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authorCliff Click <cliffc@acm.org>2023-10-20 15:21:08 -0700
committerCliff Click <cliffc@acm.org>2026-10-04 13:30:41 -0700
commit26c9ce808557ed4c7f6c2c84d9e8f8cd7ebced49 (patch)
tree1d78e5c3789663914a617388f5c7f1f89b0f3758 /docs
parentbafb37e0078950acdf0d0218a977beaf05e0b6ac (diff)
downloadSimple-26c9ce808557ed4c7f6c2c84d9e8f8cd7ebced49.tar.gz
Simple-26c9ce808557ed4c7f6c2c84d9e8f8cd7ebced49.zip
Chapter 4: External Argument and Comparisons
Co-authored-by: Dibyendu Majumdar <mobile@majumdar.org.uk> Co-authored-by: Hsiang-Ying Fu <66062782+fuhsnn@users.noreply.github.com> Co-authored-by: Yichen Yan <oraluben@outlook.com> Co-authored-by: Thalia Archibald <thalia@archibald.dev> Co-authored-by: Tamas Hadhazy <helsgithub15@gmail.com> Co-authored-by: Hels15 <helsgithub15@gmail.com> Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com> Co-authored-by: Symious <14933944+symious@users.noreply.github.com> Co-authored-by: Claude Opus 5 <noreply@anthropic.com> Co-authored-by: tannal <tannal2409@gmail.com> Co-authored-by: hadha <helsgithub15@gmail.com> Co-authored-by: Tamás Hadházy <85063808+Hels15@users.noreply.github.com> Co-authored-by: RobertObkircher <robert.obkircher@gmail.com>
Diffstat (limited to 'docs')
-rw-r--r--docs/chapter04/04-arg1.json16
-rw-r--r--docs/chapter04/04-arg1.svg81
-rw-r--r--docs/chapter04/04-arg2.json16
-rw-r--r--docs/chapter04/04-arg2.svg82
-rw-r--r--docs/chapter04/04-dce1.svg100
-rw-r--r--docs/chapter04/04-dce2.svg59
-rw-r--r--docs/chapter04/04-dce3.svg116
-rw-r--r--docs/chapter04/04-grammar.md72
-rw-r--r--docs/chapter04/04-post-peephole.gv43
-rw-r--r--docs/chapter04/04-post-peephole.json18
-rw-r--r--docs/chapter04/04-post-peephole.svg90
-rw-r--r--docs/chapter04/04-pre-peephole.gv47
-rw-r--r--docs/chapter04/04-pre-peephole.json20
-rw-r--r--docs/chapter04/04-pre-peephole.svg98
-rw-r--r--docs/chapter04/Makefile1
-rw-r--r--docs/chapter04/README.md419
-rw-r--r--docs/chapter04/lattice.gv97
-rw-r--r--docs/chapter04/lattice.svg305
-rw-r--r--docs/chapter04/projnode.json14
-rw-r--r--docs/chapter04/projnode.pngbin0 -> 6061 bytes
-rw-r--r--docs/chapter04/projnode.svg74
21 files changed, 1768 insertions, 0 deletions
diff --git a/docs/chapter04/04-arg1.json b/docs/chapter04/04-arg1.json
new file mode 100644
index 00000000..b16dc51b
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+++ b/docs/chapter04/04-arg1.json
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+{
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+ "comp": "chapter04/docs/04-arg1.svg",
+ "step": 1,
+ "roots": [],
+ "scope": 0,
+ "nodes": [
+ {"id": 1, "label": "Scope", "type": null, "kind": "SCOPE", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": "0: $ctrl"}, {"idx": 1, "def": 5, "role": "ASSOC", "label": "0: arg"}], "proj": null},
+ {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+ {"id": 4, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+ {"id": 5, "label": "2", "type": null, "kind": "DATA", "edges": [], "proj": null},
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diff --git a/docs/chapter04/04-arg1.svg b/docs/chapter04/04-arg1.svg
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+<svg aria-label="Compiler graph" width="518" height="246" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 518 246" style="font-family: sans-serif;"><style>
+ html, body { height:100%; margin:0; font-family:sans-serif; }
+ .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+ .source { padding:8px; border-bottom:1px solid #ccc; }
+ #program { width:min(600px,80vw); vertical-align:middle; }
+ #status { margin-top:4px; }
+ #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+ #elk { width:100%; height:100%; }
+ #graph svg { display:block; }
+ .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
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+ .edge.bundle.selected { stroke-width:6; }
+ .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+ .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+ .node { cursor:pointer; }
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+ .row { stroke:#b6afcf; stroke-width:1; }
+ .bind { font-size:12px; fill:#152330; }
+ .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+ #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+ max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+ background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+ .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+ .button { color:white; background:black; font-size:20px; min-width:30px; }
+ .button:disabled { background:grey; }
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+ #N { width:6ch; }
+ #scrub { width:clamp(120px,35vw,600px); }
+ </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge ASSOC" id="e1i1" d="M242,115 C242,139 465.5,0 465.5,24" stroke="#9396a3" marker-start="url(#arrow-ASSOC)" style="opacity: 1;"><title>#1[1] → #5 · ASSOC · 0: arg</title></path><path class="edge CTRL" id="e6i0" d="M84,118 L84,166" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#6[0] → #4 · CTRL</title></path><path class="edge DATA" id="e6i1" d="M242,118 L242,123 Q242,128 237,128 L132,128 Q124,128 124,136 L124,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#6[1] → #5 · DATA</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(374,24)" style="opacity: 1;"><path class="box" d="M4,0H116Q120,0 120,4V52Q120,56 116,56H4Q0,56 0,52V4Q0,0 4,0Z" fill="#e5e0ff"/><text class="label" text-anchor="middle" x="60" y="48"><tspan>Scope</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 Scope
+Type not computed
+
+[0] → — ASSOC 0: $ctrl
+[1] → #5 ASSOC 0: arg</title><line class="row" x1="0" x2="120" y1="30" y2="30"/><line class="row" x1="63" x2="63" y1="0" y2="30"/><text class="bind" x="31.5" y="20" text-anchor="middle">0: $ctrl</text><text class="bind" x="91.5" y="20" text-anchor="middle">0: arg</text><circle class="port" cx="31.5" cy="0" r="3" fill="white"/><circle class="port" cx="91.5" cy="0" r="3" fill="#536477"/><text class="slot" x="31.5" y="-7" text-anchor="middle">0</text><text class="slot" x="91.5" y="-7" text-anchor="middle">1</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #4/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2 CTRL</title></g><g class="node" id="n5" data-id="5" transform="translate(182,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>2</tspan><tspan class="node-id">  #5</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#5 2
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(44,172)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #6</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 Return
+Type not computed
+
+[0] → #4 CTRL
+[1] → #5 DATA</title><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="40" y="-10" text-anchor="middle">0</text><text class="slot" x="80" y="-10" text-anchor="middle">1</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter04/04-arg2.json b/docs/chapter04/04-arg2.json
new file mode 100644
index 00000000..5d2d7fde
--- /dev/null
+++ b/docs/chapter04/04-arg2.json
@@ -0,0 +1,16 @@
+{
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+ "comp": "chapter04/docs/04-arg2.svg",
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+ {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+ {"id": 4, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+ {"id": 5, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 4, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "DATA", "label": null}], "proj": null},
+ {"id": 6, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 1}}
+ ],
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+ ]
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diff --git a/docs/chapter04/04-arg2.svg b/docs/chapter04/04-arg2.svg
new file mode 100644
index 00000000..6083ae9b
--- /dev/null
+++ b/docs/chapter04/04-arg2.svg
@@ -0,0 +1,82 @@
+<svg aria-label="Compiler graph" width="486" height="246" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 486 246" style="font-family: sans-serif;"><style>
+ html, body { height:100%; margin:0; font-family:sans-serif; }
+ .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+ .source { padding:8px; border-bottom:1px solid #ccc; }
+ #program { width:min(600px,80vw); vertical-align:middle; }
+ #status { margin-top:4px; }
+ #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+ #elk { width:100%; height:100%; }
+ #graph svg { display:block; }
+ .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+ .hint { color:#616c78; }
+ .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+ .edge { fill:none; stroke-width:1.5; }
+ .edge.CTRL { stroke-width:2; }
+ .edge.ASSOC { stroke-dasharray:4 4; }
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+ .edge.bundle.selected { stroke-width:6; }
+ .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+ .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+ .node { cursor:pointer; }
+ .box { stroke:#758191; stroke-width:1; }
+ .node.held .box { stroke-dasharray:5 3; }
+ .node.near .box { stroke:#c18221; stroke-width:2; }
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+ .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
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+ max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+ background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+ .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+ .button { color:white; background:black; font-size:20px; min-width:30px; }
+ .button:disabled { background:grey; }
+ .count { font-size:20px; min-width:35px; text-align:center; }
+ #N { width:6ch; }
+ #scrub { width:clamp(120px,35vw,600px); }
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+Type not computed
+
+[0] → — ASSOC 0: $ctrl
+[1] → #6 ASSOC 0: arg</title><line class="row" x1="0" x2="120" y1="30" y2="30"/><line class="row" x1="63" x2="63" y1="0" y2="30"/><text class="bind" x="31.5" y="20" text-anchor="middle">0: $ctrl</text><text class="bind" x="91.5" y="20" text-anchor="middle">0: arg</text><circle class="port" cx="31.5" cy="0" r="3" fill="white"/><circle class="port" cx="91.5" cy="0" r="3" fill="#536477"/><text class="slot" x="31.5" y="-7" text-anchor="middle">0</text><text class="slot" x="91.5" y="-7" text-anchor="middle">1</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
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+Type not computed
+
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+Projection 1 of #2
+Type not computed
+
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diff --git a/docs/chapter04/04-dce2.svg b/docs/chapter04/04-dce2.svg
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+<!-- Con_6 -->
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+<path fill="none" stroke="#000000" d="M89.6664,-52.0265C94.8444,-64.2017 101.7707,-80.4878 107.5926,-94.1772"/>
+<polygon fill="#000000" stroke="#000000" points="104.4613,-95.7577 111.5959,-103.5903 110.903,-93.0181 104.4613,-95.7577"/>
+<text text-anchor="middle" x="87.4428" y="-54.4265" font-family="Helvetica,sans-Serif" font-size="8.00" fill="#000000">1</text>
+</g>
+</g>
+</svg> \ No newline at end of file
diff --git a/docs/chapter04/04-grammar.md b/docs/chapter04/04-grammar.md
new file mode 100644
index 00000000..0600679e
--- /dev/null
+++ b/docs/chapter04/04-grammar.md
@@ -0,0 +1,72 @@
+# Grammar for Chapter 1
+
+```antlrv4
+grammar SimpleLanguage;
+
+program
+ : statement+ EOF
+ ;
+
+statement
+ : returnStatement
+ | declStatement
+ | blockStatment
+ | expressionStatement
+ ;
+
+
+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
+ | '(' 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/chapter04/04-post-peephole.gv b/docs/chapter04/04-post-peephole.gv
new file mode 100644
index 00000000..b893874f
--- /dev/null
+++ b/docs/chapter04/04-post-peephole.gv
@@ -0,0 +1,43 @@
+digraph chapter04 {
+/*
+return 1+arg+2;
+*/
+ rankdir=BT;
+ ordering="in";
+ concentrate="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>>
+ ];
+ Con_10 [ label="#3" ];
+ Add11 [ label="+" ];
+ Return12 [ shape=box style=filled fillcolor=yellow label="Return" ];
+ }
+ node [shape=plaintext];
+ subgraph cluster_Scope1_0 {
+ Scope1_0 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope1_0_$ctrl">$ctrl</TD><TD PORT="Scope1_0_arg">arg</TD></TR>
+ </TABLE>>];
+ subgraph cluster_Scope1_1 {
+ Scope1_1 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">1</TD></TR>
+ </TABLE>>];
+ }
+ }
+ edge [ fontname=Helvetica, fontsize=8 ];
+ Add11 -> Start2:p1[taillabel=1];
+ Add11 -> Con_10[taillabel=2];
+ Return12 -> Start2:p0[taillabel=0; color=red];
+ Return12 -> Add11[taillabel=1];
+ edge [style=dashed color=cornflowerblue];
+ Scope1_0:"Scope1_0_arg" -> Start2:p1;
+}
diff --git a/docs/chapter04/04-post-peephole.json b/docs/chapter04/04-post-peephole.json
new file mode 100644
index 00000000..4890ca67
--- /dev/null
+++ b/docs/chapter04/04-post-peephole.json
@@ -0,0 +1,18 @@
+{
+ "ver": 1,
+ "comp": "chapter04/docs/04-post-peephole.svg",
+ "step": 1,
+ "roots": [],
+ "scope": 0,
+ "nodes": [
+ {"id": 1, "label": "Scope", "type": null, "kind": "SCOPE", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": "0: $ctrl"}, {"idx": 1, "def": 5, "role": "ASSOC", "label": "0: arg"}], "proj": null},
+ {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+ {"id": 4, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+ {"id": 5, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 1}},
+ {"id": 10, "label": "#3", "type": null, "kind": "DATA", "edges": [], "proj": null},
+ {"id": 11, "label": "+", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 5, "role": "DATA", "label": null}, {"idx": 2, "def": 10, "role": "DATA", "label": null}], "proj": null},
+ {"id": 12, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 4, "role": "CTRL", "label": null}, {"idx": 1, "def": 11, "role": "DATA", "label": null}], "proj": null}
+ ],
+ "groups": [
+ ]
+}
diff --git a/docs/chapter04/04-post-peephole.svg b/docs/chapter04/04-post-peephole.svg
new file mode 100644
index 00000000..d03218d6
--- /dev/null
+++ b/docs/chapter04/04-post-peephole.svg
@@ -0,0 +1,90 @@
+<svg aria-label="Compiler graph" width="638" height="350" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 638 350" style="font-family: sans-serif;"><style>
+ html, body { height:100%; margin:0; font-family:sans-serif; }
+ .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+ .source { padding:8px; border-bottom:1px solid #ccc; }
+ #program { width:min(600px,80vw); vertical-align:middle; }
+ #status { margin-top:4px; }
+ #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+ #elk { width:100%; height:100%; }
+ #graph svg { display:block; }
+ .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+ .hint { color:#616c78; }
+ .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+ .edge { fill:none; stroke-width:1.5; }
+ .edge.CTRL { stroke-width:2; }
+ .edge.ASSOC { stroke-dasharray:4 4; }
+ .edge.PARSER { stroke-dasharray:5 4; }
+ .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+ .edge.selected { stroke-width:3.5; }
+ .edge.bundle { stroke-width:4; }
+ .edge.bundle.selected { stroke-width:6; }
+ .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+ .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+ .node { cursor:pointer; }
+ .box { stroke:#758191; stroke-width:1; }
+ .node.held .box { stroke-dasharray:5 3; }
+ .node.near .box { stroke:#c18221; stroke-width:2; }
+ .node.focus .box { stroke:#9c4900; stroke-width:3; }
+ .node.selected .box { stroke:#1569b9; stroke-width:3; }
+ .node.folded .box { stroke-width:4; }
+ .node.folding .box { fill:#f4ccd7; }
+ .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+ .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+ .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+ .node.error .box { stroke:#b42318; stroke-width:4; }
+ #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+ .peep-ghosts { pointer-events:none; }
+ .region-box { stroke:#9da9b8; stroke-width:1.5; }
+ .fold-btn { cursor:pointer; }
+ .fold-btn rect { fill:white; stroke:#596674; }
+ .fold-btn text { font-size:14px; fill:#152330; }
+ .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+ .shortcut { cursor:pointer; }
+ .shortcut path { fill:none; stroke-width:1.5; }
+ .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+ .shortcut text { font-size:11px; fill:#783030; }
+ .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+ .label { font-size:12px; fill:#152330; font-weight:600; }
+ .node-id { font-size:10px; fill:#596674; font-weight:400; }
+ .type { font-size:11px; fill:#455768; }
+ .port { stroke:#536477; stroke-width:1; }
+ .row { stroke:#b6afcf; stroke-width:1; }
+ .bind { font-size:12px; fill:#152330; }
+ .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+ #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+ max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+ background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+ .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+ .button { color:white; background:black; font-size:20px; min-width:30px; }
+ .button:disabled { background:grey; }
+ .count { font-size:20px; min-width:35px; text-align:center; }
+ #N { width:6ch; }
+ #scrub { width:clamp(120px,35vw,600px); }
+ </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge ASSOC" id="e1i1" d="M204,115 C204,139 585.5,0 585.5,24" stroke="#9396a3" marker-start="url(#arrow-ASSOC)" style="opacity: 1;"><title>#1[1] → #5 · ASSOC · 0: arg</title></path><path class="edge DATA" id="e11i1" d="M204,118 L204,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#11[1] → #5 · DATA</title></path><path class="edge DATA" id="e11i2" d="M362,118 L362,123 Q362,128 357,128 L242,128 Q234,128 234,136 L234,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#11[2] → #10 · DATA</title></path><path class="edge CTRL" id="e12i0" d="M84,118 L84,270" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#12[0] → #4 · CTRL</title></path><path class="edge DATA" id="e12i1" d="M204,222 L204,227 Q204,232 199,232 L132,232 Q124,232 124,240 L124,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[1] → #11 · DATA</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(494,24)" style="opacity: 1;"><path class="box" d="M4,0H116Q120,0 120,4V52Q120,56 116,56H4Q0,56 0,52V4Q0,0 4,0Z" fill="#e5e0ff"/><text class="label" text-anchor="middle" x="60" y="48"><tspan>Scope</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 Scope
+Type not computed
+
+[0] → — ASSOC 0: $ctrl
+[1] → #5 ASSOC 0: arg</title><line class="row" x1="0" x2="120" y1="30" y2="30"/><line class="row" x1="63" x2="63" y1="0" y2="30"/><text class="bind" x="31.5" y="20" text-anchor="middle">0: $ctrl</text><text class="bind" x="91.5" y="20" text-anchor="middle">0: arg</text><circle class="port" cx="31.5" cy="0" r="3" fill="white"/><circle class="port" cx="91.5" cy="0" r="3" fill="#536477"/><text class="slot" x="31.5" y="-7" text-anchor="middle">0</text><text class="slot" x="91.5" y="-7" text-anchor="middle">1</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #4/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2 CTRL</title></g><g class="node" id="n5" data-id="5" transform="translate(144,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #5/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#5 arg
+Projection 1 of #2
+Type not computed
+
+[0] → #2 DATA</title></g><g class="node" id="n10" data-id="10" transform="translate(302,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#3</tspan><tspan class="node-id">  #10</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#10 #3
+Type not computed
+
+</title></g><g class="node" id="n11" data-id="11" transform="translate(144,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>+</tspan><tspan class="node-id">  #11</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#11 +
+Type not computed
+
+[0] → — DATA
+[1] → #5 DATA
+[2] → #10 DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n12" data-id="12" transform="translate(44,276)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #12</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#12 Return
+Type not computed
+
+[0] → #4 CTRL
+[1] → #11 DATA</title><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="40" y="-10" text-anchor="middle">0</text><text class="slot" x="80" y="-10" text-anchor="middle">1</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter04/04-pre-peephole.gv b/docs/chapter04/04-pre-peephole.gv
new file mode 100644
index 00000000..d0d7cb0c
--- /dev/null
+++ b/docs/chapter04/04-pre-peephole.gv
@@ -0,0 +1,47 @@
+digraph chapter04 {
+/*
+return 1+arg+2;
+*/
+ rankdir=BT;
+ ordering="in";
+ concentrate="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>>
+ ];
+ Con_5 [ label="#1" ];
+ Con_6 [ label="#2" ];
+ Add7 [ label="+" ];
+ Add8 [ label="+" ];
+ Return9 [ shape=box style=filled fillcolor=yellow label="Return" ];
+ }
+ node [shape=plaintext];
+ subgraph cluster_Scope1_0 {
+ Scope1_0 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope1_0_$ctrl">$ctrl</TD><TD PORT="Scope1_0_arg">arg</TD></TR>
+ </TABLE>>];
+ subgraph cluster_Scope1_1 {
+ Scope1_1 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">1</TD></TR>
+ </TABLE>>];
+ }
+ }
+ edge [ fontname=Helvetica, fontsize=8 ];
+ Add7 -> Start2:p1[taillabel=1];
+ Add7 -> Con_6[taillabel=2];
+ Add8 -> Con_5[taillabel=1];
+ Add8 -> Add7[taillabel=2];
+ Return9 -> Start2:p0[taillabel=0; color=red];
+ Return9 -> Add8[taillabel=1];
+ edge [style=dashed color=cornflowerblue];
+ Scope1_0:"Scope1_0_arg" -> Start2:p1;
+}
diff --git a/docs/chapter04/04-pre-peephole.json b/docs/chapter04/04-pre-peephole.json
new file mode 100644
index 00000000..839c16e7
--- /dev/null
+++ b/docs/chapter04/04-pre-peephole.json
@@ -0,0 +1,20 @@
+{
+ "ver": 1,
+ "comp": "chapter04/docs/04-pre-peephole.svg",
+ "step": 1,
+ "roots": [],
+ "scope": 0,
+ "nodes": [
+ {"id": 1, "label": "Scope", "type": null, "kind": "SCOPE", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": "0: $ctrl"}, {"idx": 1, "def": 10, "role": "ASSOC", "label": "0: arg"}], "proj": null},
+ {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+ {"id": 4, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+ {"id": 5, "label": "#1", "type": null, "kind": "DATA", "edges": [], "proj": null},
+ {"id": 6, "label": "#2", "type": null, "kind": "DATA", "edges": [], "proj": null},
+ {"id": 7, "label": "+", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 10, "role": "DATA", "label": null}, {"idx": 2, "def": 6, "role": "DATA", "label": null}], "proj": null},
+ {"id": 8, "label": "+", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 5, "role": "DATA", "label": null}, {"idx": 2, "def": 7, "role": "DATA", "label": null}], "proj": null},
+ {"id": 9, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 4, "role": "CTRL", "label": null}, {"idx": 1, "def": 8, "role": "DATA", "label": null}], "proj": null},
+ {"id": 10, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 1}}
+ ],
+ "groups": [
+ ]
+}
diff --git a/docs/chapter04/04-pre-peephole.svg b/docs/chapter04/04-pre-peephole.svg
new file mode 100644
index 00000000..813a48dd
--- /dev/null
+++ b/docs/chapter04/04-pre-peephole.svg
@@ -0,0 +1,98 @@
+<svg aria-label="Compiler graph" width="638" height="454" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 638 454" style="font-family: sans-serif;"><style>
+ html, body { height:100%; margin:0; font-family:sans-serif; }
+ .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+ .source { padding:8px; border-bottom:1px solid #ccc; }
+ #program { width:min(600px,80vw); vertical-align:middle; }
+ #status { margin-top:4px; }
+ #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+ #elk { width:100%; height:100%; }
+ #graph svg { display:block; }
+ .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+ .hint { color:#616c78; }
+ .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+ .edge { fill:none; stroke-width:1.5; }
+ .edge.CTRL { stroke-width:2; }
+ .edge.ASSOC { stroke-dasharray:4 4; }
+ .edge.PARSER { stroke-dasharray:5 4; }
+ .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+ .edge.selected { stroke-width:3.5; }
+ .edge.bundle { stroke-width:4; }
+ .edge.bundle.selected { stroke-width:6; }
+ .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+ .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+ .node { cursor:pointer; }
+ .box { stroke:#758191; stroke-width:1; }
+ .node.held .box { stroke-dasharray:5 3; }
+ .node.near .box { stroke:#c18221; stroke-width:2; }
+ .node.focus .box { stroke:#9c4900; stroke-width:3; }
+ .node.selected .box { stroke:#1569b9; stroke-width:3; }
+ .node.folded .box { stroke-width:4; }
+ .node.folding .box { fill:#f4ccd7; }
+ .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+ .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+ .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+ .node.error .box { stroke:#b42318; stroke-width:4; }
+ #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+ .peep-ghosts { pointer-events:none; }
+ .region-box { stroke:#9da9b8; stroke-width:1.5; }
+ .fold-btn { cursor:pointer; }
+ .fold-btn rect { fill:white; stroke:#596674; }
+ .fold-btn text { font-size:14px; fill:#152330; }
+ .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+ .shortcut { cursor:pointer; }
+ .shortcut path { fill:none; stroke-width:1.5; }
+ .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+ .shortcut text { font-size:11px; fill:#783030; }
+ .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+ .label { font-size:12px; fill:#152330; font-weight:600; }
+ .node-id { font-size:10px; fill:#596674; font-weight:400; }
+ .type { font-size:11px; fill:#455768; }
+ .port { stroke:#536477; stroke-width:1; }
+ .row { stroke:#b6afcf; stroke-width:1; }
+ .bind { font-size:12px; fill:#152330; }
+ .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+ #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+ max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+ background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+ .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+ .button { color:white; background:black; font-size:20px; min-width:30px; }
+ .button:disabled { background:grey; }
+ .count { font-size:20px; min-width:35px; text-align:center; }
+ #N { width:6ch; }
+ #scrub { width:clamp(120px,35vw,600px); }
+ </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge ASSOC" id="e1i1" d="M204,115 C204,139 585.5,0 585.5,24" stroke="#9396a3" marker-start="url(#arrow-ASSOC)" style="opacity: 1;"><title>#1[1] → #10 · ASSOC · 0: arg</title></path><path class="edge DATA" id="e7i1" d="M204,118 L204,123 Q204,128 209,128 L299,128 Q307,128 307,136 L307,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#7[1] → #10 · DATA</title></path><path class="edge DATA" id="e7i2" d="M362,118 L362,123 Q362,128 357,128 L345,128 Q337,128 337,136 L337,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#7[2] → #6 · DATA</title></path><path class="edge DATA" id="e8i1" d="M155,222 L155,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#8[1] → #5 · DATA</title></path><path class="edge DATA" id="e8i2" d="M307,222 L307,227 Q307,232 302,232 L193,232 Q185,232 185,240 L185,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#8[2] → #7 · DATA</title></path><path class="edge CTRL" id="e9i0" d="M84,118 L84,374" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#9[0] → #4 · CTRL</title></path><path class="edge DATA" id="e9i1" d="M155,326 L155,331 Q155,336 150,336 L132,336 Q124,336 124,344 L124,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#9[1] → #8 · DATA</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(494,24)" style="opacity: 1;"><path class="box" d="M4,0H116Q120,0 120,4V52Q120,56 116,56H4Q0,56 0,52V4Q0,0 4,0Z" fill="#e5e0ff"/><text class="label" text-anchor="middle" x="60" y="48"><tspan>Scope</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 Scope
+Type not computed
+
+[0] → — ASSOC 0: $ctrl
+[1] → #10 ASSOC 0: arg</title><line class="row" x1="0" x2="120" y1="30" y2="30"/><line class="row" x1="63" x2="63" y1="0" y2="30"/><text class="bind" x="31.5" y="20" text-anchor="middle">0: $ctrl</text><text class="bind" x="91.5" y="20" text-anchor="middle">0: arg</text><circle class="port" cx="31.5" cy="0" r="3" fill="white"/><circle class="port" cx="91.5" cy="0" r="3" fill="#536477"/><text class="slot" x="31.5" y="-7" text-anchor="middle">0</text><text class="slot" x="91.5" y="-7" text-anchor="middle">1</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #4/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2 CTRL</title></g><g class="node" id="n5" data-id="5" transform="translate(95,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#1</tspan><tspan class="node-id">  #5</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#5 #1
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(302,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#2</tspan><tspan class="node-id">  #6</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 #2
+Type not computed
+
+</title></g><g class="node" id="n7" data-id="7" transform="translate(247,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>+</tspan><tspan class="node-id">  #7</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#7 +
+Type not computed
+
+[0] → — DATA
+[1] → #10 DATA
+[2] → #6 DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n8" data-id="8" transform="translate(95,276)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>+</tspan><tspan class="node-id">  #8</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#8 +
+Type not computed
+
+[0] → — DATA
+[1] → #5 DATA
+[2] → #7 DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n9" data-id="9" transform="translate(44,380)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 Return
+Type not computed
+
+[0] → #4 CTRL
+[1] → #8 DATA</title><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="40" y="-10" text-anchor="middle">0</text><text class="slot" x="80" y="-10" text-anchor="middle">1</text></g><g class="node" id="n10" data-id="10" transform="translate(144,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #10/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#10 arg
+Projection 1 of #2
+Type not computed
+
+[0] → #2 DATA</title></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter04/Makefile b/docs/chapter04/Makefile
new file mode 100644
index 00000000..6fa0f057
--- /dev/null
+++ b/docs/chapter04/Makefile
@@ -0,0 +1 @@
+include ../../graph/docs.mk
diff --git a/docs/chapter04/README.md b/docs/chapter04/README.md
new file mode 100644
index 00000000..837941b2
--- /dev/null
+++ b/docs/chapter04/README.md
@@ -0,0 +1,419 @@
+# Chapter 4: External Argument and Comparisons
+
+[Previous: Chapter 3](../chapter03/README.md) |
+[Next: Chapter 5](../chapter05/README.md)
+
+# Table of Contents
+
+1. [Extensions to Intermediate Representation](#extensions-to-intermediate-representation)
+2. [Projection Nodes](#projection-nodes)
+3. [Visualisation](#visualisation)
+4. [Initial values](#initial-values)
+5. [When Is Control Not-Null?](#when-is-control-not-null)
+6. [Note Regarding Visualizations](#note-regarding-visualizations)
+7. [Changes to Type System](#changes-to-type-system)
+8. [Tuple Types](#tuple-types)
+9. [$ctrl name binding](#ctrl-name-binding)
+10. [More Peephole Optimizations](#more-peephole-optimizations)
+11. [Peephole Walkthrough](#peephole-walkthrough)
+12. [Dead Code Elimination(DCE)](#dead-code-eliminationdce)
+
+You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter04) 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-chapter03...linear-chapter04) it to the previous chapter.
+
+
+In this chapter we extend the language grammar with the following features:
+
+* The program receives a single argument named `arg` of integer type from the external environment.
+* Expressions support comparison operators.
+* We introduce a scope sensitive name binding `$ctrl` for the current incoming
+ control node. Thus, our Return is no longer hard-wired to Start, instead it
+ tracks the in scope `$ctrl` binding.
+
+Here is the [complete language grammar](04-grammar.md) for this chapter.
+
+
+
+## Extensions to Intermediate Representation
+
+In this chapter we add some new nodes and revise some existing nodes.
+Following are revised or new nodes
+
+| Node Name | Type | Description | Inputs | Value |
+|-----------|----------------|------------------------------------------------|-----------------------|----------------------------------------------------------------------------|
+| MultiNode | Abstract class | A node that has a tuple result | | A tuple |
+| Start | Control | Start of function, now a MultiNode | | A tuple with a ctrl token and an `arg` data node |
+| Proj | Data / Control | Projection nodes extract values from MultiNode | A MultiNode and index | Result is the extracted value from the input MultiNode at offset index |
+| Bool | Data | Represents results of a comparison operator | Two data nodes | Result is a comparison, represented as integer value where 1=true, 0=false |
+| Not | Data | Logical not | One data node | Result converts 0 to 1 and vice versa |
+
+> A `Proj` is a control node when it projects the control slot: `Proj#0` off `Start`.
+> Every other projection is a data node. See `ProjNode.isCFG()`.
+
+We keep all other nodes from prior chapters.
+
+
+## Projection Nodes
+
+We add projection nodes that are used to extract a specific tuple member from a multi-valued node.
+Each projection node contains an index of the field to extract from its input node.
+Projection nodes allow us to maintain labeled use-def edges as simple Node references.
+
+In the visuals, projection nodes are shown as rectangular boxes inside the node to which they are attached.
+
+### Visualisation
+
+![Start and its control and argument projections](./projnode.svg)
+
+In the visual above, the projection nodes have been tagged by the names
+associated with the outputs of the Start node. Both MultiNodes that contain
+Control and Control nodes are yellow. `$ctrl` and `arg` are outputs (users) of
+StartNode(`START`) and have their MultiNode as their only input in slot 0. The
+`label` has no semantics and is used during debug printing.
+
+```java
+public ProjNode(MultiNode ctrl, int idx, String label) {
+ super(ctrl);
+```
+
+```java
+_scope.define(ScopeNode.CTRL, new ProjNode(START, 0, ScopeNode.CTRL).peephole());
+_scope.define(ScopeNode.ARG0, new ProjNode(START, 1, ScopeNode.ARG0).peephole());
+```
+
+These projection nodes are going to extract the types for `CTRL` and `ARG0` from the `START` MultiNode.
+The MultiNode holds the types as a TypeTuple:
+
+```java
+public StartNode(Type[] args) {
+ super();
+ _args = new TypeTuple(args);
+```
+
+Extracting the types is based on the `_idx`:
+```java
+return t instanceof TypeTuple tt ? tt._types[_idx] : Type.BOTTOM;
+```
+
+### Initial values
+
+An argument is always provided, and defaults to `TypeInteger.BOT`. Individual
+tests can (and do) pass in other integer values by calling `new Parser` with
+an argument:
+
+```java
+Parser parser = new Parser("return arg; ", TypeInteger.constant(2));
+```
+
+The graph:
+
+![ProjNode](./04-arg1.svg)
+
+- `$ctrl` and `arg` are both defined in the outermost symbol table, at lexical depth 0.
+- There is an empty global-scope symbol table created at depth 1; in the future
+ global variables will be defined here.
+- There is no line for the scope `$ctrl` because control is dead after the
+ return. It is manually set to null, which calls `setDef` to kill the node
+ (and killed nodes are not part of the program and not visualized).
+
+```
+ ctrl(null); // Kill control
+```
+
+- The `arg` projection node is not included in the cluster because arg is a
+ constant. The `arg` was originally defined by a ProjNode; but when peephole
+ is called the computed type is a constant, and the ProjNode gets replaced
+ with a ConstantNode:
+
+```java
+public final Node peephole( ) {
+ Type type = _type = compute();
+ /* type = {TypeInteger@1527} "2" */
+
+ // ProjNode is not a constant unlike its type.
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ /* Create Constant(2) */
+ return deadCodeElim(new ConstantNode(type).peephole());
+
+ /* won't get called */
+ ...
+```
+
+If you don't pass an argument you get `TypeInteger.BOT`
+
+```java
+ Parser parser = new Parser("return arg; ");
+ ...
+
+public Parser(String source) {
+ this(source, TypeInteger.BOT);
+}
+
+```
+
+We clearly see this is not a constant:
+
+```java
+public final static TypeInteger BOT = new TypeInteger(false, 1);
+ /* _is_con = false */
+```
+
+So the `arg` projection node remains in the cluster:
+
+![ArgNode](./04-arg2.svg)
+
+
+#### When Is Control Not-Null?
+
+In later chapters, `$ctrl` will point to other control nodes, such as
+`If` and `Region` (and `Loop`), but for now with no other control flow it always gets set to null after a `Return`.
+
+#### Note Regarding Visualizations
+
+From this chapter onwards we omit the edges from Constants to Start node, mainly to reduce
+clutter and help draw the reader's attention to the more important aspects of the graph.
+
+
+
+## Changes to Type System
+
+In [Chapter 2](../chapter02/README.md) we introduced the Type System.
+
+We have annotated Nodes with Types and the Type annotation serves two purposes:
+
+* It defines the set of operations allowed on the Node, and
+* it defines the set of values the Node takes on.
+
+We mentioned in [Chapter 2](../chapter02/README.md) that the set of values
+associated with a Type at a specific Node can be conveniently represented as a
+[lattice](https://en.wikipedia.org/wiki/Lattice_(order)).
+
+The type itself is identified by the Java class `Type` and subtypes. The type
+implementation uses Java classes as a convenient way to deal with a Type's internal
+structure - but the Java classes have no relation to a Type's place in the
+lattice.
+
+In this chapter we extend the Type hierarchy as follows:
+
+```
+Type (Enhanced - now has Control, and a global Top and Bottom)
++-- TypeInteger (Enhanced - now has Top and Bottom types)
++-- TypeTuple (New - represents multi-valued result)
+```
+
+Our enhanced Lattice looks like this:
+
+![Lattice](./lattice.svg)
+
+
+In this chapter we introduce the possibility of a program input variable named
+`arg`; all we know about this variable is that it is some integer value, but we
+do not know whether it is a constant or not.
+
+To support the requirements for non-constant integer values, we enhance
+`TypeInteger` to allow it to represent `IntTop` and `IntBot` integer types in
+addition to the earlier constant value.
+
+Now that integer values may be constants or non-constants, we need to introduce
+the *meet* operator over our lattice. The `meet` operator describes rules that
+define the resulting type when we combine integer values. In the lattice
+diagram you can start from the two elements being `meet` and follow the
+two arrows down the graph to the first point they meet.
+
+| | IntBot | Con1 | Con2 | IntTop |
+|--------|--------|--------|--------|--------|
+| IntBot | IntBot | IntBot | IntBot | IntBot |
+| Con1 | IntBot | Con1 | IntBot | Con1 |
+| IntTop | IntBot | Con1 | Con2 | IntTop |
+
+In the table above `Con1` and `Con2` represent two distinct integer values, and serve to explain the rules below.
+
+* The `meet` of `IntTop` with any integer constant is that constant.
+* The `meet` of `IntBot` with any integer value is `IntBot`.
+* The `meet` of any integer with itself is that integer.
+* The `meet` of two unrelated integer constants is `IntBot`.
+
+Currently, all our integer valued nodes are either a constant or an `IntBot` integer type.
+When we start optimizing loops, we will start seeing `IntTop` values.
+
+
+### Tuple Types
+
+Tuple types need a little more explanation: they are a fixed-size grouping of
+types; literally a `Type[]`. Tuples represent a collection of otherwise
+unrelated types, and come from `MultiNode`s. `ProjNode`s will take the
+appropriate `Type` array element out of a Tuple. The `StartNode` now produces
+a 2-element `TypeTuple` with control and the type of `arg`: `[ctrl, TypeInteger.INTBOT]`
+
+The lattice `meet` operator on Tuples is done element by element; each array
+element recursively calls `meet`. Tuples of mixed sizes are an internal
+compiler error, and the `meet` uses Bottom for them.
+
+
+## `$ctrl` name binding
+
+In previous chapters, we had a hard coded control input edge from Start to
+Return. In this chapter we no longer have such a hard-wired edge. Instead, we
+track the current in-scope control node via the name `$ctrl`. This means that
+when we need to create an edge to the predecessor control node, we simply look
+up this name in the current scope.
+
+
+## More Peephole Optimizations
+
+Now that we have non-constant integer values, we can do additional
+optimizations, rearranging algebraic expressions to enable constant
+folding. For example:
+
+```
+return 1 + arg + 2;
+```
+
+We would expect the compiler to output `arg+3` here, but as it stands what we get is:
+
+![Graph1](./04-pre-peephole.svg)
+
+We need to perform some algebraic simplifications to enable a better outcome. For
+example, we need to rearrange the expression as follows:
+
+```
+arg + (1 + 2)
+```
+
+This then enables constant folding and the final outcome is shown below. By
+canonicalizing expressions we fold common addressing math constants, remove
+algebraic identities and generally simplify the code.
+
+![Graph1](./04-post-peephole.svg)
+
+Here is a list of peepholes introduced in this Chapter, more will be introduced in later chapters:
+
+| Before | After | Description |
+|-----------------------|-----------------------|------------------------------------------------|
+| (arg + 0 ) | arg | Add of zero identity |
+| (arg - 0 ) | arg | Sub of zero identity |
+| (arg * 1 ) | arg | Multiply by one identity |
+| (con + arg) | (arg + con) | Move constants to right, to encourage folding |
+| (con * arg) | (arg * con) | Move constants to right, to encourage folding |
+| (con1 + (arg + con2)) | (arg + (con1 + con2)) | Move constants to right, to encourage folding |
+| ((arg1 + con) + arg2) | ((arg1 + arg2) + con) | Move constants to right, to encourage folding |
+| (arg + arg) | (arg * 2) | Sum-of-products form |
+| (arg - arg) | 0 | Sub of same is 0
+| (0 - arg) | (-arg) | Sub from 0 is negation
+| (arg1 - (-arg2)) | (arg1 + arg2) | Sub of negation is add
+| ((-arg1) - arg2) | -(arg1 + arg2) | Sub from negation is negation of sum
+| (con / 1) | con | Division by one
+| (arg == arg) | 1 | Compare of same
+| (arg != arg) | 0 | Compare of same
+| (arg < arg) | 0 | Compare of same
+| (arg > arg) | 0 | Compare of same
+| (arg <= arg) | 1 | Compare of same
+| (arg >= arg) | 1 | Compare of same
+
+
+## Peephole Walkthrough
+
+The peephole optimizations introduced in this chapter are all local. They are triggered during parsing
+as new nodes are created, before the newly created node has any uses.
+
+For example, when we parse a unary expression, and create a Node for the parsed expression,
+`peephole()` is invoked on the newly created `MinusNode`:
+
+```java
+private Node parseUnary() {
+ if (match("-")) return new MinusNode(parseUnary()).peephole();
+ return parsePrimary();
+}
+```
+
+As another example, here is the parsing of comparison operators, also introduced in this chapter:
+
+```java
+private Node parseComparison() {
+ var lhs = parseAddition();
+ if (match("==")) return new BoolNode.EQNode(lhs, parseComparison()).peephole();
+ if (match("!=")) return new BoolNode.NENode(lhs, parseComparison()).peephole();
+ if (match("<=")) return new BoolNode.LENode(lhs, parseComparison()).peephole();
+ if (match("<" )) return new BoolNode.LTNode(lhs, parseComparison()).peephole();
+ if (match(">=")) return new BoolNode.GENode(lhs, parseComparison()).peephole();
+ if (match(">" )) return new BoolNode.GTNode(lhs, parseComparison()).peephole();
+ return lhs;
+}
+```
+
+The implementation of `peephole()` is in the main `Node` class, and is thus shared
+by all subclasses of `Node`.
+
+```java
+public final Node peephole( ) {
+ // Compute initial or improved Type
+ Type type = _type = compute();
+
+ // Replace constant computations from non-constants with a constant node
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ return deadCodeElim(new ConstantNode(type).peephole());
+
+ // Ask each node for a better replacement
+ Node n = idealize();
+ if( n != null ) // Something changed
+ // Recursively optimize
+ return deadCodeElim(n.peephole());
+
+ return this; // No progress
+}
+```
+
+The peephole method does the following:
+
+- Compute a Type for the node.
+- If the Type is a Constant and the node is not a ConstantNode, replace with a
+ ConstantNode, recursively invoking peephole on the new constant.
+- Otherwise, ask the Node for a better replacement via a call to `idealize()`.
+ The "better replacement" is things like `(1+2)` becomes `3` and `1+(x+2)`
+ becomes `(x+(1+2))`.
+- Each Node subtype is responsible for deciding what the `idealize()` step
+ should do. If there is a better replacement then the node returns a non
+ `null` value.
+- If we see a non `null` value, something changed, so we invoke `peephole()`
+ again and then also run dead code elimination on the (now dead and replaced)
+ `this` node.
+
+`peephole()` calls `deadCodeElim()` which is shown below.
+
+
+## Dead Code Elimination(DCE)
+
+We call `kill` every time a Node makes the 1-user-to-0-users transition during
+graph editing. This commonly happens when replacing via peeps and exiting
+scopes. This recursive `kill` amounts to Dead Code Elimination in many other
+compilers; here we call it in a very fine-grained way. Many Nodes will be
+created by the parser, only to be killed before the very next lexeme is parsed.
+
+For more information please read the [appendix section](appendix/dce.md#appendix) on dead code elimination.
+
+The suggestively called `deadCodeElim` function is a thin wrapper over `kill`
+used by `peepholeOpt` to avoid prematurely killing a Node which only briefly
+makes the 1->0 users transition.
+
+```java
+// m is the new Node, self is the old.
+// Return 'm', which may have zero uses but is alive nonetheless.
+// If self has zero uses (and is not 'm'), {@link #kill} self.
+private Node deadCodeElim(Node m) {
+ // If self is going dead and not being returned here (Nodes returned
+ // from peephole commonly have no uses (yet)), then kill self.
+ if( m != this && isUnused() ) {
+ // Killing self - and since self recursively kills self's inputs we
+ // might end up killing 'm', which we are returning as a live Node.
+ // So we add a bogus extra null output edge to stop kill().
+ m.addUse(null); // Add bogus null use to keep m alive
+ kill(); // Kill self because replacing with 'm'
+ m.delUse(null); // Remove bogus null.
+ }
+ return m;
+}
+```
+
+Note the temporary add of a bogus user to the Node `m`. The reason this is
+done is that we know `m` is the new replacement and is alive, but since it is
+not yet hooked into the graph, it has no users yet. By adding a bogus user we
+prevent it being mistaken for dead and being killed.
diff --git a/docs/chapter04/lattice.gv b/docs/chapter04/lattice.gv
new file mode 100644
index 00000000..6efef107
--- /dev/null
+++ b/docs/chapter04/lattice.gv
@@ -0,0 +1,97 @@
+digraph Lattice {
+ compound = true;
+ // Define nodes
+ splines=false;
+ node [shape=circle, style=filled];
+ nodesep=0.6;
+
+ TOP [label=<<B>⊤</B >>, fillcolor=black, fontcolor=white];
+ BOT [label=<<B>⊥</B>>, fillcolor=black, fontcolor=white];
+
+ // ----------------------
+ // Control
+ CTRL [label="ctrl", fillcolor=yellow, shape=oval];
+
+ TOP -> CTRL;
+ CTRL -> BOT;
+
+ // ----------------------
+ // Integers
+ INT_TOP [label=<<B>⊤</B >:int>, fillcolor=lightblue, shape=oval];
+ INT_BOT [label=<<B>⊥</B>:int>, fillcolor=lightblue, shape=oval];
+
+ INT_MIN [label="-n" , fillcolor=lightblue];
+ INT_MINDOTS [label="...", fillcolor=lightblue shape=oval];
+ INT_MINUS [label="-1" , fillcolor=lightblue];
+ INT_ZERO [label="0" , fillcolor=lightblue];
+ INT_PLUS [label="1" , fillcolor=lightblue];
+ INT_MAXDOTS [label="...", fillcolor=lightblue, shape=oval];
+ INT_MAX [label="+n" , fillcolor=lightblue];
+
+ TOP -> INT_TOP;
+ INT_TOP -> INT_MIN;
+ INT_TOP -> INT_MINDOTS;
+ INT_TOP -> INT_MINUS;
+ INT_TOP -> INT_ZERO;
+ INT_TOP -> INT_PLUS;
+ INT_TOP -> INT_MAXDOTS;
+ INT_TOP -> INT_MAX;
+ INT_MIN -> INT_BOT;
+ INT_MINDOTS -> INT_BOT;
+ INT_MINUS -> INT_BOT;
+ INT_ZERO -> INT_BOT;
+ INT_PLUS -> INT_BOT;
+ INT_MAXDOTS -> INT_BOT;
+ INT_MAX -> INT_BOT;
+ INT_BOT -> BOT;
+
+ INT_MIN -> INT_MINDOTS -> INT_MINUS -> INT_ZERO -> INT_PLUS -> INT_MAXDOTS -> INT_MAX [style=invis];
+
+ // ----------------------
+ // Tuples
+
+ TUPLE_TOP [label=<<B>⊤</B >:tuple>, fillcolor=pink, shape=oval];
+ TUPLE_BOT [label=<<B>⊥</B>:tuple>, fillcolor=pink, shape=oval];
+
+ TUPLE1 [shape=none, fillcolor=none, label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TH><TD BGCOLOR="pink">tuple</TD></TH>
+ <TR><TD BGCOLOR="black" ><FONT color="white">type</FONT></TD></TR>
+ </TABLE>
+ >];
+ TUPLE2 [shape=none, fillcolor=none, label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TH><TD BGCOLOR="pink">tuple</TD></TH>
+ <TR><TD BGCOLOR="black" ><FONT color="white">type</FONT></TD></TR>
+ <TR><TD BGCOLOR="black" ><FONT color="white">type</FONT></TD></TR>
+ </TABLE>
+ >];
+ TUPLEN [shape=none, fillcolor=none, label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TH><TD BGCOLOR="pink">tuple</TD></TH>
+ <TR><TD BGCOLOR="black" ><FONT color="white">type</FONT></TD></TR>
+ <TR><TD BGCOLOR="black" ><FONT color="white">...</FONT></TD></TR>
+ <TR><TD BGCOLOR="black" ><FONT color="white">type</FONT></TD></TR>
+ </TABLE>
+ >];
+
+
+ TOP -> TUPLE_TOP;
+ TUPLE_TOP -> TUPLE1;
+ TUPLE_TOP -> TUPLE2;
+ TUPLE_TOP -> TUPLEN;
+ TUPLE1 -> TUPLE_BOT;
+ TUPLE2 -> TUPLE_BOT;
+ TUPLEN -> TUPLE_BOT;
+ TUPLE_BOT -> BOT;
+
+ // Additional customization
+ {rank=same; TOP}
+ {rank=same; INT_TOP; TUPLE_TOP}
+ {rank=same;
+ CTRL;
+ INT_MIN; INT_MINDOTS; INT_MINUS; INT_ZERO; INT_PLUS; INT_MAXDOTS; INT_MAX;
+ }
+ {rank=same; INT_BOT, TUPLE_BOT}
+ {rank=same; BOT;}
+}
diff --git a/docs/chapter04/lattice.svg b/docs/chapter04/lattice.svg
new file mode 100644
index 00000000..35cb9296
--- /dev/null
+++ b/docs/chapter04/lattice.svg
@@ -0,0 +1,305 @@
+<?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 12.2.0 (20241103.1931)
+ -->
+<!-- Title: Lattice Pages: 1 -->
+<svg width="952pt" height="406pt"
+ viewBox="0.00 0.00 952.00 406.50" 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(4 402.5)">
+<title>Lattice</title>
+<polygon fill="white" stroke="none" points="-4,4 -4,-402.5 948,-402.5 948,4 -4,4"/>
+<!-- TOP -->
+<g id="node1" class="node">
+<title>TOP</title>
+<ellipse fill="black" stroke="black" cx="374" cy="-377.37" rx="21.12" ry="21.12"/>
+<text text-anchor="start" x="366.12" y="-372.95" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00" fill="white">⊤</text>
+</g>
+<!-- CTRL -->
+<g id="node3" class="node">
+<title>CTRL</title>
+<ellipse fill="yellow" stroke="black" cx="27" cy="-199.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">ctrl</text>
+</g>
+<!-- TOP&#45;&gt;CTRL -->
+<g id="edge1" class="edge">
+<title>TOP&#45;&gt;CTRL</title>
+<path fill="none" stroke="black" d="M354.85,-367.54C297.95,-338.34 129.51,-251.87 58.81,-215.58"/>
+<polygon fill="black" stroke="black" points="60.56,-212.54 50.07,-211.09 57.36,-218.77 60.56,-212.54"/>
+</g>
+<!-- INT_TOP -->
+<g id="node4" class="node">
+<title>INT_TOP</title>
+<ellipse fill="lightblue" stroke="black" cx="374" cy="-302.25" rx="33.95" ry="18"/>
+<text text-anchor="start" x="357.12" y="-298.2" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊤</text>
+<text text-anchor="start" x="372.88" y="-298.2" font-family="Times New Roman,serif" font-size="14.00">:int</text>
+</g>
+<!-- TOP&#45;&gt;INT_TOP -->
+<g id="edge3" class="edge">
+<title>TOP&#45;&gt;INT_TOP</title>
+<path fill="none" stroke="black" d="M374,-356C374,-348.51 374,-339.87 374,-331.79"/>
+<polygon fill="black" stroke="black" points="377.5,-332.05 374,-322.05 370.5,-332.05 377.5,-332.05"/>
+</g>
+<!-- TUPLE_TOP -->
+<g id="node13" class="node">
+<title>TUPLE_TOP</title>
+<ellipse fill="pink" stroke="black" cx="771" cy="-302.25" rx="42.65" ry="18"/>
+<text text-anchor="start" x="747.75" y="-298.2" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊤</text>
+<text text-anchor="start" x="763.5" y="-298.2" font-family="Times New Roman,serif" font-size="14.00">:tuple</text>
+</g>
+<!-- TOP&#45;&gt;TUPLE_TOP -->
+<g id="edge25" class="edge">
+<title>TOP&#45;&gt;TUPLE_TOP</title>
+<path fill="none" stroke="black" d="M395.06,-372.49C455.97,-361.27 633.5,-328.57 721.03,-312.45"/>
+<polygon fill="black" stroke="black" points="721.57,-315.91 730.77,-310.66 720.3,-309.03 721.57,-315.91"/>
+</g>
+<!-- BOT -->
+<g id="node2" class="node">
+<title>BOT</title>
+<ellipse fill="black" stroke="black" cx="374" cy="-21.12" rx="21.12" ry="21.12"/>
+<text text-anchor="start" x="366.12" y="-16.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00" fill="white">⊥</text>
+</g>
+<!-- CTRL&#45;&gt;BOT -->
+<g id="edge2" class="edge">
+<title>CTRL&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M48.71,-188.11C108.7,-157.31 276.83,-71 344.87,-36.08"/>
+<polygon fill="black" stroke="black" points="346.26,-39.3 353.55,-31.62 343.06,-33.07 346.26,-39.3"/>
+</g>
+<!-- INT_MIN -->
+<g id="node6" class="node">
+<title>INT_MIN</title>
+<ellipse fill="lightblue" stroke="black" cx="116" cy="-199.25" rx="18.6" ry="18.6"/>
+<text text-anchor="middle" x="116" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">&#45;n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MIN -->
+<g id="edge4" class="edge">
+<title>INT_TOP&#45;&gt;INT_MIN</title>
+<path fill="none" stroke="black" d="M347.36,-290.82C298.27,-271.6 193.98,-230.78 143.94,-211.18"/>
+<polygon fill="black" stroke="black" points="145.28,-207.95 134.69,-207.56 142.73,-214.47 145.28,-207.95"/>
+</g>
+<!-- INT_MINDOTS -->
+<g id="node7" class="node">
+<title>INT_MINDOTS</title>
+<ellipse fill="lightblue" stroke="black" cx="205" cy="-199.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="205" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINDOTS -->
+<g id="edge5" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINDOTS</title>
+<path fill="none" stroke="black" d="M352.25,-288.25C322.2,-270.29 267.88,-237.83 234.28,-217.75"/>
+<polygon fill="black" stroke="black" points="236.25,-214.85 225.87,-212.72 232.66,-220.85 236.25,-214.85"/>
+</g>
+<!-- INT_MINUS -->
+<g id="node8" class="node">
+<title>INT_MINUS</title>
+<ellipse fill="lightblue" stroke="black" cx="294" cy="-199.25" rx="18.6" ry="18.6"/>
+<text text-anchor="middle" x="294" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">&#45;1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINUS -->
+<g id="edge6" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINUS</title>
+<path fill="none" stroke="black" d="M361.5,-285.47C348.27,-268.76 327.25,-242.23 312.18,-223.21"/>
+<polygon fill="black" stroke="black" points="315.02,-221.14 306.06,-215.48 309.53,-225.49 315.02,-221.14"/>
+</g>
+<!-- INT_ZERO -->
+<g id="node9" class="node">
+<title>INT_ZERO</title>
+<ellipse fill="lightblue" stroke="black" cx="374" cy="-199.25" rx="18" ry="18"/>
+<text text-anchor="middle" x="374" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">0</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_ZERO -->
+<g id="edge7" class="edge">
+<title>INT_TOP&#45;&gt;INT_ZERO</title>
+<path fill="none" stroke="black" d="M374,-284.12C374,-269.02 374,-246.74 374,-228.93"/>
+<polygon fill="black" stroke="black" points="377.5,-228.98 374,-218.98 370.5,-228.98 377.5,-228.98"/>
+</g>
+<!-- INT_PLUS -->
+<g id="node10" class="node">
+<title>INT_PLUS</title>
+<ellipse fill="lightblue" stroke="black" cx="453" cy="-199.25" rx="18" ry="18"/>
+<text text-anchor="middle" x="453" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_PLUS -->
+<g id="edge8" class="edge">
+<title>INT_TOP&#45;&gt;INT_PLUS</title>
+<path fill="none" stroke="black" d="M386.34,-285.47C399.49,-268.67 420.4,-241.93 435.3,-222.88"/>
+<polygon fill="black" stroke="black" points="437.93,-225.2 441.33,-215.17 432.41,-220.89 437.93,-225.2"/>
+</g>
+<!-- INT_MAXDOTS -->
+<g id="node11" class="node">
+<title>INT_MAXDOTS</title>
+<ellipse fill="lightblue" stroke="black" cx="541" cy="-199.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="541" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAXDOTS -->
+<g id="edge9" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAXDOTS</title>
+<path fill="none" stroke="black" d="M395.83,-288.04C425.56,-270.07 478.84,-237.84 511.93,-217.83"/>
+<polygon fill="black" stroke="black" points="513.46,-221 520.2,-212.83 509.84,-215.01 513.46,-221"/>
+</g>
+<!-- INT_MAX -->
+<g id="node12" class="node">
+<title>INT_MAX</title>
+<ellipse fill="lightblue" stroke="black" cx="632" cy="-199.25" rx="21.15" ry="21.15"/>
+<text text-anchor="middle" x="632" y="-194.2" font-family="Times New Roman,serif" font-size="14.00">+n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAX -->
+<g id="edge10" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAX</title>
+<path fill="none" stroke="black" d="M400.64,-290.82C449,-271.89 550.91,-231.99 601.78,-212.08"/>
+<polygon fill="black" stroke="black" points="602.96,-215.38 610.99,-208.47 600.41,-208.86 602.96,-215.38"/>
+</g>
+<!-- INT_BOT -->
+<g id="node5" class="node">
+<title>INT_BOT</title>
+<ellipse fill="lightblue" stroke="black" cx="374" cy="-96.25" rx="33.95" ry="18"/>
+<text text-anchor="start" x="357.12" y="-92.2" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text>
+<text text-anchor="start" x="372.88" y="-92.2" font-family="Times New Roman,serif" font-size="14.00">:int</text>
+</g>
+<!-- INT_BOT&#45;&gt;BOT -->
+<g id="edge18" class="edge">
+<title>INT_BOT&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M374,-77.92C374,-70.74 374,-62.18 374,-53.95"/>
+<polygon fill="black" stroke="black" points="377.5,-54.22 374,-44.22 370.5,-54.22 377.5,-54.22"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_BOT -->
+<g id="edge11" class="edge">
+<title>INT_MIN&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M133.33,-191.46C174.74,-175.25 280.22,-133.96 336.8,-111.81"/>
+<polygon fill="black" stroke="black" points="337.98,-115.11 346.02,-108.2 335.43,-108.59 337.98,-115.11"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_MINDOTS -->
+<!-- INT_MINDOTS&#45;&gt;INT_BOT -->
+<g id="edge12" class="edge">
+<title>INT_MINDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M224.72,-186.46C253.64,-169.18 307.88,-136.76 342.4,-116.13"/>
+<polygon fill="black" stroke="black" points="343.92,-119.3 350.71,-111.17 340.33,-113.29 343.92,-119.3"/>
+</g>
+<!-- INT_MINDOTS&#45;&gt;INT_MINUS -->
+<!-- INT_MINUS&#45;&gt;INT_BOT -->
+<g id="edge13" class="edge">
+<title>INT_MINUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M305.12,-184.2C317.82,-168.18 338.81,-141.67 354.29,-122.13"/>
+<polygon fill="black" stroke="black" points="356.98,-124.37 360.45,-114.35 351.5,-120.02 356.98,-124.37"/>
+</g>
+<!-- INT_MINUS&#45;&gt;INT_ZERO -->
+<!-- INT_ZERO&#45;&gt;INT_BOT -->
+<g id="edge14" class="edge">
+<title>INT_ZERO&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M374,-181.12C374,-166.02 374,-143.74 374,-125.93"/>
+<polygon fill="black" stroke="black" points="377.5,-125.98 374,-115.98 370.5,-125.98 377.5,-125.98"/>
+</g>
+<!-- INT_ZERO&#45;&gt;INT_PLUS -->
+<!-- INT_PLUS&#45;&gt;INT_BOT -->
+<g id="edge15" class="edge">
+<title>INT_PLUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M442.35,-184.63C429.9,-168.71 409.04,-142.04 393.63,-122.35"/>
+<polygon fill="black" stroke="black" points="396.42,-120.23 387.5,-114.51 390.9,-124.54 396.42,-120.23"/>
+</g>
+<!-- INT_PLUS&#45;&gt;INT_MAXDOTS -->
+<!-- INT_MAXDOTS&#45;&gt;INT_BOT -->
+<g id="edge16" class="edge">
+<title>INT_MAXDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M521.52,-186.46C492.93,-169.18 439.34,-136.76 405.22,-116.13"/>
+<polygon fill="black" stroke="black" points="407.39,-113.35 397.03,-111.17 403.77,-119.34 407.39,-113.35"/>
+</g>
+<!-- INT_MAXDOTS&#45;&gt;INT_MAX -->
+<!-- INT_MAX&#45;&gt;INT_BOT -->
+<g id="edge17" class="edge">
+<title>INT_MAX&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M612.61,-190.66C569.87,-173.93 466.96,-133.64 411.28,-111.84"/>
+<polygon fill="black" stroke="black" points="412.8,-108.68 402.21,-108.29 410.25,-115.2 412.8,-108.68"/>
+</g>
+<!-- TUPLE1 -->
+<g id="node15" class="node">
+<title>TUPLE1</title>
+<polygon fill="none" stroke="none" points="750,-225.75 696,-225.75 696,-172.75 750,-172.75 750,-225.75"/>
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+<polygon fill="black" stroke="none" points="706.5,-176.75 706.5,-199.25 739.5,-199.25 739.5,-176.75 706.5,-176.75"/>
+<polygon fill="none" stroke="black" points="706.5,-176.75 706.5,-199.25 739.5,-199.25 739.5,-176.75 706.5,-176.75"/>
+<text text-anchor="start" x="711.38" y="-182.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text>
+</g>
+<!-- TUPLE_TOP&#45;&gt;TUPLE1 -->
+<g id="edge26" class="edge">
+<title>TUPLE_TOP&#45;&gt;TUPLE1</title>
+<path fill="none" stroke="black" d="M762.86,-284.12C756.58,-270.91 747.69,-252.2 739.89,-235.8"/>
+<polygon fill="black" stroke="black" points="743.07,-234.33 735.62,-226.8 736.75,-237.34 743.07,-234.33"/>
+</g>
+<!-- TUPLE2 -->
+<g id="node16" class="node">
+<title>TUPLE2</title>
+<polygon fill="none" stroke="none" points="847,-237 793,-237 793,-161.5 847,-161.5 847,-237"/>
+<polygon fill="pink" stroke="none" points="803.5,-210.5 803.5,-233 836.5,-233 836.5,-210.5 803.5,-210.5"/>
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+<text text-anchor="start" x="808.38" y="-171.7" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text>
+</g>
+<!-- TUPLE_TOP&#45;&gt;TUPLE2 -->
+<g id="edge27" class="edge">
+<title>TUPLE_TOP&#45;&gt;TUPLE2</title>
+<path fill="none" stroke="black" d="M779.31,-284.12C784.32,-273.8 790.95,-260.12 797.41,-246.81"/>
+<polygon fill="black" stroke="black" points="800.41,-248.65 801.62,-238.13 794.11,-245.6 800.41,-248.65"/>
+</g>
+<!-- TUPLEN -->
+<g id="node17" class="node">
+<title>TUPLEN</title>
+<polygon fill="none" stroke="none" points="944,-248.25 890,-248.25 890,-150.25 944,-150.25 944,-248.25"/>
+<polygon fill="pink" stroke="none" points="900.5,-221.75 900.5,-244.25 933.5,-244.25 933.5,-221.75 900.5,-221.75"/>
+<polygon fill="none" stroke="black" points="900.5,-221.75 900.5,-244.25 933.5,-244.25 933.5,-221.75 900.5,-221.75"/>
+<text text-anchor="start" x="903.5" y="-227.95" font-family="Times New Roman,serif" font-size="14.00">tuple</text>
+<polygon fill="black" stroke="none" points="900.5,-199.25 900.5,-221.75 933.5,-221.75 933.5,-199.25 900.5,-199.25"/>
+<polygon fill="none" stroke="black" points="900.5,-199.25 900.5,-221.75 933.5,-221.75 933.5,-199.25 900.5,-199.25"/>
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+<polygon fill="none" stroke="black" points="900.5,-176.75 900.5,-199.25 933.5,-199.25 933.5,-176.75 900.5,-176.75"/>
+<text text-anchor="start" x="911.38" y="-182.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">...</text>
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+<polygon fill="none" stroke="black" points="900.5,-154.25 900.5,-176.75 933.5,-176.75 933.5,-154.25 900.5,-154.25"/>
+<text text-anchor="start" x="905.38" y="-160.45" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text>
+</g>
+<!-- TUPLE_TOP&#45;&gt;TUPLEN -->
+<g id="edge28" class="edge">
+<title>TUPLE_TOP&#45;&gt;TUPLEN</title>
+<path fill="none" stroke="black" d="M792.54,-286.35C815.75,-270.29 853.06,-244.48 880.79,-225.3"/>
+<polygon fill="black" stroke="black" points="882.68,-228.25 888.91,-219.68 878.7,-222.49 882.68,-228.25"/>
+</g>
+<!-- TUPLE_BOT -->
+<g id="node14" class="node">
+<title>TUPLE_BOT</title>
+<ellipse fill="pink" stroke="black" cx="771" cy="-96.25" rx="42.65" ry="18"/>
+<text text-anchor="start" x="747.75" y="-92.2" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text>
+<text text-anchor="start" x="763.5" y="-92.2" font-family="Times New Roman,serif" font-size="14.00">:tuple</text>
+</g>
+<!-- TUPLE_BOT&#45;&gt;BOT -->
+<g id="edge32" class="edge">
+<title>TUPLE_BOT&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M732.57,-88.17C654.42,-73.77 478.23,-41.32 405.9,-28"/>
+<polygon fill="black" stroke="black" points="406.78,-24.6 396.31,-26.23 405.51,-31.49 406.78,-24.6"/>
+</g>
+<!-- TUPLE1&#45;&gt;TUPLE_BOT -->
+<g id="edge29" class="edge">
+<title>TUPLE1&#45;&gt;TUPLE_BOT</title>
+<path fill="none" stroke="black" d="M735.11,-172.76C742.13,-158 750.96,-139.41 758.11,-124.38"/>
+<polygon fill="black" stroke="black" points="761.18,-126.06 762.31,-115.53 754.86,-123.06 761.18,-126.06"/>
+</g>
+<!-- TUPLE2&#45;&gt;TUPLE_BOT -->
+<g id="edge30" class="edge">
+<title>TUPLE2&#45;&gt;TUPLE_BOT</title>
+<path fill="none" stroke="black" d="M802.17,-161.5C796.24,-149.27 789.75,-135.89 784.23,-124.51"/>
+<polygon fill="black" stroke="black" points="787.46,-123.15 779.94,-115.69 781.16,-126.21 787.46,-123.15"/>
+</g>
+<!-- TUPLEN&#45;&gt;TUPLE_BOT -->
+<g id="edge31" class="edge">
+<title>TUPLEN&#45;&gt;TUPLE_BOT</title>
+<path fill="none" stroke="black" d="M890.22,-179.72C865.26,-162.45 828.04,-136.71 801.84,-118.58"/>
+<polygon fill="black" stroke="black" points="803.85,-115.72 793.64,-112.91 799.87,-121.47 803.85,-115.72"/>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter04/projnode.json b/docs/chapter04/projnode.json
new file mode 100644
index 00000000..3d4d20cf
--- /dev/null
+++ b/docs/chapter04/projnode.json
@@ -0,0 +1,14 @@
+{
+ "ver": 1,
+ "comp": "chapter04/docs/projnode.svg",
+ "step": 1,
+ "roots": [],
+ "scope": 0,
+ "nodes": [
+ {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+ {"id": 4, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+ {"id": 6, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 1}}
+ ],
+ "groups": [
+ ]
+}
diff --git a/docs/chapter04/projnode.png b/docs/chapter04/projnode.png
new file mode 100644
index 00000000..bf7493f2
--- /dev/null
+++ b/docs/chapter04/projnode.png
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diff --git a/docs/chapter04/projnode.svg b/docs/chapter04/projnode.svg
new file mode 100644
index 00000000..b1291cdb
--- /dev/null
+++ b/docs/chapter04/projnode.svg
@@ -0,0 +1,74 @@
+<svg aria-label="Compiler graph" width="294" height="142" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 294 142" style="font-family: sans-serif;"><style>
+ html, body { height:100%; margin:0; font-family:sans-serif; }
+ .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+ .source { padding:8px; border-bottom:1px solid #ccc; }
+ #program { width:min(600px,80vw); vertical-align:middle; }
+ #status { margin-top:4px; }
+ #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+ #elk { width:100%; height:100%; }
+ #graph svg { display:block; }
+ .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+ .hint { color:#616c78; }
+ .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+ .edge { fill:none; stroke-width:1.5; }
+ .edge.CTRL { stroke-width:2; }
+ .edge.ASSOC { stroke-dasharray:4 4; }
+ .edge.PARSER { stroke-dasharray:5 4; }
+ .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+ .edge.selected { stroke-width:3.5; }
+ .edge.bundle { stroke-width:4; }
+ .edge.bundle.selected { stroke-width:6; }
+ .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+ .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+ .node { cursor:pointer; }
+ .box { stroke:#758191; stroke-width:1; }
+ .node.held .box { stroke-dasharray:5 3; }
+ .node.near .box { stroke:#c18221; stroke-width:2; }
+ .node.focus .box { stroke:#9c4900; stroke-width:3; }
+ .node.selected .box { stroke:#1569b9; stroke-width:3; }
+ .node.folded .box { stroke-width:4; }
+ .node.folding .box { fill:#f4ccd7; }
+ .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+ .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+ .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+ .node.error .box { stroke:#b42318; stroke-width:4; }
+ #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+ .peep-ghosts { pointer-events:none; }
+ .region-box { stroke:#9da9b8; stroke-width:1.5; }
+ .fold-btn { cursor:pointer; }
+ .fold-btn rect { fill:white; stroke:#596674; }
+ .fold-btn text { font-size:14px; fill:#152330; }
+ .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+ .shortcut { cursor:pointer; }
+ .shortcut path { fill:none; stroke-width:1.5; }
+ .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+ .shortcut text { font-size:11px; fill:#783030; }
+ .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+ .label { font-size:12px; fill:#152330; font-weight:600; }
+ .node-id { font-size:10px; fill:#596674; font-weight:400; }
+ .type { font-size:11px; fill:#455768; }
+ .port { stroke:#536477; stroke-width:1; }
+ .row { stroke:#b6afcf; stroke-width:1; }
+ .bind { font-size:12px; fill:#152330; }
+ .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+ #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+ max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+ background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+ .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+ .button { color:white; background:black; font-size:20px; min-width:30px; }
+ .button:disabled { background:grey; }
+ .count { font-size:20px; min-width:35px; text-align:center; }
+ #N { width:6ch; }
+ #scrub { width:clamp(120px,35vw,600px); }
+ </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"/><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #4/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2 CTRL</title></g><g class="node" id="n6" data-id="6" transform="translate(144,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 arg
+Projection 1 of #2
+Type not computed
+
+[0] → #2 DATA</title></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>