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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 | |
| parent | fa7d56f72455828826d0ab7e1c142ca814e6e2aa (diff) | |
| download | Simple-3ba6686fc991998a0a420709dfb0012bbddf77ab.tar.gz Simple-3ba6686fc991998a0a420709dfb0012bbddf77ab.zip | |
Backport lazy memory splits to ch10, split into ch10a and bch10ab
30 files changed, 1625 insertions, 1262 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"> 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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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<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" 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="none" stroke="none" points="487.38,-234.25 401.63,-234.25 401.63,-198.25 487.38,-198.25 487.38,-234.25"/> -<polygon fill="lightgreen" stroke="none" points="409.63,-205 409.63,-227.5 440.38,-227.5 440.38,-205 409.63,-205"/> -<polygon fill="none" stroke="black" 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xmlns="http://www.w3.org/2000/svg" width="61" height="20" viewBox="0 0 61 20" role="img" aria-labelledby="title"> + <title id="title">Control</title> + <rect width="61" height="20" rx="2" fill="#ffff00"/> + <text x="30.5" y="14" text-anchor="middle" font-family="Arial, sans-serif" font-size="13" fill="#000000">Control</text> +</svg> diff --git a/chapter10a/docs/type-integer.svg b/chapter10a/docs/type-integer.svg new file mode 100644 index 00000000..97d03372 --- /dev/null +++ b/chapter10a/docs/type-integer.svg @@ -0,0 +1,5 @@ +<svg xmlns="http://www.w3.org/2000/svg" width="60" height="20" viewBox="0 0 60 20" role="img" aria-labelledby="title"> + <title id="title">Integer</title> + <rect width="60" height="20" rx="2" fill="#add8e6"/> + <text x="30.0" y="14" text-anchor="middle" font-family="Arial, sans-serif" font-size="13" fill="#000000">Integer</text> +</svg> diff --git a/chapter10a/docs/type-memory.svg b/chapter10a/docs/type-memory.svg new file mode 100644 index 00000000..16b5121f --- 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fill="#000000">Tuple</text> +</svg> diff --git a/chapter10b/#README.md# b/chapter10b/#README.md# new file mode 100644 index 00000000..6380b79e --- /dev/null +++ b/chapter10b/#README.md# @@ -0,0 +1,174 @@ +# Chapter 10b: Splitting Memory + +[Previous: Chapter 10a](../chapter10a/README.md) | +[Next: Chapter 11](../chapter11/README.md) + +Chapter 10a made memory effects explicit with one SSA memory value. This +chapter keeps exactly that parser model and recovers independent memory chains +through graph rewrites. There is no new language syntax; the +[grammar](docs/10-grammar.md), pointer types, and null checks are unchanged. + +## Why split memory? + +```java +struct Point { int x; int y; } +Point p = new Point; +p.x = 42; +while (arg > 0) { + p.y = p.y + arg; + arg = arg - 1; +} +return p.x; +``` + +The loop changes `y`, so it cannot affect `x`. With one memory chain the load +of `x` follows the loop's stores. Splitting the fields lets ordinary +load-after-store forwarding turn the return value into 42. + + + +Control, pointer, and value edges are omitted when they do not explain memory. + +## Equivalence-class aliasing + +Each struct field has an integer alias identity. Two different fields receive +different identities, even if they have the same spelling in different structs. +Two instances of the same struct share their field aliases. Thus different +classes never alias; accesses in the same class **may alias**. Same-class does +not mean same-address: forwarding still checks pointer identity. + +The parser assigns field identities at struct declarations, beginning at 2. +These identities are independent of Start's output indices. The default slot +of a memory aggregate is 1; precise slots are greater than 1. + +We do not allocate a Start projection, scope binding, or loop Phi for every +declared field. Start supplies one memory value, Scope holds one `$mem` binding, +and Return consumes one complete memory value. The optimizer introduces slices +only where graph operations require them. + +## Three memory nodes + +| Node | Meaning | +|---|---| +| `MemMerge` | A complete memory state: a default plus precise alias overrides | +| `MemPhi` | One alias selected according to the incoming control path | +| `BulkMemPhi` | All aliases except an explicit exclusion set, selected by control | + +`MemMerge` combines independent pieces of memory at one program point. It is +not a control-flow merge. For example, after storing to alias `x`: + +```text +prior = current memory +store = Store_x(prior, pointer, value) +current memory = MemMerge(default=prior, x=store) +``` + +The Store selects its precise input from any incoming MemMerge. Loads and +precise memory Phis do the same. A missing precise entry falls back to the +default, provided that default still covers the requested alias. + +The explicit entries override the default: the semantic slices are disjoint, +and their union covers all memory. Flattening stacked aggregates preserves +entries that the outer aggregate has not replaced. This allows an `x` store +and a later `y` store to remain visible together at Return. + + + +## Splitting a memory Phi + +Scope initially creates a BulkMemPhi wherever the ordinary SSA algorithm needs +to merge memory. Its empty exclusion set means that it covers every alias. +After the Region is complete, the Phi inspects its memory inputs and users. +When they require a precise alias, it splits out that alias: + +```text +BulkPhi(R, left, right) + becomes +MemMerge( + default = BulkPhi_except{x}(R, left, right), + x = MemPhi_x(R, slice(left,x), slice(right,x))) +``` + +The new precise Phi and the remaining bulk Phi share a Region and matching +control-path indices. A loop uses the same transformation, with the backedge +among those inputs. Each further split preserves all previously extracted +slices; replacing a bulk Phi must never drop their parallel precise Phis. + + + +A bulk Phi can bypass an incoming aggregate only when all of that aggregate's +explicit slices are already excluded from the Phi. A precise consumer can +select one entry. A whole-memory consumer cannot just select the default: +that would lose the explicit updates. + +## Types and the worklist + +The memory type lattice adds a flat element `MEM#N` for each precise alias. +Meeting different aliases gives `TypeMem.BOT`. It does not track field values, +private objects, or escape information. Bulk exclusion sets belong to the +graph nodes, not to an expanded type lattice. + + + +Scalar Phis remain ordinary PhiNodes. The scope's Phi factory chooses a +BulkMemPhi for whole memory; splitting constructs MemPhis explicitly. Generic +arithmetic factoring through Phis must not factor a memory aggregate. + +Memory splitting can increase node count. Progress comes from extracting an +alias from a bulk Phi and simplifying its precise chain, rather than from +requiring every rewrite to shrink the graph. Nodes must have conservative +initial types before introducing cyclic inputs. New bulk and precise Phis are +queued, so a recursive peephole cannot start another split halfway through the +first one. + +This also extends the worklist lesson from Chapter 9. A bulk Phi inspects its +users, so changes to a user's partition must wake the producer. Selecting a +slice from an aggregate can expose a new bulk-Phi user; that selected definition +must be queued too. The optimizer's worklist completeness assertion remains +enabled and checks these dependencies. + +## Evaluation and ordering + +MemMerge is a dependency node; it emits no heap operation. Its evaluator result +is a memory token, while Store mutates the object's fields. The scheduler must +distinguish aggregation from overwriting memory. A MemMerge is not a clobber, +and stores in different alias classes do not impose load/store anti-dependencies. + + + +Tests cover independent-field folding, parallel memory Phis, multiple field +updates surviving at Return, early returns, nested loops with break/continue, +and reads before subsequent stores through potentially aliased pointers. + +## What remains for later chapters? + +Chapter 10b knows every access's alias while parsing. What is lazy here is the +construction of memory partitions. Chapter 25 also allows an existing access's +alias to become known later, using the same representation. Its private +constructor memory, escape tracking, incomplete types, and module alias +remapping are separate extensions and are not needed here. + +Chapters 11-24 currently retain their older parser-managed memory chains. +Forwarding this representation through those snapshots is tracked in the +[backport queue](../docs/chapter-backports.md). Chapter 11's scheduling lesson +therefore still shows the older graph construction, with the same language. + +## Build and test + +With JDK 21 or newer, from this directory: + +```sh +make lib +make tests +make release +make view +``` + +Make builds this complete snapshot without Maven. `make release` writes +`build/release/simple.jar`; `make view` launches the shared graph viewer. +Both the root Maven reactor and the supplied IDEA module descriptor include +the chapter. From the repository root, test both halves with: + +```sh +make tests CHAPTERS="chapter10a chapter10b" +``` diff --git a/chapter10b/.#README.md b/chapter10b/.#README.md new file mode 100644 index 00000000..c657b199 --- /dev/null +++ b/chapter10b/.#README.md @@ -0,0 +1 @@ +cliffc@DESKTOP-DAD.21980:1790387027
\ No newline at end of file diff --git a/chapter10b/README.md b/chapter10b/README.md index 1779be50..795d2233 100644 --- a/chapter10b/README.md +++ b/chapter10b/README.md @@ -28,6 +28,8 @@ load-after-store forwarding turn the return value into 42.  These are schematic dependency graphs, with arrows from uses to their definitions. +In horizontal diagrams, definitions appear on the left and uses on the right; +in vertical diagrams, definitions appear above uses. Control, pointer, and value edges are omitted when they do not explain memory. ## Equivalence-class aliasing @@ -104,13 +106,26 @@ that would lose the explicit updates. ## Types and the worklist -The memory type lattice adds a flat element `MEM#N` for each precise alias. -Meeting different aliases gives `TypeMem.BOT`. It does not track field values, -private objects, or escape information. Bulk exclusion sets belong to the -graph nodes, not to an expanded type lattice. +The type lattice retains Chapter 10a's six domains, colors, and notation: +`⊤` means top, `⊥` means bottom, and a suffix names the domain. The other five +domains are unchanged; memory now adds a flat element `MEM#N` for each precise +alias between memory top (`TypeMem.TOP`) and memory bottom (`TypeMem.BOT`).  +The parallel `MEM#2`, `MEM#3`, and further alias elements describe independent +field slices. For the first `Point` declaration above, these two aliases identify +`Point.x` and `Point.y`. Meeting different aliases gives memory bottom; joining +them gives memory top. Each precise alias is its own dual. The ellipsis stands +for more parallel aliases, not a type representing a set of aliases. + +Memory bottom covers all memory. The default aggregate slot numbered 1 is a +graph input position, not a precise field alias in this diagram. Types do not +track field values, private objects, or escape information. Bulk exclusion sets +and the default-plus-overrides structure of MemMerge belong to graph nodes, +not to an expanded type lattice. As in Chapter 10a, diagram edges show lattice +order, with top above bottom; field and tuple-element type lattices are elided. + Scalar Phis remain ordinary PhiNodes. The scope's Phi factory chooses a BulkMemPhi for whole memory; splitting constructs MemPhis explicitly. Generic arithmetic factoring through Phis must not factor a memory aggregate. diff --git a/chapter10b/docs/example1.gv b/chapter10b/docs/example1.gv index 2194ae8f..0b0a5feb 100644 --- a/chapter10b/docs/example1.gv +++ b/chapter10b/docs/example1.gv @@ -1,11 +1,13 @@ digraph Memory { - rankdir=LR; + rankdir=BT; node [shape=box]; M [label="Initial memory"]; X [label="Store x = 42"]; Y [label="Loop: Store y"]; - L [label="Load x -> 42"]; + L [label="Load x (42)"]; L -> X -> M [color=blue]; Y -> M [color=green]; MemMerge -> X [color=blue]; MemMerge -> Y [color=green]; Return -> MemMerge; Return -> L; + { rank=same; MemMerge -> L [style=invis]; } + Y -> X [style=invis]; // Layout only: keep the stores in code order. } diff --git a/chapter10b/docs/example1.svg b/chapter10b/docs/example1.svg index c441bc7b..384b6e12 100644 --- a/chapter10b/docs/example1.svg +++ b/chapter10b/docs/example1.svg @@ -4,88 +4,90 @@ <!-- Generated by graphviz version 12.2.0 (20241103.1931) --> <!-- Title: Memory 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MemMerge->B --> <g id="edge8" class="edge"> <title>MemMerge->B</title> -<path fill="none" stroke="black" d="M82.03,-83.78C100.1,-87.29 122.25,-91.6 144.12,-95.85"/> -<polygon fill="black" stroke="black" points="143.19,-99.23 153.67,-97.71 144.52,-92.36 143.19,-99.23"/> -<text text-anchor="middle" x="118.75" y="-97.06" font-family="Times New Roman,serif" font-size="14.00">default</text> +<path fill="none" stroke="black" d="M365.72,-83.78C347.65,-87.29 325.5,-91.6 303.63,-95.85"/> +<polygon fill="black" stroke="black" points="303.23,-92.36 294.08,-97.71 304.56,-99.23 303.23,-92.36"/> +<text text-anchor="middle" x="329" y="-97.06" font-family="Times New Roman,serif" font-size="14.00">default</text> </g> </g> </svg> diff --git a/chapter10b/docs/example2c.gv b/chapter10b/docs/example2c.gv index 7a0562ee..4fae3bba 100644 --- a/chapter10b/docs/example2c.gv +++ b/chapter10b/docs/example2c.gv @@ -1,5 +1,5 @@ digraph Memory { - rankdir=LR; + rankdir=RL; node [shape=box]; M [label="Prior x memory"]; L [label="Load p.x"]; diff --git a/chapter10b/docs/example2c.svg b/chapter10b/docs/example2c.svg index 1d51ccca..8249d677 100644 --- a/chapter10b/docs/example2c.svg +++ b/chapter10b/docs/example2c.svg @@ -12,45 +12,45 @@ <!-- M --> <g id="node1" class="node"> <title>M</title> -<polygon fill="none" stroke="black" points="474.25,-59 370.5,-59 370.5,-23 474.25,-23 474.25,-59"/> -<text text-anchor="middle" x="422.38" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Prior x memory</text> +<polygon fill="none" stroke="black" points="103.75,-59 0,-59 0,-23 103.75,-23 103.75,-59"/> +<text text-anchor="middle" x="51.88" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Prior x memory</text> </g> <!-- L --> <g id="node2" class="node"> <title>L</title> -<polygon fill="none" stroke="black" points="333.5,-36 268.75,-36 268.75,0 333.5,0 333.5,-36"/> -<text text-anchor="middle" x="301.12" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">Load p.x</text> +<polygon fill="none" stroke="black" points="205.5,-36 140.75,-36 140.75,0 205.5,0 205.5,-36"/> +<text text-anchor="middle" x="173.12" 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="M333.77,-24.1C341.63,-25.62 350.33,-27.3 359.1,-28.99"/> -<polygon fill="blue" stroke="blue" points="358.23,-32.39 368.71,-30.84 359.56,-25.51 358.23,-32.39"/> +<path fill="none" stroke="blue" d="M140.48,-24.1C132.62,-25.62 123.92,-27.3 115.15,-28.99"/> +<polygon fill="blue" stroke="blue" points="114.69,-25.51 105.54,-30.84 116.02,-32.39 114.69,-25.51"/> </g> <!-- S --> <g id="node3" class="node"> <title>S</title> -<polygon fill="none" stroke="black" points="102.25,-59 36.75,-59 36.75,-23 102.25,-23 102.25,-59"/> -<text text-anchor="middle" x="69.5" y="-35.95" font-family="Times New Roman,serif" font-size="14.00">Store p.x</text> +<polygon fill="none" stroke="black" points="437.5,-59 372,-59 372,-23 437.5,-23 437.5,-59"/> +<text text-anchor="middle" x="404.75" 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="M102.48,-45.13C118.77,-47.03 138.91,-49.06 157,-50 226.01,-53.58 305.22,-49.84 358.81,-46.15"/> -<polygon fill="blue" stroke="blue" points="358.94,-49.65 368.67,-45.45 358.44,-42.67 358.94,-49.65"/> +<path fill="none" stroke="blue" d="M371.77,-45.13C355.48,-47.03 335.34,-49.06 317.25,-50 248.24,-53.58 169.03,-49.84 115.44,-46.15"/> +<polygon fill="blue" stroke="blue" points="115.81,-42.67 105.58,-45.45 115.31,-49.65 115.81,-42.67"/> </g> <!-- S->L --> <g id="edge3" class="edge"> <title>S->L</title> -<path fill="none" stroke="black" stroke-dasharray="5,2" d="M102.43,-37.8C142.7,-33.77 212.1,-26.82 257.04,-22.32"/> -<polygon fill="black" stroke="black" points="257.36,-25.8 266.96,-21.32 256.66,-18.84 257.36,-25.8"/> -<text text-anchor="middle" x="203.88" y="-35.44" font-family="Times New Roman,serif" font-size="14.00">execute load first</text> +<path fill="none" stroke="black" stroke-dasharray="5,2" d="M371.82,-37.8C331.55,-33.77 262.15,-26.82 217.21,-22.32"/> +<polygon fill="black" stroke="black" points="217.59,-18.84 207.29,-21.32 216.89,-25.8 217.59,-18.84"/> +<text text-anchor="middle" x="270.38" y="-35.44" font-family="Times New Roman,serif" font-size="14.00">execute load first</text> </g> <!-- Y --> <g id="node4" class="node"> <title>Y</title> -<polygon fill="none" stroke="black" points="139,-113 0,-113 0,-77 139,-77 139,-113"/> -<text text-anchor="middle" x="69.5" y="-89.95" font-family="Times New Roman,serif" font-size="14.00">Store p.y: independent</text> +<polygon fill="none" stroke="black" points="474.25,-113 335.25,-113 335.25,-77 474.25,-77 474.25,-113"/> +<text text-anchor="middle" x="404.75" y="-89.95" font-family="Times New Roman,serif" font-size="14.00">Store p.y: independent</text> </g> </g> </svg> diff --git a/chapter10b/docs/lattice.gv b/chapter10b/docs/lattice.gv index f87acfed..f9fb2b09 100644 --- a/chapter10b/docs/lattice.gv +++ b/chapter10b/docs/lattice.gv @@ -1,161 +1,114 @@ 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]; - MEM_ALIAS1 [label="#2" , fillcolor=blue, fontcolor=white]; - MEM_ALIASDOTS [label="..." , fillcolor=blue, fontcolor=white, shape=oval]; - MEM_ALIASN [label="#n" , fillcolor=blue, fontcolor=white]; - - TOP -> MEM_TOP; - MEM_TOP -> MEM_ALIAS1; - MEM_TOP -> MEM_ALIASDOTS; - MEM_TOP -> MEM_ALIASN; - MEM_ALIAS1 -> MEM_BOT; - MEM_ALIASDOTS -> MEM_BOT; - MEM_ALIASN -> MEM_BOT; - MEM_BOT -> BOT; - - MEM_ALIAS1 -> MEM_ALIASDOTS -> MEM_ALIASN [style=invis]; - - // ---------------------- - // Tuples - - TUPLE_TOP [label=<<B>⊤</B >:tuple>, fillcolor=pink, shape=oval]; - TUPLE_BOT [label=<<B>⊥</B>:tuple>, fillcolor=pink, shape=oval]; - - TUPLE1 [shape=none, fillcolor=none, label=< - <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0"> - <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; - MEM_ALIAS1; MEM_ALIASDOTS; MEM_ALIASN;} - {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\nprecise alias slices"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#00008b", fontcolor=white]; + MEM_TOP [label="⊤:mem"]; + MEM_BOT [label="⊥:mem"]; + MEM_ALIAS2 [label="MEM#2"]; + MEM_ALIAS3 [label="MEM#3"]; + MEM_MORE [label="…"]; + {rank=same; MEM_ALIAS2; MEM_ALIAS3; MEM_MORE;} + MEM_ALIAS2 -> MEM_ALIAS3 -> MEM_MORE [style=invis]; + MEM_TOP -> {MEM_ALIAS2 MEM_ALIAS3 MEM_MORE}; + {MEM_ALIAS2 MEM_ALIAS3 MEM_MORE} -> 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/chapter10b/docs/lattice.svg b/chapter10b/docs/lattice.svg index 4023b68c..a11452b9 100644 --- a/chapter10b/docs/lattice.svg +++ b/chapter10b/docs/lattice.svg @@ -4,513 +4,617 @@ <!-- Generated by graphviz version 12.2.0 (20241103.1931) --> <!-- Title: Lattice Pages: 1 --> -<svg width="1308pt" height="440pt" - viewBox="0.00 0.00 1307.51 440.50" 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="1827pt" height="533pt" + viewBox="0.00 0.00 1827.00 533.45" 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(4 529.45)"> <title>Lattice</title> -<polygon fill="white" stroke="none" points="-4,4 -4,-436.5 1303.51,-436.5 1303.51,4 -4,4"/> +<polygon fill="white" stroke="none" points="-4,4 -4,-529.45 1823,-529.45 1823,4 -4,4"/> +<g id="clust1" class="cluster"> +<title>cluster_control</title> +<polygon fill="none" stroke="#cccccc" points="8,-85.99 8,-454.71 98,-454.71 98,-85.99 8,-85.99"/> +<text text-anchor="middle" x="53" y="-437.41" 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,-454.71 404,-454.71 404,-85.99 106,-85.99"/> +<text text-anchor="middle" x="255" y="-437.41" 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,-465.7 893,-465.7 893,-75 412,-75"/> +<text text-anchor="middle" x="652.5" y="-448.4" 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,-481.45 1237,-481.45 1237,-75 901,-75"/> +<text text-anchor="middle" x="1069" y="-464.15" font-family="Arial" font-size="14.00">Struct</text> +<text text-anchor="middle" x="1069" y="-448.4" 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="1245,-85.99 1245,-470.46 1527,-470.46 1527,-85.99 1245,-85.99"/> +<text text-anchor="middle" x="1386" y="-453.16" font-family="Arial" font-size="14.00">Memory</text> +<text text-anchor="middle" x="1386" y="-437.41" font-family="Arial" font-size="14.00">precise alias slices</text> +</g> +<g id="clust21" class="cluster"> +<title>cluster_tuple</title> +<polygon fill="none" stroke="#cccccc" points="1535,-85.99 1535,-470.46 1811,-470.46 1811,-85.99 1535,-85.99"/> +<text text-anchor="middle" x="1673" y="-453.16" font-family="Arial" font-size="14.00">Tuple</text> +<text text-anchor="middle" x="1673" y="-437.41" 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="478.51" cy="-411.37" rx="21.12" ry="21.12"/> -<text text-anchor="start" x="470.63" y="-406.95" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00" fill="white">⊤</text> +<ellipse fill="black" stroke="black" cx="887" cy="-507.45" rx="27" ry="18"/> +<text text-anchor="middle" x="887" y="-503.35" font-family="DejaVu Sans" font-size="13.00" fill="white">⊤</text> </g> <!-- XCTRL --> <g id="node3" class="node"> <title>XCTRL</title> -<ellipse fill="yellow" stroke="black" cx="36.51" cy="-327.75" rx="36.51" ry="18"/> -<text text-anchor="start" x="17.76" y="-323.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊤</text> -<text text-anchor="start" x="33.51" y="-323.7" font-family="Times New Roman,serif" font-size="14.00">:ctrl</text> +<ellipse fill="#ffff00" stroke="black" cx="53" cy="-404.96" rx="36.51" ry="18"/> +<text text-anchor="middle" x="53" y="-400.86" font-family="DejaVu Sans" font-size="13.00">⊤:ctrl</text> </g> <!-- TOP->XCTRL --> -<g id="edge1" class="edge"> +<g id="edge60" class="edge"> <title>TOP->XCTRL</title> -<path fill="none" stroke="black" d="M457.49,-406.49C389.63,-393.96 175.41,-354.4 81.44,-337.04"/> -<polygon fill="black" stroke="black" points="82.28,-333.64 71.81,-335.27 81.01,-340.53 82.28,-333.64"/> +<path fill="none" stroke="#555555" d="M859.92,-506.29C725.56,-505.4 135.66,-500.43 102,-481.45 82.17,-470.27 69.05,-447.37 61.41,-429.71"/> +<polygon fill="#555555" stroke="#555555" points="63.45,-429.15 59.23,-424.39 59.57,-430.74 63.45,-429.15"/> </g> <!-- INT_TOP --> <g id="node5" class="node"> <title>INT_TOP</title> -<ellipse fill="lightblue" stroke="black" cx="220.51" cy="-327.75" rx="33.95" ry="18"/> -<text text-anchor="start" x="203.63" y="-323.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊤</text> -<text text-anchor="start" x="219.38" y="-323.7" font-family="Times New Roman,serif" font-size="14.00">:int</text> +<ellipse fill="#add8e6" stroke="black" cx="353" cy="-404.96" rx="33.44" ry="18"/> +<text text-anchor="middle" x="353" y="-400.86" font-family="DejaVu Sans" font-size="13.00">⊤:int</text> </g> <!-- TOP->INT_TOP --> -<g id="edge4" class="edge"> +<g id="edge61" class="edge"> <title>TOP->INT_TOP</title> -<path fill="none" stroke="black" d="M458.26,-403.97C415.59,-390.47 315.75,-358.88 259.97,-341.23"/> -<polygon fill="black" stroke="black" points="261.14,-337.93 250.55,-338.25 259.03,-344.61 261.14,-337.93"/> +<path fill="none" stroke="#555555" d="M859.8,-506.38C764.27,-505.97 447.72,-502.97 408,-481.45 387.23,-470.19 372.29,-447.31 363.27,-429.67"/> +<polygon fill="#555555" stroke="#555555" points="365.18,-428.79 360.66,-424.32 361.41,-430.63 365.18,-428.79"/> </g> -<!-- PTR --> +<!-- PTR_TOP --> <g id="node10" class="node"> -<title>PTR</title> -<polygon fill="none" stroke="none" points="387.51,-354.25 333.51,-354.25 333.51,-301.25 387.51,-301.25 387.51,-354.25"/> -<polygon fill="green" stroke="none" points="342.51,-327.75 342.51,-350.25 378.51,-350.25 378.51,-327.75 342.51,-327.75"/> -<polygon fill="none" stroke="black" points="342.51,-327.75 342.51,-350.25 378.51,-350.25 378.51,-327.75 342.51,-327.75"/> -<text text-anchor="start" x="349.63" y="-333.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">*ptr</text> -<polygon fill="lightgreen" stroke="none" points="342.51,-305.25 342.51,-327.75 378.51,-327.75 378.51,-305.25 342.51,-305.25"/> -<polygon fill="none" stroke="black" points="342.51,-305.25 342.51,-327.75 378.51,-327.75 378.51,-305.25 342.51,-305.25"/> -<text text-anchor="start" x="345.51" y="-311.45" font-family="Times New Roman,serif" font-size="14.00">struct</text> -</g> -<!-- TOP->PTR --> -<g id="edge14" class="edge"> -<title>TOP->PTR</title> -<path fill="none" stroke="black" d="M461.35,-398.5C444.42,-386.79 418.03,-368.54 396.49,-353.64"/> -<polygon fill="black" stroke="black" points="398.75,-350.95 388.54,-348.14 394.77,-356.7 398.75,-350.95"/> +<title>PTR_TOP</title> +<ellipse 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font-family="Times New Roman,serif" font-size="14.00">:struct</text> +<ellipse fill="#90ee90" stroke="black" cx="1020" cy="-404.96" rx="64.35" ry="28.99"/> +<text text-anchor="middle" x="1020" y="-409.11" font-family="DejaVu Sans" font-size="13.00">⊤:struct</text> +<text text-anchor="middle" x="1020" y="-392.61" font-family="DejaVu Sans" font-size="13.00">[struct top]</text> </g> <!-- TOP->STRUCT_TOP --> -<g id="edge17" class="edge"> +<g id="edge63" class="edge"> <title>TOP->STRUCT_TOP</title> -<path fill="none" stroke="black" d="M486.86,-391.44C491.45,-381.02 497.24,-367.9 502.33,-356.35"/> -<polygon fill="black" stroke="black" points="505.5,-357.86 506.33,-347.29 499.09,-355.03 505.5,-357.86"/> +<path fill="none" stroke="#555555" d="M904.39,-493.31C923.88,-478.58 956.09,-454.25 981.56,-435"/> +<polygon fill="#555555" stroke="#555555" points="982.82,-436.68 986.34,-431.39 980.29,-433.33 982.82,-436.68"/> </g> <!-- MEM_TOP --> -<g id="node17" class="node"> +<g id="node26" class="node"> <title>MEM_TOP</title> -<ellipse fill="blue" stroke="black" cx="853.51" cy="-327.75" rx="43.67" ry="18"/> -<text text-anchor="start" x="829.51" y="-323.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00" fill="white">⊤</text> -<text text-anchor="start" x="845.26" y="-323.7" font-family="Times New Roman,serif" font-size="14.00" fill="white">:mem</text> +<ellipse fill="#00008b" stroke="black" cx="1351" cy="-404.96" rx="44.7" ry="18"/> +<text text-anchor="middle" x="1351" y="-400.86" font-family="DejaVu Sans" font-size="13.00" fill="white">⊤:mem</text> </g> <!-- TOP->MEM_TOP --> -<g id="edge27" class="edge"> +<g id="edge64" class="edge"> <title>TOP->MEM_TOP</title> -<path fill="none" stroke="black" d="M499.2,-405.87C556.98,-393.29 721.22,-357.54 804.21,-339.48"/> -<polygon fill="black" stroke="black" points="804.86,-342.92 813.89,-337.37 803.37,-336.08 804.86,-342.92"/> +<path fill="none" stroke="#555555" d="M914.33,-506.36C986.5,-505.84 1180.8,-502.47 1241,-481.45 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1074.87,-335.25"/> -<polygon fill="black" stroke="black" points="1074.97,-338.77 1084.46,-334.05 1074.1,-331.82 1074.97,-338.77"/> +<path fill="none" stroke="#555555" d="M914.36,-506.76C1030.08,-507.88 1475.84,-510.27 1531,-481.45 1552.39,-470.27 1568.01,-447.05 1577.43,-429.3"/> +<polygon fill="#555555" stroke="#555555" points="1579.08,-430.68 1579.93,-424.38 1575.34,-428.78 1579.08,-430.68"/> </g> <!-- BOT --> <g id="node2" class="node"> <title>BOT</title> -<ellipse fill="black" stroke="black" cx="448.51" cy="-21.12" rx="21.12" ry="21.12"/> -<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,-386.63C53,-337.1 53,-194.83 53,-137.43"/> +<polygon fill="#555555" stroke="#555555" points="55.1,-137.74 53,-131.74 50.9,-137.74 55.1,-137.74"/> </g> +<!-- XCTRL->INT_TOP --> <!-- 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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="M328.95,-391.93C297.31,-376.11 241.45,-348.19 204.83,-329.88"/> +<polygon fill="#555555" stroke="#555555" points="205.88,-328.06 199.58,-327.25 204,-331.81 205.88,-328.06"/> </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="-310.97" rx="27" ry="18"/> +<text text-anchor="middle" x="267" y="-306.87" 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="M338.41,-388.35C323.94,-372.88 301.71,-349.1 285.9,-332.18"/> +<polygon fill="#555555" stroke="#555555" points="287.47,-330.79 281.84,-327.84 284.4,-333.66 287.47,-330.79"/> </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="-310.97" rx="43.16" ry="18"/> +<text text-anchor="middle" x="353" y="-306.87" 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,-386.65C353,-372.52 353,-352.37 353,-336.56"/> +<polygon fill="#555555" stroke="#555555" points="355.1,-336.7 353,-330.7 350.9,-336.7 355.1,-336.7"/> </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="289" cy="-111.99" rx="33.44" ry="18"/> +<text text-anchor="middle" x="289" y="-107.89" font-family="DejaVu Sans" font-size="13.00">⊥:int</text> </g> <!-- INT_BOT->BOT --> -<g id="edge11" class="edge"> +<g id="edge67" 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="M316.06,-101.31C339.95,-93.13 375.88,-81.69 408,-75 571.35,-40.97 770.86,-25.89 849.65,-20.95"/> +<polygon fill="#555555" stroke="#555555" points="849.52,-23.07 855.38,-20.6 849.26,-18.87 849.52,-23.07"/> </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="M179.44,-292.83C201.14,-257.2 251.13,-175.15 275.35,-135.4"/> +<polygon fill="#555555" stroke="#555555" points="276.89,-136.9 278.22,-130.68 273.31,-134.72 276.89,-136.9"/> </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="M268.91,-292.83C272.82,-257.83 281.73,-178.04 286.26,-137.55"/> +<polygon fill="#555555" stroke="#555555" points="288.33,-137.93 286.91,-131.73 284.15,-137.46 288.33,-137.93"/> +</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="M347.43,-292.83C336.04,-257.76 310.03,-177.71 296.9,-137.29"/> +<polygon fill="#555555" stroke="#555555" points="298.92,-136.72 295.07,-131.67 294.92,-138.02 298.92,-136.72"/> </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="799" cy="-310.97" rx="27.3" ry="18"/> +<text text-anchor="middle" x="799" y="-306.87" font-family="DejaVu Sans" font-size="13.00" fill="white">null</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="M738.85,-377.84C752,-363.43 768.1,-345.8 780.33,-332.41"/> +<polygon fill="#555555" stroke="#555555" points="781.8,-333.91 784.3,-328.06 778.7,-331.08 781.8,-333.91"/> </g> -<!-- STRUCT_S1 --> +<!-- PTR_PERSON --> <g id="node14" class="node"> +<title>PTR_PERSON</title> +<ellipse fill="#008000" stroke="black" cx="542" cy="-310.97" rx="45.72" ry="18"/> +<text text-anchor="middle" x="542" y="-306.87" 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="M674.88,-382.62C644.57,-366.5 603.47,-344.65 575.04,-329.54"/> +<polygon fill="#555555" stroke="#555555" points="576.08,-327.71 569.8,-326.75 574.11,-331.42 576.08,-327.71"/> +</g> +<!-- PTR_S1 --> +<g id="node15" class="node"> +<title>PTR_S1</title> +<ellipse fill="#008000" stroke="black" cx="631" cy="-310.97" rx="27" ry="18"/> +<text text-anchor="middle" x="631" y="-306.87" 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="M691.15,-377.84C678,-363.43 661.9,-345.8 649.67,-332.41"/> +<polygon fill="#555555" stroke="#555555" points="651.3,-331.08 645.7,-328.06 648.2,-333.91 651.3,-331.08"/> +</g> +<!-- PTR_MORE --> +<g id="node16" class="node"> +<title>PTR_MORE</title> +<ellipse fill="#008000" stroke="black" cx="715" cy="-310.97" rx="40.6" ry="18"/> +<text text-anchor="middle" x="715" y="-306.87" 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="M715,-375.61C715,-363.22 715,-348.82 715,-336.86"/> +<polygon fill="#555555" stroke="#555555" points="717.1,-336.91 715,-330.91 712.9,-336.91 717.1,-336.91"/> +</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="edge68" 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="M779.65,-297.94C754.63,-282.39 710.79,-255.14 681.32,-236.82"/> +<polygon fill="#555555" stroke="#555555" points="682.76,-235.24 676.55,-233.86 680.54,-238.81 682.76,-235.24"/> +</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="M789.88,-293.52C781.74,-278.83 769.73,-257.16 760.65,-240.8"/> +<polygon fill="#555555" stroke="#555555" points="762.69,-240.14 757.94,-235.91 759.02,-242.18 762.69,-240.14"/> +</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="M806.33,-293.52C812.78,-279.05 822.24,-257.81 829.5,-241.54"/> +<polygon fill="#555555" stroke="#555555" points="831.32,-242.62 831.84,-236.28 827.48,-240.91 831.32,-242.62"/> +</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="M534.66,-293.09C529.74,-281.77 523.08,-266.45 517.05,-252.6"/> +<polygon fill="#555555" stroke="#555555" points="519.08,-251.99 514.76,-247.33 515.23,-253.67 519.08,-251.99"/> +</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="M560.49,-294.36C578.62,-279.06 606.38,-255.63 626.38,-238.76"/> +<polygon fill="#555555" stroke="#555555" points="627.67,-240.42 630.9,-234.94 624.96,-237.21 627.67,-240.42"/> +</g> +<!-- PTR_S1->PTR_ANY --> +<g id="edge21" class="edge"> +<title>PTR_S1->PTR_ANY</title> +<path fill="none" stroke="#555555" d="M613.06,-297.17C595.19,-284.43 567.11,-264.41 543.66,-247.68"/> +<polygon fill="#555555" stroke="#555555" points="545.14,-246.16 539.04,-244.39 542.7,-249.58 545.14,-246.16"/> +</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="M648.01,-296.59C668.14,-280.76 701.78,-254.32 724.41,-236.52"/> +<polygon fill="#555555" stroke="#555555" points="725.59,-238.26 729.01,-232.91 722.99,-234.96 725.59,-238.26"/> +</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="M686.72,-297.75C654.45,-283.81 600.84,-260.66 559.66,-242.88"/> +<polygon fill="#555555" stroke="#555555" points="560.63,-241.01 554.29,-240.56 558.97,-244.86 560.63,-241.01"/> +</g> +<!-- PTR_MORE->PTR_MORE_NIL --> +<g id="edge25" class="edge"> +<title>PTR_MORE->PTR_MORE_NIL</title> +<path fill="none" stroke="#555555" d="M735.36,-294.98C756.57,-279.37 789.9,-254.84 813.23,-237.67"/> +<polygon fill="#555555" stroke="#555555" points="814.42,-239.4 818.01,-234.16 811.93,-236.02 814.42,-239.4"/> +</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="M1008.47,-376.11C993.72,-340.49 968.36,-279.23 953.91,-244.33"/> +<polygon fill="#555555" stroke="#555555" points="955.99,-243.86 951.75,-239.12 952.11,-245.47 955.99,-243.86"/> +</g> +<!-- STRUCT_S1 --> +<g id="node23" class="node"> <title>STRUCT_S1</title> -<polygon fill="none" stroke="none" points="487.38,-234.25 401.63,-234.25 401.63,-198.25 487.38,-198.25 487.38,-234.25"/> -<polygon fill="lightgreen" stroke="none" points="409.63,-205 409.63,-227.5 440.38,-227.5 440.38,-205 409.63,-205"/> -<polygon fill="none" stroke="black" points="409.63,-205 409.63,-227.5 440.38,-227.5 440.38,-205 409.63,-205"/> -<text text-anchor="start" x="412.63" y="-211.2" font-family="Times New Roman,serif" font-size="14.00">field</text> -<defs> -<linearGradient id="l_0" gradientUnits="userSpaceOnUse" x1="446.1" y1="-224.2" x2="473.67" y2="-208.29" > -<stop offset="0" style="stop-color:lightblue;stop-opacity:1.;"/> -<stop offset="1" style="stop-color:green;stop-opacity:1.;"/> -</linearGradient> -</defs> -<polygon fill="url(#l_0)" stroke="none" points="440.38,-205 440.38,-227.5 479.38,-227.5 479.38,-205 440.38,-205"/> -<polygon fill="none" stroke="black" points="440.38,-205 440.38,-227.5 479.38,-227.5 479.38,-205 440.38,-205"/> -<text text-anchor="start" x="443.38" y="-211.2" font-family="Times New Roman,serif" font-size="14.00">int/ptr</text> +<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="edge18" class="edge"> +<g id="edge37" class="edge"> <title>STRUCT_TOP->STRUCT_S1</title> -<path fill="none" stroke="black" d="M503.88,-310.12C492.57,-292.43 474.53,-264.21 461.3,-243.51"/> -<polygon fill="black" stroke="black" points="464.39,-241.85 456.06,-235.31 458.49,-245.62 464.39,-241.85"/> +<path fill="none" stroke="#555555" d="M1020,-375.71C1020,-340.38 1020,-280.29 1020,-245.36"/> +<polygon fill="#555555" stroke="#555555" points="1022.1,-245.4 1020,-239.4 1017.9,-245.4 1022.1,-245.4"/> </g> <!-- STRUCT_S2 --> -<g id="node15" class="node"> +<g id="node24" class="node"> <title>STRUCT_S2</title> -<polygon fill="none" stroke="none" points="616.38,-242.75 530.63,-242.75 530.63,-189.75 616.38,-189.75 616.38,-242.75"/> -<polygon fill="lightgreen" stroke="none" points="538.63,-216.25 538.63,-238.75 569.38,-238.75 569.38,-216.25 538.63,-216.25"/> -<polygon fill="none" stroke="black" points="538.63,-216.25 538.63,-238.75 569.38,-238.75 569.38,-216.25 538.63,-216.25"/> -<text text-anchor="start" x="541.63" y="-222.45" font-family="Times New Roman,serif" font-size="14.00">field</text> -<defs> -<linearGradient id="l_1" gradientUnits="userSpaceOnUse" x1="575.1" y1="-235.45" x2="602.67" y2="-219.54" > -<stop offset="0" style="stop-color:lightblue;stop-opacity:1.;"/> -<stop offset="1" style="stop-color:green;stop-opacity:1.;"/> -</linearGradient> -</defs> -<polygon fill="url(#l_1)" stroke="none" points="569.38,-216.25 569.38,-238.75 608.38,-238.75 608.38,-216.25 569.38,-216.25"/> -<polygon fill="none" stroke="black" points="569.38,-216.25 569.38,-238.75 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d="M1045.31,-378.1C1081.09,-341.53 1145.91,-275.3 1179.87,-240.58"/> +<polygon fill="#555555" stroke="#555555" points="1181.3,-242.13 1183.99,-236.38 1178.3,-239.19 1181.3,-242.13"/> </g> +<!-- STRUCT_TOP->MEM_TOP --> <!-- STRUCT_BOT --> -<g id="node13" class="node"> +<g id="node21" class="node"> <title>STRUCT_BOT</title> -<ellipse fill="lightgreen" stroke="black" cx="512.51" cy="-104.75" rx="44.7" ry="18"/> -<text text-anchor="start" x="487.76" y="-100.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text> -<text text-anchor="start" x="503.51" y="-100.7" font-family="Times New Roman,serif" font-size="14.00">:struct</text> +<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 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Roman,serif" font-size="14.00" fill="white">...</text> -</g> -<!-- MEM_TOP->MEM_ALIASDOTS --> -<g id="edge29" class="edge"> -<title>MEM_TOP->MEM_ALIASDOTS</title> -<path fill="none" stroke="black" d="M860.54,-309.64C867.71,-292.18 878.96,-264.82 887.35,-244.4"/> -<polygon fill="black" stroke="black" points="890.54,-245.86 891.1,-235.28 884.06,-243.2 890.54,-245.86"/> -</g> -<!-- MEM_ALIASN --> -<g id="node21" class="node"> -<title>MEM_ALIASN</title> -<ellipse fill="blue" stroke="black" cx="988.51" cy="-216.25" rx="20.13" ry="20.13"/> -<text text-anchor="middle" x="988.51" y="-211.2" font-family="Times New Roman,serif" font-size="14.00" fill="white">#n</text> -</g> -<!-- MEM_TOP->MEM_ALIASN --> -<g id="edge30" class="edge"> -<title>MEM_TOP->MEM_ALIASN</title> -<path fill="none" stroke="black" d="M872.56,-311.29C896.65,-291.76 938.11,-258.13 964.38,-236.82"/> -<polygon fill="black" stroke="black" points="966.57,-239.55 972.13,-230.53 962.16,-234.11 966.57,-239.55"/> +<path fill="none" 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1340.66,-137.66"/> +</g> +<!-- MEM_ALIAS2->MEM_ALIAS3 --> +<!-- MEM_ALIAS3->MEM_BOT --> +<g id="edge50" class="edge"> +<title>MEM_ALIAS3->MEM_BOT</title> +<path fill="none" stroke="#555555" d="M1395.25,-198.97C1386.5,-181.97 1372.98,-155.71 1363.19,-136.68"/> +<polygon fill="#555555" stroke="#555555" points="1365.07,-135.74 1360.46,-131.37 1361.34,-137.66 1365.07,-135.74"/> +</g> +<!-- MEM_ALIAS3->MEM_MORE --> +<!-- MEM_MORE->MEM_BOT --> +<g id="edge51" class="edge"> +<title>MEM_MORE->MEM_BOT</title> +<path fill="none" stroke="#555555" d="M1475.42,-202.39C1469.65,-197.74 1463.09,-192.57 1457,-187.98 1430.93,-168.37 1400.47,-146.96 1378.9,-132.06"/> +<polygon fill="#555555" stroke="#555555" points="1380.17,-130.38 1374.03,-128.71 1377.78,-133.84 1380.17,-130.38"/> </g> <!-- TUPLE1 --> -<g id="node24" class="node"> +<g id="node33" class="node"> <title>TUPLE1</title> -<polygon fill="none" stroke="none" points="1105.51,-242.75 1051.51,-242.75 1051.51,-189.75 1105.51,-189.75 1105.51,-242.75"/> -<polygon fill="pink" stroke="none" points="1059.76,-216.25 1059.76,-238.75 1097.26,-238.75 1097.26,-216.25 1059.76,-216.25"/> -<polygon fill="none" stroke="black" points="1059.76,-216.25 1059.76,-238.75 1097.26,-238.75 1097.26,-216.25 1059.76,-216.25"/> -<text text-anchor="start" x="1062.76" y="-222.45" font-family="Times New Roman,serif" font-size="14.00">Tuple</text> -<polygon fill="black" stroke="none" points="1059.76,-193.75 1059.76,-216.25 1097.26,-216.25 1097.26,-193.75 1059.76,-193.75"/> -<polygon fill="none" stroke="black" points="1059.76,-193.75 1059.76,-216.25 1097.26,-216.25 1097.26,-193.75 1059.76,-193.75"/> -<text text-anchor="start" x="1066.88" y="-199.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text> +<polygon fill="#ffc0cb" stroke="black" points="1598.88,-328.97 1543.12,-328.97 1543.12,-292.97 1598.88,-292.97 1598.88,-328.97"/> +<text text-anchor="middle" x="1571" y="-306.87" font-family="DejaVu Sans" font-size="13.00">(type)</text> </g> <!-- TUPLE_TOP->TUPLE1 --> -<g id="edge38" class="edge"> +<g id="edge54" class="edge"> <title>TUPLE_TOP->TUPLE1</title> -<path fill="none" stroke="black" d="M1119.01,-309.64C1112.37,-294.48 1102.45,-271.87 1094.1,-252.81"/> -<polygon fill="black" stroke="black" points="1097.35,-251.51 1090.13,-243.76 1090.94,-254.32 1097.35,-251.51"/> +<path fill="none" stroke="#555555" d="M1584.8,-386.65C1582.19,-372.52 1578.47,-352.37 1575.54,-336.56"/> +<polygon fill="#555555" stroke="#555555" points="1577.61,-336.2 1574.46,-330.68 1573.48,-336.96 1577.61,-336.2"/> </g> <!-- TUPLE2 --> -<g id="node25" class="node"> +<g id="node34" class="node"> <title>TUPLE2</title> -<polygon fill="none" stroke="none" points="1202.51,-254 1148.51,-254 1148.51,-178.5 1202.51,-178.5 1202.51,-254"/> -<polygon fill="pink" stroke="none" points="1156.76,-227.5 1156.76,-250 1194.26,-250 1194.26,-227.5 1156.76,-227.5"/> -<polygon fill="none" stroke="black" points="1156.76,-227.5 1156.76,-250 1194.26,-250 1194.26,-227.5 1156.76,-227.5"/> -<text text-anchor="start" x="1159.76" y="-233.7" font-family="Times New Roman,serif" font-size="14.00">Tuple</text> -<polygon fill="black" stroke="none" points="1156.76,-205 1156.76,-227.5 1194.26,-227.5 1194.26,-205 1156.76,-205"/> -<polygon fill="none" stroke="black" points="1156.76,-205 1156.76,-227.5 1194.26,-227.5 1194.26,-205 1156.76,-205"/> -<text text-anchor="start" x="1163.88" y="-211.2" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text> -<polygon fill="black" stroke="none" points="1156.76,-182.5 1156.76,-205 1194.26,-205 1194.26,-182.5 1156.76,-182.5"/> -<polygon fill="none" stroke="black" points="1156.76,-182.5 1156.76,-205 1194.26,-205 1194.26,-182.5 1156.76,-182.5"/> -<text text-anchor="start" x="1163.88" y="-188.7" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text> +<polygon fill="#ffc0cb" stroke="black" points="1709,-328.97 1615,-328.97 1615,-292.97 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y="-199.95" font-family="Times New Roman,serif" font-size="14.00" fill="white">...</text> -<polygon fill="black" stroke="none" points="1253.76,-171.25 1253.76,-193.75 1291.26,-193.75 1291.26,-171.25 1253.76,-171.25"/> -<polygon fill="none" stroke="black" points="1253.76,-171.25 1253.76,-193.75 1291.26,-193.75 1291.26,-171.25 1253.76,-171.25"/> -<text text-anchor="start" x="1260.88" y="-177.45" font-family="Times New Roman,serif" font-size="14.00" fill="white">type</text> +<polygon fill="#ffc0cb" stroke="black" points="1802.75,-328.97 1725.25,-328.97 1725.25,-292.97 1802.75,-292.97 1802.75,-328.97"/> +<text text-anchor="middle" x="1764" y="-306.87" font-family="DejaVu Sans" font-size="13.00">(type, …)</text> </g> <!-- TUPLE_TOP->TUPLEN --> -<g id="edge40" class="edge"> +<g id="edge56" class="edge"> <title>TUPLE_TOP->TUPLEN</title> -<path fill="none" stroke="black" d="M1146.81,-311.52C1169.97,-294.15 1208.28,-265.42 1236.53,-244.23"/> -<polygon fill="black" stroke="black" points="1238.58,-247.07 1244.48,-238.27 1234.38,-241.47 1238.58,-247.07"/> +<path fill="none" stroke="#555555" d="M1614.35,-390.18C1643.39,-375.01 1690.42,-350.42 1724.01,-332.87"/> +<polygon fill="#555555" stroke="#555555" points="1724.85,-334.8 1729.2,-330.16 1722.91,-331.07 1724.85,-334.8"/> </g> <!-- TUPLE_BOT --> -<g id="node23" class="node"> +<g id="node32" class="node"> <title>TUPLE_BOT</title> -<ellipse fill="pink" stroke="black" cx="1126.51" cy="-104.75" rx="42.65" ry="18"/> -<text text-anchor="start" x="1103.26" y="-100.7" font-family="Times New Roman,serif" font-weight="bold" font-size="14.00">⊥</text> -<text text-anchor="start" x="1119.01" y="-100.7" font-family="Times New Roman,serif" font-size="14.00">:tuple</text> +<ellipse fill="#ffc0cb" stroke="black" cx="1625" cy="-111.99" rx="44.7" ry="18"/> +<text text-anchor="middle" x="1625" y="-107.89" font-family="DejaVu Sans" font-size="13.00">⊥:tuple</text> </g> <!-- TUPLE_BOT->BOT --> -<g id="edge44" class="edge"> +<g 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