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| author | Cliff Click <cliffc@acm.org> | 2026-09-29 12:34:58 -0700 |
|---|---|---|
| committer | Cliff Click <cliffc@acm.org> | 2026-09-29 12:34:58 -0700 |
| commit | 502e7e752f3efdb069a36b23ab51ac22f9d74e9e (patch) | |
| tree | d2b3c84357be365b5a6cc674285d1d2778c0072c /docs/chapter10a | |
| parent | fdfc4e4b824e97952110069558de70cd16c725a1 (diff) | |
| download | Simple-502e7e752f3efdb069a36b23ab51ac22f9d74e9e.tar.gz Simple-502e7e752f3efdb069a36b23ab51ac22f9d74e9e.zip | |
Chapter 10a: Structs and Memorylinear-chapter10a
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| -rw-r--r-- | docs/chapter10a/10-grammar.md | 125 | ||||
| -rw-r--r-- | docs/chapter10a/Makefile | 14 | ||||
| -rw-r--r-- | docs/chapter10a/README.md | 290 | ||||
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diff --git a/docs/chapter10a/10-grammar.md b/docs/chapter10a/10-grammar.md new file mode 100644 index 00000000..5b9b680e --- /dev/null +++ b/docs/chapter10a/10-grammar.md @@ -0,0 +1,125 @@ +# Grammar for Chapter 10a + +```antlrv4 +grammar SimpleLanguage; + +program + : statement+ EOF + ; + +statement + : returnStatement + | structDeclaration + | declStatement + | blockStatment + | expressionStatement + | ifStatement + | whileStatement + | breakStatement + | continueStatment + ; + +field + : 'int' IDENTIFIER ';' + ; + +fields + : field+ + ; + +structDeclaration + : 'struct' IDENTIFIER '{' fields '}' + ; + +whileStatement + : 'while' '(' expression ')' statement + ; + +breakStatement + : 'break' ';' + ; + +continueStatement + : 'continue' ';' + ; + +ifStatement + : 'if' '(' expression ')' statement ('else' statement)? + ; + + +expressionStatement + : IDENTIFIER '=' expression ';' + | fieldExpression '=' expression ';' + ; + +blockStatement + : '{' statement+ '}' + ; + +structName + : IDENTIFIER + ; + +declStatement + : 'int' IDENTIFIER '=' expression ';' + | structName ('?')? IDENTIFIER '=' expression ';' + ; + +returnStatement + : 'return' expression ';' + ; + +expression + : comparisonExpression + ; + +comparisonExpression + : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)* + ; + +additiveExpression + : multiplicativeExpression (('+' | '-') multiplicativeExpression)* + ; + +multiplicativeExpression + : unaryExpression (('*' | '/') unaryExpression)* + ; + +unaryExpression + : ('-') unaryExpression + | '!' unaryExpression + | primaryExpression + ; + +newExpression + : 'new' IDENTIFIER + ; + +fieldExpression + : primaryExpresson '.' IDENTIFIER + ; + +primaryExpression + : IDENTIFIER + | INTEGER_LITERAL + | 'true' + | 'false' + | 'null' + | newExpression + | '(' expression ')' + | fieldExpression + ; + +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/chapter10a/Makefile b/docs/chapter10a/Makefile new file mode 100644 index 00000000..055882b2 --- /dev/null +++ b/docs/chapter10a/Makefile @@ -0,0 +1,14 @@ +GV := $(wildcard *.gv) +SVG := $(patsubst %.gv,%.svg,$(GV)) +.DELETE_ON_ERROR: + +.PHONY: all +all: $(SVG) + +%.svg: %.gv + dot -Tsvg $< > $@ + @sed -i 's/\r$$//' $@ + +.PHONY: clean +clean: + @rm -f $(SVG) diff --git a/docs/chapter10a/README.md b/docs/chapter10a/README.md new file mode 100644 index 00000000..8aaf779c --- /dev/null +++ b/docs/chapter10a/README.md @@ -0,0 +1,290 @@ +# Chapter 10a: Structs and Memory + +[Previous: Chapter 9](../chapter09/README.md) | +[Next: Chapter 10b](../chapter10b/README.md) + +This chapter adds user-defined structs, pointers, allocation, field loads and +stores, and null checking. It also introduces an evaluator that executes the +graph, including its memory effects. The [grammar](10-grammar.md) is the +same in 10a and 10b; the next chapter improves the memory representation. + +## One memory value + +Arithmetic nodes depend on the values they use, similarly a load also depends +on when it observes memory. In this chapter every store consumes the preceding +memory state and produces the next one, and a load consumes memory without +changing it. This makes the source program's memory ordering explicit in the +graph. + +```java +struct Point { int x; int y; } +Point p = new Point; +p.x = 3; +p.y = arg; +return p.x; +``` + +`NewNode` produces the pointer. The parser emits stores of zero for both fields, +then stores 3 into `x` and `arg` into `y`. The final load observes the memory +after the `y` store. We deliberately keep that dependency here, even though +different fields are independent. Chapter 10b will remove it. + + + +| Node | Inputs | Result | +|----------|---|---| +| `New` | Control and a struct type | A fresh, non-null object pointer | +| `Store` | Memory, pointer, field name, value | The updated whole-memory state | +| `Load` | Memory, pointer, field name | The value of the field | +| `Start` | External entry | Control, initial memory, and `arg` | +| `Return` | Control, result, memory | Completion with all preceding effects retained | + +The memory edge is a dependency, not a copy of the heap. The graph determines +the legal execution order. In hardware, a Store updates physical memory +directly. In the evaluator, a Store updates an objects' attached memory array. + +## Memory is an SSA variable + +The parser keeps one hidden binding named `$mem`. Source identifiers cannot +contain `$`, so user code cannot name it. Reading and updating memory uses the +same `ScopeNode` lookup and update operations as a local variable. + +For an `if`, the two branches can finish with different memory values. An +ordinary Phi selects the memory from the branch that executed: + + + +Loops reuse Chapter 8's lazy Phi construction. Reading or updating `$mem` in a +loop creates an initially incomplete memory Phi. Closing the loop supplies its +backedge. `break`, `continue`, nested loops, and early returns use the same scope +mechanics as scalar variables. + + + +Every Return consumes the current whole-memory value. This keeps stores alive +even when the returned scalar does not depend on them, or when the program +returns the modified object itself. + +## Local memory optimizations + +A load immediately following a store to the **same pointer and field** can use +the stored value. A store immediately following another store to the same +address can discard the earlier store when no other user needs it. Both the +pointer and field checks matter: two different fields of one object are +different addresses, as are the same fields of two different objects. + +A load can also move through a memory Phi when doing so exposes a useful +load-after-store fold. On a loop, the backedge must fold, preventing this rewrite +from repeatedly moving the load around the cycle. + +The single chain is conservative. A store to `y` can prevent forwarding an +earlier store to `x`, even when the objects are identical. This is a missed +optimization, not a correctness problem; it motivates the next chapter. + +## Enhanced Type Lattice + +The Type Lattice for Simple has a major revision in this chapter. + + + +The diagram uses `⊤` for **top** and `⊥` for **bottom**. A suffix names the +domain: `⊤:struct` is *struct top*, while the bare `⊤` is global top. In the +prose we use those words; in code examples we use the actual Java constants. +The implementation's `$TOP` and `$BOT` names need not appear in the diagram: + +| Diagram | Prose | Java constant | Internal struct name | +|---|---|---|---| +| `⊤:struct` | struct top | `TypeStruct.TOP` | `$TOP` | +| `⊥:struct` | struct bottom | `TypeStruct.BOT` | `$BOT` | + +Edges in this diagram show lattice order, with top above bottom. They are not +the use-to-definition edges of the program graphs elsewhere in the chapter. +Boxes containing an ellipsis abbreviate further parallel alternatives; they +are not extra union types. Field and tuple-element type lattices are elided. + +Within the type lattice, we now have the following domains: + +*  represents control flow: unreachable control + at control top, and reachable control at control bottom. +*  has integer top, integer bottom, and parallel + constants between them. The ellipses stand for the other integer constants. +*  (new) combines a struct type with nullability. + * The prefix `*` means pointer-to: `*Person` is a non-null pointer to a Person. + The suffix `?` includes null, so `*Person?` permits a Person pointer or null. + * The pointer domain contains the whole struct lattice twice, once without + null and once with it. The diagram expands named alternatives in both + copies. It is not just two individual pointer types. + * `null` combines struct top with the nullable flag: it has no non-null + object alternative. The diagram labels it `*⊤:struct?` as well as `null`. + * A pointer to struct bottom can point to any struct. The diagram shows the + non-null form as `*⊥:struct` and the nullable form as `*⊥:struct?`. + The latter is pointer bottom; pointer top is `*⊤:struct`. + * Null evaluates to false; non-null pointers evaluate to true. + + > C analogy: the non-null pointer to struct bottom is akin to `void *`, except + > that C's `void *` may also be null. Simple names this constant + > `TypeMemPtr.VOIDPTR` and prints it as `*void`. Struct bottom itself is the + > common lower bound of struct types, not C's `void` type. + +*  (new) represents user-defined named structs. + Fields have integer types in this chapter. + * Struct top lies above every named struct; struct bottom lies below every + named struct. Top is the high/empty struct alternative, while bottom + conservatively includes any struct name. + * `Person`, `s1`, `s2`, and further names are parallel alternatives. There is + no inheritance, so different named structs do not nest beneath one another, + even if they have identical fields. + * There is no fixed bound on the names a program can declare. The diagram's + ellipsis stands for more named alternatives, not a distinguished unnamed + struct. Each named box abbreviates its own field-type lattice. +*  (new) represents the whole-memory token. + Memory top and memory bottom are `TypeMem.TOP` and `TypeMem.BOT`. Neither + records the values stored in individual fields. +*  represents a collection of results from one node, + such as Start's control, memory, and argument. The displayed shapes abbreviate + tuples of different lengths and their element-type lattices. + +We use the following operations on the lattice: + +* **Meet** computes the greatest lower bound. For these examples, think of + combining the alternatives represented by its inputs. + * The meet of `Person` and `s1` is struct bottom. There is no separate type + representing exactly those two names. + * The meet of `*Person` and `*s1` is the non-null pointer to struct bottom. + * The meet of `*Person` and `null` is `*Person?`. + * The meet of the non-null pointer to struct bottom and `null` is pointer bottom. + * The meet of `1` and `2` is integer bottom. +* **Dual** reflects the lattice about its centerline: top and bottom exchange + places, and applying dual twice returns the original type. + * Struct top and struct bottom are duals. + * `null` and the non-null pointer to struct bottom are duals. + * A pointer's dual also duals its struct's fields and flips nullability. Thus + the dual of `*Person` is not generally the original `*Person?`: the field + types must be dualed too. Those field details are omitted in the diagram. +* **Join** computes the least upper bound. It is defined through meet and dual: + `JOIN(x,y) = MEET(x.dual(),y.dual()).dual()`. + * The join of `Person` and `s1` is struct top. + * The join of `*Person` and `*s1` is pointer top. + * The join of the non-null pointer to struct bottom and `null` is pointer top. + * The join of `1` and `2` is integer top. + +As we construct the Sea of Nodes graph, we ensure that values stay inside the +domain they are created in - that is ptr fields will never contain ints +(obviously)... nor even the generic `TOP` and `BOT`. There are a couple of +nuances worth highlighting. + +* When Phis are created, the initial type of the Phi is based on the declared + type of its first input. This is a pessimistic type assignment because we do + not yet know what other types will be met. + +* When all the inputs of the Phi are known, we start with the local Top of the + declared type, and then compute a meet of all the input types. This + computation results in a more refined type for the Phi. + +## Parser Enhancements + +In previous chapters the only available type was Integer. Now, variables can +be of Integer type or pointer to Struct types. To support this, the Parser now +tracks the declared type of a variable (used to only be Integer!). The +declared type of a variable defines the set of values that can be legitimately +assigned to the variable. The Sea of Nodes graph also tracks the actual type +of values assigned to variables, these type transitions are defined by the Type +lattice described in the previous section. + +## Null Pointer Analysis + +The Simple language syntax allows a pointer variable to be specified as +null-able - and it prevents ever throwing a Null Pointer Exception. The +compiler decides if a null check is needed, and if needed and missing +the compiler rejects the program (asking the user to insert a null check). + +When the Parser encounters conditions that test the truthiness of a pointer variable, it uses this knowledge to refine the type information in the branches that follow. + +Here are two motivating examples: + +```java +struct Bar { int a; } +Bar? bar = new Bar; +if (arg) bar = null; +if( bar ) bar.a = 1; +``` + +If `bar` is not `null` above, then we would like to allow the assignment to +`bar.a`. If the final line lacked the null check, e.g. a plain `bar.a = 1;`, +then `Java` would compile this program but throw a NPE, and Simple rejects the +program pointing out a null check is required. + + +```java +struct Bar { int a; } +Bar? bar = new Bar; +if (arg) bar = null; +int rez = 3; +if( !bar ) rez=4; +else bar.a = 1; +``` + +If `bar` is `null` then we would like `!bar` to evaluate to `true`. In the else +branch we know `bar` is not null, hence the assignment to `bar.a` should be +allowed. + +To enable this behaviour, we make following enhancements. + +* We track the null-ness of a pointer in the Type system, and hence in every + Node that ptr type flows through. + +* We "wrap" the predicate of an `If` node with an up-cast when we see that the + predicate is a ptr value. The up-cast removes the null possibility on the + true branch making it legal to use the pointer. + +* The up-cast uses a `Cast` with the non-null pointer to struct bottom + (`TypeMemPtr.VOIDPTR`). It joins the original pointer type with that type, + corresponding to `*⊥:struct` in the diagram. This JOIN operation preserves + everything we already know about ptr, and also adds the new knowledge that + the ptr is not-null. + +* The up-cast is represented by the `CastNode` op, and if applicable, we + replace all occurrences of the original predicate with the up-cast in the + current scope. The change is local to each branch of the `If`; occuring + separately for the true and the false branches of the `If` (and the false + branch inverts the predicate). + +* The up-cast peepholes normally; if its input's type is a super type of the + up-cast, then the `CastNode` can be removed. See `ScopeNode.upcast()` method, + and `CastNode`. + +* When computing a type for Not, we produce an Integer type when its input is a + ptr. When the input is a `null` we convert to `1` and when is a not `null` + ptr value, we convert to `0`. See `NotNode.compute()`. + + +## Executing the graph + +The evaluator includes a small late scheduler. A load must execute before a +later store that consumes the same memory definition, even though there is no +ordinary data edge from the load to that store. These load/store +anti-dependencies supplement the explicit graph edges. + + + +The scheduler is sufficient to execute this chapter. Chapter 11 develops +global code motion and scheduling as a separate topic. + +## Build and test + +From this directory, with JDK 21 or newer, Make, and a shell: + +```sh +make lib +make tests +make release +make view +``` + +Make builds this snapshot directly, without Maven. `make release` produces +`build/release/simple.jar`; `make view` launches the shared interactive graph +viewer. Maven and IDEA module descriptions are also supplied. Tests include all +earlier chapters, memory ordering, returned object contents, and nested loops. + +Next, [Chapter 10b](../chapter10b/README.md) keeps this one parser binding while +splitting the graph into independent memory slices. diff --git a/docs/chapter10a/example1.gv b/docs/chapter10a/example1.gv new file mode 100644 index 00000000..d399b562 --- /dev/null +++ b/docs/chapter10a/example1.gv @@ -0,0 +1,10 @@ +digraph Memory { + rankdir=RL; + node [shape=box]; + M0 [label="Initial memory"]; + X [label="Store p.x = 3"]; + Y [label="Store p.y = arg"]; + L [label="Load p.x"]; + L -> Y -> X -> M0 [color=blue]; + Return -> Y [color=blue]; Return -> L; +} diff --git a/docs/chapter10a/example1.svg b/docs/chapter10a/example1.svg new file mode 100644 index 00000000..d1c5e3bd --- /dev/null +++ b/docs/chapter10a/example1.svg @@ -0,0 +1,73 @@ +<?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: Memory Pages: 1 --> +<svg width="556pt" height="67pt" + viewBox="0.00 0.00 555.75 67.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> +<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 63)"> +<title>Memory</title> +<polygon fill="white" stroke="none" points="-4,4 -4,-63 551.75,-63 551.75,4 -4,4"/> +<!-- M0 --> +<g id="node1" class="node"> +<title>M0</title> +<polygon fill="none" stroke="black" points="98.5,-59 0,-59 0,-23 98.5,-23 98.5,-59"/> +<text text-anchor="middle" x="49.25" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Initial memory</text> +</g> +<!-- X --> +<g id="node2" class="node"> +<title>X</title> +<polygon fill="none" stroke="black" points="222.5,-59 134.5,-59 134.5,-23 222.5,-23 222.5,-59"/> +<text text-anchor="middle" x="178.5" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.x = 3</text> +</g> +<!-- X->M0 --> +<g id="edge3" class="edge"> +<title>X->M0</title> +<path fill="none" stroke="blue" d="M134.06,-41C126.33,-41 118.16,-41 110.06,-41"/> +<polygon fill="blue" stroke="blue" points="110.24,-37.5 100.24,-41 110.24,-44.5 110.24,-37.5"/> +</g> +<!-- Y --> +<g id="node3" class="node"> +<title>Y</title> +<polygon fill="none" stroke="black" points="357,-59 258.5,-59 258.5,-23 357,-23 357,-59"/> +<text text-anchor="middle" x="307.75" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.y = arg</text> +</g> +<!-- Y->X --> +<g id="edge2" class="edge"> +<title>Y->X</title> +<path fill="none" stroke="blue" d="M258.28,-41C250.45,-41 242.29,-41 234.32,-41"/> +<polygon fill="blue" stroke="blue" points="234.35,-37.5 224.35,-41 234.35,-44.5 234.35,-37.5"/> +</g> +<!-- L --> +<g id="node4" class="node"> +<title>L</title> +<polygon fill="none" stroke="black" points="457.75,-36 393,-36 393,0 457.75,0 457.75,-36"/> +<text text-anchor="middle" x="425.38" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Load p.x</text> +</g> +<!-- L->Y --> +<g id="edge1" class="edge"> +<title>L->Y</title> +<path fill="none" stroke="blue" d="M392.78,-24.28C385.16,-25.8 376.76,-27.47 368.31,-29.15"/> +<polygon fill="blue" stroke="blue" points="367.85,-25.68 358.73,-31.06 369.22,-32.54 367.85,-25.68"/> +</g> +<!-- Return --> +<g id="node5" class="node"> +<title>Return</title> +<polygon fill="none" stroke="black" points="547.75,-59 493.75,-59 493.75,-23 547.75,-23 547.75,-59"/> +<text text-anchor="middle" x="520.75" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Return</text> +</g> +<!-- Return->Y --> +<g id="edge4" class="edge"> +<title>Return->Y</title> +<path fill="none" stroke="blue" d="M493.52,-43.07C482.49,-43.84 469.5,-44.62 457.75,-45 428.99,-45.93 421.77,-45.68 393,-45 385.14,-44.81 376.87,-44.53 368.71,-44.2"/> +<polygon fill="blue" stroke="blue" points="368.95,-40.7 358.81,-43.76 368.65,-47.7 368.95,-40.7"/> +</g> +<!-- Return->L --> +<g id="edge5" class="edge"> +<title>Return->L</title> +<path fill="none" stroke="black" d="M493.74,-34.59C486.17,-32.73 477.69,-30.64 469.38,-28.59"/> +<polygon fill="black" stroke="black" points="470.24,-25.2 459.7,-26.21 468.57,-32 470.24,-25.2"/> +</g> +</g> +</svg> diff --git a/docs/chapter10a/example2a.gv b/docs/chapter10a/example2a.gv new file mode 100644 index 00000000..ec5afbdc --- /dev/null +++ b/docs/chapter10a/example2a.gv @@ -0,0 +1,10 @@ +digraph Memory { + rankdir=RL; + node [shape=box]; + M [label="Incoming memory"]; + A [label="True: Store x"]; + B [label="False: Store y"]; + P [label="Phi(memory)"]; + P -> A -> M [color=blue]; P -> B -> M [color=blue]; + P -> Region [style=dashed]; Return -> P [color=blue]; +} diff --git a/docs/chapter10a/example2a.svg b/docs/chapter10a/example2a.svg new file mode 100644 index 00000000..f9a9b4fd --- /dev/null +++ b/docs/chapter10a/example2a.svg @@ -0,0 +1,85 @@ +<?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: Memory Pages: 1 --> +<svg width="469pt" height="152pt" + viewBox="0.00 0.00 469.25 152.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> +<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 148)"> +<title>Memory</title> +<polygon fill="white" stroke="none" points="-4,4 -4,-148 465.25,-148 465.25,4 -4,4"/> +<!-- M --> +<g id="node1" class="node"> +<title>M</title> +<polygon fill="none" stroke="black" points="118.75,-117 0,-117 0,-81 118.75,-81 118.75,-117"/> +<text text-anchor="middle" x="59.38" y="-93.95" font-family="Times New Roman,serif" font-size="14.00">Incoming memory</text> +</g> +<!-- A --> +<g id="node2" class="node"> +<title>A</title> +<polygon fill="none" stroke="black" points="244.25,-144 156.25,-144 156.25,-108 244.25,-108 244.25,-144"/> +<text text-anchor="middle" x="200.25" y="-120.95" font-family="Times New Roman,serif" font-size="14.00">True: Store x</text> +</g> +<!-- A->M --> +<g id="edge2" class="edge"> +<title>A->M</title> +<path fill="none" stroke="blue" d="M156.07,-117.61C147.84,-116.01 139.03,-114.29 130.22,-112.58"/> +<polygon fill="blue" stroke="blue" points="131.06,-109.18 120.58,-110.7 129.72,-116.05 131.06,-109.18"/> +</g> +<!-- B --> +<g id="node3" class="node"> +<title>B</title> +<polygon fill="none" stroke="black" points="245.75,-90 154.75,-90 154.75,-54 245.75,-54 245.75,-90"/> +<text text-anchor="middle" x="200.25" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">False: Store y</text> +</g> +<!-- B->M --> +<g id="edge4" class="edge"> +<title>B->M</title> +<path fill="none" stroke="blue" d="M154.54,-80.69C146.8,-82.2 138.59,-83.79 130.37,-85.39"/> +<polygon fill="blue" stroke="blue" points="129.83,-81.93 120.68,-87.28 131.16,-88.8 129.83,-81.93"/> +</g> +<!-- P --> +<g id="node4" class="node"> +<title>P</title> +<polygon fill="none" stroke="black" points="371.25,-90 281.75,-90 281.75,-54 371.25,-54 371.25,-90"/> +<text text-anchor="middle" x="326.5" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">Phi(memory)</text> +</g> +<!-- P->A --> +<g id="edge1" class="edge"> +<title>P->A</title> +<path fill="none" stroke="blue" d="M283.09,-90.43C273.69,-94.52 263.62,-98.89 253.88,-103.13"/> +<polygon fill="blue" stroke="blue" points="252.64,-99.85 244.86,-107.05 255.43,-106.27 252.64,-99.85"/> +</g> +<!-- P->B --> +<g id="edge3" class="edge"> +<title>P->B</title> +<path fill="none" stroke="blue" d="M281.34,-72C273.66,-72 265.57,-72 257.61,-72"/> +<polygon fill="blue" stroke="blue" points="257.62,-68.5 247.62,-72 257.62,-75.5 257.62,-68.5"/> +</g> +<!-- Region --> +<g id="node5" class="node"> +<title>Region</title> +<polygon fill="none" stroke="black" points="227.75,-36 172.75,-36 172.75,0 227.75,0 227.75,-36"/> +<text text-anchor="middle" x="200.25" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Region</text> +</g> +<!-- P->Region --> +<g id="edge5" class="edge"> +<title>P->Region</title> +<path fill="none" stroke="black" stroke-dasharray="5,2" d="M283.09,-53.57C268.52,-47.24 252.34,-40.21 238.24,-34.08"/> +<polygon fill="black" stroke="black" points="239.88,-30.97 229.31,-30.2 237.09,-37.39 239.88,-30.97"/> +</g> +<!-- Return --> +<g id="node6" class="node"> +<title>Return</title> +<polygon fill="none" stroke="black" points="461.25,-90 407.25,-90 407.25,-54 461.25,-54 461.25,-90"/> +<text text-anchor="middle" x="434.25" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">Return</text> +</g> +<!-- Return->P --> +<g id="edge6" class="edge"> +<title>Return->P</title> +<path fill="none" stroke="blue" d="M406.84,-72C399.52,-72 391.29,-72 382.97,-72"/> +<polygon fill="blue" stroke="blue" points="383.17,-68.5 373.17,-72 383.17,-75.5 383.17,-68.5"/> +</g> 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+<!-- Title: Memory Pages: 1 --> +<svg width="422pt" height="98pt" + viewBox="0.00 0.00 421.75 98.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> +<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 94)"> +<title>Memory</title> +<polygon fill="white" stroke="none" points="-4,4 -4,-94 417.75,-94 417.75,4 -4,4"/> +<!-- P --> +<g id="node1" class="node"> +<title>P</title> +<polygon fill="none" stroke="black" points="179.5,-63 90,-63 90,-27 179.5,-27 179.5,-63"/> +<text text-anchor="middle" x="134.75" y="-39.95" font-family="Times New Roman,serif" font-size="14.00">Phi(memory)</text> +</g> +<!-- S --> +<g id="node2" class="node"> +<title>S</title> +<polygon fill="none" stroke="black" points="323.75,-40 215.5,-40 215.5,-4 323.75,-4 323.75,-40"/> +<text text-anchor="middle" x="269.62" y="-16.95" font-family="Times New Roman,serif" font-size="14.00">Loop-body Store</text> +</g> +<!-- P->S --> +<g id="edge2" class="edge"> +<title>P->S</title> +<path fill="none" stroke="blue" d="M179.67,-43.79C187.52,-42.69 195.84,-41.37 204.12,-39.91"/> +<polygon fill="blue" stroke="blue" points="204.65,-43.37 213.86,-38.13 203.39,-36.49 204.65,-43.37"/> +</g> +<!-- Entry --> +<g id="node3" class="node"> +<title>Entry</title> +<polygon fill="none" stroke="black" points="54,-90 0,-90 0,-54 54,-54 54,-90"/> +<text text-anchor="middle" x="27" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">Entry</text> +</g> +<!-- P->Entry --> +<g id="edge1" class="edge"> +<title>P->Entry</title> +<path fill="none" stroke="blue" d="M89.52,-56.29C81.45,-58.35 73.12,-60.48 65.28,-62.48"/> +<polygon fill="blue" stroke="blue" points="64.54,-59.06 55.72,-64.92 66.27,-65.84 64.54,-59.06"/> +</g> +<!-- Loop --> +<g id="node4" class="node"> +<title>Loop</title> +<polygon fill="none" stroke="black" points="54,-36 0,-36 0,0 54,0 54,-36"/> +<text text-anchor="middle" x="27" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Loop</text> +</g> +<!-- P->Loop --> +<g id="edge4" class="edge"> +<title>P->Loop</title> +<path fill="none" stroke="black" stroke-dasharray="5,2" d="M89.52,-33.71C81.45,-31.65 73.12,-29.52 65.28,-27.52"/> +<polygon fill="black" stroke="black" points="66.27,-24.16 55.72,-25.08 64.54,-30.94 66.27,-24.16"/> +</g> +<!-- S->P --> +<g id="edge3" class="edge"> +<title>S->P</title> +<path fill="none" stroke="blue" d="M215.35,-24.59C207.3,-25.84 198.98,-27.27 190.89,-28.79"/> +<polygon fill="blue" stroke="blue" points="190.29,-25.34 181.15,-30.71 191.64,-32.21 190.29,-25.34"/> +</g> +<!-- Return --> +<g id="node5" class="node"> +<title>Return</title> +<polygon fill="none" stroke="black" points="413.75,-63 359.75,-63 359.75,-27 413.75,-27 413.75,-63"/> +<text text-anchor="middle" x="386.75" y="-39.95" font-family="Times New Roman,serif" font-size="14.00">Return</text> +</g> +<!-- Return->P --> +<g id="edge5" class="edge"> +<title>Return->P</title> +<path fill="none" stroke="blue" d="M359.52,-47.07C348.49,-47.84 335.5,-48.62 323.75,-49 275.66,-50.55 263.6,-50.21 215.5,-49 207.59,-48.8 199.24,-48.49 191.04,-48.13"/> +<polygon fill="blue" stroke="blue" points="191.28,-44.64 181.12,-47.67 190.95,-51.63 191.28,-44.64"/> +</g> +<!-- Return->S --> +</g> +</svg> diff --git a/docs/chapter10a/example2c.gv b/docs/chapter10a/example2c.gv new file mode 100644 index 00000000..ef8a5fc8 --- /dev/null +++ b/docs/chapter10a/example2c.gv @@ -0,0 +1,9 @@ +digraph Memory { + rankdir=RL; + node [shape=box]; + M [label="Prior memory"]; + L [label="Load p.x"]; + S [label="Store p.x"]; + L -> M [color=blue]; S -> M [color=blue]; + S -> L [style=dashed,label="execute load first"]; +} diff --git a/docs/chapter10a/example2c.svg b/docs/chapter10a/example2c.svg new file mode 100644 index 00000000..c7b37912 --- /dev/null +++ b/docs/chapter10a/example2c.svg @@ -0,0 +1,50 @@ +<?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: Memory Pages: 1 --> +<svg width="398pt" height="67pt" + viewBox="0.00 0.00 398.25 67.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> +<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 63)"> +<title>Memory</title> +<polygon fill="white" stroke="none" points="-4,4 -4,-63 394.25,-63 394.25,4 -4,4"/> +<!-- M --> +<g id="node1" class="node"> +<title>M</title> +<polygon fill="none" stroke="black" points="93.25,-59 0,-59 0,-23 93.25,-23 93.25,-59"/> +<text text-anchor="middle" x="46.62" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Prior memory</text> +</g> +<!-- L --> +<g id="node2" class="node"> +<title>L</title> +<polygon fill="none" stroke="black" points="195,-36 130.25,-36 130.25,0 195,0 195,-36"/> +<text text-anchor="middle" x="162.62" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Load p.x</text> +</g> +<!-- L->M --> +<g id="edge1" class="edge"> +<title>L->M</title> +<path fill="none" stroke="blue" d="M129.87,-24.41C122.08,-25.98 113.51,-27.71 104.92,-29.44"/> +<polygon fill="blue" stroke="blue" points="104.29,-26 95.18,-31.41 105.68,-32.86 104.29,-26"/> +</g> +<!-- S --> +<g id="node3" class="node"> +<title>S</title> +<polygon fill="none" stroke="black" points="390.25,-59 324.75,-59 324.75,-23 390.25,-23 390.25,-59"/> +<text text-anchor="middle" x="357.5" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.x</text> +</g> +<!-- S->M --> +<g id="edge2" class="edge"> +<title>S->M</title> +<path fill="none" stroke="blue" d="M324.5,-47.66C318.62,-48.63 312.52,-49.48 306.75,-50 237.56,-56.21 157.62,-51.66 105.04,-47.07"/> +<polygon fill="blue" stroke="blue" points="105.37,-43.59 95.1,-46.17 104.74,-50.56 105.37,-43.59"/> +</g> +<!-- S->L --> +<g id="edge3" class="edge"> +<title>S->L</title> +<path fill="none" stroke="black" stroke-dasharray="5,2" d="M324.41,-35.96C318.54,-35.1 312.47,-34.24 306.75,-33.5 273.09,-29.14 234.87,-25.05 206.4,-22.16"/> +<polygon fill="black" stroke="black" points="207.03,-18.71 196.73,-21.19 206.33,-25.67 207.03,-18.71"/> +<text text-anchor="middle" x="259.88" y="-36.7" font-family="Times New Roman,serif" font-size="14.00">execute load first</text> +</g> +</g> +</svg> diff --git a/docs/chapter10a/lattice.gv b/docs/chapter10a/lattice.gv new file mode 100644 index 00000000..733a5287 --- /dev/null +++ b/docs/chapter10a/lattice.gv @@ -0,0 +1,108 @@ +digraph Lattice { + rankdir=TB; + newrank=true; + // Preserve the same-rank ordering edges through cluster layout. + remincross=false; + nodesep=0.22; + ranksep=0.65; + node [shape=ellipse, style=filled, fontname="DejaVu Sans", fontsize=13]; + edge [color="#555555", arrowsize=0.6]; + + // These arrows are lattice-order edges, not use/definition edges. + TOP [label="⊤", fillcolor=black, fontcolor=white]; + BOT [label="⊥", fillcolor=black, fontcolor=white]; + + subgraph cluster_control { + label="Control"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#ffff00"]; + XCTRL [label="⊤:ctrl"]; + CTRL [label="⊥:ctrl"]; + XCTRL -> CTRL; + } + + subgraph cluster_integer { + label="Integer"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#add8e6"]; + INT_TOP [label="⊤:int"]; + INT_BOT [label="⊥:int"]; + INT_NEG [label="… −2, −1"]; + INT_ZERO [label="0"]; + INT_POS [label="1, 2, …"]; + {rank=same; INT_NEG; INT_ZERO; INT_POS;} + INT_NEG -> INT_ZERO -> INT_POS [style=invis]; + INT_TOP -> {INT_NEG INT_ZERO INT_POS}; + {INT_NEG INT_ZERO INT_POS} -> INT_BOT; + } + + subgraph cluster_pointer { + label="Pointer = nullability × struct type"; + fontname="Arial"; color="#cccccc"; + node [fillcolor="#008000", fontcolor=white]; + PTR_TOP [label="⊤:ptr\n[*⊤:struct]"]; + PTR_BOT [label="⊥:ptr\n[*⊥:struct?]"]; + PTR_NULL [label="null"]; + PTR_ANY [label="*⊥:struct\n[ptr any struct]"]; + PTR_PERSON [label="*Person"]; + PTR_S1 [label="*s1"]; + PTR_MORE [label="*s2, …"]; + PTR_PERSON_NIL [label="*Person?"]; + PTR_S1_NIL [label="*s1?"]; + PTR_MORE_NIL [label="*s2?, …"]; + {rank=same; PTR_PERSON; PTR_S1; PTR_MORE; PTR_NULL;} + {rank=same; PTR_ANY; PTR_PERSON_NIL; PTR_S1_NIL; PTR_MORE_NIL;} + PTR_PERSON -> PTR_S1 -> PTR_MORE -> PTR_NULL [style=invis]; + PTR_ANY -> PTR_PERSON_NIL -> PTR_S1_NIL -> PTR_MORE_NIL [style=invis]; + PTR_TOP -> {PTR_PERSON PTR_S1 PTR_MORE PTR_NULL}; + {PTR_PERSON PTR_S1 PTR_MORE} -> PTR_ANY; + PTR_PERSON -> PTR_PERSON_NIL; + PTR_S1 -> PTR_S1_NIL; + PTR_MORE -> PTR_MORE_NIL; + PTR_NULL -> {PTR_PERSON_NIL PTR_S1_NIL PTR_MORE_NIL}; + {PTR_ANY PTR_PERSON_NIL PTR_S1_NIL PTR_MORE_NIL} -> PTR_BOT; + } + + subgraph cluster_struct { + label="Struct\nnamed collection of named scalar types"; + fontname="Arial"; color="#cccccc"; + node [fillcolor="#90ee90"]; + STRUCT_TOP [label="⊤:struct\n[struct top]"]; + STRUCT_BOT [label="⊥:struct\n[struct bottom]"]; + STRUCT_PERSON [label="Person\nage: int", shape=box]; + STRUCT_S1 [label="s1\nx: int", shape=box]; + STRUCT_S2 [label="s2\nx: int, y: *s1", shape=box]; + STRUCT_MORE [label="…", shape=box]; + {rank=same; STRUCT_PERSON; STRUCT_S1; STRUCT_S2; STRUCT_MORE;} + STRUCT_PERSON -> STRUCT_S1 -> STRUCT_S2 -> STRUCT_MORE [style=invis]; + STRUCT_TOP -> {STRUCT_PERSON STRUCT_S1 STRUCT_S2 STRUCT_MORE}; + {STRUCT_PERSON STRUCT_S1 STRUCT_S2 STRUCT_MORE} -> STRUCT_BOT; + } + + subgraph cluster_memory { + label="Memory"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#00008b", fontcolor=white]; + MEM_TOP [label="⊤:mem"]; + MEM_BOT [label="⊥:mem"]; + MEM_TOP -> MEM_BOT; + } + + subgraph cluster_tuple { + label="Tuple\ncollection of types"; + fontname="Arial"; color="#cccccc"; + node [fillcolor="#ffc0cb"]; + TUPLE_TOP [label="⊤:tuple"]; + TUPLE_BOT [label="⊥:tuple"]; + TUPLE1 [label="(type)", shape=box]; + TUPLE2 [label="(type, type)", shape=box]; + TUPLEN [label="(type, …)", shape=box]; + {rank=same; TUPLE1; TUPLE2; TUPLEN;} + TUPLE1 -> TUPLE2 -> TUPLEN [style=invis]; + TUPLE_TOP -> {TUPLE1 TUPLE2 TUPLEN}; + {TUPLE1 TUPLE2 TUPLEN} -> TUPLE_BOT; + } + + TOP -> {XCTRL INT_TOP PTR_TOP STRUCT_TOP MEM_TOP TUPLE_TOP}; + {CTRL INT_BOT PTR_BOT STRUCT_BOT MEM_BOT TUPLE_BOT} -> BOT; + {rank=same; XCTRL; INT_TOP; PTR_TOP; STRUCT_TOP; MEM_TOP; TUPLE_TOP;} + {rank=same; CTRL; INT_BOT; PTR_BOT; STRUCT_BOT; MEM_BOT; TUPLE_BOT;} + XCTRL -> INT_TOP -> PTR_TOP -> STRUCT_TOP -> MEM_TOP -> TUPLE_TOP [style=invis]; +} diff --git a/docs/chapter10a/lattice.svg b/docs/chapter10a/lattice.svg new file mode 100644 index 00000000..24c0de8c --- /dev/null +++ b/docs/chapter10a/lattice.svg @@ -0,0 +1,570 @@ +<?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="1647pt" height="555pt" + viewBox="0.00 0.00 1647.00 555.43" 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(4 551.43)"> +<title>Lattice</title> +<polygon fill="white" stroke="none" points="-4,4 -4,-551.43 1643,-551.43 1643,4 -4,4"/> +<g id="clust1" class="cluster"> +<title>cluster_control</title> +<polygon fill="none" stroke="#cccccc" points="8,-85.99 8,-476.69 98,-476.69 98,-85.99 8,-85.99"/> +<text text-anchor="middle" x="53" y="-459.39" font-family="Arial" font-size="14.00">Control</text> +</g> +<g id="clust2" class="cluster"> +<title>cluster_integer</title> +<polygon fill="none" stroke="#cccccc" points="106,-85.99 106,-476.69 404,-476.69 404,-85.99 106,-85.99"/> +<text text-anchor="middle" x="255" y="-459.39" font-family="Arial" font-size="14.00">Integer</text> +</g> +<g id="clust6" class="cluster"> +<title>cluster_pointer</title> +<polygon fill="none" stroke="#cccccc" points="412,-75 412,-487.68 893,-487.68 893,-75 412,-75"/> +<text text-anchor="middle" x="652.5" y="-470.38" font-family="Arial" font-size="14.00">Pointer = nullability × struct type</text> +</g> +<g id="clust13" class="cluster"> +<title>cluster_struct</title> +<polygon fill="none" stroke="#cccccc" points="901,-75 901,-503.43 1233,-503.43 1233,-75 901,-75"/> +<text text-anchor="middle" x="1067" y="-486.13" font-family="Arial" font-size="14.00">Struct</text> +<text text-anchor="middle" x="1067" y="-470.38" font-family="Arial" font-size="14.00">named collection of named scalar types</text> +</g> +<g id="clust17" class="cluster"> +<title>cluster_memory</title> +<polygon fill="none" stroke="#cccccc" points="1241,-85.99 1241,-476.69 1347,-476.69 1347,-85.99 1241,-85.99"/> +<text text-anchor="middle" x="1294" y="-459.39" font-family="Arial" font-size="14.00">Memory</text> +</g> +<g id="clust18" class="cluster"> +<title>cluster_tuple</title> +<polygon fill="none" stroke="#cccccc" points="1355,-85.99 1355,-492.44 1631,-492.44 1631,-85.99 1355,-85.99"/> +<text text-anchor="middle" x="1493" y="-475.14" font-family="Arial" font-size="14.00">Tuple</text> +<text text-anchor="middle" x="1493" y="-459.39" font-family="Arial" font-size="14.00">collection of types</text> +</g> +<!-- TOP --> +<g id="node1" class="node"> +<title>TOP</title> +<ellipse fill="black" stroke="black" cx="845" cy="-529.43" rx="27" ry="18"/> +<text text-anchor="middle" x="845" y="-525.33" font-family="DejaVu Sans" font-size="13.00" fill="white">⊤</text> +</g> +<!-- XCTRL --> +<g id="node3" class="node"> +<title>XCTRL</title> +<ellipse fill="#ffff00" stroke="black" cx="53" cy="-426.94" rx="36.51" ry="18"/> +<text text-anchor="middle" x="53" y="-422.84" font-family="DejaVu Sans" font-size="13.00">⊤:ctrl</text> +</g> +<!-- TOP->XCTRL --> +<g id="edge53" class="edge"> +<title>TOP->XCTRL</title> +<path fill="none" stroke="#555555" d="M817.66,-528.22C687.28,-527.11 133.71,-521.35 102,-503.43 82.18,-492.23 69.06,-469.34 61.42,-451.68"/> +<polygon fill="#555555" stroke="#555555" points="63.46,-451.12 59.24,-446.37 59.57,-452.72 63.46,-451.12"/> +</g> +<!-- INT_TOP --> +<g id="node5" class="node"> +<title>INT_TOP</title> +<ellipse fill="#add8e6" stroke="black" cx="353" cy="-426.94" rx="33.44" ry="18"/> +<text text-anchor="middle" x="353" y="-422.84" font-family="DejaVu Sans" font-size="13.00">⊤:int</text> +</g> +<!-- TOP->INT_TOP --> +<g id="edge54" class="edge"> +<title>TOP->INT_TOP</title> +<path fill="none" stroke="#555555" d="M817.72,-528.22C727.72,-527.33 443.86,-522.98 408,-503.43 387.26,-492.12 372.32,-469.24 363.29,-451.62"/> +<polygon fill="#555555" stroke="#555555" points="365.2,-450.74 360.67,-446.28 361.42,-452.59 365.2,-450.74"/> +</g> +<!-- PTR_TOP --> +<g id="node10" class="node"> +<title>PTR_TOP</title> +<ellipse fill="#008000" stroke="black" cx="685" cy="-426.94" rx="61.7" ry="28.99"/> +<text text-anchor="middle" x="685" y="-431.09" font-family="DejaVu Sans" font-size="13.00" fill="white">⊤:ptr</text> +<text text-anchor="middle" x="685" y="-414.59" font-family="DejaVu Sans" font-size="13.00" fill="white">[*⊤:struct]</text> +</g> +<!-- TOP->PTR_TOP --> +<g id="edge55" class="edge"> +<title>TOP->PTR_TOP</title> +<path fill="none" stroke="#555555" d="M825.7,-516.31C801.54,-501.14 759.48,-474.72 727.62,-454.71"/> +<polygon fill="#555555" stroke="#555555" points="728.87,-453.01 722.67,-451.6 726.64,-456.57 728.87,-453.01"/> +</g> +<!-- STRUCT_TOP --> +<g id="node20" class="node"> +<title>STRUCT_TOP</title> +<ellipse fill="#90ee90" stroke="black" cx="996" cy="-426.94" rx="64.35" ry="28.99"/> +<text text-anchor="middle" x="996" y="-431.09" font-family="DejaVu Sans" font-size="13.00">⊤:struct</text> +<text text-anchor="middle" x="996" y="-414.59" font-family="DejaVu Sans" font-size="13.00">[struct top]</text> +</g> +<!-- TOP->STRUCT_TOP --> +<g id="edge56" class="edge"> +<title>TOP->STRUCT_TOP</title> +<path fill="none" stroke="#555555" d="M867.28,-518.93C876.68,-514.61 887.61,-509.19 897,-503.43 919.21,-489.82 942.45,-472.29 960.83,-457.55"/> +<polygon fill="#555555" stroke="#555555" points="961.85,-459.43 965.2,-454.02 959.21,-456.16 961.85,-459.43"/> +</g> +<!-- MEM_TOP --> +<g id="node26" class="node"> +<title>MEM_TOP</title> +<ellipse fill="#00008b" stroke="black" cx="1294" cy="-426.94" rx="44.7" ry="18"/> +<text text-anchor="middle" x="1294" y="-422.84" font-family="DejaVu Sans" font-size="13.00" fill="white">⊤:mem</text> +</g> +<!-- TOP->MEM_TOP --> +<g id="edge57" class="edge"> +<title>TOP->MEM_TOP</title> +<path fill="none" stroke="#555555" d="M872.35,-528C956.06,-526.49 1205.1,-520.6 1237,-503.43 1258.25,-491.99 1273.89,-468.81 1283.35,-451.14"/> +<polygon fill="#555555" stroke="#555555" points="1284.99,-452.55 1285.86,-446.25 1281.25,-450.62 1284.99,-452.55"/> +</g> +<!-- TUPLE_TOP --> +<g id="node28" class="node"> +<title>TUPLE_TOP</title> +<ellipse fill="#ffc0cb" stroke="black" cx="1408" cy="-426.94" rx="44.7" ry="18"/> +<text text-anchor="middle" x="1408" y="-422.84" font-family="DejaVu Sans" font-size="13.00">⊤:tuple</text> +</g> +<!-- TOP->TUPLE_TOP --> +<g id="edge58" class="edge"> +<title>TOP->TUPLE_TOP</title> +<path fill="none" stroke="#555555" d="M872.34,-528.42C971.49,-528.22 1308.63,-525.85 1351,-503.43 1372.33,-492.14 1387.95,-468.94 1397.39,-451.22"/> +<polygon fill="#555555" stroke="#555555" points="1399.04,-452.62 1399.9,-446.32 1395.3,-450.7 1399.04,-452.62"/> +</g> +<!-- BOT --> +<g id="node2" class="node"> +<title>BOT</title> +<ellipse fill="black" stroke="black" cx="884" cy="-18" rx="27" ry="18"/> +<text text-anchor="middle" x="884" y="-13.9" font-family="DejaVu Sans" font-size="13.00" fill="white">⊥</text> +</g> +<!-- CTRL --> +<g id="node4" class="node"> +<title>CTRL</title> +<ellipse fill="#ffff00" stroke="black" cx="53" cy="-111.99" rx="36.51" ry="18"/> +<text text-anchor="middle" x="53" y="-107.89" font-family="DejaVu Sans" font-size="13.00">⊥:ctrl</text> +</g> +<!-- XCTRL->CTRL --> +<g id="edge1" class="edge"> +<title>XCTRL->CTRL</title> +<path fill="none" stroke="#555555" d="M53,-408.67C53,-356.2 53,-198.53 53,-137.49"/> +<polygon fill="#555555" stroke="#555555" points="55.1,-137.72 53,-131.72 50.9,-137.72 55.1,-137.72"/> +</g> +<!-- XCTRL->INT_TOP --> +<!-- CTRL->BOT --> +<g id="edge59" class="edge"> +<title>CTRL->BOT</title> +<path fill="none" stroke="#555555" d="M69.29,-95.39C78.22,-87.83 89.91,-79.45 102,-75 242.26,-23.4 717.31,-19.12 849.57,-18.95"/> +<polygon fill="#555555" stroke="#555555" points="849.19,-21.05 855.19,-18.94 849.18,-16.85 849.19,-21.05"/> +</g> +<!-- INT_NEG --> +<g id="node7" class="node"> +<title>INT_NEG</title> +<ellipse fill="#add8e6" stroke="black" cx="169" cy="-216.97" rx="55.45" ry="18"/> +<text text-anchor="middle" x="169" y="-212.87" font-family="DejaVu Sans" font-size="13.00">… −2, −1</text> +</g> +<!-- INT_TOP->INT_NEG --> +<g id="edge4" class="edge"> +<title>INT_TOP->INT_NEG</title> +<path fill="none" stroke="#555555" d="M339.17,-410.31C306.78,-373.7 225.91,-282.29 188.52,-240.04"/> +<polygon fill="#555555" stroke="#555555" points="190.31,-238.89 184.76,-235.78 187.16,-241.67 190.31,-238.89"/> +</g> +<!-- INT_ZERO --> +<g id="node8" class="node"> +<title>INT_ZERO</title> +<ellipse fill="#add8e6" stroke="black" cx="267" cy="-216.97" rx="27" ry="18"/> +<text text-anchor="middle" x="267" y="-212.87" font-family="DejaVu Sans" font-size="13.00">0</text> +</g> +<!-- INT_TOP->INT_ZERO --> +<g id="edge5" class="edge"> +<title>INT_TOP->INT_ZERO</title> +<path fill="none" stroke="#555555" d="M345.96,-408.92C330.64,-371.87 294.24,-283.85 276.74,-241.52"/> +<polygon fill="#555555" stroke="#555555" points="278.71,-240.79 274.47,-236.05 274.83,-242.39 278.71,-240.79"/> +</g> +<!-- INT_POS --> +<g id="node9" class="node"> +<title>INT_POS</title> +<ellipse fill="#add8e6" stroke="black" cx="353" cy="-216.97" rx="43.16" ry="18"/> +<text text-anchor="middle" x="353" y="-212.87" font-family="DejaVu Sans" font-size="13.00">1, 2, …</text> +</g> +<!-- INT_TOP->INT_POS --> +<g id="edge6" class="edge"> +<title>INT_TOP->INT_POS</title> +<path fill="none" stroke="#555555" d="M353,-408.57C353,-371.71 353,-285.59 353,-242.89"/> +<polygon fill="#555555" stroke="#555555" points="355.1,-242.96 353,-236.96 350.9,-242.96 355.1,-242.96"/> +</g> +<!-- INT_TOP->PTR_TOP --> +<!-- INT_BOT --> +<g id="node6" class="node"> +<title>INT_BOT</title> +<ellipse fill="#add8e6" stroke="black" cx="310" cy="-111.99" rx="33.44" ry="18"/> +<text text-anchor="middle" x="310" y="-107.89" font-family="DejaVu Sans" font-size="13.00">⊥:int</text> +</g> +<!-- INT_BOT->BOT --> +<g id="edge60" class="edge"> +<title>INT_BOT->BOT</title> +<path fill="none" stroke="#555555" d="M335.28,-99.84C354.78,-91.7 382.61,-81.07 408,-75 570.29,-36.22 770.4,-23.83 849.5,-20.29"/> +<polygon fill="#555555" stroke="#555555" points="849.36,-22.39 855.26,-20.04 849.17,-18.2 849.36,-22.39"/> +</g> +<!-- INT_NEG->INT_BOT --> +<g id="edge7" class="edge"> +<title>INT_NEG->INT_BOT</title> +<path fill="none" stroke="#555555" d="M190.72,-200.11C216.15,-181.54 258.17,-150.85 284.95,-131.29"/> +<polygon fill="#555555" stroke="#555555" points="285.92,-133.18 289.52,-127.95 283.44,-129.79 285.92,-133.18"/> +</g> +<!-- INT_NEG->INT_ZERO --> +<!-- INT_ZERO->INT_BOT --> +<g id="edge8" class="edge"> +<title>INT_ZERO->INT_BOT</title> +<path fill="none" stroke="#555555" d="M273.91,-199.43C281.01,-182.41 292.14,-155.76 300.16,-136.55"/> +<polygon fill="#555555" stroke="#555555" points="302.01,-137.58 302.38,-131.24 298.13,-135.96 302.01,-137.58"/> +</g> +<!-- INT_ZERO->INT_POS --> +<!-- INT_POS->INT_BOT --> +<g id="edge9" class="edge"> +<title>INT_POS->INT_BOT</title> +<path fill="none" stroke="#555555" d="M345.9,-198.97C338.83,-182.05 327.93,-155.94 319.99,-136.93"/> +<polygon fill="#555555" stroke="#555555" points="321.94,-136.15 317.69,-131.42 318.07,-137.76 321.94,-136.15"/> +</g> +<!-- PTR_NULL --> +<g id="node12" class="node"> +<title>PTR_NULL</title> +<ellipse fill="#008000" stroke="black" cx="808" cy="-321.96" rx="66.47" ry="28.99"/> +<text text-anchor="middle" x="808" y="-326.11" font-family="DejaVu Sans" font-size="13.00" fill="white">null</text> +<text text-anchor="middle" x="808" y="-309.61" font-family="DejaVu Sans" font-size="13.00" fill="white">[*⊤:struct?]</text> +</g> +<!-- PTR_TOP->PTR_NULL --> +<g id="edge16" class="edge"> +<title>PTR_TOP->PTR_NULL</title> +<path fill="none" stroke="#555555" d="M714.46,-401.27C731.85,-386.71 753.98,-368.18 772.35,-352.8"/> +<polygon fill="#555555" stroke="#555555" points="773.51,-354.57 776.76,-349.11 770.82,-351.35 773.51,-354.57"/> +</g> +<!-- PTR_PERSON --> +<g id="node14" class="node"> +<title>PTR_PERSON</title> +<ellipse fill="#008000" stroke="black" cx="512" cy="-321.96" rx="45.72" ry="18"/> +<text text-anchor="middle" x="512" y="-317.86" font-family="DejaVu Sans" font-size="13.00" fill="white">*Person</text> +</g> +<!-- PTR_TOP->PTR_PERSON --> +<g id="edge17" class="edge"> +<title>PTR_TOP->PTR_PERSON</title> +<path fill="none" stroke="#555555" d="M647.46,-403.59C616.14,-384.95 572.05,-358.7 542.78,-341.28"/> +<polygon fill="#555555" stroke="#555555" points="543.94,-339.52 537.71,-338.26 541.79,-343.13 543.94,-339.52"/> +</g> +<!-- PTR_S1 --> +<g id="node15" class="node"> +<title>PTR_S1</title> +<ellipse fill="#008000" stroke="black" cx="601" cy="-321.96" rx="27" ry="18"/> +<text text-anchor="middle" x="601" y="-317.86" font-family="DejaVu Sans" font-size="13.00" fill="white">*s1</text> +</g> +<!-- PTR_TOP->PTR_S1 --> +<g id="edge18" class="edge"> +<title>PTR_TOP->PTR_S1</title> +<path fill="none" stroke="#555555" d="M663.37,-399.42C649.25,-382.12 631.09,-359.85 618.01,-343.81"/> +<polygon fill="#555555" stroke="#555555" points="619.81,-342.7 614.39,-339.38 616.56,-345.36 619.81,-342.7"/> +</g> +<!-- PTR_MORE --> +<g id="node16" class="node"> +<title>PTR_MORE</title> +<ellipse fill="#008000" stroke="black" cx="685" cy="-321.96" rx="40.6" ry="18"/> +<text text-anchor="middle" x="685" y="-317.86" font-family="DejaVu Sans" font-size="13.00" fill="white">*s2, …</text> +</g> +<!-- PTR_TOP->PTR_MORE --> +<g id="edge19" class="edge"> +<title>PTR_TOP->PTR_MORE</title> +<path fill="none" stroke="#555555" d="M685,-397.53C685,-381.91 685,-362.73 685,-347.73"/> +<polygon fill="#555555" stroke="#555555" points="687.1,-347.82 685,-341.82 682.9,-347.82 687.1,-347.82"/> +</g> +<!-- PTR_TOP->STRUCT_TOP --> +<!-- PTR_BOT --> +<g id="node11" class="node"> +<title>PTR_BOT</title> +<ellipse fill="#008000" stroke="black" cx="748" cy="-111.99" rx="66.47" ry="28.99"/> +<text text-anchor="middle" x="748" y="-116.14" font-family="DejaVu Sans" font-size="13.00" fill="white">⊥:ptr</text> +<text text-anchor="middle" x="748" y="-99.64" font-family="DejaVu Sans" font-size="13.00" fill="white">[*⊥:struct?]</text> +</g> +<!-- PTR_BOT->BOT --> +<g id="edge61" class="edge"> +<title>PTR_BOT->BOT</title> +<path fill="none" stroke="#555555" d="M783.38,-87.06C807.3,-70.88 838.29,-49.92 859.52,-35.56"/> +<polygon fill="#555555" stroke="#555555" points="860.46,-37.46 864.25,-32.36 858.1,-33.98 860.46,-37.46"/> +</g> +<!-- PTR_PERSON_NIL --> +<g id="node17" class="node"> +<title>PTR_PERSON_NIL</title> +<ellipse fill="#008000" stroke="black" cx="651" cy="-216.97" rx="50.33" ry="18"/> +<text text-anchor="middle" x="651" y="-212.87" font-family="DejaVu Sans" font-size="13.00" fill="white">*Person?</text> +</g> +<!-- PTR_NULL->PTR_PERSON_NIL --> +<g id="edge26" class="edge"> +<title>PTR_NULL->PTR_PERSON_NIL</title> +<path fill="none" stroke="#555555" d="M771.98,-297.33C744.16,-279.08 706.14,-254.14 680.2,-237.12"/> +<polygon fill="#555555" stroke="#555555" points="681.63,-235.56 675.47,-234.02 679.33,-239.07 681.63,-235.56"/> +</g> +<!-- PTR_S1_NIL --> +<g id="node18" class="node"> +<title>PTR_S1_NIL</title> +<ellipse fill="#008000" stroke="black" cx="748" cy="-216.97" rx="30.37" ry="18"/> +<text text-anchor="middle" x="748" y="-212.87" font-family="DejaVu Sans" font-size="13.00" fill="white">*s1?</text> +</g> +<!-- PTR_NULL->PTR_S1_NIL --> +<g id="edge27" class="edge"> +<title>PTR_NULL->PTR_S1_NIL</title> +<path fill="none" stroke="#555555" d="M791.92,-293.36C782.32,-276.89 770.28,-256.22 761.24,-240.69"/> +<polygon fill="#555555" stroke="#555555" points="763.16,-239.82 758.32,-235.69 759.53,-241.93 763.16,-239.82"/> +</g> +<!-- PTR_MORE_NIL --> +<g id="node19" class="node"> +<title>PTR_MORE_NIL</title> +<ellipse fill="#008000" stroke="black" cx="840" cy="-216.97" rx="45.21" ry="18"/> +<text text-anchor="middle" x="840" y="-212.87" font-family="DejaVu Sans" font-size="13.00" fill="white">*s2?, …</text> +</g> +<!-- PTR_NULL->PTR_MORE_NIL --> +<g id="edge28" class="edge"> +<title>PTR_NULL->PTR_MORE_NIL</title> +<path fill="none" stroke="#555555" d="M816.74,-292.82C821.67,-276.95 827.77,-257.33 832.48,-242.16"/> +<polygon fill="#555555" stroke="#555555" points="834.45,-242.91 834.23,-236.56 830.44,-241.66 834.45,-242.91"/> +</g> +<!-- PTR_ANY --> +<g id="node13" class="node"> +<title>PTR_ANY</title> +<ellipse fill="#008000" stroke="black" cx="502" cy="-216.97" rx="82.38" ry="28.99"/> +<text text-anchor="middle" x="502" y="-221.12" font-family="DejaVu Sans" font-size="13.00" fill="white">*⊥:struct</text> +<text text-anchor="middle" x="502" y="-204.62" font-family="DejaVu Sans" font-size="13.00" fill="white">[ptr any struct]</text> +</g> +<!-- PTR_ANY->PTR_BOT --> +<g id="edge29" class="edge"> +<title>PTR_ANY->PTR_BOT</title> +<path fill="none" stroke="#555555" d="M554.17,-194.13C595.32,-176.91 652.51,-152.97 694.1,-135.56"/> +<polygon fill="#555555" stroke="#555555" points="694.78,-137.55 699.5,-133.29 693.15,-133.67 694.78,-137.55"/> +</g> +<!-- PTR_ANY->PTR_PERSON_NIL --> +<!-- PTR_PERSON->PTR_ANY --> +<g id="edge20" class="edge"> +<title>PTR_PERSON->PTR_ANY</title> +<path fill="none" stroke="#555555" d="M510.3,-303.49C508.98,-289.83 507.09,-270.39 505.45,-253.5"/> +<polygon fill="#555555" stroke="#555555" points="507.58,-253.71 504.91,-247.94 503.4,-254.12 507.58,-253.71"/> +</g> +<!-- PTR_PERSON->PTR_S1 --> +<!-- PTR_PERSON->PTR_PERSON_NIL --> +<g id="edge23" class="edge"> +<title>PTR_PERSON->PTR_PERSON_NIL</title> +<path fill="none" stroke="#555555" d="M532.81,-305.54C557.17,-287.49 597.57,-257.56 624.25,-237.8"/> +<polygon fill="#555555" stroke="#555555" points="625.26,-239.66 628.83,-234.4 622.76,-236.28 625.26,-239.66"/> +</g> +<!-- PTR_S1->PTR_ANY --> +<g id="edge21" class="edge"> +<title>PTR_S1->PTR_ANY</title> +<path fill="none" stroke="#555555" d="M586.82,-306.2C572.74,-291.56 550.72,-268.65 532.64,-249.85"/> +<polygon fill="#555555" stroke="#555555" points="534.38,-248.62 528.7,-245.75 531.35,-251.53 534.38,-248.62"/> +</g> +<!-- PTR_S1->PTR_MORE --> +<!-- PTR_S1->PTR_S1_NIL --> +<g id="edge24" class="edge"> +<title>PTR_S1->PTR_S1_NIL</title> +<path fill="none" stroke="#555555" d="M617.46,-307.22C623.23,-302.56 629.81,-297.42 636,-292.97 667.33,-270.44 677.09,-267.67 709,-245.97 713.75,-242.74 718.77,-239.22 723.56,-235.8"/> +<polygon fill="#555555" stroke="#555555" points="724.61,-237.64 728.26,-232.43 722.16,-234.22 724.61,-237.64"/> +</g> +<!-- PTR_MORE->PTR_NULL --> +<!-- PTR_MORE->PTR_ANY --> +<g id="edge22" class="edge"> +<title>PTR_MORE->PTR_ANY</title> +<path fill="none" stroke="#555555" d="M660.85,-307.1C652.94,-302.58 644.1,-297.55 636,-292.97 608.08,-277.18 576.81,-259.67 551.5,-245.54"/> +<polygon fill="#555555" stroke="#555555" points="552.79,-243.85 546.52,-242.76 550.74,-247.52 552.79,-243.85"/> +</g> +<!-- PTR_MORE->PTR_MORE_NIL --> +<g id="edge25" class="edge"> +<title>PTR_MORE->PTR_MORE_NIL</title> +<path fill="none" stroke="#555555" d="M706.88,-306.42C734.22,-288.25 781.1,-257.11 811.3,-237.04"/> +<polygon fill="#555555" stroke="#555555" points="812.38,-238.85 816.22,-233.78 810.06,-235.35 812.38,-238.85"/> +</g> +<!-- PTR_PERSON_NIL->PTR_BOT --> +<g id="edge30" class="edge"> +<title>PTR_PERSON_NIL->PTR_BOT</title> +<path fill="none" stroke="#555555" d="M666.58,-199.43C680.58,-184.56 701.51,-162.35 718.65,-144.16"/> +<polygon fill="#555555" stroke="#555555" points="719.75,-146.05 722.33,-140.24 716.69,-143.17 719.75,-146.05"/> +</g> +<!-- PTR_PERSON_NIL->PTR_S1_NIL --> +<!-- PTR_S1_NIL->PTR_BOT --> +<g id="edge31" class="edge"> +<title>PTR_S1_NIL->PTR_BOT</title> +<path fill="none" stroke="#555555" d="M748,-198.5C748,-184.97 748,-165.76 748,-148.97"/> +<polygon fill="#555555" stroke="#555555" points="750.1,-148.97 748,-142.97 745.9,-148.97 750.1,-148.97"/> +</g> +<!-- PTR_S1_NIL->PTR_MORE_NIL --> +<!-- PTR_MORE_NIL->PTR_BOT --> +<g id="edge32" class="edge"> +<title>PTR_MORE_NIL->PTR_BOT</title> +<path fill="none" stroke="#555555" d="M825.62,-199.88C812.53,-185.22 792.8,-163.14 776.51,-144.9"/> +<polygon fill="#555555" stroke="#555555" points="778.14,-143.58 772.58,-140.51 775.01,-146.38 778.14,-143.58"/> +</g> +<!-- STRUCT_PERSON --> +<g id="node22" class="node"> +<title>STRUCT_PERSON</title> +<polygon fill="#90ee90" stroke="black" points="976.5,-237.47 909.5,-237.47 909.5,-196.47 976.5,-196.47 976.5,-237.47"/> +<text text-anchor="middle" x="943" y="-221.12" font-family="DejaVu Sans" font-size="13.00">Person</text> +<text text-anchor="middle" x="943" y="-204.62" font-family="DejaVu Sans" font-size="13.00">age: int</text> +</g> +<!-- STRUCT_TOP->STRUCT_PERSON --> +<g id="edge36" class="edge"> +<title>STRUCT_TOP->STRUCT_PERSON</title> +<path fill="none" stroke="#555555" d="M988.85,-397.89C978.61,-357.71 959.89,-284.26 949.83,-244.77"/> +<polygon fill="#555555" stroke="#555555" points="951.95,-244.58 948.43,-239.28 947.88,-245.61 951.95,-244.58"/> +</g> +<!-- STRUCT_S1 --> +<g id="node23" class="node"> +<title>STRUCT_S1</title> +<polygon fill="#90ee90" stroke="black" points="1047,-237.47 993,-237.47 993,-196.47 1047,-196.47 1047,-237.47"/> +<text text-anchor="middle" x="1020" y="-221.12" font-family="DejaVu Sans" font-size="13.00">s1</text> +<text text-anchor="middle" x="1020" y="-204.62" font-family="DejaVu Sans" font-size="13.00">x: int</text> +</g> +<!-- STRUCT_TOP->STRUCT_S1 --> +<g id="edge37" class="edge"> +<title>STRUCT_TOP->STRUCT_S1</title> +<path fill="none" stroke="#555555" d="M999.24,-397.89C1003.85,-357.88 1012.28,-284.87 1016.85,-245.27"/> +<polygon fill="#555555" stroke="#555555" points="1018.94,-245.52 1017.54,-239.32 1014.76,-245.04 1018.94,-245.52"/> +</g> +<!-- STRUCT_S2 --> +<g id="node24" class="node"> +<title>STRUCT_S2</title> +<polygon fill="#90ee90" stroke="black" points="1154.88,-237.47 1063.12,-237.47 1063.12,-196.47 1154.88,-196.47 1154.88,-237.47"/> +<text text-anchor="middle" x="1109" y="-221.12" font-family="DejaVu Sans" font-size="13.00">s2</text> +<text text-anchor="middle" x="1109" y="-204.62" font-family="DejaVu Sans" font-size="13.00">x: int, y: int</text> +</g> +<!-- STRUCT_TOP->STRUCT_S2 --> +<g id="edge38" class="edge"> +<title>STRUCT_TOP->STRUCT_S2</title> +<path fill="none" stroke="#555555" d="M1011.01,-398.32C1032.86,-358.11 1073.16,-283.94 1094.64,-244.41"/> +<polygon fill="#555555" stroke="#555555" points="1096.43,-245.51 1097.45,-239.24 1092.74,-243.51 1096.43,-245.51"/> +</g> +<!-- STRUCT_MORE --> +<g id="node25" class="node"> +<title>STRUCT_MORE</title> +<polygon fill="#90ee90" stroke="black" points="1225,-234.97 1171,-234.97 1171,-198.97 1225,-198.97 1225,-234.97"/> +<text text-anchor="middle" x="1198" y="-212.87" font-family="DejaVu Sans" font-size="13.00">…</text> +</g> +<!-- STRUCT_TOP->STRUCT_MORE --> +<g id="edge39" class="edge"> +<title>STRUCT_TOP->STRUCT_MORE</title> +<path fill="none" stroke="#555555" d="M1021.18,-400.02C1061.16,-358.86 1138.49,-279.24 1176.23,-240.39"/> +<polygon fill="#555555" stroke="#555555" points="1177.33,-242.26 1180.01,-236.5 1174.32,-239.34 1177.33,-242.26"/> +</g> +<!-- STRUCT_TOP->MEM_TOP --> +<!-- STRUCT_BOT --> +<g id="node21" class="node"> +<title>STRUCT_BOT</title> +<ellipse fill="#90ee90" stroke="black" cx="1020" cy="-111.99" rx="82.91" ry="28.99"/> +<text text-anchor="middle" x="1020" y="-116.14" font-family="DejaVu Sans" font-size="13.00">⊥:struct</text> +<text text-anchor="middle" x="1020" y="-99.64" font-family="DejaVu Sans" font-size="13.00">[struct bottom]</text> +</g> +<!-- STRUCT_BOT->BOT --> +<g id="edge62" class="edge"> +<title>STRUCT_BOT->BOT</title> +<path fill="none" stroke="#555555" d="M982.84,-85.85C959.17,-69.85 929.19,-49.57 908.49,-35.56"/> +<polygon fill="#555555" stroke="#555555" points="909.78,-33.9 903.63,-32.28 907.42,-37.38 909.78,-33.9"/> +</g> +<!-- STRUCT_PERSON->STRUCT_BOT --> +<g id="edge40" class="edge"> +<title>STRUCT_PERSON->STRUCT_BOT</title> +<path fill="none" stroke="#555555" d="M957.85,-196.12C968.43,-181.96 982.92,-162.59 995.24,-146.11"/> +<polygon fill="#555555" stroke="#555555" points="996.85,-147.46 998.76,-141.4 993.49,-144.94 996.85,-147.46"/> +</g> +<!-- STRUCT_PERSON->STRUCT_S1 --> +<!-- STRUCT_S1->STRUCT_BOT --> +<g id="edge41" class="edge"> +<title>STRUCT_S1->STRUCT_BOT</title> +<path fill="none" stroke="#555555" d="M1020,-196.12C1020,-182.64 1020,-164.43 1020,-148.49"/> +<polygon fill="#555555" stroke="#555555" points="1022.1,-148.87 1020,-142.87 1017.9,-148.87 1022.1,-148.87"/> +</g> +<!-- STRUCT_S1->STRUCT_S2 --> +<!-- STRUCT_S2->STRUCT_BOT --> +<g id="edge42" class="edge"> +<title>STRUCT_S2->STRUCT_BOT</title> +<path fill="none" stroke="#555555" d="M1091.84,-196.12C1079.5,-181.83 1062.57,-162.25 1048.25,-145.68"/> +<polygon fill="#555555" stroke="#555555" points="1050,-144.5 1044.49,-141.33 1046.82,-147.24 1050,-144.5"/> +</g> +<!-- STRUCT_S2->STRUCT_MORE --> +<!-- STRUCT_MORE->STRUCT_BOT --> +<g id="edge43" class="edge"> +<title>STRUCT_MORE->STRUCT_BOT</title> +<path fill="none" stroke="#555555" d="M1177.76,-198.72C1173.05,-195 1167.95,-191.22 1163,-187.98 1135.19,-169.81 1102.49,-152.39 1075.38,-138.93"/> +<polygon fill="#555555" stroke="#555555" points="1076.64,-137.21 1070.33,-136.44 1074.78,-140.97 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+<title>TUPLE_TOP->TUPLE2</title> +<path fill="none" stroke="#555555" d="M1419.89,-409.39C1432.2,-392.26 1451.54,-365.35 1465.37,-346.1"/> +<polygon fill="#555555" stroke="#555555" points="1466.97,-347.48 1468.76,-341.38 1463.56,-345.02 1466.97,-347.48"/> +</g> +<!-- TUPLEN --> +<g id="node32" class="node"> +<title>TUPLEN</title> +<polygon fill="#ffc0cb" stroke="black" points="1622.75,-339.96 1545.25,-339.96 1545.25,-303.96 1622.75,-303.96 1622.75,-339.96"/> +<text text-anchor="middle" x="1584" y="-317.86" font-family="DejaVu Sans" font-size="13.00">(type, …)</text> +</g> +<!-- TUPLE_TOP->TUPLEN --> +<g id="edge49" class="edge"> +<title>TUPLE_TOP->TUPLEN</title> +<path fill="none" stroke="#555555" d="M1432.78,-411.64C1458.78,-396.61 1500.83,-372.23 1537,-350.95 1540.81,-348.7 1544.8,-346.35 1548.76,-344"/> +<polygon fill="#555555" stroke="#555555" points="1549.56,-345.97 1553.64,-341.1 1547.41,-342.36 1549.56,-345.97"/> +</g> +<!-- TUPLE_BOT --> +<g id="node29" class="node"> 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