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digraph Lattice {
rankdir=TB;
newrank=true;
// Preserve the same-rank ordering edges through cluster layout.
remincross=false;
nodesep=0.22;
ranksep=0.65;
node [shape=ellipse, style=filled, fontname="DejaVu Sans", fontsize=13];
edge [color="#555555", arrowsize=0.6];
// These arrows are lattice-order edges, not use/definition edges.
TOP [label="⊤", fillcolor=black, fontcolor=white];
BOT [label="⊥", fillcolor=black, fontcolor=white];
subgraph cluster_control {
label="Control"; fontname="Arial"; color="#cccccc";
node [fillcolor="#ffff00"];
XCTRL [label="⊤:ctrl"];
CTRL [label="⊥:ctrl"];
XCTRL -> CTRL;
}
subgraph cluster_integer {
label="Integer ranges (schematic)"; fontname="Arial"; color="#cccccc";
INT_TOP [label=<<B>⊤</B >:int>, fillcolor=lightblue, shape=oval];
INT_BOT [label=<<B>⊥</B>:int>, fillcolor=lightblue, shape=oval];
INT_HI [label="max < min" , fillcolor=lightblue, shape=oval];
INT_XBOOL [label="1...0", fillcolor=lightblue, shape=oval];
INT_CON [label="constants", fillcolor=lightblue, shape=oval];
INT_CON0 [label="0", fillcolor=lightblue];
INT_CON1 [label="1", fillcolor=lightblue];
INT_BOOL [label="0...1", fillcolor=lightblue,shape=oval];
INT_LO [label="max > min" , fillcolor=lightblue, shape=oval];
INT_TOP -> INT_HI;
INT_HI -> INT_XBOOL;
INT_XBOOL -> INT_CON0;
INT_XBOOL -> INT_CON1;
INT_HI -> INT_CON;
INT_CON0 -> INT_BOOL;
INT_CON1 -> INT_BOOL;
INT_BOOL -> INT_LO;
INT_CON -> INT_LO;
INT_LO -> INT_BOT;
INT_CON0 -> INT_CON1 -> INT_CON [style=invis];
{rank=same; INT_CON0; INT_CON1; INT_CON;}
}
subgraph cluster_float {
label="Float"; fontname="Arial"; color="#cccccc";
FLT_TOP [label=<<B>⊤</B >:flt>, fillcolor=aqua, shape=oval];
FLT_BOT [label=<<B>⊥</B>:flt>, fillcolor=aqua, shape=oval];
FLT_CON64 [label="64b consts\n[excludes\n32b consts]" , fillcolor=aqua, shape=oval];
FLT_CON32 [label="32b consts", fillcolor=aqua, shape=oval];
FLT_CONPI [label="3.14159...", fillcolor=aqua, shape=oval];
FLT_X32 [label="~f32", fillcolor=aqua];
FLT_CON0 [label="0." , fillcolor=aqua];
FLT_32 [label="f32" , fillcolor=aqua];
FLT_TOP -> FLT_CON64
FLT_TOP -> FLT_CONPI
FLT_CON64 -> FLT_BOT
FLT_CONPI -> FLT_BOT
FLT_TOP -> FLT_X32;
FLT_X32 -> FLT_CON0;
FLT_X32 -> FLT_CON32;
FLT_CON0 -> FLT_32;
FLT_CON32 -> FLT_32;
FLT_32 -> FLT_BOT
FLT_CON0 -> FLT_CON32 -> FLT_CONPI -> FLT_CON64 [style=invis];
{rank=same; FLT_CON0; FLT_CON32; FLT_CONPI; FLT_CON64;}
}
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"];
// Each black element stands for a recursively nested type lattice.
TUPLE1 [shape=plain, label=<
<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
<TR><TD BGCOLOR="#ffc0cb">tuple</TD></TR>
<TR><TD BGCOLOR="black"><FONT COLOR="white">type</FONT></TD></TR>
</TABLE>
>];
TUPLE2 [shape=plain, label=<
<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
<TR><TD BGCOLOR="#ffc0cb">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=plain, label=<
<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
<TR><TD BGCOLOR="#ffc0cb">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>
>];
{rank=same; TUPLE1; TUPLE2; TUPLEN;}
TUPLE1 -> TUPLE2 -> TUPLEN [style=invis];
TUPLE_TOP -> {TUPLE1 TUPLE2 TUPLEN};
{TUPLE1 TUPLE2 TUPLEN} -> TUPLE_BOT;
}
TOP -> {XCTRL INT_TOP FLT_TOP PTR_TOP STRUCT_TOP MEM_TOP TUPLE_TOP};
{CTRL INT_BOT FLT_BOT PTR_BOT STRUCT_BOT MEM_BOT TUPLE_BOT} -> BOT;
{rank=same; XCTRL; INT_TOP; FLT_TOP; PTR_TOP; STRUCT_TOP; MEM_TOP; TUPLE_TOP;}
{rank=same; CTRL; INT_BOT; FLT_BOT; PTR_BOT; STRUCT_BOT; MEM_BOT; TUPLE_BOT;}
XCTRL -> INT_TOP -> FLT_TOP -> PTR_TOP -> STRUCT_TOP -> MEM_TOP -> TUPLE_TOP [style=invis];
}
|
