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=<⊤:int>, fillcolor=lightblue, shape=oval]; INT_BOT [label=<⊥: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=<⊤:flt>, fillcolor=aqua, shape=oval]; FLT_BOT [label=<⊥: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=<
tuple
type
>]; TUPLE2 [shape=plain, label=<
tuple
type
type
>]; TUPLEN [shape=plain, label=<
tuple
type
…
type
>]; {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]; }