
+			<key>Points</key>
+			<array>
+				<string>{377.50001495583831, 169.00119742870976}</string>
+				<string>{456.4999856486923, 169.00429896269634}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>12</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{457, 149.0000114440918}, {60, 40}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>ID</key>
+			<integer>15</integer>
+			<key>Shape</key>
+			<string>Circle</string>
+			<key>Style</key>
+			<dict/>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'91\'ce\'8f\'db
+\f1 d}</string>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{261.50000035484334, 155.00001462960023}, {29, 28}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>14</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>13</integer>
+				<key>Position</key>
+				<real>0.42957744002342224</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'8e\'cb
+\f1 g}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>12</integer>
+			</dict>
+			<key>ID</key>
+			<integer>13</integer>
+			<key>Points</key>
+			<array>
+				<string>{245.50001500358479, 169.00001462960023}</string>
+				<string>{316.49998499641208, 169.00001462960023}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{317, 149}, {60, 40}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>ID</key>
+			<integer>12</integer>
+			<key>Shape</key>
+			<string>Circle</string>
+			<key>Style</key>
+			<dict/>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'91\'ce\'8f\'db
+\f1 c}</string>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{185, 149}, {60, 40}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>ID</key>
+			<integer>11</integer>
+			<key>Shape</key>
+			<string>Circle</string>
+			<key>Style</key>
+			<dict/>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'91\'ce\'8f\'db
+\f1 b}</string>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{53, 149.03311157226562}, {60, 40}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>ID</key>
+			<integer>3</integer>
+			<key>Shape</key>
+			<string>Circle</string>
+			<key>Style</key>
+			<dict/>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1265
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;\f1\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 \'91\'ce\'8f\'db
+\f1 a}</string>
+			</dict>
+		</dict>
+	</array>
+	<key>GridInfo</key>
+	<dict/>
+	<key>GuidesLocked</key>
+	<string>NO</string>
+	<key>GuidesVisible</key>
+	<string>YES</string>
+	<key>HPages</key>
+	<integer>1</integer>
+	<key>ImageCounter</key>
+	<integer>1</integer>
+	<key>KeepToScale</key>
+	<false/>
+	<key>Layers</key>
+	<array>
+		<dict>
+			<key>Lock</key>
+			<string>NO</string>
+			<key>Name</key>
+			<string>Layer 1</string>
+			<key>Print</key>
+			<string>YES</string>
+			<key>View</key>
+			<string>YES</string>
+		</dict>
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+	<dict>
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+		<string>{{1107, 886}, {710, 872}}</string>
+		<key>ListView</key>
+		<true/>
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+		<integer>142</integer>
+		<key>RightSidebar</key>
+		<false/>
+		<key>ShowRuler</key>
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+		<key>Sidebar</key>
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+		<key>SidebarWidth</key>
+		<integer>120</integer>
+		<key>VisibleRegion</key>
+		<string>{{0, 0}, {575, 733}}</string>
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+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 Nodes.fmap(show)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{189.6250848180986, 43.66126331704875}, {89, 24}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>25</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>17</integer>
+				<key>Offset</key>
+				<real>13.314260482788086</real>
+				<key>Position</key>
+				<real>0.45270270109176636</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 flatten(Integer)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>20</integer>
+			<key>Points</key>
+			<array>
+				<string>{333.1530314376655, 76}</string>
+				<string>{333.1530314376655, 139}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>19</integer>
+			<key>Points</key>
+			<array>
+				<string>{176.1020326163983, 145.99214674557442}</string>
+				<string>{303.6530489245975, 145.96543499668616}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+			<key>ID</key>
+			<integer>18</integer>
+			<key>Points</key>
+			<array>
+				<string>{138.60285108587959, 76}</string>
+				<string>{138.61021731121093, 139}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+			<key>ID</key>
+			<integer>17</integer>
+			<key>Points</key>
+			<array>
+				<string>{179.10203261639833, 68.989622731029371}</string>
+				<string>{300.65302748944521, 68.958477857759092}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{303.6530489245975, 139}, {59, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>11</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 List(String)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{101.10203261639833, 139}, {75, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>10</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 Nodes(String)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{300.65302748944521, 62}, {65, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>9</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 List(Integer)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{98.102032616398333, 62}, {81, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>8</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 Nodes(Integer)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+	</array>
+	<key>GridInfo</key>
+	<dict/>
+	<key>GuidesLocked</key>
+	<string>NO</string>
+	<key>GuidesVisible</key>
+	<string>YES</string>
+	<key>HPages</key>
+	<integer>1</integer>
+	<key>ImageCounter</key>
+	<integer>1</integer>
+	<key>KeepToScale</key>
+	<false/>
+	<key>Layers</key>
+	<array>
+		<dict>
+			<key>Lock</key>
+			<string>NO</string>
+			<key>Name</key>
+			<string>Layer 1</string>
+			<key>Print</key>
+			<string>YES</string>
+			<key>View</key>
+			<string>YES</string>
+		</dict>
+	</array>
+	<key>LayoutInfo</key>
+	<dict>
+		<key>Animate</key>
+		<string>NO</string>
+		<key>circoMinDist</key>
+		<real>18</real>
+		<key>circoSeparation</key>
+		<real>0.0</real>
+		<key>layoutEngine</key>
+		<string>dot</string>
+		<key>neatoSeparation</key>
+		<real>0.0</real>
+		<key>twopiSeparation</key>
+		<real>0.0</real>
+	</dict>
+	<key>LinksVisible</key>
+	<string>NO</string>
+	<key>MagnetsVisible</key>
+	<string>NO</string>
+	<key>MasterSheets</key>
+	<array/>
+	<key>ModificationDate</key>
+	<string>2013-07-08 10:44:31 +0000</string>
+	<key>Modifier</key>
+	<string>Shinji KONO</string>
+	<key>NotesVisible</key>
+	<string>NO</string>
+	<key>Orientation</key>
+	<integer>2</integer>
+	<key>OriginVisible</key>
+	<string>NO</string>
+	<key>PageBreaks</key>
+	<string>YES</string>
+	<key>PrintInfo</key>
+	<dict>
+		<key>NSBottomMargin</key>
+		<array>
+			<string>float</string>
+			<string>41</string>
+		</array>
+		<key>NSHorizonalPagination</key>
+		<array>
+			<string>coded</string>
+			<string>BAtzdHJlYW10eXBlZIHoA4QBQISEhAhOU051bWJlcgCEhAdOU1ZhbHVlAISECE5TT2JqZWN0AIWEASqEhAFxlwCG</string>
+		</array>
+		<key>NSLeftMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+		<key>NSPaperSize</key>
+		<array>
+			<string>size</string>
+			<string>{595, 842}</string>
+		</array>
+		<key>NSPrintReverseOrientation</key>
+		<array>
+			<string>int</string>
+			<string>0</string>
+		</array>
+		<key>NSPrinter</key>
+		<array>
+			<string>coded</string>
+			<string>BAtzdHJlYW10eXBlZIHoA4QBQISEhAlOU1ByaW50ZXIAhIQITlNPYmplY3QAhZKEhIQITlNTdHJpbmcBlIQBKyFjaW5uYW1vbi5jci5pZS51LXJ5dWt5dS5hYy5qcC1scGSGhg==</string>
+		</array>
+		<key>NSPrinterName</key>
+		<array>
+			<string>string</string>
+			<string>cinnamon.cr.ie.u-ryukyu.ac.jp-lpd</string>
+		</array>
+		<key>NSRightMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+		<key>NSTopMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+	</dict>
+	<key>PrintOnePage</key>
+	<false/>
+	<key>ReadOnly</key>
+	<string>NO</string>
+	<key>RowAlign</key>
+	<integer>1</integer>
+	<key>RowSpacing</key>
+	<real>36</real>
+	<key>SheetTitle</key>
+	<string>Canvas 1</string>
+	<key>SmartAlignmentGuidesActive</key>
+	<string>YES</string>
+	<key>SmartDistanceGuidesActive</key>
+	<string>YES</string>
+	<key>UniqueID</key>
+	<integer>1</integer>
+	<key>UseEntirePage</key>
+	<false/>
+	<key>VPages</key>
+	<integer>1</integer>
+	<key>WindowInfo</key>
+	<dict>
+		<key>CurrentSheet</key>
+		<integer>0</integer>
+		<key>ExpandedCanvases</key>
+		<array>
+			<dict>
+				<key>name</key>
+				<string>Canvas 1</string>
+			</dict>
+		</array>
+		<key>Frame</key>
+		<string>{{1060, 195}, {693, 922}}</string>
+		<key>ListView</key>
+		<true/>
+		<key>OutlineWidth</key>
+		<integer>142</integer>
+		<key>RightSidebar</key>
+		<false/>
+		<key>ShowRuler</key>
+		<true/>
+		<key>Sidebar</key>
+		<true/>
+		<key>SidebarWidth</key>
+		<integer>120</integer>
+		<key>VisibleRegion</key>
+		<string>{{0, 0}, {558, 783}}</string>
+		<key>Zoom</key>
+		<real>1</real>
+		<key>ZoomValues</key>
+		<array>
+			<array>
+				<string>Canvas 1</string>
+				<real>1</real>
+				<real>1</real>
+			</array>
+		</array>
+	</dict>
+</dict>
+</plist>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/presen/fig/flatten.svg	Sat Jan 11 09:48:32 2014 +0900
@@ -0,0 +1,3 @@
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+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>4</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>4</integer>
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+			<integer>16</integer>
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+			<array>
+				<string>{114, 125}</string>
+				<string>{144.50003906683062, 124.61874951166462}</string>
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+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{315, 92}, {79, 66}}</string>
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+			<string>ShapedGraphic</string>
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+				<string>{1, 0}</string>
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+			<key>Shape</key>
+			<string>Diamond</string>
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+			<dict/>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
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+
+\f0\fs24 \cf0 T1(out1)}</string>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{145, 104}, {98, 40}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>ID</key>
+			<integer>4</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
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+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
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+
+\f0\fs24 \cf0 in-&gt; T(out1)}</string>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{97, 118}, {10, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
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+			<dict>
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+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
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+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
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+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
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+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
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+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
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+
+\f0\fs24 \cf0 in}</string>
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+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{15, 82}, {532, 206}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
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+			<integer>29</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+		</dict>
+	</array>
+	<key>GridInfo</key>
+	<dict/>
+	<key>GuidesLocked</key>
+	<string>NO</string>
+	<key>GuidesVisible</key>
+	<string>YES</string>
+	<key>HPages</key>
+	<integer>1</integer>
+	<key>ImageCounter</key>
+	<integer>1</integer>
+	<key>KeepToScale</key>
+	<false/>
+	<key>Layers</key>
+	<array>
+		<dict>
+			<key>Lock</key>
+			<string>NO</string>
+			<key>Name</key>
+			<string>Layer 1</string>
+			<key>Print</key>
+			<string>YES</string>
+			<key>View</key>
+			<string>YES</string>
+		</dict>
+	</array>
+	<key>LayoutInfo</key>
+	<dict>
+		<key>Animate</key>
+		<string>NO</string>
+		<key>circoMinDist</key>
+		<real>18</real>
+		<key>circoSeparation</key>
+		<real>0.0</real>
+		<key>layoutEngine</key>
+		<string>dot</string>
+		<key>neatoSeparation</key>
+		<real>0.0</real>
+		<key>twopiSeparation</key>
+		<real>0.0</real>
+	</dict>
+	<key>LinksVisible</key>
+	<string>NO</string>
+	<key>MagnetsVisible</key>
+	<string>NO</string>
+	<key>MasterSheets</key>
+	<array/>
+	<key>ModificationDate</key>
+	<string>2013-07-08 11:15:32 +0000</string>
+	<key>Modifier</key>
+	<string>Shinji KONO</string>
+	<key>NotesVisible</key>
+	<string>NO</string>
+	<key>Orientation</key>
+	<integer>2</integer>
+	<key>OriginVisible</key>
+	<string>NO</string>
+	<key>PageBreaks</key>
+	<string>YES</string>
+	<key>PrintInfo</key>
+	<dict>
+		<key>NSBottomMargin</key>
+		<array>
+			<string>float</string>
+			<string>41</string>
+		</array>
+		<key>NSHorizonalPagination</key>
+		<array>
+			<string>coded</string>
+			<string>BAtzdHJlYW10eXBlZIHoA4QBQISEhAhOU051bWJlcgCEhAdOU1ZhbHVlAISECE5TT2JqZWN0AIWEASqEhAFxlwCG</string>
+		</array>
+		<key>NSLeftMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+		<key>NSPaperSize</key>
+		<array>
+			<string>size</string>
+			<string>{595, 842}</string>
+		</array>
+		<key>NSPrintReverseOrientation</key>
+		<array>
+			<string>int</string>
+			<string>0</string>
+		</array>
+		<key>NSRightMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+		<key>NSTopMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+	</dict>
+	<key>PrintOnePage</key>
+	<false/>
+	<key>ReadOnly</key>
+	<string>NO</string>
+	<key>RowAlign</key>
+	<integer>1</integer>
+	<key>RowSpacing</key>
+	<real>36</real>
+	<key>SheetTitle</key>
+	<string>Canvas 1</string>
+	<key>SmartAlignmentGuidesActive</key>
+	<string>YES</string>
+	<key>SmartDistanceGuidesActive</key>
+	<string>YES</string>
+	<key>UniqueID</key>
+	<integer>1</integer>
+	<key>UseEntirePage</key>
+	<false/>
+	<key>VPages</key>
+	<integer>1</integer>
+	<key>WindowInfo</key>
+	<dict>
+		<key>CurrentSheet</key>
+		<integer>0</integer>
+		<key>ExpandedCanvases</key>
+		<array>
+			<dict>
+				<key>name</key>
+				<string>Canvas 1</string>
+			</dict>
+		</array>
+		<key>Frame</key>
+		<string>{{1175, 776}, {693, 922}}</string>
+		<key>ListView</key>
+		<true/>
+		<key>OutlineWidth</key>
+		<integer>142</integer>
+		<key>RightSidebar</key>
+		<false/>
+		<key>ShowRuler</key>
+		<true/>
+		<key>Sidebar</key>
+		<true/>
+		<key>SidebarWidth</key>
+		<integer>120</integer>
+		<key>VisibleRegion</key>
+		<string>{{0, 0}, {558, 783}}</string>
+		<key>Zoom</key>
+		<real>1</real>
+		<key>ZoomValues</key>
+		<array>
+			<array>
+				<string>Canvas 1</string>
+				<real>1</real>
+				<real>1</real>
+			</array>
+		</array>
+	</dict>
+</dict>
+</plist>
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+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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+	<array>
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+		<string>139.17.0.185490</string>
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+	<key>AutoAdjust</key>
+	<true/>
+	<key>BackgroundGraphic</key>
+	<dict>
+		<key>Bounds</key>
+		<string>{{0, 0}, {559, 783}}</string>
+		<key>Class</key>
+		<string>SolidGraphic</string>
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+		<key>Style</key>
+		<dict>
+			<key>shadow</key>
+			<dict>
+				<key>Draws</key>
+				<string>NO</string>
+			</dict>
+			<key>stroke</key>
+			<dict>
+				<key>Draws</key>
+				<string>NO</string>
+			</dict>
+		</dict>
+	</dict>
+	<key>BaseZoom</key>
+	<integer>0</integer>
+	<key>CanvasOrigin</key>
+	<string>{0, 0}</string>
+	<key>ColumnAlign</key>
+	<integer>1</integer>
+	<key>ColumnSpacing</key>
+	<real>36</real>
+	<key>CreationDate</key>
+	<string>2013-07-08 10:40:31 +0000</string>
+	<key>Creator</key>
+	<string>Shinji KONO</string>
+	<key>DisplayScale</key>
+	<string>1.000 cm = 1.000 cm</string>
+	<key>GraphDocumentVersion</key>
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+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>29</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
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+			<key>Text</key>
+			<dict>
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+
+\f0\fs24 \cf0 G(f)t(a) = t(b)F(f)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
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+			<key>Wrap</key>
+			<string>NO</string>
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+			<string>{{173.80101990847274, 96.317317531050094}, {33, 28}}</string>
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+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
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+				<key>Font</key>
+				<string>Helvetica</string>
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+			</dict>
+			<key>ID</key>
+			<integer>28</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>20</integer>
+				<key>Offset</key>
+				<real>18.75</real>
+				<key>Position</key>
+				<real>0.56648933887481689</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fnil\fcharset128 HiraKakuProN-W3;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 G(f)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{103.50780663622498, 145.58183742626861}, {28, 24}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>27</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>19</integer>
+				<key>Offset</key>
+				<real>-12.95334529876709</real>
+				<key>Position</key>
+				<real>0.39506173133850098</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 t(b)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{41.025492314390476, 94.387673184812911}, {29, 24}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>26</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>18</integer>
+				<key>Offset</key>
+				<real>-23.525527954101562</real>
+				<key>Position</key>
+				<real>0.50411403179168701</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 F(f)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{107.51385403407693, 42.314231644713416}, {28, 24}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>FontInfo</key>
+			<dict>
+				<key>Color</key>
+				<dict>
+					<key>w</key>
+					<string>0</string>
+				</dict>
+				<key>Font</key>
+				<string>Helvetica</string>
+				<key>Size</key>
+				<real>12</real>
+			</dict>
+			<key>ID</key>
+			<integer>25</integer>
+			<key>Line</key>
+			<dict>
+				<key>ID</key>
+				<integer>17</integer>
+				<key>Offset</key>
+				<real>13.314260482788086</real>
+				<key>Position</key>
+				<real>0.45270270109176636</real>
+				<key>RotationType</key>
+				<integer>0</integer>
+			</dict>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 t(a)}</string>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>20</integer>
+			<key>Points</key>
+			<array>
+				<string>{171.55101990847274, 74.628489181936629}</string>
+				<string>{171.55101990847274, 137.62848918193663}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>11</integer>
+			</dict>
+			<key>ID</key>
+			<integer>19</integer>
+			<key>Points</key>
+			<array>
+				<string>{90.051016308199166, 144.62849212750152}</string>
+				<string>{159.55101630819917, 144.62849212750152}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>10</integer>
+			</dict>
+			<key>ID</key>
+			<integer>18</integer>
+			<key>Points</key>
+			<array>
+				<string>{79.051020268492039, 74.628489181936629}</string>
+				<string>{79.051020268492039, 137.62848918193663}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Class</key>
+			<string>LineGraphic</string>
+			<key>Head</key>
+			<dict>
+				<key>ID</key>
+				<integer>9</integer>
+			</dict>
+			<key>ID</key>
+			<integer>17</integer>
+			<key>Points</key>
+			<array>
+				<string>{90.051016308199166, 67.628492127501502}</string>
+				<string>{159.55101630819917, 67.628492127501502}</string>
+			</array>
+			<key>Style</key>
+			<dict>
+				<key>stroke</key>
+				<dict>
+					<key>HeadArrow</key>
+					<string>FilledArrow</string>
+					<key>Legacy</key>
+					<true/>
+					<key>TailArrow</key>
+					<string>0</string>
+				</dict>
+			</dict>
+			<key>Tail</key>
+			<dict>
+				<key>ID</key>
+				<integer>8</integer>
+			</dict>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{159.55101630819917, 137.62848918193663}, {24, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>11</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 G(b)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{68.051016308199166, 137.62848918193663}, {22, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>10</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 F(b)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{159.55101630819917, 60.628489181936629}, {24, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>9</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 G(a)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+		<dict>
+			<key>Bounds</key>
+			<string>{{68.051016308199166, 60.628489181936629}, {22, 14}}</string>
+			<key>Class</key>
+			<string>ShapedGraphic</string>
+			<key>FitText</key>
+			<string>YES</string>
+			<key>Flow</key>
+			<string>Resize</string>
+			<key>ID</key>
+			<integer>8</integer>
+			<key>Shape</key>
+			<string>Rectangle</string>
+			<key>Style</key>
+			<dict>
+				<key>fill</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>shadow</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+				<key>stroke</key>
+				<dict>
+					<key>Draws</key>
+					<string>NO</string>
+				</dict>
+			</dict>
+			<key>Text</key>
+			<dict>
+				<key>Pad</key>
+				<integer>0</integer>
+				<key>Text</key>
+				<string>{\rtf1\ansi\ansicpg1252\cocoartf1187\cocoasubrtf390
+\cocoascreenfonts1{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
+{\colortbl;\red255\green255\blue255;}
+\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\pardirnatural\qc
+
+\f0\fs24 \cf0 F(a)}</string>
+				<key>VerticalPad</key>
+				<integer>0</integer>
+			</dict>
+			<key>Wrap</key>
+			<string>NO</string>
+		</dict>
+	</array>
+	<key>GridInfo</key>
+	<dict/>
+	<key>GuidesLocked</key>
+	<string>NO</string>
+	<key>GuidesVisible</key>
+	<string>YES</string>
+	<key>HPages</key>
+	<integer>1</integer>
+	<key>ImageCounter</key>
+	<integer>1</integer>
+	<key>KeepToScale</key>
+	<false/>
+	<key>Layers</key>
+	<array>
+		<dict>
+			<key>Lock</key>
+			<string>NO</string>
+			<key>Name</key>
+			<string>Layer 1</string>
+			<key>Print</key>
+			<string>YES</string>
+			<key>View</key>
+			<string>YES</string>
+		</dict>
+	</array>
+	<key>LayoutInfo</key>
+	<dict>
+		<key>Animate</key>
+		<string>NO</string>
+		<key>circoMinDist</key>
+		<real>18</real>
+		<key>circoSeparation</key>
+		<real>0.0</real>
+		<key>layoutEngine</key>
+		<string>dot</string>
+		<key>neatoSeparation</key>
+		<real>0.0</real>
+		<key>twopiSeparation</key>
+		<real>0.0</real>
+	</dict>
+	<key>LinksVisible</key>
+	<string>NO</string>
+	<key>MagnetsVisible</key>
+	<string>NO</string>
+	<key>MasterSheets</key>
+	<array/>
+	<key>ModificationDate</key>
+	<string>2013-07-09 04:19:31 +0000</string>
+	<key>Modifier</key>
+	<string>Shinji KONO</string>
+	<key>NotesVisible</key>
+	<string>NO</string>
+	<key>Orientation</key>
+	<integer>2</integer>
+	<key>OriginVisible</key>
+	<string>NO</string>
+	<key>PageBreaks</key>
+	<string>YES</string>
+	<key>PrintInfo</key>
+	<dict>
+		<key>NSBottomMargin</key>
+		<array>
+			<string>float</string>
+			<string>41</string>
+		</array>
+		<key>NSHorizonalPagination</key>
+		<array>
+			<string>coded</string>
+			<string>BAtzdHJlYW10eXBlZIHoA4QBQISEhAhOU051bWJlcgCEhAdOU1ZhbHVlAISECE5TT2JqZWN0AIWEASqEhAFxlwCG</string>
+		</array>
+		<key>NSLeftMargin</key>
+		<array>
+			<string>float</string>
+			<string>18</string>
+		</array>
+		<key>NSPaperSize</key>
+		<array>
+			<string>size</string>
+			<string>{595, 842}</string>
+		</array>
+		<key>NSPrintReverseOrientation</key>
+		<array>
+			<string>int</string>
+			<string>0</string>
+		</array>
+		<key>NSRightMargin</key>
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+		<key>ListView</key>
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
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