Documentation updates (#76)

* More clearly explain why we do not have an AST in the implementation

* Improve the description of type lattice.
Cross reference to future chapters.

* Minor update

* Add lattice visual
Revise the text describing meet.

* minor update

* Add a lattice visual to the text

* Update the lattice visual.
Add description of the new edges in the SoN graph

4 files changed, 293 insertions, 36 deletions

diff --git a/chapter04/README.md b/chapter04/README.md
index f938f468..4ae4d432 100644
--- a/chapter04/README.md
+++ b/chapter04/README.md
@@ -19,22 +19,22 @@ Following are revised or new nodes
 |-----------|----------------|------------------------------------------------|-----------------------|----------------------------------------------------------------------------|
 | 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      | ?              | Projection nodes extract values from MultiNode | A MultiNode and index | Result is the extracted value from the input MultiNode at offset index     | 
+| Proj      | Data           | 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                                      |
 
 Below is our list of Nodes from [Chapter 3](../chapter03/README.md):
 
-| Node Name | Type    | Description                        | Inputs                                                           | Value                        |
-|-----------|---------|------------------------------------|------------------------------------------------------------------|------------------------------|
-| Return    | Control | End of function                    | Predecessor control node, Data node value                        | Return value of the function |
-| Constant  | Data    | Constants such as integer literals | None, however Start node is set as input to enable graph walking | Value of the constant        |
-| Add       | Data    | Add two values                     | Two data nodes, values are added, order not important            | Result of the add operation  |
-| Sub       | Data    | Subtract a value from another      | Two data nodes, values are subtracted, order matters             | Result of the subtract       |
-| Mul       | Data    | Multiply two values                | Two data nodes, values are multiplied, order not important       | Result of the multiply       |
-| Div       | Data    | Divide a value by another          | Two data nodes, values are divided, order matters                | Result of the division       |
-| Minus     | Data    | Negate a value                     | One data node, value is negated                                  | Result of the unary minus    |
-| Scope     | ?       | Represents scopes in the graph     | All nodes that define variables                                  | None                         |
+| Node Name | Type         | Description                        | Inputs                                                           | Value                        |
+|-----------|--------------|------------------------------------|------------------------------------------------------------------|------------------------------|
+| Return    | Control      | End of function                    | Predecessor control node, Data node value                        | Return value of the function |
+| Constant  | Data         | Constants such as integer literals | None, however Start node is set as input to enable graph walking | Value of the constant        |
+| Add       | Data         | Add two values                     | Two data nodes, values are added, order not important            | Result of the add operation  |
+| Sub       | Data         | Subtract a value from another      | Two data nodes, values are subtracted, order matters             | Result of the subtract       |
+| Mul       | Data         | Multiply two values                | Two data nodes, values are multiplied, order not important       | Result of the multiply       |
+| Div       | Data         | Divide a value by another          | Two data nodes, values are divided, order matters                | Result of the division       |
+| Minus     | Data         | Negate a value                     | One data node, value is negated                                  | Result of the unary minus    |
+| Scope     | Symbol Table | Represents scopes in the graph     | All nodes that define variables                                  | None                         |
 
 ## Projection Nodes
 
@@ -51,13 +51,13 @@ Start node.
 
 ## Changes to Type System
 
-In [Chapter 2](../chapter02/README.md) we introduced the Type System.  Here is a summary of key points:
+In [Chapter 2](../chapter02/README.md) we introduced the Type System. 
 
 We annotate Nodes with Types.
 
 The Type annotation serves two purposes:
 
-* it defines the set of operations allowed on the Node, and
+* It defines the set of operations allowed on the Node, and
 * it defines the set of values the Node takes on.
 
 The type itself is identified by the Java class sub-typing relationship; all
@@ -76,40 +76,37 @@ Type
 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".
 
-Our lattice elements can be one of three types:
+Our enhanced Lattice looks like this.
 
-* the highest element is "top", denoted by T.
-* The lowest is bottom, denoted by ⊥,
-* All elements in the middle are constants.
+![Lattice](./docs/lattice.svg)
 
-Assigning ⊥ means that the Node's value is known to be not a compile time
-constant, whereas assigning T means that the Node's value may be some (as yet)
-undetermined constant. The transition of the Node's type can occur from T to
-some constant to ⊥.
 
 In this chapter we introduce the possibility of a program input variable named
-`arg`; this variable is usually unknown so ⊥ .
+`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 `Top` and `Bot` integer types in addition to the earlier constant value.
+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
-in our lattice. The meet operator describes rules that define the resulting type when we combine
+Now that integer values may be constants or non-constants, we need to introduce the "meet" operator
+in our lattice. The `meet` operator describes rules that define the resulting type when we combine
 integer values.
 
-|      | ⊥ | Con1 | Con2 | T    |
-|------|---|------|------|------|
-| ⊥    | ⊥ | ⊥    | ⊥    | ⊥    |
-| Con1 | ⊥ | Con1 | ⊥    | Con1 |
-| T    | ⊥ | Con1 | Con2 | T    | 
+|        | 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 a `IntBot` integer type.
+When we start optimizing loops, we will start seeing `IntTop` values.
 
-The `meet` of `Top` with anything is that thing.
-The `meet` of `Bot` with anything is `Bot`.
-The `meet` of anything with itself is that thing.
-The `meet` of two unrelated constants is `Bot`.
-Currently, all our integer valued nodes are either a constant or a Bottom integer type.
-When we start optimizing loops, we will start seeing Top values.
 
 ## `$ctrl` name binding
 
diff --git a/chapter04/docs/build-graphs.sh b/chapter04/docs/build-graphs.sh
new file mode 100644
index 00000000..d8038602
--- /dev/null
+++ b/chapter04/docs/build-graphs.sh
@@ -0,0 +1,2 @@
+dot -Tsvg  lattice.gv > lattice.svg
+
diff --git a/chapter04/docs/lattice.gv b/chapter04/docs/lattice.gv
new file mode 100644
index 00000000..2644448e
--- /dev/null
+++ b/chapter04/docs/lattice.gv
@@ -0,0 +1,63 @@
+digraph Lattice {
+    // Define nodes
+    splines=false;
+    node [shape=circle, style=filled, fillcolor=lightblue];
+    nodesep=0.6;
+
+    TOP [label="⊤"];
+    BOT [label="⊥"];
+
+    CTRL [label="Ctrl"];
+
+    INT_TOP [label="IntTop"];
+    INT_BOT [label="IntBot"];
+
+    INT_MIN [label="-n"];
+    INT_MINDOTS [label="..." shape=none style=none];
+    INT_MINUS [label="-1"];
+    INT_ZERO [label="0"];
+    INT_PLUS [label="1"];
+    INT_MAXDOTS [label="..." shape=none style=none];
+    INT_MAX [label="+n"];
+
+    TUPLE [label="TUPLE"];
+
+    // Define edges
+    edge [arrowhead=none];
+
+    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];
+
+    TOP          -> TUPLE;
+    TUPLE        -> BOT;
+
+    TOP          -> CTRL;
+    CTRL         -> BOT;
+
+
+    // Additional customization
+    {rank=same; TOP}
+    {rank=same; INT_TOP}
+    {rank=same; CTRL; INT_MIN; INT_MINDOTS;
+                INT_MINUS; INT_ZERO;
+                INT_PLUS; INT_MAXDOTS;
+                INT_MAX; TUPLE}
+    {rank=same; INT_BOT}
+    {rank=same; BOT;}
+}
\ No newline at end of file
diff --git a/chapter04/docs/lattice.svg b/chapter04/docs/lattice.svg
new file mode 100644
index 00000000..0d403c20
--- /dev/null
+++ b/chapter04/docs/lattice.svg
@@ -0,0 +1,195 @@
+<?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: Lattice Pages: 1 -->
+<svg width="802pt" height="478pt"
+ viewBox="0.00 0.00 802.14 478.27" 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(4 474.27)">
+<title>Lattice</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-474.27 798.14,-474.27 798.14,4 -4,4"/>
+<!-- TOP -->
+<g id="node1" class="node">
+<title>TOP</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-450.77" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="377.6" y="-447.07" font-family="Times,serif" font-size="14.00">⊤</text>
+</g>
+<!-- CTRL -->
+<g id="node3" class="node">
+<title>CTRL</title>
+<ellipse fill="lightblue" stroke="black" cx="28.6" cy="-235.14" rx="28.7" ry="28.7"/>
+<text text-anchor="middle" x="28.6" y="-231.44" font-family="Times,serif" font-size="14.00">Ctrl</text>
+</g>
+<!-- TOP&#45;&gt;CTRL -->
+<g id="edge25" class="edge">
+<title>TOP&#45;&gt;CTRL</title>
+<path fill="none" stroke="black" d="M360.76,-440.37C304.12,-405.37 120.24,-291.76 53.28,-250.38"/>
+</g>
+<!-- INT_TOP -->
+<g id="node4" class="node">
+<title>INT_TOP</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-354.98" rx="40.09" ry="40.09"/>
+<text text-anchor="middle" x="377.6" y="-351.28" font-family="Times,serif" font-size="14.00">IntTop</text>
+</g>
+<!-- TOP&#45;&gt;INT_TOP -->
+<g id="edge1" class="edge">
+<title>TOP&#45;&gt;INT_TOP</title>
+<path fill="none" stroke="black" d="M377.6,-431.24C377.6,-420.99 377.6,-407.84 377.6,-395.42"/>
+</g>
+<!-- TUPLE -->
+<g id="node13" class="node">
+<title>TUPLE</title>
+<ellipse fill="lightblue" stroke="black" cx="750.6" cy="-235.14" rx="43.59" ry="43.59"/>
+<text text-anchor="middle" x="750.6" y="-231.44" font-family="Times,serif" font-size="14.00">TUPLE</text>
+</g>
+<!-- TOP&#45;&gt;TUPLE -->
+<g id="edge23" class="edge">
+<title>TOP&#45;&gt;TUPLE</title>
+<path fill="none" stroke="black" d="M394.59,-440.95C451.03,-408.32 633.13,-303.05 712.75,-257.02"/>
+</g>
+<!-- BOT -->
+<g id="node2" class="node">
+<title>BOT</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-19.5" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="377.6" y="-15.8" font-family="Times,serif" font-size="14.00">⊥</text>
+</g>
+<!-- CTRL&#45;&gt;BOT -->
+<g id="edge26" class="edge">
+<title>CTRL&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M53.14,-219.97C120.01,-178.65 304.22,-64.84 360.83,-29.86"/>
+</g>
+<!-- INT_MIN -->
+<g id="node6" class="node">
+<title>INT_MIN</title>
+<ellipse fill="lightblue" stroke="black" cx="119.6" cy="-235.14" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="119.6" y="-231.44" font-family="Times,serif" font-size="14.00">&#45;n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MIN -->
+<g id="edge2" class="edge">
+<title>INT_TOP&#45;&gt;INT_MIN</title>
+<path fill="none" stroke="black" d="M341.18,-337.34C284.92,-311.65 179.02,-263.28 137.21,-244.18"/>
+</g>
+<!-- INT_MINDOTS -->
+<g id="node7" class="node">
+<title>INT_MINDOTS</title>
+<text text-anchor="middle" x="208.6" y="-231.44" font-family="Times,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINDOTS -->
+<g id="edge3" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINDOTS</title>
+<path fill="none" stroke="black" d="M345.01,-331.26C312.3,-308.45 262.65,-273.83 233.14,-253.25"/>
+</g>
+<!-- INT_MINUS -->
+<g id="node8" class="node">
+<title>INT_MINUS</title>
+<ellipse fill="lightblue" stroke="black" cx="297.6" cy="-235.14" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="297.6" y="-231.44" font-family="Times,serif" font-size="14.00">&#45;1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINUS -->
+<g id="edge4" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINUS</title>
+<path fill="none" stroke="black" d="M355.31,-321.15C339.96,-298.54 320.25,-269.51 308.29,-251.89"/>
+</g>
+<!-- INT_ZERO -->
+<g id="node9" class="node">
+<title>INT_ZERO</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-235.14" rx="18" ry="18"/>
+<text text-anchor="middle" x="377.6" y="-231.44" font-family="Times,serif" font-size="14.00">0</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_ZERO -->
+<g id="edge5" class="edge">
+<title>INT_TOP&#45;&gt;INT_ZERO</title>
+<path fill="none" stroke="black" d="M377.6,-314.41C377.6,-293.68 377.6,-269.36 377.6,-253.39"/>
+</g>
+<!-- INT_PLUS -->
+<g id="node10" class="node">
+<title>INT_PLUS</title>
+<ellipse fill="lightblue" stroke="black" cx="456.6" cy="-235.14" rx="18" ry="18"/>
+<text text-anchor="middle" x="456.6" y="-231.44" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_PLUS -->
+<g id="edge6" class="edge">
+<title>INT_TOP&#45;&gt;INT_PLUS</title>
+<path fill="none" stroke="black" d="M399.6,-321.15C415.13,-298 435.17,-268.1 446.88,-250.63"/>
+</g>
+<!-- INT_MAXDOTS -->
+<g id="node11" class="node">
+<title>INT_MAXDOTS</title>
+<text text-anchor="middle" x="544.6" y="-231.44" font-family="Times,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAXDOTS -->
+<g id="edge7" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAXDOTS</title>
+<path fill="none" stroke="black" d="M410.19,-330.98C442.56,-308.14 491.43,-273.65 520.47,-253.16"/>
+</g>
+<!-- INT_MAX -->
+<g id="node12" class="node">
+<title>INT_MAX</title>
+<ellipse fill="lightblue" stroke="black" cx="639.6" cy="-235.14" rx="24.9" ry="24.9"/>
+<text text-anchor="middle" x="639.6" y="-231.44" font-family="Times,serif" font-size="14.00">+n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAX -->
+<g id="edge8" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAX</title>
+<path fill="none" stroke="black" d="M414.03,-337.59C469.15,-312.8 572.09,-266.5 617.32,-246.16"/>
+</g>
+<!-- INT_BOT -->
+<g id="node5" class="node">
+<title>INT_BOT</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-115.29" rx="40.09" ry="40.09"/>
+<text text-anchor="middle" x="377.6" y="-111.59" font-family="Times,serif" font-size="14.00">IntBot</text>
+</g>
+<!-- INT_BOT&#45;&gt;BOT -->
+<g id="edge16" class="edge">
+<title>INT_BOT&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M377.6,-74.79C377.6,-62.37 377.6,-49.25 377.6,-39.01"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_BOT -->
+<g id="edge9" class="edge">
+<title>INT_MIN&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M137.33,-226.04C179.23,-206.9 285.02,-158.58 341.21,-132.91"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_MINDOTS -->
+<!-- INT_MINDOTS&#45;&gt;INT_BOT -->
+<g id="edge10" class="edge">
+<title>INT_MINDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M233.17,-217C262.65,-196.45 312.17,-161.91 344.87,-139.11"/>
+</g>
+<!-- INT_MINDOTS&#45;&gt;INT_MINUS -->
+<!-- INT_MINUS&#45;&gt;INT_BOT -->
+<g id="edge11" class="edge">
+<title>INT_MINUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M308.39,-218.24C320.33,-200.65 339.91,-171.81 355.2,-149.29"/>
+</g>
+<!-- INT_MINUS&#45;&gt;INT_ZERO -->
+<!-- INT_ZERO&#45;&gt;INT_BOT -->
+<g id="edge12" class="edge">
+<title>INT_ZERO&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M377.6,-217C377.6,-201.04 377.6,-176.66 377.6,-155.88"/>
+</g>
+<!-- INT_ZERO&#45;&gt;INT_PLUS -->
+<!-- INT_PLUS&#45;&gt;INT_BOT -->
+<g id="edge13" class="edge">
+<title>INT_PLUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M446.91,-219.69C435.21,-202.23 415.16,-172.33 399.63,-149.16"/>
+</g>
+<!-- INT_PLUS&#45;&gt;INT_MAXDOTS -->
+<!-- INT_MAXDOTS&#45;&gt;INT_BOT -->
+<g id="edge14" class="edge">
+<title>INT_MAXDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M520.31,-217C491.28,-196.51 442.55,-162.13 410.24,-139.33"/>
+</g>
+<!-- INT_MAXDOTS&#45;&gt;INT_MAX -->
+<!-- INT_MAX&#45;&gt;INT_BOT -->
+<g id="edge15" class="edge">
+<title>INT_MAX&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M617.26,-224.09C572.09,-203.77 469.52,-157.64 414.35,-132.82"/>
+</g>
+<!-- TUPLE&#45;&gt;BOT -->
+<g id="edge24" class="edge">
+<title>TUPLE&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M712.78,-213.27C633.14,-167.23 450.85,-61.85 394.51,-29.27"/>
+</g>
+</g>
+</svg>