Chapter 7: While Statementlinear-chapter07

Co-authored-by: Cliff Click <cliffc@acm.org>
Co-authored-by: Thalia Archibald <thalia@archibald.dev>
Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
Co-authored-by: Robert Obkircher <robert.obkircher@gmail.com>

11 files changed, 1860 insertions, 0 deletions

diff --git a/docs/chapter07/07-grammar.md b/docs/chapter07/07-grammar.md
new file mode 100644
index 00000000..29a730b6
--- /dev/null
+++ b/docs/chapter07/07-grammar.md
@@ -0,0 +1,88 @@
+# Grammar for Chapter 6
+
+```antlrv4
+grammar SimpleLanguage;
+
+program
+    : statement+ EOF
+    ;
+
+statement
+    : returnStatement
+    | declStatement
+    | blockStatment
+    | expressionStatement
+    | ifStatement
+    | whileStatement
+    | metaStatement
+    ;
+
+whileStatement
+    : 'while' '(' expression ')' statement
+    ;
+
+ifStatement
+    : 'if' '(' expression ')' statement ('else' statement)?
+    ;
+
+metaStatement
+    : '#showGraph' ';'
+    ;
+
+expressionStatement
+    : IDENTIFIER '=' expression ';'
+    ;
+
+blockStatement
+    : '{' statement+ '}'
+    ;
+
+declStatement
+    : 'int' IDENTIFIER '=' expression ';'
+    ;
+
+returnStatement
+    : 'return' expression ';'
+    ;
+
+expression
+    : comparisonExpression
+    ;
+
+comparisonExpression
+    : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)*
+    ;
+
+additiveExpression
+    : multiplicativeExpression (('+' | '-') multiplicativeExpression)*
+    ;
+
+multiplicativeExpression
+    : unaryExpression (('*' | '/') unaryExpression)*
+    ;
+
+unaryExpression
+    : ('-') unaryExpression
+    | primaryExpression
+    ;
+
+primaryExpression
+    : IDENTIFIER
+    | INTEGER_LITERAL
+    | 'true'
+    | 'false'
+    | '(' expression ')'
+    ;
+
+INTEGER_LITERAL
+    : [1-9][0-9]*
+    | [0]
+    ;
+
+IDENTIFIER
+    : NON_DIGIT (NON_DIGIT | DIGIT)*
+    ;
+
+NON_DIGIT: [a-zA-Z_];
+DEC_DIGIT: [0-9];
+```
diff --git a/docs/chapter07/07-graph1.gv b/docs/chapter07/07-graph1.gv
new file mode 100644
index 00000000..ba806a28
--- /dev/null
+++ b/docs/chapter07/07-graph1.gv
@@ -0,0 +1,107 @@
+digraph chapter07 {
+/*
+while(arg < 10) {
+    arg = arg + 1;
+    #showGraph;
+}
+return arg;
+
+*/
+	rankdir=BT;
+	ordering="in";
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Loop6 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_arg8 [ style=filled fillcolor=lightyellow label="&phi;_arg" ];
+		Con_9 [ label="10" ];
+		LT10 [ label="<" ];
+		If11 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_15 [ label="1" ];
+		Add16 [ label="+" ];
+		{ rank=same; Loop6;Phi_arg8;}
+	}
+	node [shape=plaintext];
+	subgraph cluster_Scope7_1 {
+		Scope7_1 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">2</TD></TR>
+			</TABLE>>];
+	subgraph cluster_Scope7_2 {
+		Scope7_2 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">1</TD></TR>
+			</TABLE>>];
+	subgraph cluster_Scope7_3 {
+		Scope7_3 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope7_3_$ctrl">$ctrl</TD><TD PORT="Scope7_3_arg">arg</TD></TR>
+			</TABLE>>];
+	}
+	}
+	}
+	node [shape=plaintext];
+	subgraph cluster_Scope1_1 {
+		Scope1_1 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">1</TD></TR>
+			</TABLE>>];
+	subgraph cluster_Scope1_2 {
+		Scope1_2 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope1_2_$ctrl">$ctrl</TD><TD PORT="Scope1_2_arg">arg</TD></TR>
+			</TABLE>>];
+	}
+	}
+	node [shape=plaintext];
+	subgraph cluster_Scope14_1 {
+		Scope14_1 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">1</TD></TR>
+			</TABLE>>];
+	subgraph cluster_Scope14_2 {
+		Scope14_2 [label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+			<TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope14_2_$ctrl">$ctrl</TD><TD PORT="Scope14_2_arg">arg</TD></TR>
+			</TABLE>>];
+	}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Loop6 -> Start2:p0[taillabel=1 color=red];
+	Phi_arg8 -> Loop6 [style=dotted taillabel=0];
+	Phi_arg8 -> Start2:p1[taillabel=1];
+	LT10 -> Phi_arg8[taillabel=1];
+	LT10 -> Con_9[taillabel=2];
+	If11 -> Loop6[taillabel=0 color=red];
+	If11 -> LT10[taillabel=1];
+	Add16 -> Phi_arg8[taillabel=1];
+	Add16 -> Con_15[taillabel=2];
+	edge [style=dashed color=cornflowerblue];
+	Scope7_3:"Scope7_3_$ctrl" -> If11:p0;
+	Scope7_3:"Scope7_3_arg" -> Add16;
+	edge [style=dashed color=cornflowerblue];
+	Scope1_2:"Scope1_2_$ctrl" -> Loop6;
+	Scope1_2:"Scope1_2_arg" -> Phi_arg8;
+	edge [style=dashed color=cornflowerblue];
+	Scope14_2:"Scope14_2_$ctrl" -> If11:p1;
+	Scope14_2:"Scope14_2_arg" -> Phi_arg8;
+}
diff --git a/docs/chapter07/07-graph1.svg b/docs/chapter07/07-graph1.svg
new file mode 100644
index 00000000..94248cfb
--- /dev/null
+++ b/docs/chapter07/07-graph1.svg
@@ -0,0 +1,268 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter07 Pages: 1 -->
+<svg width="726pt" height="440pt"
+ viewBox="0.00 0.00 726.00 440.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 436)">
+<title>chapter07</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-436 722,-436 722,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="196,-100 196,-424 502,-424 502,-100 196,-100"/>
+</g>
+<g id="clust3" class="cluster">
+<title>cluster_Scope7_1</title>
+<polygon fill="none" stroke="black" points="8,-8 8,-92 288,-92 288,-8 8,-8"/>
+</g>
+<g id="clust4" class="cluster">
+<title>cluster_Scope7_2</title>
+<polygon fill="none" stroke="black" points="80,-16 80,-84 280,-84 280,-16 80,-16"/>
+</g>
+<g id="clust5" class="cluster">
+<title>cluster_Scope7_3</title>
+<polygon fill="none" stroke="black" points="152,-24 152,-76 272,-76 272,-24 152,-24"/>
+</g>
+<g id="clust6" class="cluster">
+<title>cluster_Scope1_1</title>
+<polygon fill="none" stroke="black" points="510,-192 510,-260 710,-260 710,-192 510,-192"/>
+</g>
+<g id="clust7" class="cluster">
+<title>cluster_Scope1_2</title>
+<polygon fill="none" stroke="black" points="582,-200 582,-252 702,-252 702,-200 582,-200"/>
+</g>
+<g id="clust8" class="cluster">
+<title>cluster_Scope14_1</title>
+<polygon fill="none" stroke="black" points="296,-16 296,-84 496,-84 496,-16 296,-16"/>
+</g>
+<g id="clust9" class="cluster">
+<title>cluster_Scope14_2</title>
+<polygon fill="none" stroke="black" points="368,-24 368,-76 488,-76 488,-24 368,-24"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="365,-387 365,-412 446,-412 446,-387 365,-387"/>
+<polygon fill="none" stroke="black" points="365,-387 365,-412 446,-412 446,-387 365,-387"/>
+<text text-anchor="start" x="387" y="-395.8" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="365,-356 365,-387 446,-387 446,-356 365,-356"/>
+<polygon fill="yellow" stroke="transparent" points="370,-361 370,-382 410,-382 410,-361 370,-361"/>
+<polygon fill="none" stroke="black" points="370,-361 370,-382 410,-382 410,-361 370,-361"/>
+<text text-anchor="start" x="373" y="-367.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="410,-361 410,-382 441,-382 441,-361 410,-361"/>
+<text text-anchor="start" x="413" y="-367.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Loop6 -->
+<g id="node2" class="node">
+<title>Loop6</title>
+<polygon fill="yellow" stroke="black" points="494,-316 440,-316 440,-280 494,-280 494,-316"/>
+<text text-anchor="middle" x="467" y="-294.3" font-family="Times,serif" font-size="14.00">Loop</text>
+</g>
+<!-- Loop6&#45;&gt;Start2 -->
+<g id="edge1" class="edge">
+<title>Loop6&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M439.64,-314.34C422.52,-324.68 402.19,-338.54 393.85,-350.32"/>
+<polygon fill="red" stroke="red" points="390.45,-349.41 390,-360 396.95,-352 390.45,-349.41"/>
+<text text-anchor="middle" x="436.64" y="-307.94" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_arg8 -->
+<g id="node3" class="node">
+<title>Phi_arg8</title>
+<ellipse fill="lightyellow" stroke="black" cx="385" cy="-298" rx="37.09" ry="18"/>
+<text text-anchor="middle" x="385" y="-294.3" font-family="Times,serif" font-size="14.00">φ_arg</text>
+</g>
+<!-- Phi_arg8&#45;&gt;Start2 -->
+<g id="edge3" class="edge">
+<title>Phi_arg8&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M402.63,-314.22C411.57,-323.35 421.25,-335.86 424.7,-349.71"/>
+<polygon fill="black" stroke="black" points="421.27,-350.52 426,-360 428.22,-349.64 421.27,-350.52"/>
+<text text-anchor="middle" x="399.63" y="-316.82" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_arg8&#45;&gt;Loop6 -->
+<g id="edge2" class="edge">
+<title>Phi_arg8&#45;&gt;Loop6</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M422.16,-298C424.62,-298 427.08,-298 429.55,-298"/>
+<polygon fill="black" stroke="black" points="429.67,-301.5 439.67,-298 429.67,-294.5 429.67,-301.5"/>
+<text text-anchor="middle" x="425.16" y="-291.6" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Con_9 -->
+<g id="node4" class="node">
+<title>Con_9</title>
+<ellipse fill="none" stroke="black" cx="303" cy="-298" rx="27" ry="18"/>
+<text text-anchor="middle" x="303" y="-294.3" font-family="Times,serif" font-size="14.00">10</text>
+</g>
+<!-- LT10 -->
+<g id="node5" class="node">
+<title>LT10</title>
+<ellipse fill="none" stroke="black" cx="374" cy="-226" rx="27" ry="18"/>
+<text text-anchor="middle" x="374" y="-222.3" font-family="Times,serif" font-size="14.00">&lt;</text>
+</g>
+<!-- LT10&#45;&gt;Phi_arg8 -->
+<g id="edge4" class="edge">
+<title>LT10&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="black" d="M376.66,-243.95C377.87,-251.65 379.34,-260.97 380.7,-269.64"/>
+<polygon fill="black" stroke="black" points="377.28,-270.39 382.29,-279.72 384.19,-269.3 377.28,-270.39"/>
+<text text-anchor="middle" x="373.66" y="-246.55" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- LT10&#45;&gt;Con_9 -->
+<g id="edge5" class="edge">
+<title>LT10&#45;&gt;Con_9</title>
+<path fill="none" stroke="black" d="M359.29,-241.5C349.39,-251.27 336.16,-264.31 325.01,-275.3"/>
+<polygon fill="black" stroke="black" points="322.36,-273 317.69,-282.51 327.27,-277.99 322.36,-273"/>
+<text text-anchor="middle" x="356.29" y="-244.1" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- If11 -->
+<g id="node6" class="node">
+<title>If11</title>
+<polygon fill="yellow" stroke="transparent" points="327,-143 327,-168 421,-168 421,-143 327,-143"/>
+<polygon fill="none" stroke="black" points="327,-143 327,-168 421,-168 421,-143 327,-143"/>
+<text text-anchor="start" x="368.5" y="-151.8" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="327,-112 327,-143 421,-143 421,-112 327,-112"/>
+<polygon fill="yellow" stroke="transparent" points="332,-117 332,-138 372,-138 372,-117 332,-117"/>
+<polygon fill="none" stroke="black" points="332,-117 332,-138 372,-138 372,-117 332,-117"/>
+<text text-anchor="start" x="335" y="-123.8" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="372,-117 372,-138 416,-138 416,-117 372,-117"/>
+<polygon fill="none" stroke="black" points="372,-117 372,-138 416,-138 416,-117 372,-117"/>
+<text text-anchor="start" x="375" y="-123.8" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- If11&#45;&gt;Loop6 -->
+<g id="edge6" class="edge">
+<title>If11&#45;&gt;Loop6</title>
+<path fill="none" stroke="red" d="M396.87,-172.17C401.36,-178.63 405.94,-185.46 410,-192 426.23,-218.13 442.79,-249.22 453.84,-270.75"/>
+<polygon fill="red" stroke="red" points="450.85,-272.6 458.51,-279.92 457.09,-269.42 450.85,-272.6"/>
+<text text-anchor="middle" x="393.87" y="-174.77" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If11&#45;&gt;LT10 -->
+<g id="edge7" class="edge">
+<title>If11&#45;&gt;LT10</title>
+<path fill="none" stroke="black" d="M374,-172.28C374,-180.58 374,-189.48 374,-197.56"/>
+<polygon fill="black" stroke="black" points="370.5,-197.6 374,-207.6 377.5,-197.6 370.5,-197.6"/>
+<text text-anchor="middle" x="371" y="-174.88" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_15 -->
+<g id="node7" class="node">
+<title>Con_15</title>
+<ellipse fill="none" stroke="black" cx="231" cy="-298" rx="27" ry="18"/>
+<text text-anchor="middle" x="231" y="-294.3" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Add16 -->
+<g id="node8" class="node">
+<title>Add16</title>
+<ellipse fill="none" stroke="black" cx="241" cy="-226" rx="27" ry="18"/>
+<text text-anchor="middle" x="241" y="-222.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Add16&#45;&gt;Phi_arg8 -->
+<g id="edge8" class="edge">
+<title>Add16&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="black" d="M262.25,-237.33C285.48,-248.62 323.06,-266.89 350.53,-280.24"/>
+<polygon fill="black" stroke="black" points="349.26,-283.52 359.78,-284.74 352.32,-277.22 349.26,-283.52"/>
+<text text-anchor="middle" x="265.25" y="-239.93" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add16&#45;&gt;Con_15 -->
+<g id="edge9" class="edge">
+<title>Add16&#45;&gt;Con_15</title>
+<path fill="none" stroke="black" d="M238.58,-243.95C237.48,-251.65 236.15,-260.97 234.91,-269.64"/>
+<polygon fill="black" stroke="black" points="231.42,-269.33 233.47,-279.72 238.35,-270.32 231.42,-269.33"/>
+<text text-anchor="middle" x="235.58" y="-246.55" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Scope7_1 -->
+<g id="node9" class="node">
+<title>Scope7_1</title>
+<polygon fill="cyan" stroke="transparent" points="35,-39 35,-60 51,-60 51,-39 35,-39"/>
+<polygon fill="none" stroke="black" points="35,-39 35,-60 51,-60 51,-39 35,-39"/>
+<text text-anchor="start" x="38" y="-45.8" font-family="Times,serif" font-size="14.00">2</text>
+</g>
+<!-- Scope7_2 -->
+<g id="node10" class="node">
+<title>Scope7_2</title>
+<polygon fill="cyan" stroke="transparent" points="107,-39 107,-60 123,-60 123,-39 107,-39"/>
+<polygon fill="none" stroke="black" points="107,-39 107,-60 123,-60 123,-39 107,-39"/>
+<text text-anchor="start" x="110" y="-45.8" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Scope7_3 -->
+<g id="node11" class="node">
+<title>Scope7_3</title>
+<polygon fill="cyan" stroke="transparent" points="169,-39 169,-60 185,-60 185,-39 169,-39"/>
+<polygon fill="none" stroke="black" points="169,-39 169,-60 185,-60 185,-39 169,-39"/>
+<text text-anchor="start" x="172" y="-45.8" font-family="Times,serif" font-size="14.00">0</text>
+<polygon fill="none" stroke="black" points="185,-39 185,-60 225,-60 225,-39 185,-39"/>
+<text text-anchor="start" x="188" y="-45.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="225,-39 225,-60 256,-60 256,-39 225,-39"/>
+<text text-anchor="start" x="228" y="-45.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Scope7_3&#45;&gt;If11 -->
+<g id="edge10" class="edge">
+<title>Scope7_3:Scope7_3_$ctrl&#45;&gt;If11:p0</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M205,-61C205,-74.83 289.37,-114.99 321.05,-124.81"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="320.48,-128.27 331,-127 321.98,-121.43 320.48,-128.27"/>
+</g>
+<!-- Scope7_3&#45;&gt;Add16 -->
+<g id="edge11" class="edge">
+<title>Scope7_3:Scope7_3_arg&#45;&gt;Add16</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M241,-61C241,-109.09 241,-165.12 241,-197.67"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="237.5,-197.76 241,-207.76 244.5,-197.76 237.5,-197.76"/>
+</g>
+<!-- Scope1_1 -->
+<g id="node12" class="node">
+<title>Scope1_1</title>
+<polygon fill="cyan" stroke="transparent" points="537,-215 537,-236 553,-236 553,-215 537,-215"/>
+<polygon fill="none" stroke="black" points="537,-215 537,-236 553,-236 553,-215 537,-215"/>
+<text text-anchor="start" x="540" y="-221.8" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Scope1_2 -->
+<g id="node13" class="node">
+<title>Scope1_2</title>
+<polygon fill="cyan" stroke="transparent" points="599,-215 599,-236 615,-236 615,-215 599,-215"/>
+<polygon fill="none" stroke="black" points="599,-215 599,-236 615,-236 615,-215 599,-215"/>
+<text text-anchor="start" x="602" y="-221.8" font-family="Times,serif" font-size="14.00">0</text>
+<polygon fill="none" stroke="black" points="615,-215 615,-236 655,-236 655,-215 615,-215"/>
+<text text-anchor="start" x="618" y="-221.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="655,-215 655,-236 686,-236 686,-215 655,-215"/>
+<text text-anchor="start" x="658" y="-221.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Scope1_2&#45;&gt;Loop6 -->
+<g id="edge12" class="edge">
+<title>Scope1_2:Scope1_2_$ctrl&#45;&gt;Loop6</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M635,-237C635,-264.54 553.92,-282.77 504.41,-291.34"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="503.65,-287.92 494.37,-293.02 504.81,-294.82 503.65,-287.92"/>
+</g>
+<!-- Scope1_2&#45;&gt;Phi_arg8 -->
+<g id="edge13" class="edge">
+<title>Scope1_2:Scope1_2_arg&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M671,-237C671,-275.71 624.96,-252.41 587,-260 518.46,-273.71 498.88,-263.33 431,-280 428.04,-280.73 425,-281.58 421.97,-282.52"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="420.79,-279.23 412.41,-285.72 423.01,-285.86 420.79,-279.23"/>
+</g>
+<!-- Scope14_1 -->
+<g id="node14" class="node">
+<title>Scope14_1</title>
+<polygon fill="cyan" stroke="transparent" points="323,-39 323,-60 339,-60 339,-39 323,-39"/>
+<polygon fill="none" stroke="black" points="323,-39 323,-60 339,-60 339,-39 323,-39"/>
+<text text-anchor="start" x="326" y="-45.8" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Scope14_2 -->
+<g id="node15" class="node">
+<title>Scope14_2</title>
+<polygon fill="cyan" stroke="transparent" points="385,-39 385,-60 401,-60 401,-39 385,-39"/>
+<polygon fill="none" stroke="black" points="385,-39 385,-60 401,-60 401,-39 385,-39"/>
+<text text-anchor="start" x="388" y="-45.8" font-family="Times,serif" font-size="14.00">0</text>
+<polygon fill="none" stroke="black" points="401,-39 401,-60 441,-60 441,-39 401,-39"/>
+<text text-anchor="start" x="404" y="-45.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="441,-39 441,-60 472,-60 472,-39 441,-39"/>
+<text text-anchor="start" x="444" y="-45.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Scope14_2&#45;&gt;Phi_arg8 -->
+<g id="edge15" class="edge">
+<title>Scope14_2:Scope14_2_arg&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M457,-61C457,-151.88 449.62,-178.21 410,-260 408.01,-264.11 405.61,-268.3 403.09,-272.3"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="400.15,-270.4 397.51,-280.67 405.97,-274.28 400.15,-270.4"/>
+</g>
+<!-- Scope14_2&#45;&gt;If11 -->
+<g id="edge14" class="edge">
+<title>Scope14_2:Scope14_2_$ctrl&#45;&gt;If11:p1</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M421,-61C421,-84.4 401.06,-88.09 395.45,-105.95"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="391.97,-105.6 394,-116 398.89,-106.6 391.97,-105.6"/>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter07/07-graph2.gv b/docs/chapter07/07-graph2.gv
new file mode 100644
index 00000000..f4cfcb45
--- /dev/null
+++ b/docs/chapter07/07-graph2.gv
@@ -0,0 +1,62 @@
+digraph chapter07 {
+/*
+while(arg < 10) {
+    arg = arg + 1;
+    #showGraph;
+}
+return arg;
+
+*/
+	rankdir=BT;
+	ordering="in";
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Loop6 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_arg8 [ style=filled fillcolor=lightyellow label="&phi;_arg" ];
+		Con_9 [ label="10" ];
+		LT10 [ label="<" ];
+		If11 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_15 [ label="1" ];
+		Add16 [ label="+" ];
+		Return17 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop6;Phi_arg8;}
+	}
+	node [shape=plaintext];
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return17[taillabel=0 color=red];
+	Loop6 -> Start2:p0[taillabel=1 color=red];
+	Loop6 -> If11:p0[taillabel=2 color=red constraint=false];
+	Phi_arg8 -> Loop6 [style=dotted taillabel=0];
+	Phi_arg8 -> Start2:p1[taillabel=1];
+	Phi_arg8 -> Add16[taillabel=2 constraint=false];
+	LT10 -> Phi_arg8[taillabel=1];
+	LT10 -> Con_9[taillabel=2];
+	If11 -> Loop6[taillabel=0 color=red];
+	If11 -> LT10[taillabel=1];
+	Add16 -> Phi_arg8[taillabel=1];
+	Add16 -> Con_15[taillabel=2];
+	Return17 -> If11:p1[taillabel=0 color=red];
+	Return17 -> Phi_arg8[taillabel=1];
+	edge [style=dashed color=cornflowerblue];
+}
\ No newline at end of file
diff --git a/docs/chapter07/07-graph2.svg b/docs/chapter07/07-graph2.svg
new file mode 100644
index 00000000..1fec9556
--- /dev/null
+++ b/docs/chapter07/07-graph2.svg
@@ -0,0 +1,184 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter07 Pages: 1 -->
+<svg width="330pt" height="492pt"
+ viewBox="0.00 0.00 330.00 492.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 488)">
+<title>chapter07</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-488 326,-488 326,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="8,-8 8,-476 314,-476 314,-8 8,-8"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="141,-439 141,-464 222,-464 222,-439 141,-439"/>
+<polygon fill="none" stroke="black" points="141,-439 141,-464 222,-464 222,-439 141,-439"/>
+<text text-anchor="start" x="163" y="-447.8" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="141,-408 141,-439 222,-439 222,-408 141,-408"/>
+<polygon fill="yellow" stroke="transparent" points="146,-413 146,-434 186,-434 186,-413 146,-413"/>
+<polygon fill="none" stroke="black" points="146,-413 146,-434 186,-434 186,-413 146,-413"/>
+<text text-anchor="start" x="149" y="-419.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="186,-413 186,-434 217,-434 217,-413 186,-413"/>
+<text text-anchor="start" x="189" y="-419.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Stop3 -->
+<g id="node2" class="node">
+<title>Stop3</title>
+<polygon fill="yellow" stroke="black" points="153,-52 99,-52 99,-16 153,-16 153,-52"/>
+<text text-anchor="middle" x="126" y="-30.3" font-family="Times,serif" font-size="14.00">Stop</text>
+</g>
+<!-- Return17 -->
+<g id="node10" class="node">
+<title>Return17</title>
+<polygon fill="yellow" stroke="black" points="159,-124 93,-124 93,-88 159,-88 159,-124"/>
+<text text-anchor="middle" x="126" y="-102.3" font-family="Times,serif" font-size="14.00">Return</text>
+</g>
+<!-- Stop3&#45;&gt;Return17 -->
+<g id="edge1" class="edge">
+<title>Stop3&#45;&gt;Return17</title>
+<path fill="none" stroke="red" d="M126,-52.3C126,-60.02 126,-69.29 126,-77.89"/>
+<polygon fill="red" stroke="red" points="122.5,-77.9 126,-87.9 129.5,-77.9 122.5,-77.9"/>
+<text text-anchor="middle" x="123" y="-54.9" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Loop6 -->
+<g id="node3" class="node">
+<title>Loop6</title>
+<polygon fill="yellow" stroke="black" points="306,-368 252,-368 252,-332 306,-332 306,-368"/>
+<text text-anchor="middle" x="279" y="-346.3" font-family="Times,serif" font-size="14.00">Loop</text>
+</g>
+<!-- Loop6&#45;&gt;Start2 -->
+<g id="edge2" class="edge">
+<title>Loop6&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M251.93,-364.13C226.34,-376.71 189.56,-395.24 173.73,-405.41"/>
+<polygon fill="red" stroke="red" points="171.34,-402.85 166,-412 175.88,-408.18 171.34,-402.85"/>
+<text text-anchor="middle" x="248.93" y="-357.73" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- If11 -->
+<g id="node7" class="node">
+<title>If11</title>
+<polygon fill="yellow" stroke="transparent" points="32,-195 32,-220 126,-220 126,-195 32,-195"/>
+<polygon fill="none" stroke="black" points="32,-195 32,-220 126,-220 126,-195 32,-195"/>
+<text text-anchor="start" x="73.5" y="-203.8" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="32,-164 32,-195 126,-195 126,-164 32,-164"/>
+<polygon fill="yellow" stroke="transparent" points="37,-169 37,-190 77,-190 77,-169 37,-169"/>
+<polygon fill="none" stroke="black" points="37,-169 37,-190 77,-190 77,-169 37,-169"/>
+<text text-anchor="start" x="40" y="-175.8" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="77,-169 77,-190 121,-190 121,-169 77,-169"/>
+<polygon fill="none" stroke="black" points="77,-169 77,-190 121,-190 121,-169 77,-169"/>
+<text text-anchor="start" x="80" y="-175.8" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- Loop6&#45;&gt;If11 -->
+<g id="edge3" class="edge">
+<title>Loop6&#45;&gt;If11:p0</title>
+<path fill="none" stroke="red" d="M251.78,-335.24C248.86,-334.04 245.9,-332.93 243,-332 156.98,-304.48 103.76,-362.82 43,-296 18.41,-268.96 14.64,-203.69 27.49,-184.44"/>
+<polygon fill="red" stroke="red" points="29.46,-187.33 36,-179 25.69,-181.43 29.46,-187.33"/>
+<text text-anchor="middle" x="248.78" y="-328.84" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_arg8 -->
+<g id="node4" class="node">
+<title>Phi_arg8</title>
+<ellipse fill="lightyellow" stroke="black" cx="125" cy="-350" rx="37.09" ry="18"/>
+<text text-anchor="middle" x="125" y="-346.3" font-family="Times,serif" font-size="14.00">φ_arg</text>
+</g>
+<!-- Phi_arg8&#45;&gt;Start2 -->
+<g id="edge5" class="edge">
+<title>Phi_arg8&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M154.55,-360.93C173.21,-369 194.84,-382.27 200.56,-401.87"/>
+<polygon fill="black" stroke="black" points="197.12,-402.59 202,-412 204.05,-401.61 197.12,-402.59"/>
+<text text-anchor="middle" x="151.55" y="-363.53" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_arg8&#45;&gt;Loop6 -->
+<g id="edge4" class="edge">
+<title>Phi_arg8&#45;&gt;Loop6</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M143.47,-334.01C153.54,-326.34 166.66,-317.98 180,-314 203,-307.14 211.35,-306.06 234,-314 241.14,-316.5 247.99,-320.67 254.09,-325.3"/>
+<polygon fill="black" stroke="black" points="251.99,-328.1 261.92,-331.78 256.45,-322.71 251.99,-328.1"/>
+<text text-anchor="middle" x="140.47" y="-327.61" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Add16 -->
+<g id="node9" class="node">
+<title>Add16</title>
+<ellipse fill="none" stroke="black" cx="203" cy="-278" rx="27" ry="18"/>
+<text text-anchor="middle" x="203" y="-274.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Con_9 -->
+<g id="node5" class="node">
+<title>Con_9</title>
+<ellipse fill="none" stroke="black" cx="43" cy="-350" rx="27" ry="18"/>
+<text text-anchor="middle" x="43" y="-346.3" font-family="Times,serif" font-size="14.00">10</text>
+</g>
+<!-- LT10 -->
+<g id="node6" class="node">
+<title>LT10</title>
+<ellipse fill="none" stroke="black" cx="79" cy="-278" rx="27" ry="18"/>
+<text text-anchor="middle" x="79" y="-274.3" font-family="Times,serif" font-size="14.00">&lt;</text>
+</g>
+<!-- LT10&#45;&gt;Phi_arg8 -->
+<g id="edge7" class="edge">
+<title>LT10&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="black" d="M89.44,-294.88C95.12,-303.53 102.28,-314.42 108.68,-324.17"/>
+<polygon fill="black" stroke="black" points="105.87,-326.26 114.28,-332.69 111.72,-322.41 105.87,-326.26"/>
+<text text-anchor="middle" x="86.44" y="-297.48" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- LT10&#45;&gt;Con_9 -->
+<g id="edge8" class="edge">
+<title>LT10&#45;&gt;Con_9</title>
+<path fill="none" stroke="black" d="M70.65,-295.24C66.29,-303.72 60.85,-314.29 55.96,-323.8"/>
+<polygon fill="black" stroke="black" points="52.77,-322.36 51.3,-332.85 58.99,-325.56 52.77,-322.36"/>
+<text text-anchor="middle" x="67.65" y="-297.84" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- If11&#45;&gt;Loop6 -->
+<g id="edge9" class="edge">
+<title>If11&#45;&gt;Loop6</title>
+<path fill="none" stroke="red" d="M134.07,-205.07C167.93,-214.93 210.21,-231.94 239,-260 256.28,-276.84 266.71,-302.48 272.57,-321.93"/>
+<polygon fill="red" stroke="red" points="269.24,-323.03 275.3,-331.72 275.98,-321.15 269.24,-323.03"/>
+<text text-anchor="middle" x="137.07" y="-198.67" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If11&#45;&gt;LT10 -->
+<g id="edge10" class="edge">
+<title>If11&#45;&gt;LT10</title>
+<path fill="none" stroke="black" d="M79,-224.28C79,-232.58 79,-241.48 79,-249.56"/>
+<polygon fill="black" stroke="black" points="75.5,-249.6 79,-259.6 82.5,-249.6 75.5,-249.6"/>
+<text text-anchor="middle" x="76" y="-226.88" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_15 -->
+<g id="node8" class="node">
+<title>Con_15</title>
+<ellipse fill="none" stroke="black" cx="207" cy="-350" rx="27" ry="18"/>
+<text text-anchor="middle" x="207" y="-346.3" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Add16&#45;&gt;Phi_arg8 -->
+<g id="edge11" class="edge">
+<title>Add16&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="black" d="M180.01,-299.63C170.41,-308.25 159.23,-318.28 149.47,-327.04"/>
+<polygon fill="black" stroke="black" points="182.48,-302.11 187.59,-292.83 177.81,-296.9 182.48,-302.11"/>
+<polygon fill="black" stroke="black" points="147.11,-324.46 142,-333.74 151.78,-329.67 147.11,-324.46"/>
+<text text-anchor="middle" x="184.59" y="-295.43" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add16&#45;&gt;Con_15 -->
+<g id="edge12" class="edge">
+<title>Add16&#45;&gt;Con_15</title>
+<path fill="none" stroke="black" d="M203.99,-296.3C204.43,-304.02 204.96,-313.29 205.45,-321.89"/>
+<polygon fill="black" stroke="black" points="201.96,-322.11 206.02,-331.9 208.95,-321.71 201.96,-322.11"/>
+<text text-anchor="middle" x="200.99" y="-298.9" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Return17&#45;&gt;Phi_arg8 -->
+<g id="edge14" class="edge">
+<title>Return17&#45;&gt;Phi_arg8</title>
+<path fill="none" stroke="black" d="M133.07,-124.33C136.84,-134.53 141.09,-147.78 143,-160 151.97,-217.35 140.08,-285.24 131.79,-322.03"/>
+<polygon fill="black" stroke="black" points="128.33,-321.44 129.46,-331.97 135.14,-323.03 128.33,-321.44"/>
+<text text-anchor="middle" x="130.07" y="-126.93" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Return17&#45;&gt;If11 -->
+<g id="edge13" class="edge">
+<title>Return17&#45;&gt;If11:p1</title>
+<path fill="none" stroke="red" d="M113.92,-124C108.25,-133.3 102.24,-145.44 99.95,-157.94"/>
+<polygon fill="red" stroke="red" points="96.46,-157.71 99,-168 103.43,-158.38 96.46,-157.71"/>
+<text text-anchor="middle" x="110.92" y="-126.6" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter07/07-graph3.gv b/docs/chapter07/07-graph3.gv
new file mode 100644
index 00000000..4482100b
--- /dev/null
+++ b/docs/chapter07/07-graph3.gv
@@ -0,0 +1,108 @@
+digraph chapter07 {
+/*
+int sum = 0;
+int i = 0;
+while(i < arg) {
+    i = i + 1;
+    int j = 0;
+    while( j < arg ) {
+        sum = sum + j;
+        j = j + 1;
+    }
+}
+return sum;
+
+*/
+	rankdir=BT;
+	ordering="in";
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_6 [ label="0" ];
+		Con_7 [ label="0" ];
+		Loop8 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_sum11 [ style=filled fillcolor=lightyellow label="&phi;_sum" ];
+		Phi_i12 [ style=filled fillcolor=lightyellow label="&phi;_i" ];
+		LT13 [ label="<" ];
+		If14 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_18 [ label="1" ];
+		Add19 [ label="+" ];
+		Con_20 [ label="0" ];
+		Loop21 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_sum24 [ style=filled fillcolor=lightyellow label="&phi;_sum" ];
+		Phi_j26 [ style=filled fillcolor=lightyellow label="&phi;_j" ];
+		LT27 [ label="<" ];
+		If28 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Add32 [ label="+" ];
+		Con_33 [ label="1" ];
+		Add34 [ label="+" ];
+		Return35 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop8;Phi_sum11;Phi_i12;}
+		{ rank=same; Loop21;Phi_sum24;Phi_j26;}
+	}
+	node [shape=plaintext];
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return35[taillabel=0 color=red];
+	Loop8 -> Start2:p0[taillabel=1 color=red];
+	Loop8 -> If28:p1[taillabel=2 color=red constraint=false];
+	Phi_sum11 -> Loop8 [style=dotted taillabel=0];
+	Phi_sum11 -> Con_6[taillabel=1];
+	Phi_sum11 -> Phi_sum24[taillabel=2 constraint=false];
+	Phi_i12 -> Loop8 [style=dotted taillabel=0];
+	Phi_i12 -> Con_7[taillabel=1];
+	Phi_i12 -> Add19[taillabel=2 constraint=false];
+	LT13 -> Phi_i12[taillabel=1];
+	LT13 -> Start2:p1[taillabel=2];
+	If14 -> Loop8[taillabel=0 color=red];
+	If14 -> LT13[taillabel=1];
+	Add19 -> Phi_i12[taillabel=1];
+	Add19 -> Con_18[taillabel=2];
+	Loop21 -> If14:p0[taillabel=1 color=red];
+	Loop21 -> If28:p0[taillabel=2 color=red constraint=false];
+	Phi_sum24 -> Loop21 [style=dotted taillabel=0];
+	Phi_sum24 -> Phi_sum11[taillabel=1];
+	Phi_sum24 -> Add32[taillabel=2 constraint=false];
+	Phi_j26 -> Loop21 [style=dotted taillabel=0];
+	Phi_j26 -> Con_20[taillabel=1];
+	Phi_j26 -> Add34[taillabel=2 constraint=false];
+	LT27 -> Phi_j26[taillabel=1];
+	LT27 -> Start2:p1[taillabel=2];
+	If28 -> Loop21[taillabel=0 color=red];
+	If28 -> LT27[taillabel=1];
+	Add32 -> Phi_j26[taillabel=1];
+	Add32 -> Phi_sum24[taillabel=2];
+	Add34 -> Phi_j26[taillabel=1];
+	Add34 -> Con_33[taillabel=2];
+	Return35 -> If14:p1[taillabel=0 color=red];
+	Return35 -> Phi_sum11[taillabel=1];
+	edge [style=dashed color=cornflowerblue];
+}
\ No newline at end of file
diff --git a/docs/chapter07/07-graph3.svg b/docs/chapter07/07-graph3.svg
new file mode 100644
index 00000000..a9a0e8d0
--- /dev/null
+++ b/docs/chapter07/07-graph3.svg
@@ -0,0 +1,373 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter07 Pages: 1 -->
+<svg width="462pt" height="592pt"
+ viewBox="0.00 0.00 462.00 592.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 588)">
+<title>chapter07</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-588 458,-588 458,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="8,-8 8,-576 446,-576 446,-8 8,-8"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="148,-539 148,-564 229,-564 229,-539 148,-539"/>
+<polygon fill="none" stroke="black" points="148,-539 148,-564 229,-564 229,-539 148,-539"/>
+<text text-anchor="start" x="170" y="-547.8" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="148,-508 148,-539 229,-539 229,-508 148,-508"/>
+<polygon fill="yellow" stroke="transparent" points="153,-513 153,-534 193,-534 193,-513 153,-513"/>
+<polygon fill="none" stroke="black" points="153,-513 153,-534 193,-534 193,-513 153,-513"/>
+<text text-anchor="start" x="156" y="-519.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="193,-513 193,-534 224,-534 224,-513 193,-513"/>
+<text text-anchor="start" x="196" y="-519.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Stop3 -->
+<g id="node2" class="node">
+<title>Stop3</title>
+<polygon fill="yellow" stroke="black" points="432,-152 378,-152 378,-116 432,-116 432,-152"/>
+<text text-anchor="middle" x="405" y="-130.3" font-family="Times,serif" font-size="14.00">Stop</text>
+</g>
+<!-- Return35 -->
+<g id="node21" class="node">
+<title>Return35</title>
+<polygon fill="yellow" stroke="black" points="438,-224 372,-224 372,-188 438,-188 438,-224"/>
+<text text-anchor="middle" x="405" y="-202.3" font-family="Times,serif" font-size="14.00">Return</text>
+</g>
+<!-- Stop3&#45;&gt;Return35 -->
+<g id="edge1" class="edge">
+<title>Stop3&#45;&gt;Return35</title>
+<path fill="none" stroke="red" d="M405,-152.3C405,-160.02 405,-169.29 405,-177.89"/>
+<polygon fill="red" stroke="red" points="401.5,-177.9 405,-187.9 408.5,-177.9 401.5,-177.9"/>
+<text text-anchor="middle" x="402" y="-154.9" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Con_6 -->
+<g id="node3" class="node">
+<title>Con_6</title>
+<ellipse fill="none" stroke="black" cx="94" cy="-536" rx="27" ry="18"/>
+<text text-anchor="middle" x="94" y="-532.3" font-family="Times,serif" font-size="14.00">0</text>
+</g>
+<!-- Con_7 -->
+<g id="node4" class="node">
+<title>Con_7</title>
+<ellipse fill="none" stroke="black" cx="282" cy="-536" rx="27" ry="18"/>
+<text text-anchor="middle" x="282" y="-532.3" font-family="Times,serif" font-size="14.00">0</text>
+</g>
+<!-- Loop8 -->
+<g id="node5" class="node">
+<title>Loop8</title>
+<polygon fill="yellow" stroke="black" points="426,-468 372,-468 372,-432 426,-432 426,-468"/>
+<text text-anchor="middle" x="399" y="-446.3" font-family="Times,serif" font-size="14.00">Loop</text>
+</g>
+<!-- Loop8&#45;&gt;Start2 -->
+<g id="edge2" class="edge">
+<title>Loop8&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M371.74,-464.61C368.82,-465.84 365.87,-467 363,-468 325.58,-481 197.82,-470.79 176.14,-502.03"/>
+<polygon fill="red" stroke="red" points="172.67,-501.41 173,-512 179.34,-503.51 172.67,-501.41"/>
+<text text-anchor="middle" x="368.74" y="-458.21" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- If28 -->
+<g id="node17" class="node">
+<title>If28</title>
+<polygon fill="yellow" stroke="transparent" points="142,-51 142,-76 236,-76 236,-51 142,-51"/>
+<polygon fill="none" stroke="black" points="142,-51 142,-76 236,-76 236,-51 142,-51"/>
+<text text-anchor="start" x="183.5" y="-59.8" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="142,-20 142,-51 236,-51 236,-20 142,-20"/>
+<polygon fill="yellow" stroke="transparent" points="147,-25 147,-46 187,-46 187,-25 147,-25"/>
+<polygon fill="none" stroke="black" points="147,-25 147,-46 187,-46 187,-25 147,-25"/>
+<text text-anchor="start" x="150" y="-31.8" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="187,-25 187,-46 231,-46 231,-25 187,-25"/>
+<polygon fill="none" stroke="black" points="187,-25 187,-46 231,-46 231,-25 187,-25"/>
+<text text-anchor="start" x="190" y="-31.8" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- Loop8&#45;&gt;If28 -->
+<g id="edge3" class="edge">
+<title>Loop8&#45;&gt;If28:p1</title>
+<path fill="none" stroke="red" d="M371.72,-435.44C368.81,-434.2 365.86,-433.02 363,-432 300.87,-409.81 259.6,-448 219,-396 176.78,-341.93 243.11,-308.12 292,-260 311.77,-240.54 330.24,-248.63 343,-224 350.36,-209.79 353.65,-199.94 343,-188 248.88,-82.54 121.12,-257.46 27,-152 16.35,-140.06 16.65,-128.2 27,-116 90.22,-41.43 180.78,-154.57 244,-80 259.81,-61.35 261.04,-42.53 244,-25 236.29,-17.07 221.85,-12.04 214.15,-15.39"/>
+<polygon fill="red" stroke="red" points="211.13,-13.62 209,-24 217.14,-17.22 211.13,-13.62"/>
+<text text-anchor="middle" x="368.72" y="-429.04" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_sum11 -->
+<g id="node6" class="node">
+<title>Phi_sum11</title>
+<ellipse fill="lightyellow" stroke="black" cx="149" cy="-450" rx="40.89" ry="18"/>
+<text text-anchor="middle" x="149" y="-446.3" font-family="Times,serif" font-size="14.00">φ_sum</text>
+</g>
+<!-- Phi_sum11&#45;&gt;Con_6 -->
+<g id="edge5" class="edge">
+<title>Phi_sum11&#45;&gt;Con_6</title>
+<path fill="none" stroke="black" d="M138.13,-467.6C130.07,-479.91 118.95,-496.89 109.89,-510.73"/>
+<polygon fill="black" stroke="black" points="106.84,-509.01 104.29,-519.29 112.69,-512.84 106.84,-509.01"/>
+<text text-anchor="middle" x="135.13" y="-470.2" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_sum11&#45;&gt;Loop8 -->
+<g id="edge4" class="edge">
+<title>Phi_sum11&#45;&gt;Loop8</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M173.66,-435.44C188.78,-427.38 208.85,-418.16 228,-414 282.73,-402.12 301.16,-395.46 354,-414 361.14,-416.5 367.99,-420.67 374.09,-425.3"/>
+<polygon fill="black" stroke="black" points="371.99,-428.1 381.92,-431.78 376.45,-422.71 371.99,-428.1"/>
+<text text-anchor="middle" x="170.66" y="-429.04" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Phi_sum24 -->
+<g id="node14" class="node">
+<title>Phi_sum24</title>
+<ellipse fill="lightyellow" stroke="black" cx="149" cy="-206" rx="40.89" ry="18"/>
+<text text-anchor="middle" x="149" y="-202.3" font-family="Times,serif" font-size="14.00">φ_sum</text>
+</g>
+<!-- Phi_i12 -->
+<g id="node7" class="node">
+<title>Phi_i12</title>
+<ellipse fill="lightyellow" stroke="black" cx="255" cy="-450" rx="27" ry="18"/>
+<text text-anchor="middle" x="255" y="-446.3" font-family="Times,serif" font-size="14.00">φ_i</text>
+</g>
+<!-- Phi_i12&#45;&gt;Con_7 -->
+<g id="edge8" class="edge">
+<title>Phi_i12&#45;&gt;Con_7</title>
+<path fill="none" stroke="black" d="M260.46,-468C264.22,-479.69 269.28,-495.44 273.56,-508.73"/>
+<polygon fill="black" stroke="black" points="270.24,-509.86 276.64,-518.31 276.91,-507.72 270.24,-509.86"/>
+<text text-anchor="middle" x="257.46" y="-470.6" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_i12&#45;&gt;Loop8 -->
+<g id="edge7" class="edge">
+<title>Phi_i12&#45;&gt;Loop8</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M269.22,-434.43C277.37,-426.68 288.29,-418.11 300,-414 322.65,-406.06 331.35,-406.06 354,-414 361.14,-416.5 367.99,-420.67 374.09,-425.3"/>
+<polygon fill="black" stroke="black" points="371.99,-428.1 381.92,-431.78 376.45,-422.71 371.99,-428.1"/>
+<text text-anchor="middle" x="266.22" y="-428.03" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Add19 -->
+<g id="node11" class="node">
+<title>Add19</title>
+<ellipse fill="none" stroke="black" cx="327" cy="-378" rx="27" ry="18"/>
+<text text-anchor="middle" x="327" y="-374.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- LT13 -->
+<g id="node8" class="node">
+<title>LT13</title>
+<ellipse fill="none" stroke="black" cx="255" cy="-378" rx="27" ry="18"/>
+<text text-anchor="middle" x="255" y="-374.3" font-family="Times,serif" font-size="14.00">&lt;</text>
+</g>
+<!-- LT13&#45;&gt;Start2 -->
+<g id="edge11" class="edge">
+<title>LT13&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M241.85,-394.14C233.87,-404.19 224.26,-418.05 219,-432 207.64,-462.12 208.62,-473.77 208.94,-501.81"/>
+<polygon fill="black" stroke="black" points="205.44,-502.02 209,-512 212.44,-501.98 205.44,-502.02"/>
+<text text-anchor="middle" x="238.85" y="-396.74" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- LT13&#45;&gt;Phi_i12 -->
+<g id="edge10" class="edge">
+<title>LT13&#45;&gt;Phi_i12</title>
+<path fill="none" stroke="black" d="M255,-396.3C255,-404.02 255,-413.29 255,-421.89"/>
+<polygon fill="black" stroke="black" points="251.5,-421.9 255,-431.9 258.5,-421.9 251.5,-421.9"/>
+<text text-anchor="middle" x="252" y="-398.9" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- If14 -->
+<g id="node9" class="node">
+<title>If14</title>
+<polygon fill="yellow" stroke="transparent" points="309,-295 309,-320 403,-320 403,-295 309,-295"/>
+<polygon fill="none" stroke="black" points="309,-295 309,-320 403,-320 403,-295 309,-295"/>
+<text text-anchor="start" x="350.5" y="-303.8" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="309,-264 309,-295 403,-295 403,-264 309,-264"/>
+<polygon fill="yellow" stroke="transparent" points="314,-269 314,-290 354,-290 354,-269 314,-269"/>
+<polygon fill="none" stroke="black" points="314,-269 314,-290 354,-290 354,-269 314,-269"/>
+<text text-anchor="start" x="317" y="-275.8" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="354,-269 354,-290 398,-290 398,-269 354,-269"/>
+<polygon fill="none" stroke="black" points="354,-269 354,-290 398,-290 398,-269 354,-269"/>
+<text text-anchor="start" x="357" y="-275.8" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- If14&#45;&gt;Loop8 -->
+<g id="edge12" class="edge">
+<title>If14&#45;&gt;Loop8</title>
+<path fill="none" stroke="red" d="M364.6,-324.19C372.47,-352.77 384.02,-394.64 391.52,-421.86"/>
+<polygon fill="red" stroke="red" points="388.24,-423.15 394.27,-431.86 394.99,-421.29 388.24,-423.15"/>
+<text text-anchor="middle" x="361.6" y="-326.79" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If14&#45;&gt;LT13 -->
+<g id="edge13" class="edge">
+<title>If14&#45;&gt;LT13</title>
+<path fill="none" stroke="black" d="M318.68,-324.04C305.44,-335.05 290.9,-347.14 279.06,-356.99"/>
+<polygon fill="black" stroke="black" points="276.79,-354.32 271.34,-363.41 281.27,-359.7 276.79,-354.32"/>
+<text text-anchor="middle" x="315.68" y="-326.64" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_18 -->
+<g id="node10" class="node">
+<title>Con_18</title>
+<ellipse fill="none" stroke="black" cx="327" cy="-450" rx="27" ry="18"/>
+<text text-anchor="middle" x="327" y="-446.3" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Add19&#45;&gt;Phi_i12 -->
+<g id="edge14" class="edge">
+<title>Add19&#45;&gt;Phi_i12</title>
+<path fill="none" stroke="black" d="M304.96,-400.43C296.13,-409.01 285.99,-418.87 277.15,-427.46"/>
+<polygon fill="black" stroke="black" points="307.7,-402.65 312.43,-393.17 302.82,-397.63 307.7,-402.65"/>
+<polygon fill="black" stroke="black" points="274.53,-425.13 269.8,-434.62 279.41,-430.15 274.53,-425.13"/>
+<text text-anchor="middle" x="309.43" y="-395.77" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add19&#45;&gt;Con_18 -->
+<g id="edge15" class="edge">
+<title>Add19&#45;&gt;Con_18</title>
+<path fill="none" stroke="black" d="M327,-396.3C327,-404.02 327,-413.29 327,-421.89"/>
+<polygon fill="black" stroke="black" points="323.5,-421.9 327,-431.9 330.5,-421.9 323.5,-421.9"/>
+<text text-anchor="middle" x="324" y="-398.9" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Con_20 -->
+<g id="node12" class="node">
+<title>Con_20</title>
+<ellipse fill="none" stroke="black" cx="63" cy="-292" rx="27" ry="18"/>
+<text text-anchor="middle" x="63" y="-288.3" font-family="Times,serif" font-size="14.00">0</text>
+</g>
+<!-- Loop21 -->
+<g id="node13" class="node">
+<title>Loop21</title>
+<polygon fill="yellow" stroke="black" points="334,-224 280,-224 280,-188 334,-188 334,-224"/>
+<text text-anchor="middle" x="307" y="-202.3" font-family="Times,serif" font-size="14.00">Loop</text>
+</g>
+<!-- Loop21&#45;&gt;If14 -->
+<g id="edge16" class="edge">
+<title>Loop21&#45;&gt;If14:p0</title>
+<path fill="none" stroke="red" d="M319.08,-224C324.75,-233.3 330.76,-245.44 333.05,-257.94"/>
+<polygon fill="red" stroke="red" points="329.57,-258.38 334,-268 336.54,-257.71 329.57,-258.38"/>
+<text text-anchor="middle" x="316.08" y="-226.6" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Loop21&#45;&gt;If28 -->
+<g id="edge17" class="edge">
+<title>Loop21&#45;&gt;If28:p0</title>
+<path fill="none" stroke="red" d="M279.81,-191.15C276.88,-189.96 273.91,-188.88 271,-188 218.54,-172.13 62.82,-193.49 27,-152 -19.29,-98.38 63.73,-40.46 135.9,-35.36"/>
+<polygon fill="red" stroke="red" points="136.13,-38.86 146,-35 135.88,-31.86 136.13,-38.86"/>
+<text text-anchor="middle" x="276.81" y="-184.75" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_sum24&#45;&gt;Phi_sum11 -->
+<g id="edge19" class="edge">
+<title>Phi_sum24&#45;&gt;Phi_sum11</title>
+<path fill="none" stroke="black" d="M149,-234.1C149,-280.5 149,-374.66 149,-421.4"/>
+<polygon fill="black" stroke="black" points="152.5,-234.02 149,-224.02 145.5,-234.02 152.5,-234.02"/>
+<polygon fill="black" stroke="black" points="145.5,-421.68 149,-431.68 152.5,-421.68 145.5,-421.68"/>
+<text text-anchor="middle" x="146" y="-226.62" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_sum24&#45;&gt;Loop21 -->
+<g id="edge18" class="edge">
+<title>Phi_sum24&#45;&gt;Loop21</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M168.72,-190.18C179.62,-182.46 193.79,-173.99 208,-170 231.11,-163.51 239.35,-162.06 262,-170 269.14,-172.5 275.99,-176.67 282.09,-181.3"/>
+<polygon fill="black" stroke="black" points="279.99,-184.1 289.92,-187.78 284.45,-178.71 279.99,-184.1"/>
+<text text-anchor="middle" x="165.72" y="-183.78" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Add32 -->
+<g id="node18" class="node">
+<title>Add32</title>
+<ellipse fill="none" stroke="black" cx="142" cy="-134" rx="27" ry="18"/>
+<text text-anchor="middle" x="142" y="-130.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Phi_j26 -->
+<g id="node15" class="node">
+<title>Phi_j26</title>
+<ellipse fill="lightyellow" stroke="black" cx="63" cy="-206" rx="27" ry="18"/>
+<text text-anchor="middle" x="63" y="-202.3" font-family="Times,serif" font-size="14.00">φ_j</text>
+</g>
+<!-- Phi_j26&#45;&gt;Con_20 -->
+<g id="edge22" class="edge">
+<title>Phi_j26&#45;&gt;Con_20</title>
+<path fill="none" stroke="black" d="M63,-224.4C63,-235.74 63,-250.77 63,-263.68"/>
+<polygon fill="black" stroke="black" points="59.5,-263.9 63,-273.9 66.5,-263.9 59.5,-263.9"/>
+<text text-anchor="middle" x="60" y="-227" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_j26&#45;&gt;Loop21 -->
+<g id="edge21" class="edge">
+<title>Phi_j26&#45;&gt;Loop21</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M77.22,-190.43C85.37,-182.68 96.29,-174.11 108,-170 172.59,-147.34 197.41,-147.34 262,-170 269.14,-172.5 275.99,-176.67 282.09,-181.3"/>
+<polygon fill="black" stroke="black" points="279.99,-184.1 289.92,-187.78 284.45,-178.71 279.99,-184.1"/>
+<text text-anchor="middle" x="74.22" y="-184.03" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Add34 -->
+<g id="node20" class="node">
+<title>Add34</title>
+<ellipse fill="none" stroke="black" cx="225" cy="-134" rx="27" ry="18"/>
+<text text-anchor="middle" x="225" y="-130.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- LT27 -->
+<g id="node16" class="node">
+<title>LT27</title>
+<ellipse fill="none" stroke="black" cx="63" cy="-134" rx="27" ry="18"/>
+<text text-anchor="middle" x="63" y="-130.3" font-family="Times,serif" font-size="14.00">&lt;</text>
+</g>
+<!-- LT27&#45;&gt;Start2 -->
+<g id="edge25" class="edge">
+<title>LT27&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M49.72,-150.09C41.69,-160.12 32.07,-173.98 27,-188 11.37,-231.26 17,-245.01 17,-291 17,-291 17,-291 17,-379 17,-432.79 54.71,-437.48 99,-468 139.14,-495.66 199.24,-464.69 207.94,-501.72"/>
+<polygon fill="black" stroke="black" points="204.49,-502.41 209,-512 211.45,-501.69 204.49,-502.41"/>
+<text text-anchor="middle" x="46.72" y="-152.69" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- LT27&#45;&gt;Phi_j26 -->
+<g id="edge24" class="edge">
+<title>LT27&#45;&gt;Phi_j26</title>
+<path fill="none" stroke="black" d="M63,-152.3C63,-160.02 63,-169.29 63,-177.89"/>
+<polygon fill="black" stroke="black" points="59.5,-177.9 63,-187.9 66.5,-177.9 59.5,-177.9"/>
+<text text-anchor="middle" x="60" y="-154.9" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- If28&#45;&gt;Loop21 -->
+<g id="edge26" class="edge">
+<title>If28&#45;&gt;Loop21</title>
+<path fill="none" stroke="red" d="M227.35,-80.17C239.01,-90.79 251.3,-103.21 261,-116 275.71,-135.38 288.07,-160.15 296.27,-178.63"/>
+<polygon fill="red" stroke="red" points="293.1,-180.12 300.27,-187.92 299.53,-177.35 293.1,-180.12"/>
+<text text-anchor="middle" x="224.35" y="-82.77" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If28&#45;&gt;LT27 -->
+<g id="edge27" class="edge">
+<title>If28&#45;&gt;LT27</title>
+<path fill="none" stroke="black" d="M142.44,-80.04C124.74,-91.84 105.18,-104.88 89.9,-115.07"/>
+<polygon fill="black" stroke="black" points="87.82,-112.24 81.44,-120.7 91.71,-118.07 87.82,-112.24"/>
+<text text-anchor="middle" x="139.44" y="-82.64" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add32&#45;&gt;Phi_sum24 -->
+<g id="edge29" class="edge">
+<title>Add32&#45;&gt;Phi_sum24</title>
+<path fill="none" stroke="black" d="M144.73,-162.33C145.24,-167.45 145.78,-172.79 146.29,-177.9"/>
+<polygon fill="black" stroke="black" points="148.21,-161.91 143.73,-152.3 141.24,-162.6 148.21,-161.91"/>
+<polygon fill="black" stroke="black" points="142.81,-178.29 147.29,-187.9 149.78,-177.6 142.81,-178.29"/>
+<text text-anchor="middle" x="140.73" y="-154.9" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Add32&#45;&gt;Phi_j26 -->
+<g id="edge28" class="edge">
+<title>Add32&#45;&gt;Phi_j26</title>
+<path fill="none" stroke="black" d="M126.39,-148.83C114.92,-158.99 99.15,-172.97 86.21,-184.44"/>
+<polygon fill="black" stroke="black" points="83.74,-181.95 78.58,-191.2 88.38,-187.19 83.74,-181.95"/>
+<text text-anchor="middle" x="123.39" y="-151.43" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_33 -->
+<g id="node19" class="node">
+<title>Con_33</title>
+<ellipse fill="none" stroke="black" cx="235" cy="-206" rx="27" ry="18"/>
+<text text-anchor="middle" x="235" y="-202.3" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Add34&#45;&gt;Phi_j26 -->
+<g id="edge30" class="edge">
+<title>Add34&#45;&gt;Phi_j26</title>
+<path fill="none" stroke="black" d="M193.01,-148.01C167.45,-158.51 130.76,-173.83 99,-188 97.2,-188.8 95.36,-189.64 93.5,-190.49"/>
+<polygon fill="black" stroke="black" points="194.64,-151.12 202.57,-144.09 191.99,-144.65 194.64,-151.12"/>
+<polygon fill="black" stroke="black" points="91.85,-187.39 84.25,-194.78 94.79,-193.74 91.85,-187.39"/>
+<text text-anchor="middle" x="199.57" y="-146.69" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add34&#45;&gt;Con_33 -->
+<g id="edge31" class="edge">
+<title>Add34&#45;&gt;Con_33</title>
+<path fill="none" stroke="black" d="M227.42,-151.95C228.52,-159.65 229.85,-168.97 231.09,-177.64"/>
+<polygon fill="black" stroke="black" points="227.65,-178.32 232.53,-187.72 234.58,-177.33 227.65,-178.32"/>
+<text text-anchor="middle" x="224.42" y="-154.55" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Return35&#45;&gt;Phi_sum11 -->
+<g id="edge33" class="edge">
+<title>Return35&#45;&gt;Phi_sum11</title>
+<path fill="none" stroke="black" d="M371.93,-220.42C343.47,-232.34 305.01,-249.46 292,-260 233.39,-307.47 185.4,-383.86 162.87,-423.42"/>
+<polygon fill="black" stroke="black" points="159.79,-421.75 157.95,-432.19 165.89,-425.18 159.79,-421.75"/>
+<text text-anchor="middle" x="368.93" y="-214.02" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Return35&#45;&gt;If14 -->
+<g id="edge32" class="edge">
+<title>Return35&#45;&gt;If14:p1</title>
+<path fill="none" stroke="red" d="M391.86,-224.13C385.8,-233.37 379.43,-245.41 377.01,-257.92"/>
+<polygon fill="red" stroke="red" points="373.52,-257.7 376,-268 380.48,-258.4 373.52,-257.7"/>
+<text text-anchor="middle" x="388.86" y="-226.73" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter07/07-graph4.gv b/docs/chapter07/07-graph4.gv
new file mode 100644
index 00000000..24ace3da
--- /dev/null
+++ b/docs/chapter07/07-graph4.gv
@@ -0,0 +1,96 @@
+digraph chapter07 {
+/*
+int a = 1;
+int b = 2;
+while(a < 10) {
+    if (a == 2) a = 3;
+    else b = 4;
+}
+return b;
+
+*/
+	rankdir=BT;
+	ordering="in";
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_6 [ label="1" ];
+		Con_7 [ label="2" ];
+		Loop8 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_a11 [ style=filled fillcolor=lightyellow label="&phi;_a" ];
+		Phi_b12 [ style=filled fillcolor=lightyellow label="&phi;_b" ];
+		Con_13 [ label="10" ];
+		LT14 [ label="<" ];
+		If15 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_19 [ label="2" ];
+		EQ20 [ label="==" ];
+		If21 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_25 [ label="3" ];
+		Con_26 [ label="4" ];
+		Region27 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_a28 [ style=filled fillcolor=lightyellow label="&phi;_a" ];
+		Phi_b29 [ style=filled fillcolor=lightyellow label="&phi;_b" ];
+		Return30 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop8;Phi_a11;Phi_b12;}
+		{ rank=same; Region27;Phi_b29;Phi_a28;}
+	}
+	node [shape=plaintext];
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return30[taillabel=0 color=red];
+	Loop8 -> Start2:p0[taillabel=1 color=red];
+	Loop8 -> Region27[taillabel=2 color=red constraint=false];
+	Phi_a11 -> Loop8 [style=dotted taillabel=0];
+	Phi_a11 -> Con_6[taillabel=1];
+	Phi_a11 -> Phi_a28[taillabel=2 constraint=false];
+	Phi_b12 -> Loop8 [style=dotted taillabel=0];
+	Phi_b12 -> Con_7[taillabel=1];
+	Phi_b12 -> Phi_b29[taillabel=2 constraint=false];
+	LT14 -> Phi_a11[taillabel=1];
+	LT14 -> Con_13[taillabel=2];
+	If15 -> Loop8[taillabel=0 color=red];
+	If15 -> LT14[taillabel=1];
+	EQ20 -> Phi_a11[taillabel=1];
+	EQ20 -> Con_19[taillabel=2];
+	If21 -> If15:p0[taillabel=0 color=red];
+	If21 -> EQ20[taillabel=1];
+	Region27 -> If21:p0[taillabel=1 color=red];
+	Region27 -> If21:p1[taillabel=2 color=red];
+	Phi_a28 -> Region27 [style=dotted taillabel=0];
+	Phi_a28 -> Con_25[taillabel=1];
+	Phi_a28 -> Phi_a11[taillabel=2 constraint=false];
+	Phi_b29 -> Region27 [style=dotted taillabel=0];
+	Phi_b29 -> Phi_b12[taillabel=1];
+	Phi_b29 -> Con_26[taillabel=2 constraint=false];
+	Return30 -> If15:p1[taillabel=0 color=red];
+	Return30 -> Phi_b12[taillabel=1];
+	edge [style=dashed color=cornflowerblue];
+}
diff --git a/docs/chapter07/07-graph4.svg b/docs/chapter07/07-graph4.svg
new file mode 100644
index 00000000..cf42453d
--- /dev/null
+++ b/docs/chapter07/07-graph4.svg
@@ -0,0 +1,329 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter07 Pages: 1 -->
+<svg width="394pt" height="545pt"
+ viewBox="0.00 0.00 394.00 545.35" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 541.35)">
+<title>chapter07</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-541.35 390,-541.35 390,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="8,-33.35 8,-529.35 378,-529.35 378,-33.35 8,-33.35"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="312,-492.35 312,-517.35 362,-517.35 362,-492.35 312,-492.35"/>
+<polygon fill="none" stroke="black" points="312,-492.35 312,-517.35 362,-517.35 362,-492.35 312,-492.35"/>
+<text text-anchor="start" x="318.5" y="-501.15" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="312,-461.35 312,-492.35 362,-492.35 362,-461.35 312,-461.35"/>
+<polygon fill="yellow" stroke="transparent" points="317,-466.35 317,-487.35 357,-487.35 357,-466.35 317,-466.35"/>
+<polygon fill="none" stroke="black" points="317,-466.35 317,-487.35 357,-487.35 357,-466.35 317,-466.35"/>
+<text text-anchor="start" x="320" y="-473.15" font-family="Times,serif" font-size="14.00">$ctrl</text>
+</g>
+<!-- Stop3 -->
+<g id="node2" class="node">
+<title>Stop3</title>
+<polygon fill="yellow" stroke="black" points="370,-77.35 316,-77.35 316,-41.35 370,-41.35 370,-77.35"/>
+<text text-anchor="middle" x="343" y="-55.65" font-family="Times,serif" font-size="14.00">Stop</text>
+</g>
+<!-- Return30 -->
+<g id="node19" class="node">
+<title>Return30</title>
+<polygon fill="yellow" stroke="black" points="370,-163.35 304,-163.35 304,-127.35 370,-127.35 370,-163.35"/>
+<text text-anchor="middle" x="337" y="-141.65" font-family="Times,serif" font-size="14.00">Return</text>
+</g>
+<!-- Stop3&#45;&gt;Return30 -->
+<g id="edge1" class="edge">
+<title>Stop3&#45;&gt;Return30</title>
+<path fill="none" stroke="red" d="M341.76,-77.75C340.95,-89.09 339.87,-104.12 338.95,-117.03"/>
+<polygon fill="red" stroke="red" points="335.44,-117.03 338.22,-127.25 342.42,-117.53 335.44,-117.03"/>
+<text text-anchor="middle" x="338.76" y="-80.35" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Con_6 -->
+<g id="node3" class="node">
+<title>Con_6</title>
+<ellipse fill="none" stroke="black" cx="196" cy="-489.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="196" y="-485.65" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- Con_7 -->
+<g id="node4" class="node">
+<title>Con_7</title>
+<ellipse fill="none" stroke="black" cx="124" cy="-489.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="124" y="-485.65" font-family="Times,serif" font-size="14.00">2</text>
+</g>
+<!-- Loop8 -->
+<g id="node5" class="node">
+<title>Loop8</title>
+<polygon fill="yellow" stroke="black" points="367,-421.35 313,-421.35 313,-385.35 367,-385.35 367,-421.35"/>
+<text text-anchor="middle" x="340" y="-399.65" font-family="Times,serif" font-size="14.00">Loop</text>
+</g>
+<!-- Loop8&#45;&gt;Start2 -->
+<g id="edge2" class="edge">
+<title>Loop8&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M338.71,-421.43C338.08,-430.88 337.4,-443.1 337.13,-455.02"/>
+<polygon fill="red" stroke="red" points="333.62,-455.3 337,-465.35 340.62,-455.39 333.62,-455.3"/>
+<text text-anchor="middle" x="335.71" y="-424.03" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Region27 -->
+<g id="node16" class="node">
+<title>Region27</title>
+<polygon fill="yellow" stroke="black" points="298,-77.35 232,-77.35 232,-41.35 298,-41.35 298,-77.35"/>
+<text text-anchor="middle" x="265" y="-55.65" font-family="Times,serif" font-size="14.00">Region</text>
+</g>
+<!-- Loop8&#45;&gt;Region27 -->
+<g id="edge3" class="edge">
+<title>Loop8&#45;&gt;Region27</title>
+<path fill="none" stroke="red" d="M312.6,-389.27C286.36,-376.62 248.79,-358.1 235,-349.35 191.17,-321.51 165.74,-324.02 143,-277.35 130.54,-251.78 139.66,-241.59 143,-213.35 145.69,-190.65 153.07,-131.47 167,-113.35 174.64,-103.41 199.67,-89.94 222.53,-79.07"/>
+<polygon fill="red" stroke="red" points="224.22,-82.15 231.8,-74.74 221.25,-75.8 224.22,-82.15"/>
+<text text-anchor="middle" x="309.6" y="-382.87" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_a11 -->
+<g id="node6" class="node">
+<title>Phi_a11</title>
+<ellipse fill="lightyellow" stroke="black" cx="196" cy="-403.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="196" y="-399.65" font-family="Times,serif" font-size="14.00">φ_a</text>
+</g>
+<!-- Phi_a11&#45;&gt;Con_6 -->
+<g id="edge5" class="edge">
+<title>Phi_a11&#45;&gt;Con_6</title>
+<path fill="none" stroke="black" d="M196,-421.75C196,-433.09 196,-448.12 196,-461.03"/>
+<polygon fill="black" stroke="black" points="192.5,-461.25 196,-471.25 199.5,-461.25 192.5,-461.25"/>
+<text text-anchor="middle" x="193" y="-424.35" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_a11&#45;&gt;Loop8 -->
+<g id="edge4" class="edge">
+<title>Phi_a11&#45;&gt;Loop8</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M210.22,-387.78C218.37,-380.03 229.29,-371.45 241,-367.35 263.65,-359.4 272.35,-359.4 295,-367.35 302.14,-369.85 308.99,-374.02 315.09,-378.65"/>
+<polygon fill="black" stroke="black" points="312.99,-381.44 322.92,-385.13 317.45,-376.05 312.99,-381.44"/>
+<text text-anchor="middle" x="207.22" y="-381.38" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Phi_a28 -->
+<g id="node17" class="node">
+<title>Phi_a28</title>
+<ellipse fill="lightyellow" stroke="black" cx="187" cy="-59.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="187" y="-55.65" font-family="Times,serif" font-size="14.00">φ_a</text>
+</g>
+<!-- Phi_b12 -->
+<g id="node7" class="node">
+<title>Phi_b12</title>
+<ellipse fill="lightyellow" stroke="black" cx="124" cy="-403.35" rx="27.1" ry="18"/>
+<text text-anchor="middle" x="124" y="-399.65" font-family="Times,serif" font-size="14.00">φ_b</text>
+</g>
+<!-- Phi_b12&#45;&gt;Con_7 -->
+<g id="edge8" class="edge">
+<title>Phi_b12&#45;&gt;Con_7</title>
+<path fill="none" stroke="black" d="M124,-421.75C124,-433.09 124,-448.12 124,-461.03"/>
+<polygon fill="black" stroke="black" points="120.5,-461.25 124,-471.25 127.5,-461.25 120.5,-461.25"/>
+<text text-anchor="middle" x="121" y="-424.35" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_b12&#45;&gt;Loop8 -->
+<g id="edge7" class="edge">
+<title>Phi_b12&#45;&gt;Loop8</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M138.22,-387.78C146.37,-380.03 157.29,-371.45 169,-367.35 221.84,-348.81 242.16,-348.81 295,-367.35 302.14,-369.85 308.99,-374.02 315.09,-378.65"/>
+<polygon fill="black" stroke="black" points="312.99,-381.44 322.92,-385.13 317.45,-376.05 312.99,-381.44"/>
+<text text-anchor="middle" x="135.22" y="-381.38" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Phi_b29 -->
+<g id="node18" class="node">
+<title>Phi_b29</title>
+<ellipse fill="lightyellow" stroke="black" cx="43" cy="-59.35" rx="27.1" ry="18"/>
+<text text-anchor="middle" x="43" y="-55.65" font-family="Times,serif" font-size="14.00">φ_b</text>
+</g>
+<!-- Con_13 -->
+<g id="node8" class="node">
+<title>Con_13</title>
+<ellipse fill="none" stroke="black" cx="268" cy="-403.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="268" y="-399.65" font-family="Times,serif" font-size="14.00">10</text>
+</g>
+<!-- LT14 -->
+<g id="node9" class="node">
+<title>LT14</title>
+<ellipse fill="none" stroke="black" cx="271" cy="-331.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="271" y="-327.65" font-family="Times,serif" font-size="14.00">&lt;</text>
+</g>
+<!-- LT14&#45;&gt;Phi_a11 -->
+<g id="edge10" class="edge">
+<title>LT14&#45;&gt;Phi_a11</title>
+<path fill="none" stroke="black" d="M255.82,-346.51C245.15,-356.47 230.68,-369.98 218.65,-381.21"/>
+<polygon fill="black" stroke="black" points="216.08,-378.82 211.15,-388.2 220.85,-383.94 216.08,-378.82"/>
+<text text-anchor="middle" x="252.82" y="-349.11" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- LT14&#45;&gt;Con_13 -->
+<g id="edge11" class="edge">
+<title>LT14&#45;&gt;Con_13</title>
+<path fill="none" stroke="black" d="M270.26,-349.65C269.93,-357.36 269.53,-366.63 269.16,-375.23"/>
+<polygon fill="black" stroke="black" points="265.66,-375.1 268.73,-385.24 272.66,-375.4 265.66,-375.1"/>
+<text text-anchor="middle" x="267.26" y="-352.25" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- If15 -->
+<g id="node10" class="node">
+<title>If15</title>
+<polygon fill="yellow" stroke="transparent" points="260,-248.35 260,-273.35 354,-273.35 354,-248.35 260,-248.35"/>
+<polygon fill="none" stroke="black" points="260,-248.35 260,-273.35 354,-273.35 354,-248.35 260,-248.35"/>
+<text text-anchor="start" x="301.5" y="-257.15" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="260,-217.35 260,-248.35 354,-248.35 354,-217.35 260,-217.35"/>
+<polygon fill="yellow" stroke="transparent" points="265,-222.35 265,-243.35 305,-243.35 305,-222.35 265,-222.35"/>
+<polygon fill="none" stroke="black" points="265,-222.35 265,-243.35 305,-243.35 305,-222.35 265,-222.35"/>
+<text text-anchor="start" x="268" y="-229.15" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="305,-222.35 305,-243.35 349,-243.35 349,-222.35 305,-222.35"/>
+<polygon fill="none" stroke="black" points="305,-222.35 305,-243.35 349,-243.35 349,-222.35 305,-222.35"/>
+<text text-anchor="start" x="308" y="-229.15" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- If15&#45;&gt;Loop8 -->
+<g id="edge12" class="edge">
+<title>If15&#45;&gt;Loop8</title>
+<path fill="none" stroke="red" d="M314.79,-277.64C317.5,-288.87 320.49,-301.65 323,-313.35 327.43,-333.98 331.89,-357.43 335.12,-375.08"/>
+<polygon fill="red" stroke="red" points="331.74,-376.02 336.97,-385.24 338.63,-374.77 331.74,-376.02"/>
+<text text-anchor="middle" x="311.79" y="-280.24" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If15&#45;&gt;LT14 -->
+<g id="edge13" class="edge">
+<title>If15&#45;&gt;LT14</title>
+<path fill="none" stroke="black" d="M293.59,-277.62C289.8,-286.48 285.72,-296.01 282.08,-304.5"/>
+<polygon fill="black" stroke="black" points="278.78,-303.32 278.05,-313.89 285.21,-306.08 278.78,-303.32"/>
+<text text-anchor="middle" x="290.59" y="-280.22" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_19 -->
+<g id="node11" class="node">
+<title>Con_19</title>
+<ellipse fill="none" stroke="black" cx="130" cy="-331.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="130" y="-327.65" font-family="Times,serif" font-size="14.00">2</text>
+</g>
+<!-- EQ20 -->
+<g id="node12" class="node">
+<title>EQ20</title>
+<ellipse fill="none" stroke="black" cx="179" cy="-245.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="179" y="-241.65" font-family="Times,serif" font-size="14.00">==</text>
+</g>
+<!-- EQ20&#45;&gt;Phi_a11 -->
+<g id="edge14" class="edge">
+<title>EQ20&#45;&gt;Phi_a11</title>
+<path fill="none" stroke="black" d="M180.85,-263.34C183.79,-290.3 189.54,-343.11 193.05,-375.31"/>
+<polygon fill="black" stroke="black" points="189.59,-375.81 194.15,-385.38 196.55,-375.06 189.59,-375.81"/>
+<text text-anchor="middle" x="177.85" y="-265.94" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- EQ20&#45;&gt;Con_19 -->
+<g id="edge15" class="edge">
+<title>EQ20&#45;&gt;Con_19</title>
+<path fill="none" stroke="black" d="M169.55,-262.54C162.5,-274.63 152.74,-291.37 144.67,-305.19"/>
+<polygon fill="black" stroke="black" points="141.43,-303.8 139.42,-314.2 147.48,-307.33 141.43,-303.8"/>
+<text text-anchor="middle" x="166.55" y="-265.14" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- If21 -->
+<g id="node13" class="node">
+<title>If21</title>
+<polygon fill="yellow" stroke="transparent" points="184,-148.35 184,-173.35 278,-173.35 278,-148.35 184,-148.35"/>
+<polygon fill="none" stroke="black" points="184,-148.35 184,-173.35 278,-173.35 278,-148.35 184,-148.35"/>
+<text text-anchor="start" x="225.5" y="-157.15" font-family="Times,serif" font-size="14.00">If</text>
+<polygon fill="none" stroke="black" points="184,-117.35 184,-148.35 278,-148.35 278,-117.35 184,-117.35"/>
+<polygon fill="yellow" stroke="transparent" points="189,-122.35 189,-143.35 229,-143.35 229,-122.35 189,-122.35"/>
+<polygon fill="none" stroke="black" points="189,-122.35 189,-143.35 229,-143.35 229,-122.35 189,-122.35"/>
+<text text-anchor="start" x="192" y="-129.15" font-family="Times,serif" font-size="14.00">True</text>
+<polygon fill="yellow" stroke="transparent" points="229,-122.35 229,-143.35 273,-143.35 273,-122.35 229,-122.35"/>
+<polygon fill="none" stroke="black" points="229,-122.35 229,-143.35 273,-143.35 273,-122.35 229,-122.35"/>
+<text text-anchor="start" x="232" y="-129.15" font-family="Times,serif" font-size="14.00">False</text>
+</g>
+<!-- If21&#45;&gt;If15 -->
+<g id="edge16" class="edge">
+<title>If21&#45;&gt;If15:p0</title>
+<path fill="none" stroke="red" d="M266.11,-177.35C274.25,-187.13 281.31,-198.68 283.92,-211.16"/>
+<polygon fill="red" stroke="red" points="280.47,-211.77 285,-221.35 287.43,-211.03 280.47,-211.77"/>
+<text text-anchor="middle" x="263.11" y="-179.95" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- If21&#45;&gt;EQ20 -->
+<g id="edge17" class="edge">
+<title>If21&#45;&gt;EQ20</title>
+<path fill="none" stroke="black" d="M214.55,-177.35C207.43,-190.76 199.21,-206.25 192.47,-218.96"/>
+<polygon fill="black" stroke="black" points="189.24,-217.58 187.65,-228.05 195.42,-220.86 189.24,-217.58"/>
+<text text-anchor="middle" x="211.55" y="-179.95" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Con_25 -->
+<g id="node14" class="node">
+<title>Con_25</title>
+<ellipse fill="none" stroke="black" cx="111" cy="-145.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="111" y="-141.65" font-family="Times,serif" font-size="14.00">3</text>
+</g>
+<!-- Con_26 -->
+<g id="node15" class="node">
+<title>Con_26</title>
+<ellipse fill="none" stroke="black" cx="115" cy="-59.35" rx="27" ry="18"/>
+<text text-anchor="middle" x="115" y="-55.65" font-family="Times,serif" font-size="14.00">4</text>
+</g>
+<!-- Region27&#45;&gt;If21 -->
+<g id="edge18" class="edge">
+<title>Region27&#45;&gt;If21:p0</title>
+<path fill="none" stroke="red" d="M236.34,-77.55C225.26,-86.1 214.31,-97.52 210.45,-111.09"/>
+<polygon fill="red" stroke="red" points="206.94,-110.95 209,-121.35 213.87,-111.94 206.94,-110.95"/>
+<text text-anchor="middle" x="233.34" y="-80.15" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Region27&#45;&gt;If21 -->
+<g id="edge19" class="edge">
+<title>Region27&#45;&gt;If21:p1</title>
+<path fill="none" stroke="red" d="M258.9,-77.46C255.95,-86.91 252.79,-99.16 251.55,-111.27"/>
+<polygon fill="red" stroke="red" points="248.05,-111.17 251,-121.35 255.04,-111.55 248.05,-111.17"/>
+<text text-anchor="middle" x="255.9" y="-80.06" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_a28&#45;&gt;Phi_a11 -->
+<g id="edge22" class="edge">
+<title>Phi_a28&#45;&gt;Phi_a11</title>
+<path fill="none" stroke="black" d="M156.38,-74.81C123.24,-90.46 75.08,-113.23 75,-113.35 59.78,-137.38 66.63,-150.16 75,-177.35 90.81,-228.71 98.49,-247.23 143,-277.35 204.81,-319.16 260.23,-255.2 307,-313.35 317.03,-325.81 315.54,-335.81 307,-349.35 306.7,-349.82 259.29,-372.35 226.54,-387.88"/>
+<polygon fill="black" stroke="black" points="158.14,-77.85 165.69,-70.41 155.15,-71.52 158.14,-77.85"/>
+<polygon fill="black" stroke="black" points="224.86,-384.81 217.32,-392.25 227.86,-391.13 224.86,-384.81"/>
+<text text-anchor="middle" x="162.69" y="-73.01" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_a28&#45;&gt;Con_25 -->
+<g id="edge21" class="edge">
+<title>Phi_a28&#45;&gt;Con_25</title>
+<path fill="none" stroke="black" d="M173.41,-75.36C161.74,-88.26 144.74,-107.05 131.43,-121.77"/>
+<polygon fill="black" stroke="black" points="128.58,-119.7 124.47,-129.46 133.77,-124.39 128.58,-119.7"/>
+<text text-anchor="middle" x="170.41" y="-77.96" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_a28&#45;&gt;Region27 -->
+<g id="edge20" class="edge">
+<title>Phi_a28&#45;&gt;Region27</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M214.12,-59.35C216.58,-59.35 219.04,-59.35 221.5,-59.35"/>
+<polygon fill="black" stroke="black" points="221.61,-62.85 231.61,-59.35 221.61,-55.85 221.61,-62.85"/>
+<text text-anchor="middle" x="217.12" y="-52.95" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Phi_b29&#45;&gt;Phi_b12 -->
+<g id="edge24" class="edge">
+<title>Phi_b29&#45;&gt;Phi_b12</title>
+<path fill="none" stroke="black" d="M44.59,-87.64C48.34,-139.92 60.11,-257.16 94,-349.35 97.54,-358.97 102.7,-368.9 107.74,-377.53"/>
+<polygon fill="black" stroke="black" points="48.07,-87.25 43.91,-77.51 41.09,-87.72 48.07,-87.25"/>
+<polygon fill="black" stroke="black" points="104.9,-379.59 113.09,-386.31 110.88,-375.95 104.9,-379.59"/>
+<text text-anchor="middle" x="40.91" y="-80.11" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Phi_b29&#45;&gt;Con_26 -->
+<g id="edge25" class="edge">
+<title>Phi_b29&#45;&gt;Con_26</title>
+<path fill="none" stroke="black" d="M70.56,-59.35C73,-59.35 75.44,-59.35 77.89,-59.35"/>
+<polygon fill="black" stroke="black" points="77.92,-62.85 87.92,-59.35 77.92,-55.85 77.92,-62.85"/>
+<text text-anchor="middle" x="73.56" y="-52.95" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Phi_b29&#45;&gt;Region27 -->
+<g id="edge23" class="edge">
+<title>Phi_b29&#45;&gt;Region27</title>
+<path fill="none" stroke="black" stroke-dasharray="1,5" d="M54.68,-42.66C62.75,-32.67 74.44,-20.87 88,-15.35 139.86,5.79 161.51,4.17 214,-15.35 224.63,-19.3 234.53,-26.57 242.72,-34.08"/>
+<polygon fill="black" stroke="black" points="240.44,-36.75 250.02,-41.26 245.34,-31.75 240.44,-36.75"/>
+<text text-anchor="middle" x="51.68" y="-36.26" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Return30&#45;&gt;Phi_b12 -->
+<g id="edge27" class="edge">
+<title>Return30&#45;&gt;Phi_b12</title>
+<path fill="none" stroke="black" d="M313.98,-163.53C307.84,-168.06 301.19,-172.92 295,-177.35 272.13,-193.69 260.87,-191.65 243,-213.35 223.27,-237.31 230.02,-250.17 215,-277.35 196.27,-311.22 188.92,-318.16 166,-349.35 158.65,-359.34 150.22,-370.11 142.84,-379.32"/>
+<polygon fill="black" stroke="black" points="139.98,-377.29 136.43,-387.27 145.43,-381.68 139.98,-377.29"/>
+<text text-anchor="middle" x="310.98" y="-166.13" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Return30&#45;&gt;If15 -->
+<g id="edge26" class="edge">
+<title>Return30&#45;&gt;If15:p1</title>
+<path fill="none" stroke="red" d="M333.39,-163.54C331,-176.2 328.14,-194.14 327.27,-211.34"/>
+<polygon fill="red" stroke="red" points="323.77,-211.26 327,-221.35 330.76,-211.44 323.77,-211.26"/>
+<text text-anchor="middle" x="330.39" y="-166.14" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter07/Makefile b/docs/chapter07/Makefile
new file mode 100644
index 00000000..12659b8f
--- /dev/null
+++ b/docs/chapter07/Makefile
@@ -0,0 +1,12 @@
+GV := $(wildcard *.gv)
+SVG := $(patsubst %.gv,%.svg,$(GV))
+
+.PHONY: all
+all: $(SVG)
+
+%.svg: %.gv
+	dot -Tsvg $< > $@
+
+.PHONY: clean
+clean:
+	@rm -f $(SVG)
diff --git a/docs/chapter07/README.md b/docs/chapter07/README.md
new file mode 100644
index 00000000..203e5314
--- /dev/null
+++ b/docs/chapter07/README.md
@@ -0,0 +1,233 @@
+# Chapter 7: While Statement
+
+In this chapter we introduce the `while` statement.
+
+Here is the [complete language grammar](07-grammar.md) for this chapter.
+
+You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter07) in a linear Git revision history on the [linear](https://github.com/SeaOfNodes/Simple/tree/linear) branch and [compare](https://github.com/SeaOfNodes/Simple/compare/linear-chapter06...linear-chapter07) it to the previous chapter.
+
+## Dealing With Back Edges
+
+The complication introduced by looping constructs is that variables flow back into the body of the loop on iteration.
+For example:
+
+```java
+while(arg < 10) {
+    arg = arg + 1;
+}
+return arg;
+```
+
+The variable `arg` is assigned a new value inside the body of the loop, and this then flows back into the body of the loop.
+
+In general, we will rewrite the looping construct as follows:
+
+```java
+loop_head:
+if( !(arg < 10) )
+    goto loop_exit;
+arg = arg + 1;
+goto loop_head;
+
+loop_exit:
+```
+
+Above is for illustration only, we do not have labels and `goto` statements in the language.
+
+From an SSA[^1] point of view, since `arg` flows back, it requires a `phi` node at the head. Conceptually we would like the outcome to be:
+
+```java
+// arg1 represents incoming arg
+//
+loop_head:
+arg2 = phi(arg1, arg3);
+if( !(arg2 < 10) )
+    goto loop_exit;
+arg3 = arg2 + 1;
+goto loop_head;
+
+loop_exit:
+```
+
+Notice that the phi for `arg2` refers to `arg3`, which is not known at the time we parse the `while` loop predicate. This is the crux of the problem that we need
+to solve in order to successfully construct the Sea of Nodes graph, which is always in SSA form.
+
+Recall from [Chapter 5](../chapter05/README.md) that when parsing `if` statements, we clone the symbol tables as we go past the `if` predicate.
+Later we merge the two sets of symbol tables at a `Region` - creating phis for all names that encountered a change in definition within the two
+branches of the `if` statement. In the case of the `if` statement, the phis are created at the merge point when we already know the definitions
+that are being merged.
+
+The essential idea for loop constructs is to eagerly create phis for all names in the symbol tables *before* we enter the loop's `if` condition,
+since we do not know which names will be redefined inside the body of the loop. When the loop terminates, we go back and remove unnecessary
+phis. We call this approach the "eager phi" approach.[^2]
+
+In [Chapter 8](../chapter08) we will implement a "lazy phi" approach that creates phis only when we encounter redefinition of a name.
+
+## New Node Types
+
+Our list of nodes remains the same as in [Chapter 5](../chapter05/README.md), however, we create a subtype of `Region` named `Loop` to better
+encapsulate some of the additional logic required. A key aspect of this is to temporarily disable peepholes of the `Region` and any phis
+created until we complete parsing the loop body. This is because our phis are not fully constructed until the loop end.
+
+## Detailed Steps
+
+1. We start by creating a new subclass of `Region`, the `Loop`. The `Loop` gets two control inputs,
+   the first is the entry point, i.e. the current binding to `$ctrl`, and second (`null`) is a placeholder for the back edge that is
+   set after loop is parsed. The absence of a back edge is used as an indicator to switch off peepholes of the region and
+   associated phis.
+
+    ```java
+    ctrl(new LoopNode(ctrl(),null).peephole());
+    ```
+
+   The newly created region becomes the current control.
+
+2. We duplicate the current Scope node. This involves duplicating all the symbols at
+   every level with the scope, and creating phis for every symbol except the `$ctrl` binding.
+
+    ```java
+    // Make a new Scope for the body.
+    _scope = _scope.dup(true);
+    ```
+
+   Note that the `dup` call is given an argument `true`. This triggers creating phis. The code
+   that creates the phis in the `dup()` method is shown below.
+
+    ```java
+    // boolean loop=true if this is a loop region
+
+    String[] names = reverseNames(); // Get the variable names
+    dup.add_def(ctrl());      // Control input is just copied
+    for( int i=1; i<nIns(); i++ ) {
+       if ( !loop ) { dup.add_def(in(i)); }
+       else {
+          // Loop region
+          // Create a phi node with second input as null - to be filled in
+          // by endLoop() below
+          dup.add_def(new PhiNode(names[i], ctrl(), in(i), null).peephole());
+          // Ensure our node has the same phi in case we created one
+          set_def(i, dup.in(i));
+       }
+    }
+    ```
+
+   Inside the `else` block both the duplicated scope and the original scope get the same phi node.
+
+3. Next we set up the `if` condition, very much like we do with regular ifs.
+
+    ```java
+    // Parse predicate
+    var pred = require(parseExpression(), ")");
+    // IfNode takes current control and predicate
+    IfNode ifNode = (IfNode)new IfNode(ctrl(), pred).<IfNode>keep().peephole();
+    // Setup projection nodes
+    Node ifT = new ProjNode(ifNode, 0, "True" ).peephole();
+    ifNode.unkeep();
+    Node ifF = new ProjNode(ifNode, 1, "False").peephole();
+    ```
+
+4. We make another clone of the current scope. This will be the exit scope that will live after the loop ends,
+   therefore `$ctrl` in the exit scope is set to the `False` projection.
+   The exit scope captures any side effects of the loop's predicate.
+
+    ```java
+    // The exit scope, accounting for any side effects in the predicate
+    var exit = _scope.dup();
+    exit.ctrl(ifF);
+    ```
+
+5. We now set the control to the `True` projection and parse the loop body.
+
+    ```java
+    // Parse the true side, which corresponds to loop body
+    ctrl(ifT);              // set ctrl token to ifTrue projection
+    parseStatement();       // Parse loop body
+    ```
+
+6. After the loop body is parsed, we go back and process all the phis we created earlier.
+
+    ```java
+    // The true branch loops back, so whatever is current control gets
+    // added to head loop as input
+    head.endLoop(_scope, exit);
+    ```
+
+   The `endLoop` method sets the second control of the loop region to the control from the back edge.
+   It then goes through all the phis and sets the second data input on the phi to the corresponding entry
+   from the loop body; phis that were not used are peepholed and get replaced by the original input.
+
+    ```java
+    Node ctrl = ctrl();
+    ctrl.set_def(2,back.ctrl());
+    for( int i=1; i<nIns(); i++ ) {
+       PhiNode phi = (PhiNode)in(i);
+       assert phi.region()==ctrl && phi.in(2)==null;
+       phi.set_def(2,back.in(i));
+       // Do an eager useless-phi removal
+       Node in = phi.peephole();
+       if( in != phi )
+          phi.subsume(in);
+    }
+    ```
+
+7. Finally, both the original scope (head) we started with, and the duplicate created for the body are killed.
+   At exit the false control is the current control (step 4), and exit scope is set as the current scope.
+
+   ```java
+   // At exit the false control is the current control, and
+   // the scope is the exit scope after the exit test.
+   return (_scope = exit);
+   ```
+
+### Visualization
+
+The example quoted above is shown below at an intermediate state:
+
+![Graph1](./07-graph1.svg)
+
+* Three Scopes are shown, reading clockwise, the loop head, exit and the body.
+
+The final graph looks like this:
+
+![Graph2](./07-graph2.svg)
+
+## More Complex Examples
+
+### Nested Loops
+
+```java
+int sum = 0;
+int i = 0;
+while(i < arg) {
+    i = i + 1;
+    int j = 0;
+    while( j < arg ) {
+        sum = sum + j;
+        j = j + 1;
+    }
+}
+return sum;
+```
+
+![Graph2](./07-graph3.svg)
+
+### Loop With Nested If
+
+```java
+int a = 1;
+int b = 2;
+while(a < 10) {
+    if (a == 2) a = 3;
+    else b = 4;
+}
+return b;
+```
+
+![Graph2](./07-graph4.svg)
+
+
+[^1]: Cytron, R. et al (1991).
+    Efficiently computing static single assignment form and the control dependence graph, in ACM Transactions on Programming Languages and Systems, 13(4):451-490, 1991.
+
+[^2]: Click, C. (1995).
+    Combining Analyses, Combining Optimizations, 103.