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| author | Cliff Click <cliffc@acm.org> | 2026-09-29 12:21:46 -0700 |
|---|---|---|
| committer | Cliff Click <cliffc@acm.org> | 2026-09-29 12:21:46 -0700 |
| commit | 3ba6686fc991998a0a420709dfb0012bbddf77ab (patch) | |
| tree | 6da4371d0ac6a0e17cfc31dad2275f1331ab3edb /chapter10a | |
| parent | fa7d56f72455828826d0ab7e1c142ca814e6e2aa (diff) | |
| download | Simple-3ba6686fc991998a0a420709dfb0012bbddf77ab.tar.gz Simple-3ba6686fc991998a0a420709dfb0012bbddf77ab.zip | |
Backport lazy memory splits to ch10, split into ch10a and bch10ab
Diffstat (limited to 'chapter10a')
| -rw-r--r-- | chapter10a/README.md | 183 | ||||
| -rw-r--r-- | chapter10a/docs/example1.gv | 2 | ||||
| -rw-r--r-- | chapter10a/docs/example1.svg | 40 | ||||
| -rw-r--r-- | chapter10a/docs/example2a.gv | 2 | ||||
| -rw-r--r-- | chapter10a/docs/example2a.svg | 48 | ||||
| -rw-r--r-- | chapter10a/docs/example2b.gv | 7 | ||||
| -rw-r--r-- | chapter10a/docs/example2b.svg | 49 | ||||
| -rw-r--r-- | chapter10a/docs/example2c.gv | 2 | ||||
| -rw-r--r-- | chapter10a/docs/example2c.svg | 26 | ||||
| -rw-r--r-- | chapter10a/docs/lattice.gv | 255 | ||||
| -rw-r--r-- | chapter10a/docs/lattice.svg | 726 | ||||
| -rw-r--r-- | chapter10a/docs/type-control.svg | 5 | ||||
| -rw-r--r-- | chapter10a/docs/type-integer.svg | 5 | ||||
| -rw-r--r-- | chapter10a/docs/type-memory.svg | 5 | ||||
| -rw-r--r-- | chapter10a/docs/type-pointer.svg | 5 | ||||
| -rw-r--r-- | chapter10a/docs/type-struct.svg | 5 | ||||
| -rw-r--r-- | chapter10a/docs/type-tuple.svg | 5 |
17 files changed, 741 insertions, 629 deletions
diff --git a/chapter10a/README.md b/chapter10a/README.md index 64600fa0..2f25f681 100644 --- a/chapter10a/README.md +++ b/chapter10a/README.md @@ -10,10 +10,11 @@ same in 10a and 10b; the next chapter improves the memory representation. ## One memory value -Arithmetic nodes depend on the values they use. A load also depends on when it -observes memory. In this chapter every store consumes the preceding memory -state and produces the next one. A load consumes memory without changing it. -This makes the source program's effect ordering explicit in the graph. +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; } @@ -30,27 +31,23 @@ different fields are independent. Chapter 10b will remove it.  -These diagrams are schematic dependency graphs: arrows run from uses to their -definitions. Pointer and value inputs are omitted where they do not explain ordering. - -| 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` | +| 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 token, not a copy of the heap. In the evaluator, -objects contain mutable field arrays; executing a Store changes an array entry. -The graph determines the legal execution order. +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. Start has a -fixed tuple: control at index 0, memory at index 1, and `arg` at index 2. +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: @@ -88,69 +85,88 @@ optimization, not a correctness problem; it motivates the next chapter. The Type Lattice for Simple has a major revision in this chapter. - - -Within the Type Lattice, we now have the following type domains: - -* <font style="background-color:yellow">Control type</font> - represents control flow -* <font style="background-color:lightblue">Integer type</font> - Integer values, with a Top, Bottom and constants -* <font style="background-color:green" color="white">Pointer type</font> (new) - Represents a pointer to a struct type - * We use the prefix `*` to mean pointer-to. Thus `*S1` means pointer to - `S1`, `*$TOP` means pointer to `$TOP`. - * `?` suffix represents the union of a pointer to some type and `null`. - * The pointer lattice has only 2 entries: null or not-null. In both cases a struct lattice element is - included, and can be any member of the struct lattice. - * `null` is a pointer to non-existent memory object, i.e. `*$TOP?`, and is a - nullable. Notice that the null part of the type is low in the lattice, - while the struct part is the highest struct. - * `*void` is a synonym for `*$BOT` - i.e. it represents a non-null pointer to - all possible struct types, akin to `void *` in C except not null. It is - the inverse or *dual* of `null`, and the null part is high in the pointer - lattice, while the struct part is the lowest struct. - * `null` pointer evaluates to False and non-null pointers evaluate to True, as in C. - -* <font style="background-color:lightgreen">Struct type</font> (new) - - Represents user defined struct types, a struct type is allowed to have - members of Integer type only in this chapter, later chapters will expand - this. - * `⊤:struct` represents local Top for struct type; all we know about the type - is that it is a struct but, we do not know if it is a specific struct, or - all possible structs. In the code, we use a struct with no fields named `$TOP`. - * `⊥:struct` represents local Bottom for struct type; we definitely know the - value can take all possible struct types. In the code, we uise a struct - with no fields named `$BOT`. -* <font style="background-color:blue" color="white">Memory type</font> (new) - Represents the whole-memory token - * `⊤:mem` is `TypeMem.TOP`, the high end of the memory domain. - * `⊥:mem` is `TypeMem.BOT`, our conservative type for the whole-memory state. - * Neither token describes the values stored in individual fields. -* <font style="background-color:pink">Tuple type</font> - when a Node results in a collection of values - -We make use of following operations on the lattice. - -* The `meet` operation takes two types and computes the greatest lower bound - type. While not true for all lattices, in the our lattice this can be - thought of as set union (ORing) of its input types (as sets). - * Example, meet of `*S1` and `*S2` results in `*void` - there is no lattice - element for exactly both `{*S1,*S2}`, so we drop down to the nearest - element containing both (and maybe more), which is `*void`. - * Meet of `*S1` and pointer `null` results in `*S1?` - * Meet of `*void` and `null` results in `*$BOT?`; bear in mind that `*void` is a synonym for `*$BOT`. - * Meet of `1` and `2` results in `Int Bot`. -* The `dual` operation is symmetric across the lattice centerline. Types directly on the centerline are their own dual. - * Find the corresponding node of the lattice after inverting the lattice. - * Thus, dual of `Top` is `Bot`. - * The dual of `*$TOP` is `*$BOT?`. - * For structs, the dual is obtained by computing the dual of each struct - member. Thus, dual of `*S1` is not `*S1?`, it is some `*S1?` with dualed - fields. - -* The `join` operation takes two types and computes the least upper bound type. - Similar to `meet` this can thought of as set intersection (ANDing) of its input types. - Because our lattice structure is symmetric and complete, we compute `join` with a well known identity: - `JOIN(x,y) === MEET(x.dual,y.dual).dual` - * Example, join of `*S1` and `*S2` results in `*$TOP`. - * Join of `1` and `2` results in `Int Top`. - * Join of `*void` and `Null` results in `*$TOP`. + + +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 @@ -221,8 +237,9 @@ To enable this behaviour, we make following enhancements. 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 is done using a `Cast` op with the type `*void`. This does a - lattice JOIN of the original type and `*void`. This JOIN operation preserves +* 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. diff --git a/chapter10a/docs/example1.gv b/chapter10a/docs/example1.gv index e34c73ed..d399b562 100644 --- a/chapter10a/docs/example1.gv +++ b/chapter10a/docs/example1.gv @@ -1,5 +1,5 @@ digraph Memory { - rankdir=LR; + rankdir=RL; node [shape=box]; M0 [label="Initial memory"]; X [label="Store p.x = 3"]; diff --git a/chapter10a/docs/example1.svg b/chapter10a/docs/example1.svg index c0668ce3..d1c5e3bd 100644 --- a/chapter10a/docs/example1.svg +++ b/chapter10a/docs/example1.svg @@ -12,62 +12,62 @@ <!-- M0 --> <g id="node1" class="node"> <title>M0</title> -<polygon fill="none" stroke="black" points="547.75,-59 449.25,-59 449.25,-23 547.75,-23 547.75,-59"/> -<text text-anchor="middle" x="498.5" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Initial memory</text> +<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="413.25,-59 325.25,-59 325.25,-23 413.25,-23 413.25,-59"/> -<text text-anchor="middle" x="369.25" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.x = 3</text> +<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="M413.69,-41C421.42,-41 429.59,-41 437.69,-41"/> -<polygon fill="blue" stroke="blue" points="437.51,-44.5 447.51,-41 437.51,-37.5 437.51,-44.5"/> +<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="289.25,-59 190.75,-59 190.75,-23 289.25,-23 289.25,-59"/> -<text text-anchor="middle" x="240" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.y = arg</text> +<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="M289.47,-41C297.3,-41 305.46,-41 313.43,-41"/> -<polygon fill="blue" stroke="blue" points="313.4,-44.5 323.4,-41 313.4,-37.5 313.4,-44.5"/> +<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="154.75,-36 90,-36 90,0 154.75,0 154.75,-36"/> -<text text-anchor="middle" x="122.38" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Load p.x</text> +<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="M154.97,-24.28C162.59,-25.8 170.99,-27.47 179.44,-29.15"/> -<polygon fill="blue" stroke="blue" points="178.53,-32.54 189.02,-31.06 179.9,-25.68 178.53,-32.54"/> +<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="54,-59 0,-59 0,-23 54,-23 54,-59"/> -<text text-anchor="middle" x="27" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Return</text> +<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="M54.23,-43.07C65.26,-43.84 78.25,-44.62 90,-45 118.76,-45.93 125.98,-45.68 154.75,-45 162.61,-44.81 170.88,-44.53 179.04,-44.2"/> -<polygon fill="blue" stroke="blue" points="179.1,-47.7 188.94,-43.76 178.8,-40.7 179.1,-47.7"/> +<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="M54.01,-34.59C61.58,-32.73 70.06,-30.64 78.37,-28.59"/> -<polygon fill="black" stroke="black" points="79.18,-32 88.05,-26.21 77.51,-25.2 79.18,-32"/> +<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/chapter10a/docs/example2a.gv b/chapter10a/docs/example2a.gv index 64e774fc..ec5afbdc 100644 --- a/chapter10a/docs/example2a.gv +++ b/chapter10a/docs/example2a.gv @@ -1,5 +1,5 @@ digraph Memory { - rankdir=LR; + rankdir=RL; node [shape=box]; M [label="Incoming memory"]; A [label="True: Store x"]; diff --git a/chapter10a/docs/example2a.svg b/chapter10a/docs/example2a.svg index c6801f59..f9a9b4fd 100644 --- a/chapter10a/docs/example2a.svg +++ b/chapter10a/docs/example2a.svg @@ -12,74 +12,74 @@ <!-- M --> <g id="node1" class="node"> <title>M</title> -<polygon fill="none" stroke="black" points="461.25,-117 342.5,-117 342.5,-81 461.25,-81 461.25,-117"/> -<text text-anchor="middle" x="401.88" y="-93.95" font-family="Times New Roman,serif" font-size="14.00">Incoming memory</text> +<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="305,-144 217,-144 217,-108 305,-108 305,-144"/> -<text text-anchor="middle" x="261" y="-120.95" font-family="Times New Roman,serif" font-size="14.00">True: Store x</text> +<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="M305.18,-117.61C313.41,-116.01 322.22,-114.29 331.03,-112.58"/> -<polygon fill="blue" stroke="blue" points="331.53,-116.05 340.67,-110.7 330.19,-109.18 331.53,-116.05"/> +<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="306.5,-90 215.5,-90 215.5,-54 306.5,-54 306.5,-90"/> -<text text-anchor="middle" x="261" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">False: Store y</text> +<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="M306.71,-80.69C314.45,-82.2 322.66,-83.79 330.88,-85.39"/> -<polygon fill="blue" stroke="blue" points="330.09,-88.8 340.57,-87.28 331.42,-81.93 330.09,-88.8"/> +<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="179.5,-90 90,-90 90,-54 179.5,-54 179.5,-90"/> -<text text-anchor="middle" x="134.75" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">Phi(memory)</text> +<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="M178.16,-90.43C187.56,-94.52 197.63,-98.89 207.37,-103.13"/> -<polygon fill="blue" stroke="blue" points="205.82,-106.27 216.39,-107.05 208.61,-99.85 205.82,-106.27"/> +<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="M179.91,-72C187.59,-72 195.68,-72 203.64,-72"/> -<polygon fill="blue" stroke="blue" points="203.63,-75.5 213.63,-72 203.63,-68.5 203.63,-75.5"/> +<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="288.5,-36 233.5,-36 233.5,0 288.5,0 288.5,-36"/> -<text text-anchor="middle" x="261" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Region</text> +<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="M178.16,-53.57C192.73,-47.24 208.91,-40.21 223.01,-34.08"/> -<polygon fill="black" stroke="black" points="224.16,-37.39 231.94,-30.2 221.37,-30.97 224.16,-37.39"/> +<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="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">Return</text> +<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="M54.41,-72C61.73,-72 69.96,-72 78.28,-72"/> -<polygon fill="blue" stroke="blue" points="78.08,-75.5 88.08,-72 78.08,-68.5 78.08,-75.5"/> +<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> </g> </svg> diff --git a/chapter10a/docs/example2b.gv b/chapter10a/docs/example2b.gv index 7ccbcc99..3f3309e5 100644 --- a/chapter10a/docs/example2b.gv +++ b/chapter10a/docs/example2b.gv @@ -1,8 +1,11 @@ digraph Memory { - rankdir=LR; + rankdir=RL; node [shape=box]; P [label="Phi(memory)"]; S [label="Loop-body Store"]; - P -> Entry [color=blue]; P -> S -> P [color=blue]; + P -> Entry [color=blue]; + P -> S [color=blue,constraint=false]; // Backedge must not place Store before Phi. + S -> P [color=blue]; P -> Loop [style=dashed]; Return -> P [color=blue]; + Return -> S [style=invis]; // Layout only: Phi, Store, Return from left to right. } diff --git a/chapter10a/docs/example2b.svg b/chapter10a/docs/example2b.svg index 063a6f21..8fff33d4 100644 --- a/chapter10a/docs/example2b.svg +++ b/chapter10a/docs/example2b.svg @@ -4,70 +4,71 @@ <!-- Generated by graphviz version 12.2.0 (20241103.1931) --> <!-- Title: Memory Pages: 1 --> -<svg width="332pt" height="152pt" - viewBox="0.00 0.00 331.75 152.00" 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)"> +<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,-148 327.75,-148 327.75,4 -4,4"/> +<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,-117 90,-117 90,-81 179.5,-81 179.5,-117"/> -<text text-anchor="middle" x="134.75" y="-93.95" font-family="Times New Roman,serif" font-size="14.00">Phi(memory)</text> +<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 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<g id="node3" class="node"> <title>Entry</title> -<polygon fill="none" stroke="black" points="296.62,-90 242.62,-90 242.62,-54 296.62,-54 296.62,-90"/> -<text text-anchor="middle" x="269.62" y="-66.95" font-family="Times New Roman,serif" font-size="14.00">Entry</text> +<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="M180,-90.01C196.64,-86.63 215.39,-82.82 231.34,-79.58"/> -<polygon fill="blue" stroke="blue" points="231.8,-83.05 240.9,-77.63 230.41,-76.19 231.8,-83.05"/> +<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="296.62,-36 242.62,-36 242.62,0 296.62,0 296.62,-36"/> -<text text-anchor="middle" x="269.62" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Loop</text> +<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="M161.08,-80.66C176.5,-69.79 196.77,-56.04 215.5,-45 220.85,-41.85 226.61,-38.69 232.29,-35.7"/> -<polygon fill="black" stroke="black" points="233.69,-38.92 240.99,-31.24 230.49,-32.69 233.69,-38.92"/> +<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="M215.34,-121.8C207.37,-120.33 199.14,-118.67 191.13,-116.92"/> -<polygon fill="blue" stroke="blue" points="192,-113.53 181.47,-114.73 190.45,-120.35 192,-113.53"/> +<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="54,-117 0,-117 0,-81 54,-81 54,-117"/> -<text text-anchor="middle" x="27" y="-93.95" font-family="Times New Roman,serif" font-size="14.00">Return</text> +<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="M54.41,-99C61.73,-99 69.96,-99 78.28,-99"/> -<polygon fill="blue" stroke="blue" points="78.08,-102.5 88.08,-99 78.08,-95.5 78.08,-102.5"/> +<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/chapter10a/docs/example2c.gv b/chapter10a/docs/example2c.gv index 0c7cf67d..ef8a5fc8 100644 --- a/chapter10a/docs/example2c.gv +++ b/chapter10a/docs/example2c.gv @@ -1,5 +1,5 @@ digraph Memory { - rankdir=LR; + rankdir=RL; node [shape=box]; M [label="Prior memory"]; L [label="Load p.x"]; diff --git a/chapter10a/docs/example2c.svg b/chapter10a/docs/example2c.svg index a4d2f53e..c7b37912 100644 --- a/chapter10a/docs/example2c.svg +++ b/chapter10a/docs/example2c.svg @@ -12,39 +12,39 @@ <!-- M --> <g id="node1" class="node"> <title>M</title> -<polygon fill="none" stroke="black" points="390.25,-59 297,-59 297,-23 390.25,-23 390.25,-59"/> -<text text-anchor="middle" x="343.62" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Prior memory</text> +<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="260,-36 195.25,-36 195.25,0 260,0 260,-36"/> -<text text-anchor="middle" x="227.62" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Load p.x</text> +<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="M260.38,-24.41C268.17,-25.98 276.74,-27.71 285.33,-29.44"/> -<polygon fill="blue" stroke="blue" points="284.57,-32.86 295.07,-31.41 285.96,-26 284.57,-32.86"/> +<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="65.5,-59 0,-59 0,-23 65.5,-23 65.5,-59"/> -<text text-anchor="middle" x="32.75" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.x</text> +<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="M65.75,-47.66C71.63,-48.63 77.73,-49.48 83.5,-50 152.69,-56.21 232.63,-51.66 285.21,-47.07"/> -<polygon fill="blue" stroke="blue" points="285.51,-50.56 295.15,-46.17 284.88,-43.59 285.51,-50.56"/> +<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="M65.84,-35.96C71.71,-35.1 77.78,-34.24 83.5,-33.5 117.16,-29.14 155.38,-25.05 183.85,-22.16"/> -<polygon fill="black" stroke="black" points="183.92,-25.67 193.52,-21.19 183.22,-18.71 183.92,-25.67"/> -<text text-anchor="middle" x="130.38" y="-36.7" font-family="Times New Roman,serif" font-size="14.00">execute load first</text> +<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/chapter10a/docs/lattice.gv b/chapter10a/docs/lattice.gv index b2d8255e..733a5287 100644 --- a/chapter10a/docs/lattice.gv +++ b/chapter10a/docs/lattice.gv @@ -1,151 +1,108 @@ 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 - XCTRL [label=<<B>⊤</B >:ctrl>, fillcolor=yellow, shape=oval]; - CTRL [label=<<B>⊥</B>:ctrl>, fillcolor=yellow, shape=oval]; - - TOP -> XCTRL; - XCTRL -> 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_MINDOTS [label="...", fillcolor=lightblue, shape=oval]; - INT_ZERO [label="0" , fillcolor=lightblue]; - INT_MAXDOTS [label="...", fillcolor=lightblue, shape=oval]; - - TOP -> INT_TOP; - INT_TOP -> INT_MINDOTS; - INT_TOP -> INT_ZERO; - INT_TOP -> INT_MAXDOTS; - INT_MINDOTS -> INT_BOT; - INT_ZERO -> INT_BOT; - INT_MAXDOTS -> INT_BOT; - INT_BOT -> BOT; - - INT_MINDOTS -> INT_ZERO -> INT_MAXDOTS [style=invis]; - - // ---------------------- - // Pointers, just a boolean nil/not and a struct - PTR [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <TR><TD BGCOLOR="green"><FONT color="white">*ptr</FONT></TD></TR> - <TR><TD BGCOLOR="lightgreen">struct</TD></TR> - </TABLE> - >]; - PTR0 [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <TR><TD BGCOLOR="green"><FONT color="white">*ptr?</FONT></TD></TR> - <TR><TD BGCOLOR="lightgreen">struct</TD></TR> - </TABLE> - >]; - - TOP -> PTR; - PTR -> PTR0; - PTR0 -> BOT; - - // ---------------------- - // Structs - STRUCT_TOP [label=<<B>⊤</B >:struct>, fillcolor=lightgreen, shape=oval]; - STRUCT_BOT [label=<<B>⊥</B>:struct>, fillcolor=lightgreen, shape=oval]; - - STRUCT_S1 [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <TR><TD BGCOLOR="lightgreen">field</TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - </TABLE> - >]; - STRUCT_S2 [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <TR><TD BGCOLOR="lightgreen">field</TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - <TR><TD BGCOLOR="lightgreen">field</TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - </TABLE> - >]; - STRUCT_SN [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <TR><TD BGCOLOR="lightgreen">field</TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - <TR><TD BGCOLOR="lightgreen">... </TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - <TR><TD BGCOLOR="lightgreen">field</TD><TD BGCOLOR="lightblue:green" gradientangle="315">int/ptr</TD></TR> - </TABLE> - >]; - - - TOP -> STRUCT_TOP; - STRUCT_TOP -> STRUCT_S1; - STRUCT_TOP -> STRUCT_S2; - STRUCT_TOP -> STRUCT_SN; - STRUCT_S1 -> STRUCT_BOT; - STRUCT_S2 -> STRUCT_BOT; - STRUCT_SN -> STRUCT_BOT; - STRUCT_BOT -> BOT; - - STRUCT_S1 -> STRUCT_S2 -> STRUCT_SN [style=invis]; - - // ---------------------- - // Memory - MEM_TOP [label=<<B>⊤</B >:mem>, fillcolor=blue, fontcolor=white, shape=oval]; - MEM_BOT [label=<<B>⊥</B>:mem>, fillcolor=blue, fontcolor=white, shape=oval]; - - TOP -> MEM_TOP; - MEM_TOP -> MEM_BOT; - MEM_BOT -> BOT; - - - // ---------------------- - // 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"> - <TR><TD BGCOLOR="pink">Tuple</TD></TR> - <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"> - <TR><TD BGCOLOR="pink">Tuple</TD></TR> - <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"> - <TR><TD BGCOLOR="pink">Tuple</TD></TR> - <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; XCTRL; STRUCT_TOP; MEM_TOP; TUPLE_TOP} - {rank=same; INT_MINDOTS; INT_ZERO; INT_MAXDOTS; - STRUCT_S1; STRUCT_S2; STRUCT_SN;} - {rank=same; INT_BOT; CTRL; STRUCT_BOT; MEM_BOT; TUPLE_BOT} - {rank=same; BOT;} + 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/chapter10a/docs/lattice.svg b/chapter10a/docs/lattice.svg index aa296366..24c0de8c 100644 --- a/chapter10a/docs/lattice.svg +++ b/chapter10a/docs/lattice.svg @@ -4,463 +4,567 @@ <!-- Generated by graphviz version 12.2.0 (20241103.1931) --> <!-- Title: Lattice Pages: 1 --> -<svg width="1132pt" height="440pt" - viewBox="0.00 0.00 1131.51 440.50" 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(4 436.5)"> +<svg width="1647pt" height="555pt" + viewBox="0.00 0.00 1647.00 555.43" 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-<text text-anchor="start" x="440.63" y="-16.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00" fill="white">⊥</text> +<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="yellow" stroke="black" cx="36.51" cy="-104.75" rx="36.51" ry="18"/> -<text text-anchor="start" x="17.76" y="-100.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text> -<text text-anchor="start" x="33.51" y="-100.7" font-family="Times New Roman,serif" font-size="14.00">:ctrl</text> +<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="edge2" class="edge"> +<g id="edge1" class="edge"> <title>XCTRL->CTRL</title> -<path fill="none" stroke="black" d="M36.51,-309.5C36.51,-271.02 36.51,-181.25 36.51,-134.4"/> -<polygon fill="black" stroke="black" points="40.01,-134.45 36.51,-124.45 33.01,-134.45 40.01,-134.45"/> +<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="edge3" class="edge"> +<g id="edge59" class="edge"> <title>CTRL->BOT</title> -<path fill="none" stroke="black" d="M69.88,-97.14C147.7,-81.72 340.42,-43.54 416.69,-28.43"/> -<polygon fill="black" stroke="black" points="417.29,-31.88 426.41,-26.5 415.93,-25.01 417.29,-31.88"/> +<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_MINDOTS --> +<!-- INT_NEG --> <g id="node7" class="node"> -<title>INT_MINDOTS</title> -<ellipse fill="lightblue" stroke="black" cx="68.51" cy="-216.25" rx="27" ry="18"/> -<text text-anchor="middle" x="68.51" y="-211.2" font-family="Times New Roman,serif" font-size="14.00">...</text> +<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_MINDOTS --> -<g id="edge5" class="edge"> -<title>INT_TOP->INT_MINDOTS</title> -<path fill="none" stroke="black" d="M200.95,-312.66C174.03,-293.27 125.48,-258.29 95.24,-236.5"/> -<polygon fill="black" stroke="black" points="97.5,-233.82 87.34,-230.81 93.41,-239.5 97.5,-233.82"/> +<!-- 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="lightblue" stroke="black" cx="156.51" cy="-216.25" rx="18" ry="18"/> -<text text-anchor="middle" x="156.51" y="-211.2" font-family="Times New Roman,serif" font-size="14.00">0</text> +<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="edge6" class="edge"> +<g id="edge5" class="edge"> <title>INT_TOP->INT_ZERO</title> -<path fill="none" stroke="black" d="M210.79,-310.12C200.2,-292 183.15,-262.82 170.98,-242.01"/> -<polygon fill="black" stroke="black" points="174.12,-240.45 166.05,-233.58 168.08,-243.98 174.12,-240.45"/> +<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_MAXDOTS --> +<!-- INT_POS --> <g id="node9" class="node"> -<title>INT_MAXDOTS</title> -<ellipse fill="lightblue" stroke="black" cx="244.51" cy="-216.25" rx="27" ry="18"/> -<text text-anchor="middle" x="244.51" y="-211.2" font-family="Times New Roman,serif" font-size="14.00">...</text> +<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_MAXDOTS --> -<g id="edge7" class="edge"> -<title>INT_TOP->INT_MAXDOTS</title> -<path fill="none" stroke="black" d="M224.26,-309.64C228.03,-292.44 233.9,-265.64 238.35,-245.33"/> -<polygon fill="black" stroke="black" points="241.74,-246.23 240.46,-235.72 234.9,-244.73 241.74,-246.23"/> +<!-- 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="lightblue" stroke="black" cx="220.51" cy="-104.75" rx="33.95" ry="18"/> -<text text-anchor="start" x="203.63" y="-100.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text> -<text text-anchor="start" x="219.38" y="-100.7" font-family="Times New Roman,serif" font-size="14.00">:int</text> +<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="edge11" class="edge"> +<g id="edge60" class="edge"> <title>INT_BOT->BOT</title> -<path fill="none" stroke="black" d="M248.01,-93.9C290.83,-78.57 373.15,-49.1 417.83,-33.11"/> -<polygon fill="black" stroke="black" points="418.93,-36.43 427.17,-29.76 416.57,-29.84 418.93,-36.43"/> +<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_MINDOTS->INT_BOT --> -<g id="edge8" class="edge"> -<title>INT_MINDOTS->INT_BOT</title> -<path fill="none" stroke="black" d="M86.24,-202.47C112.22,-183.76 160.89,-148.7 191.95,-126.33"/> -<polygon fill="black" stroke="black" points="193.68,-129.39 199.75,-120.71 189.59,-123.71 193.68,-129.39"/> +<!-- 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_MINDOTS->INT_ZERO --> +<!-- INT_NEG->INT_ZERO --> <!-- INT_ZERO->INT_BOT --> -<g id="edge9" class="edge"> +<g id="edge8" class="edge"> <title>INT_ZERO->INT_BOT</title> -<path fill="none" stroke="black" d="M165.14,-200.48C175.34,-183.02 192.52,-153.64 205.04,-132.22"/> -<polygon fill="black" stroke="black" points="207.97,-134.13 210,-123.73 201.93,-130.6 207.97,-134.13"/> +<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> -<!-- INT_ZERO->INT_MAXDOTS --> -<!-- INT_MAXDOTS->INT_BOT --> -<g id="edge10" class="edge"> -<title>INT_MAXDOTS->INT_BOT</title> -<path fill="none" stroke="black" d="M240.76,-198.14C237.01,-181.04 231.18,-154.46 226.74,-134.19"/> -<polygon fill="black" stroke="black" points="230.2,-133.6 224.64,-124.58 223.36,-135.09 230.2,-133.6"/> +<!-- 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> -<!-- PTR0 --> -<g id="node11" class="node"> -<title>PTR0</title> -<polygon fill="none" stroke="none" points="387.51,-131.25 333.51,-131.25 333.51,-78.25 387.51,-78.25 387.51,-131.25"/> -<polygon fill="green" stroke="none" points="342.51,-104.75 342.51,-127.25 378.51,-127.25 378.51,-104.75 342.51,-104.75"/> -<polygon fill="none" stroke="black" points="342.51,-104.75 342.51,-127.25 378.51,-127.25 378.51,-104.75 342.51,-104.75"/> -<text text-anchor="start" x="346.63" y="-110.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">*ptr?</text> -<polygon fill="lightgreen" stroke="none" points="342.51,-82.25 342.51,-104.75 378.51,-104.75 378.51,-82.25 342.51,-82.25"/> -<polygon fill="none" stroke="black" points="342.51,-82.25 342.51,-104.75 378.51,-104.75 378.51,-82.25 342.51,-82.25"/> -<text text-anchor="start" x="345.51" y="-88.45" font-family="Times New Roman,serif" font-size="14.00">struct</text> -</g> -<!-- PTR->PTR0 --> -<g id="edge15" class="edge"> -<title>PTR->PTR0</title> -<path fill="none" stroke="black" d="M360.51,-301.29C360.51,-261.89 360.51,-187.62 360.51,-142.52"/> -<polygon fill="black" stroke="black" points="364.01,-142.68 360.51,-132.68 357.01,-142.68 364.01,-142.68"/> -</g> -<!-- PTR0->BOT --> +<!-- PTR_TOP->PTR_NULL --> <g id="edge16" class="edge"> -<title>PTR0->BOT</title> -<path fill="none" stroke="black" d="M387.39,-78.81C399.39,-67.68 413.41,-54.68 424.99,-43.94"/> -<polygon fill="black" stroke="black" points="427.24,-46.63 432.19,-37.26 422.48,-41.5 427.24,-46.63"/> +<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> -<!-- STRUCT_S1 --> +<!-- 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" 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