From 001a42d0e833dc496d8c0d8dcddd34fdf7dcd755 Mon Sep 17 00:00:00 2001 From: Cliff Click Date: Sun, 30 Jun 2024 01:58:08 +0100 Subject: Chapter 11: Splitting Memory MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Hsiang-Ying Fu <66062782+fuhsnn@users.noreply.github.com> Co-authored-by: Dibyendu Majumdar Co-authored-by: Thalia Archibald Co-authored-by: Tamás Hadházy <85063808+Hels15@users.noreply.github.com> Co-authored-by: tannal Co-authored-by: hadha Co-authored-by: fuhsnn <66062782+fuhsnn@users.noreply.github.com> Co-authored-by: Symious <14933944+symious@users.noreply.github.com> Co-authored-by: RobertObkircher Co-authored-by: Robert Obkircher Co-authored-by: Claude Opus 5 --- docs/chapter11/10-grammar.md | 125 +++++++ docs/chapter11/Makefile | 1 + docs/chapter11/README.md | 268 ++++++++++++++ docs/chapter11/example1.gv | 20 ++ docs/chapter11/example1.json | 31 ++ docs/chapter11/example1.svg | 155 ++++++++ docs/chapter11/example2a.gv | 17 + docs/chapter11/example2a.json | 20 ++ docs/chapter11/example2a.svg | 103 ++++++ docs/chapter11/example2b-final.json | 251 +++++++++++++ docs/chapter11/example2b-final.svg | 110 ++++++ docs/chapter11/example2b-merged.json | 339 ++++++++++++++++++ docs/chapter11/example2b-merged.svg | 130 +++++++ docs/chapter11/example2b-split-y.json | 486 +++++++++++++++++++++++++ docs/chapter11/example2b-split-y.svg | 157 +++++++++ docs/chapter11/example2b.gv | 19 + docs/chapter11/example2b.json | 30 ++ docs/chapter11/example2b.svg | 150 ++++++++ docs/chapter11/example2c.gv | 15 + docs/chapter11/example2c.json | 23 ++ docs/chapter11/example2c.svg | 121 +++++++ docs/chapter11/lattice.gv | 133 +++++++ docs/chapter11/lattice.svg | 644 ++++++++++++++++++++++++++++++++++ 23 files changed, 3348 insertions(+) create mode 100644 docs/chapter11/10-grammar.md create mode 100644 docs/chapter11/Makefile create mode 100644 docs/chapter11/README.md create mode 100644 docs/chapter11/example1.gv create mode 100644 docs/chapter11/example1.json create mode 100644 docs/chapter11/example1.svg create mode 100644 docs/chapter11/example2a.gv create mode 100644 docs/chapter11/example2a.json create mode 100644 docs/chapter11/example2a.svg create mode 100644 docs/chapter11/example2b-final.json create mode 100644 docs/chapter11/example2b-final.svg create mode 100644 docs/chapter11/example2b-merged.json create mode 100644 docs/chapter11/example2b-merged.svg create mode 100644 docs/chapter11/example2b-split-y.json create mode 100644 docs/chapter11/example2b-split-y.svg create mode 100644 docs/chapter11/example2b.gv create mode 100644 docs/chapter11/example2b.json create mode 100644 docs/chapter11/example2b.svg create mode 100644 docs/chapter11/example2c.gv create mode 100644 docs/chapter11/example2c.json create mode 100644 docs/chapter11/example2c.svg create mode 100644 docs/chapter11/lattice.gv create mode 100644 docs/chapter11/lattice.svg (limited to 'docs/chapter11') diff --git a/docs/chapter11/10-grammar.md b/docs/chapter11/10-grammar.md new file mode 100644 index 00000000..5a3f3778 --- /dev/null +++ b/docs/chapter11/10-grammar.md @@ -0,0 +1,125 @@ +# Grammar for Chapter 11 + +```antlrv4 +grammar SimpleLanguage; + +program + : statement+ EOF + ; + +statement + : returnStatement + | structDeclaration + | declStatement + | blockStatment + | expressionStatement + | ifStatement + | whileStatement + | breakStatement + | continueStatment + ; + +field + : 'int' IDENTIFIER ';' + ; + +fields + : field+ + ; + +structDeclaration + : 'struct' IDENTIFIER '{' fields '}' + ; + +whileStatement + : 'while' '(' expression ')' statement + ; + +breakStatement + : 'break' ';' + ; + +continueStatement + : 'continue' ';' + ; + +ifStatement + : 'if' '(' expression ')' statement ('else' statement)? + ; + + +expressionStatement + : IDENTIFIER '=' expression ';' + | fieldExpression '=' expression ';' + ; + +blockStatement + : '{' statement+ '}' + ; + +structName + : IDENTIFIER + ; + +declStatement + : 'int' IDENTIFIER '=' expression ';' + | structName ('?')? IDENTIFIER '=' expression ';' + ; + +returnStatement + : 'return' expression ';' + ; + +expression + : comparisonExpression + ; + +comparisonExpression + : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)* + ; + +additiveExpression + : multiplicativeExpression (('+' | '-') multiplicativeExpression)* + ; + +multiplicativeExpression + : unaryExpression (('*' | '/') unaryExpression)* + ; + +unaryExpression + : ('-') unaryExpression + | '!' unaryExpression + | primaryExpression + ; + +newExpression + : 'new' IDENTIFIER + ; + +fieldExpression + : primaryExpresson '.' IDENTIFIER + ; + +primaryExpression + : IDENTIFIER + | INTEGER_LITERAL + | 'true' + | 'false' + | 'null' + | newExpression + | '(' expression ')' + | fieldExpression + ; + +INTEGER_LITERAL + : [1-9][0-9]* + | [0] + ; + +IDENTIFIER + : NON_DIGIT (NON_DIGIT | DIGIT)* + ; + +NON_DIGIT: [a-zA-Z_]; +DEC_DIGIT: [0-9]; +``` diff --git a/docs/chapter11/Makefile b/docs/chapter11/Makefile new file mode 100644 index 00000000..6fa0f057 --- /dev/null +++ b/docs/chapter11/Makefile @@ -0,0 +1 @@ +include ../../graph/docs.mk diff --git a/docs/chapter11/README.md b/docs/chapter11/README.md new file mode 100644 index 00000000..22be3ebf --- /dev/null +++ b/docs/chapter11/README.md @@ -0,0 +1,268 @@ +# Chapter 11: Splitting Memory + +[Previous: Chapter 10](../chapter10/README.md) | +[Next: Chapter 12](../chapter12/README.md) + +Chapter 10 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](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. + +![Independent field dependencies](example1.svg) + +The graph shows the split chains before the final Load folds. Its memory input +goes straight to the Store of 42, bypassing the loop's `y` chain. As in +Chapter 10, small, detached True/False projections show the source branches +gating Loads and Stores. Other control-flow context, including Loops and their +Phi bindings, is omitted. The graph shows dependencies, not execution order. + +## 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). You still need to check for pointer identity. + +The parser assigns field identities at struct declarations, beginning at alias#2. + +We do not allocate a Start projection, scope binding, or loop Phi for every +declared field or alias. Start supplies one memory value, Scope holds one +`$mem` binding, and Return consumes all of memory: `{ctrl, $mem, result}`. As +with Start's outputs, control is in slot 0 and memory in slot 1. 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) +``` + +MemMerges have a default memory in slot 1, and precise aliases in other slots +if they differ from the default. Loads, Stores and MemPhis select their +precise input from any incoming MemMerge, using a precise alias input if +possible. + +The explicit aliases override the default: the alias slices are disjoint, +and their union covers all memory. Flattening stacked MemMerges preserves +entries that the outer MemMerge has not replaced. + +The graph below shows `p.x = arg; p.y = 42; return p;` after redundant +initialization stores have been removed. MemMerge takes the default memory +in slot 1 and the `x` and `y` overrides in slots 2 and 3. + +![An aggregate preserves both updates](example2a.svg) + + +## Splitting a memory Phi + +The Parser initially creates a BulkMemPhi wherever the ordinary SSA algorithm needs +to merge memory. It starts by covering all aliases and an empty exclusion set +while the merge point is finalized. Later, peeps will split out precise memory +slices from the bulk memory, lazily on demand. + +Precise single aliases can be split out from the bulk by this transformation: + +```text +BulkPhi(R, left, right) + becomes +MemMerge( + default = BulkPhi_except{x}(R, left, right), + x = MemPhi_x(R, slice(left,x), slice(right,x))) +``` + +"A BulkPhi becomes a Merge of a BulkPhi (minus the alias) and MemPhi (of the alias)". + +The new precise Phi and the remaining bulk Phi share a Region (omitted from the +illustrations) 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 (and peephole optimizations tidy up +the stacked splits). + +Here the two branches store 3 or 4 into `p.x`, then return `p`. The graph shows +the partition immediately after extracting `x`, before further simplification +of the bulk Phi and its incoming aggregates. + +```java +struct Point { int x; int y; } +Point p = new Point; +if (arg) p.x = 3; +else p.x = 4; +return p; +``` + +![Precise and bulk Phis share a control merge](example2b.svg) + +Continuing from this graph, here is one order in which the peepholes can fire: + +**Flatten the incoming MemMerges, then split `y`.** MemMerges #17 and #18 +inherit the `y` slice from #9, but their own `x` overrides win. Both now have +Start's memory as their default, and #9 becomes unused. BulkMemPhi #21 excludes +`x`, but still covers `y`, so it cannot simply bypass these MemMerges. It +extracts MemPhi #24 for `y` and creates BulkMemPhi #25, excluding both fields. +The extra MemMerge #26 combines these slices. + +![After flattening the incoming aggregates and extracting y](example2b-split-y.svg) + +**Fold the unchanged memory.** Both inputs of MemPhi #24 are the same +initializing Store #8, so it becomes that Store. BulkMemPhi #25 can now look +through #17 and #18: their explicit aliases are all excluded from its domain. +Both remaining inputs become Start's memory, so this bulk Phi also folds. +Flattening the outgoing aggregates leaves MemMerge #22 with default memory +from Start, `x` from MemPhi #20, and `y` from Store #8. + +![Only the x memory Phi still needs the branch merge](example2b-merged.svg) + +**Factor the Stores, then remove the overwritten initialization.** With the +bulk Phi and the incoming aggregates gone, Stores #14 and #16 are used only +by MemPhi #20. They store to the same pointer and alias, and share the same +incoming memory. `PhiNode` can pull the Store below the merge: + +```text +MemPhi_x(Store_x(mem, p, 3), Store_x(mem, p, 4)) + becomes +Store_x(mem, p, Phi(3, 4)) +``` + +In general, Phi refactoring can combine Loads or Stores as in Chapter 10 (pushing +up or pulling down). The Phi new memory operands can use precise MemPhis for +the alias. This peep requires precise aliases, and is otherwise blocked by +BulkMems - and thus is a trigger for splitting a BulkMem. + + +Continuing with the example, the new value Phi #28 chooses 3 on the true arm +and 4 on the false arm. Store +#27 replaces both branch Stores and their memory Phi. Now the initial +`p.x = 0` Store #7 has only that one Store as a user, so store-after-store +elimination bypasses it. The `p.y = 0` Store #8 remains: we return the object, +and its `y` field still needs initialization. + +![Final graph: one x Store of a value Phi, and the y initialization](example2b-final.svg) + +Thus the final graph has two Stores, one ordinary value Phi, and one MemMerge; +neither a MemPhi nor a BulkMemPhi remains. Other worklists order can, for +instance, bypass the original incoming MemMerges before flattening them, +avoiding the temporary `y` split. + +This memory splitting transform is invasive, and is disallowed from being +called recursively; you can end up splitting around a loop (which is good) but +then trying to split a mid-split loop head (which is bad). The new nodes from +the split are put on the worklist and visited after the current split +completes - safely allowing memory to be completely sliced around loops. + +Since bulk Phis merge a bunch of aliases, they have to take care when +peepholing vs MemMerges: there cannot be any overlap between the MemMerge +precise merges and the bulk Phi. + +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 - job for +`addDep()`. Selecting a slice from a MemMerge can expose a new bulk-Phi +user; that selected definition must be queued too. In short, any time we're +working with MemMerge, MemPhi or BulkMemPhi we can expect some non-local +dependencies. + +Memory splitting can increase node count - but Phis (Mem, Bulk or otherwise) +make no code. Progress comes from extracting an alias from a bulk Phi and +removing some Loads and Stores, rather than from requiring every rewrite +to shrink the graph. In other words, the total Load/Store count is going down +even if the MemPhi count is going up. + + +## Types + +The type lattice retains Chapter 10's six domains, colors, and notation: +`⊤` means top, `⊥` means bottom, and a suffix names the domain. The other five +domains are unchanged; however memory now adds a flat element `MEM#N` for each precise +alias between memory top (`TypeMem.TOP`) and memory bottom (`TypeMem.BOT`). + +![The type domains, including precise memory aliases](lattice.svg) + +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. (And the ellipsis stands +for more parallel aliases, not a type representing a set of aliases). + + +## Evaluation and ordering + +MemMerge is a dependency node and not a clobber; it emits no code. Its +evaluator result is a memory token, while Store actually mutates the object's +fields. The scheduler must distinguish merging memory from overwriting memory. +Stores in different alias classes do not impose load/store anti-dependencies, +but Loads in the same class require anti-dependencies. + +In `int old = p.x; p.x = arg; p.y = arg; return old;`, the Load must precede +the later `x` Store; the `y` Store has an independent memory chain. The graph +retains the Load to show this scheduling requirement before local folding. + +![Ordering applies within the affected alias](example2c.svg) + +There are a lot of tests in this chapter, to 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 11 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) and will allow +more incomplete types, module aliases, seperate compilation and a host of other +benefits. + +Chapters 12-24 use this representation. Chapter 13 adds global code motion +and load/store anti-dependencies. Chapter 15 adds allocation with partial memory and typed +alias contents. Chapter 16 extends initialization to constructor values, and +Chapter 18 carries whole memory across function calls. + +## 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="chapter10 chapter11" +``` + +Next, [Chapter 12](../chapter12/README.md) adds reference fields and recursive +structs while retaining this memory representation. diff --git a/docs/chapter11/example1.gv b/docs/chapter11/example1.gv new file mode 100644 index 00000000..5e059d77 --- /dev/null +++ b/docs/chapter11/example1.gv @@ -0,0 +1,20 @@ +digraph Memory { + // IR styles match graph/web/render.js; arrows are use -> definition. + graph [bgcolor="#fafbfc" fontname="Helvetica" nodesep=0.35 ranksep=0.55 splines=ortho]; + node [fontname="Helvetica" fontsize=12 color="#758191" fontcolor="#152330" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + edge [fontname="Helvetica" fontsize=9 color="#536477" fontcolor="#364352" arrowsize=0.7 penwidth=1.5]; + + rankdir=BT; + + M [label="Initial memory" shape=octagon style="filled" fillcolor="#dcecff"]; + X [label="Store x = 42" shape=octagon style="filled" fillcolor="#dcecff"]; + Y [label="Loop: Store y" shape=octagon style="filled" fillcolor="#dcecff"]; + L [label="Load x (42)" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + L -> X -> M [color="#2867b2"]; Y -> M [color="#2867b2"]; + MemMerge -> X [color="#2867b2"]; MemMerge -> Y [color="#2867b2"]; + Return -> MemMerge [color="#2867b2"]; Return -> L; + { rank=same; MemMerge -> L [style=invis]; } + Y -> X [style=invis]; // Layout only: keep the stores in code order. + Return [shape=box style="filled" fillcolor="#fff1c4"]; + MemMerge [shape=octagon style="filled" fillcolor="#dcecff"]; +} diff --git a/docs/chapter11/example1.json b/docs/chapter11/example1.json new file mode 100644 index 00000000..c0c28450 --- /dev/null +++ b/docs/chapter11/example1.json @@ -0,0 +1,31 @@ +{ + "ver": 1, + "comp": "chapter11/docs/example1.svg", + "step": 1, + "roots": [24], + "scope": 0, + "nodes": [ + {"id": 1, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null}, + {"id": 3, 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1, "def": 22, "role": "MEM", "label": null}, {"idx": 2, "def": 23, "role": "DATA", "label": null}], "proj": null} + ], + "groups": [ + ] +} diff --git a/docs/chapter11/example1.svg b/docs/chapter11/example1.svg new file mode 100644 index 00000000..46faf818 --- /dev/null +++ b/docs/chapter11/example1.svg @@ -0,0 +1,155 @@ +#6[0] → #1 · ASSOC#7[0] → #1 · ASSOC#8[1] → #3 · MEM#8[2] → #5 · DATA#8[3] → #7 · DATA#9[1] → #3 · MEM#9[2] → #5 · DATA#9[3] → #6 · DATA#11[1] → #9 · MEM#11[2] → #19 · MEM#12[1] → #4 · DATA#12[2] → #21 · DATA#17[0] → #15 · CTRL#17[1] → #11 · MEM#17[2] → #5 · DATA#18[1] → #17 · DATA#18[2] → #12 · DATA#19[0] → #15 · CTRL#19[1] → #11 · MEM#19[2] → #5 · DATA#19[3] → #18 · DATA#20[0] → #1 · ASSOC#21[1] → #12 · DATA#21[2] → #20 · DATA#22[1] → #3 · MEM#22[2] → #8 · MEM#22[3] → #11 · MEM#23[0] → #16 · CTRL#23[1] → #8 · MEM#23[2] → #5 · DATA#24[1] → #22 · MEM#24[2] → #23 · DATAStart  #1#1 Start +Type not computed + +$mem  #3/1#3 $mem +Projection 1 of #1 +Type not computed + +[0] → #1 MEMarg  #4/2#4 arg +Projection 2 of #1 +Type not computed + +[0] → #1 DATAnew Point  #5#5 new Point +Type not computed + +[0] → — CTRL0#0  #6#6 #0 +Type not computed + +[0] → #1 ASSOC0#42  #7#7 #42 +Type not computed + +[0] → #1 ASSOC0Store p.x  #8MEM#2#8 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #7 DATA0123Store p.y  #9MEM#3#9 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123MemPhi y  #11MEM#3#11 MemPhi y +MEM#3 + +[0] → — ASSOC +[1] → #9 MEM +[2] → #19 MEM012Phi arg  #12#12 Phi arg +Type not computed + +[0] → — ASSOC +[1] → #4 DATA +[2] → #21 DATA012True  #15/0#15 True +Projection 0 of #0 +Type not computed + +False  #16/1#16 False +Projection 1 of #0 +Type not computed + +Load p.y  #17#17 Load p.y +Type not computed + +[0] → #15 CTRL +[1] → #11 MEM +[2] → #5 DATA +[3] → — DATA0123+  #18#18 + +Type not computed + +[0] → — CTRL +[1] → #17 DATA +[2] → #12 DATA012Store p.y  #19MEM#3#19 Store p.y +MEM#3 + +[0] → #15 CTRL +[1] → #11 MEM +[2] → #5 DATA +[3] → #18 DATA0123#1  #20#20 #1 +Type not computed + +[0] → #1 ASSOC0-  #21#21 - +Type not computed + +[0] → — CTRL +[1] → #12 DATA +[2] → #20 DATA012MemMerge  #22#22 MemMerge +Type not computed + +[0] → — CTRL +[1] → #3 MEM +[2] → #8 MEM +[3] → #11 MEM0123Load p.x  #23#23 Load p.x +Type not computed + +[0] → #16 CTRL +[1] → #8 MEM +[2] → #5 DATA +[3] → — DATA0123Return  #24#24 Return +Type not computed + +[0] → — CTRL +[1] → #22 MEM +[2] → #23 DATA012 diff --git a/docs/chapter11/example2a.gv b/docs/chapter11/example2a.gv new file mode 100644 index 00000000..187e63b9 --- /dev/null +++ b/docs/chapter11/example2a.gv @@ -0,0 +1,17 @@ +digraph Memory { + // IR styles match graph/web/render.js; arrows are use -> definition. + graph [bgcolor="#fafbfc" fontname="Helvetica" nodesep=0.35 ranksep=0.55 splines=ortho]; + node [fontname="Helvetica" fontsize=12 color="#758191" fontcolor="#152330" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + edge [fontname="Helvetica" fontsize=9 color="#536477" fontcolor="#364352" arrowsize=0.7 penwidth=1.5]; + + rankdir=RL; + + M [label="Default memory" shape=octagon style="filled" fillcolor="#dcecff"]; + X [label="Store x" shape=octagon style="filled" fillcolor="#dcecff"]; + Y [label="Store y" shape=octagon style="filled" fillcolor="#dcecff"]; + X -> M [color="#2867b2"]; Y -> M [color="#2867b2"]; + MemMerge -> M [xlabel="default",color="#2867b2"]; MemMerge -> X [xlabel="x",color="#2867b2"]; + MemMerge -> Y [xlabel="y",color="#2867b2"]; Return -> MemMerge [color="#2867b2"]; + Return [shape=box style="filled" fillcolor="#fff1c4"]; + MemMerge [shape=octagon style="filled" fillcolor="#dcecff"]; +} diff --git a/docs/chapter11/example2a.json b/docs/chapter11/example2a.json new file mode 100644 index 00000000..b9e84d5a --- /dev/null +++ b/docs/chapter11/example2a.json @@ -0,0 +1,20 @@ +{ + "ver": 1, + "comp": "chapter11/docs/example2a.svg", + "step": 1, + "roots": [11], + "scope": 0, + "nodes": [ + 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DATA#16[3] → #15 · DATA#20[1] → #14 · MEM#20[2] → #16 · MEM#22[1] → #3 · MEM#22[2] → #20 · MEM#22[3] → #8 · MEM#23[1] → #22 · MEM#23[2] → #5 · DATAStart  #1#1 Start +Type not computed + +$mem  #3/1#3 $mem +Projection 1 of #1 +Type not computed + +[0] → #1 MEMnew Point  #5#5 new Point +Type not computed + +[0] → — CTRL0#0  #6#6 #0 +Type not computed + +[0] → #1 ASSOC0Store p.x  #7MEM#2#7 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123Store p.y  #8MEM#3#8 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123True  #11/0#11 True +Projection 0 of #0 +Type not computed + +False  #12/1#12 False +Projection 1 of #0 +Type not computed + +#3  #13#13 #3 +Type not computed + +[0] → #1 ASSOC0Store p.x  #14MEM#2#14 Store p.x +MEM#2 + +[0] → #11 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #13 DATA0123#4  #15#15 #4 +Type not computed + +[0] → #1 ASSOC0Store p.x  #16MEM#2#16 Store p.x +MEM#2 + +[0] → #12 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → 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null + }, + { + "idx": 3, + "def": 24, + "role": "MEM", + "label": null + } + ], + "proj": null + } + ], + "groups": [] +} diff --git a/docs/chapter11/example2b-split-y.svg b/docs/chapter11/example2b-split-y.svg new file mode 100644 index 00000000..f4d4b9b6 --- /dev/null +++ b/docs/chapter11/example2b-split-y.svg @@ -0,0 +1,157 @@ +#6[0] → #1 · ASSOC#7[1] → #3 · MEM#7[2] → #5 · DATA#7[3] → #6 · DATA#8[1] → #3 · MEM#8[2] → #5 · DATA#8[3] → #6 · DATA#13[0] → #1 · ASSOC#14[0] → #11 · CTRL#14[1] → #7 · MEM#14[2] → #5 · DATA#14[3] → #13 · DATA#15[0] → #1 · ASSOC#16[0] → #12 · CTRL#16[1] → #7 · MEM#16[2] → #5 · DATA#16[3] → #15 · DATA#17[1] → #3 · MEM#17[2] → #14 · MEM#17[3] → #8 · MEM#18[1] → #3 · MEM#18[2] → #16 · MEM#18[3] → #8 · MEM#20[1] → #14 · MEM#20[2] → #16 · MEM#22[1] → #26 · MEM#22[2] → #20 · MEM#23[1] → #22 · MEM#23[2] → #5 · DATA#24[1] → #8 · MEM#24[2] → #8 · MEM#25[1] → #17 · MEM#25[2] → #18 · MEM#26[1] → #25 · MEM#26[2] → #20 · MEM#26[3] → #24 · MEMStart  #1#1 Start +Type not computed + +$mem  #3/1#3 $mem +Projection 1 of #1 +Type not computed + +[0] → #1 MEMnew Point  #5#5 new Point +Type not computed + +[0] → — CTRL0#0  #6#6 #0 +Type not computed + +[0] → #1 ASSOC0Store p.x  #7MEM#2#7 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123Store p.y  #8MEM#3#8 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123True  #11/0#11 True +Projection 0 of #0 +Type not computed + +False  #12/1#12 False +Projection 1 of #0 +Type not computed + +#3  #13#13 #3 +Type not computed + +[0] → #1 ASSOC0Store p.x  #14MEM#2#14 Store p.x +MEM#2 + +[0] → #11 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #13 DATA0123#4  #15#15 #4 +Type not computed + +[0] → #1 ASSOC0Store p.x  #16MEM#2#16 Store p.x +MEM#2 + +[0] → #12 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #15 DATA0123MemMerge  #17#17 MemMerge +Type not computed + +[0] → — CTRL +[1] → #3 MEM +[2] → #14 MEM +[3] → #8 MEM0123MemMerge  #18#18 MemMerge +Type not computed + +[0] → — CTRL +[1] → #3 MEM +[2] → #16 MEM +[3] → #8 MEM0123MemPhi x  #20MEM#2#20 MemPhi x +MEM#2 + +[0] → — ASSOC +[1] → #14 MEM +[2] → #16 MEM012MemMerge  #22#22 MemMerge +Type not computed + +[0] → — CTRL +[1] → #26 MEM +[2] → #20 MEM012Return  #23#23 Return +Type not computed + +[0] → — CTRL +[1] → #22 MEM +[2] → #5 DATA012MemPhi y  #24MEM#3#24 MemPhi y +MEM#3 + +[0] → — ASSOC +[1] → #8 MEM +[2] → #8 MEM012BulkMemPhi except x,y  #25#25 BulkMemPhi except x,y +Type not computed + +[0] → — ASSOC +[1] → #17 MEM +[2] → #18 MEM012MemMerge  #26#26 MemMerge +Type not computed + +[0] → — CTRL +[1] → #25 MEM +[2] → #20 MEM +[3] → #24 MEM0123 diff --git a/docs/chapter11/example2b.gv b/docs/chapter11/example2b.gv new file mode 100644 index 00000000..39b87a6a --- /dev/null +++ b/docs/chapter11/example2b.gv @@ -0,0 +1,19 @@ +digraph Memory { + // IR styles match graph/web/render.js; arrows are use -> definition. + graph [bgcolor="#fafbfc" fontname="Helvetica" nodesep=0.35 ranksep=0.55 splines=ortho]; + node [fontname="Helvetica" fontsize=12 color="#758191" fontcolor="#152330" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + edge [fontname="Helvetica" fontsize=9 color="#536477" fontcolor="#364352" arrowsize=0.7 penwidth=1.5]; + + rankdir=RL; + + P [label="MemPhi(x)" shape=hexagon style="filled" fillcolor="#f5e4fa"]; + B [label="BulkMemPhi(All except x)" shape=hexagon style="filled" fillcolor="#f5e4fa"]; + P -> Left [xlabel="slice x",color="#2867b2"]; P -> Right [xlabel="slice x",color="#2867b2"]; + B -> Left [color="#2867b2"]; B -> Right [color="#2867b2"]; + P -> Region [style=dashed,color="#9396a3"]; B -> Region [style=dashed,color="#9396a3"]; + MemMerge -> P [xlabel="x",color="#2867b2"]; MemMerge -> B [xlabel="default",color="#2867b2"]; + MemMerge [shape=octagon style="filled" fillcolor="#dcecff"]; + Left [shape=octagon style="filled" fillcolor="#dcecff"]; + Right [shape=octagon style="filled" fillcolor="#dcecff"]; + Region [shape=trapezium style="filled" fillcolor="#fff1c4"]; +} diff --git a/docs/chapter11/example2b.json b/docs/chapter11/example2b.json new file mode 100644 index 00000000..702773ea --- /dev/null +++ b/docs/chapter11/example2b.json @@ -0,0 +1,30 @@ +{ + "ver": 1, + "comp": "chapter11/docs/example2b.svg", + "step": 1, + "roots": [23], + "scope": 0, + "nodes": [ + {"id": 1, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null}, + {"id": 3, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 1, "role": "MEM", "label": null}], "proj": {"par": 1, "idx": 1}}, + {"id": 5, "label": "new Point", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null}, + {"id": 6, "label": "#0", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 1, "role": "ASSOC", "label": null}], "proj": null}, + {"id": 7, "label": "Store p.x", "type": "MEM#2", "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 3, "role": "MEM", "label": null}, {"idx": 2, "def": 5, "role": "DATA", "label": null}, {"idx": 3, "def": 6, "role": "DATA", "label": null}], "proj": null}, + {"id": 8, "label": "Store p.y", "type": "MEM#3", "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 3, "role": "MEM", "label": null}, {"idx": 2, "def": 5, "role": "DATA", "label": null}, {"idx": 3, "def": 6, "role": "DATA", "label": null}], "proj": null}, + {"id": 9, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 3, "role": "MEM", "label": null}, {"idx": 2, "def": 7, "role": "MEM", "label": null}, {"idx": 3, "def": 8, "role": "MEM", "label": null}], "proj": null}, + {"id": 11, "label": "True", "type": null, "kind": "CTRL", "edges": [], "proj": {"par": 0, "idx": 0}}, + {"id": 12, "label": "False", "type": null, "kind": "CTRL", "edges": [], "proj": {"par": 0, "idx": 1}}, + {"id": 13, "label": "#3", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 1, "role": "ASSOC", "label": null}], "proj": null}, + {"id": 14, "label": "Store p.x", "type": "MEM#2", "kind": "MEM", "edges": [{"idx": 0, "def": 11, "role": "CTRL", "label": null}, {"idx": 1, "def": 7, "role": "MEM", "label": null}, {"idx": 2, "def": 5, "role": "DATA", "label": null}, {"idx": 3, "def": 13, "role": "DATA", "label": null}], "proj": null}, + {"id": 15, "label": "#4", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 1, "role": "ASSOC", "label": null}], "proj": null}, + {"id": 16, "label": "Store p.x", "type": "MEM#2", "kind": "MEM", "edges": [{"idx": 0, "def": 12, "role": "CTRL", "label": null}, {"idx": 1, "def": 7, "role": "MEM", "label": null}, {"idx": 2, "def": 5, "role": "DATA", "label": null}, {"idx": 3, "def": 15, "role": "DATA", "label": null}], "proj": null}, + {"id": 17, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 9, "role": "MEM", "label": null}, {"idx": 2, "def": 14, "role": "MEM", "label": null}], "proj": null}, + {"id": 18, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 9, "role": "MEM", "label": null}, {"idx": 2, "def": 16, "role": "MEM", "label": null}], "proj": null}, + {"id": 20, "label": "MemPhi x", "type": "MEM#2", "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 16, "role": "MEM", "label": null}], "proj": null}, + {"id": 21, "label": "BulkMemPhi except x", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 17, "role": "MEM", "label": null}, {"idx": 2, "def": 18, "role": "MEM", "label": null}], "proj": null}, + {"id": 22, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 21, "role": "MEM", "label": null}, {"idx": 2, "def": 20, "role": "MEM", "label": null}], "proj": null}, + {"id": 23, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 22, "role": "MEM", "label": null}, {"idx": 2, "def": 5, "role": "DATA", "label": null}], "proj": null} + ], + "groups": [ + ] +} diff --git a/docs/chapter11/example2b.svg b/docs/chapter11/example2b.svg new file mode 100644 index 00000000..54ddad9d --- /dev/null +++ b/docs/chapter11/example2b.svg @@ -0,0 +1,150 @@ +#6[0] → #1 · ASSOC#7[1] → #3 · MEM#7[2] → #5 · DATA#7[3] → #6 · DATA#8[1] → #3 · MEM#8[2] → #5 · DATA#8[3] → #6 · DATA#9[1] → #3 · MEM#9[2] → #7 · MEM#9[3] → #8 · MEM#13[0] → #1 · ASSOC#14[0] → #11 · CTRL#14[1] → #7 · MEM#14[2] → #5 · DATA#14[3] → #13 · DATA#15[0] → #1 · ASSOC#16[0] → #12 · CTRL#16[1] → #7 · MEM#16[2] → #5 · DATA#16[3] → #15 · DATA#17[1] → #9 · MEM#17[2] → #14 · MEM#18[1] → #9 · MEM#18[2] → #16 · MEM#20[1] → #14 · MEM#20[2] → #16 · MEM#21[1] → #17 · MEM#21[2] → #18 · MEM#22[1] → #21 · MEM#22[2] → #20 · MEM#23[1] → #22 · MEM#23[2] → #5 · DATAStart  #1#1 Start +Type not computed + +$mem  #3/1#3 $mem +Projection 1 of #1 +Type not computed + +[0] → #1 MEMnew Point  #5#5 new Point +Type not computed + +[0] → — CTRL0#0  #6#6 #0 +Type not computed + +[0] → #1 ASSOC0Store p.x  #7MEM#2#7 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123Store p.y  #8MEM#3#8 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123MemMerge  #9#9 MemMerge +Type not computed + +[0] → — CTRL +[1] → #3 MEM +[2] → #7 MEM +[3] → #8 MEM0123True  #11/0#11 True +Projection 0 of #0 +Type not computed + +False  #12/1#12 False +Projection 1 of #0 +Type not computed + +#3  #13#13 #3 +Type not computed + +[0] → #1 ASSOC0Store p.x  #14MEM#2#14 Store p.x +MEM#2 + +[0] → #11 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #13 DATA0123#4  #15#15 #4 +Type not computed + +[0] → #1 ASSOC0Store p.x  #16MEM#2#16 Store p.x +MEM#2 + +[0] → #12 CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #15 DATA0123MemMerge  #17#17 MemMerge +Type not computed + +[0] → — CTRL +[1] → #9 MEM +[2] → #14 MEM012MemMerge  #18#18 MemMerge +Type not computed + +[0] → — CTRL +[1] → #9 MEM +[2] → #16 MEM012MemPhi x  #20MEM#2#20 MemPhi x +MEM#2 + +[0] → — ASSOC +[1] → #14 MEM +[2] → #16 MEM012BulkMemPhi except x  #21#21 BulkMemPhi except x +Type not computed + +[0] → — ASSOC +[1] → #17 MEM +[2] → #18 MEM012MemMerge  #22#22 MemMerge +Type not computed + +[0] → — CTRL +[1] → #21 MEM +[2] → #20 MEM012Return  #23#23 Return +Type not computed + +[0] → — CTRL +[1] → #22 MEM +[2] → #5 DATA012 diff --git a/docs/chapter11/example2c.gv b/docs/chapter11/example2c.gv new file mode 100644 index 00000000..b32d186d --- /dev/null +++ b/docs/chapter11/example2c.gv @@ -0,0 +1,15 @@ +digraph Memory { + // IR styles match graph/web/render.js; arrows are use -> definition. + graph [bgcolor="#fafbfc" fontname="Helvetica" nodesep=0.35 ranksep=0.55 splines=ortho]; + node [fontname="Helvetica" fontsize=12 color="#758191" fontcolor="#152330" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + edge [fontname="Helvetica" fontsize=9 color="#536477" fontcolor="#364352" arrowsize=0.7 penwidth=1.5]; + + rankdir=RL; + + M [label="Prior x memory" shape=octagon style="filled" fillcolor="#dcecff"]; + L [label="Load p.x" shape=box style="rounded,filled" fillcolor="#edf3f7"]; + S [label="Store p.x" shape=octagon style="filled" fillcolor="#dcecff"]; + L -> M [color="#2867b2"]; S -> M [color="#2867b2"]; + S -> L [style=dashed,xlabel="execute load first"]; + Y [label="Store p.y: independent" shape=octagon style="filled" fillcolor="#dcecff"]; +} diff --git a/docs/chapter11/example2c.json b/docs/chapter11/example2c.json new file mode 100644 index 00000000..c25fa5b8 --- /dev/null +++ b/docs/chapter11/example2c.json @@ -0,0 +1,23 @@ +{ + "ver": 1, + "comp": "chapter11/docs/example2c.svg", + "step": 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+#6[0] → #1 · ASSOC#7[1] → #3 · MEM#7[2] → #5 · DATA#7[3] → #6 · DATA#8[1] → #3 · MEM#8[2] → #5 · DATA#8[3] → #6 · DATA#9[1] → #7 · MEM#9[2] → #5 · DATA#10[1] → #7 · MEM#10[2] → #5 · DATA#10[3] → #4 · DATA#11[1] → #8 · MEM#11[2] → #5 · DATA#11[3] → #4 · DATA#12[1] → #3 · MEM#12[2] → #10 · MEM#12[3] → #11 · MEM#13[1] → #12 · MEM#13[2] → #9 · DATAStart  #1#1 Start +Type not computed + +$mem  #3/1#3 $mem +Projection 1 of #1 +Type not computed + +[0] → #1 MEMarg  #4/2#4 arg +Projection 2 of #1 +Type not computed + +[0] → #1 DATAnew Point  #5#5 new Point +Type not computed + +[0] → — CTRL0#0  #6#6 #0 +Type not computed + +[0] → #1 ASSOC0Store p.x  #7MEM#2#7 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123Store p.y  #8MEM#3#8 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #3 MEM +[2] → #5 DATA +[3] → #6 DATA0123Load p.x  #9#9 Load p.x +Type not computed + +[0] → — CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → — DATA0123Store p.x  #10MEM#2#10 Store p.x +MEM#2 + +[0] → — CTRL +[1] → #7 MEM +[2] → #5 DATA +[3] → #4 DATA0123Store p.y  #11MEM#3#11 Store p.y +MEM#3 + +[0] → — CTRL +[1] → #8 MEM +[2] → #5 DATA +[3] → #4 DATA0123MemMerge  #12#12 MemMerge +Type not computed + +[0] → — CTRL +[1] → #3 MEM +[2] → #10 MEM +[3] → #11 MEM0123Return  #13#13 Return +Type not computed + +[0] → — CTRL +[1] → #12 MEM +[2] → #9 DATA012 diff --git a/docs/chapter11/lattice.gv b/docs/chapter11/lattice.gv new file mode 100644 index 00000000..93d99dd8 --- /dev/null +++ b/docs/chapter11/lattice.gv @@ -0,0 +1,133 @@ +digraph Lattice { + rankdir=TB; + newrank=true; + // Preserve the same-rank ordering edges through cluster layout. + remincross=false; + nodesep=0.22; + ranksep=0.65; + node [shape=ellipse, style=filled, fontname="DejaVu Sans", fontsize=13]; + edge [color="#555555", arrowsize=0.6]; + + // These arrows are lattice-order edges, not use/definition edges. + TOP [label="⊤", fillcolor=black, fontcolor=white]; + BOT [label="⊥", fillcolor=black, fontcolor=white]; + + subgraph cluster_control { + label="Control"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#ffff00"]; + XCTRL [label="⊤:ctrl"]; + CTRL [label="⊥:ctrl"]; + XCTRL -> CTRL; + } + + subgraph cluster_integer { + label="Integer"; fontname="Arial"; color="#cccccc"; + node [fillcolor="#add8e6"]; + INT_TOP [label="⊤:int"]; + INT_BOT [label="⊥:int"]; + INT_NEG [label="… −2, −1"]; + INT_ZERO [label="0"]; + INT_POS [label="1, 2, …"]; + {rank=same; INT_NEG; INT_ZERO; INT_POS;} + INT_NEG -> INT_ZERO -> INT_POS [style=invis]; + INT_TOP -> {INT_NEG INT_ZERO INT_POS}; + {INT_NEG INT_ZERO INT_POS} -> INT_BOT; + } + + subgraph cluster_pointer { + label="Pointer = nullability × struct type"; + fontname="Arial"; color="#cccccc"; + node [fillcolor="#008000", fontcolor=white]; + PTR_TOP [label="⊤:ptr\n[*⊤:struct]"]; + PTR_BOT [label="⊥:ptr\n[*⊥:struct?]"]; + PTR_NULL [label="null"]; + PTR_ANY [label="*⊥:struct\n[ptr any struct]"]; + PTR_PERSON [label="*Person"]; + PTR_S1 [label="*s1"]; + PTR_MORE [label="*s2, …"]; + PTR_PERSON_NIL [label="*Person?"]; + PTR_S1_NIL [label="*s1?"]; + PTR_MORE_NIL [label="*s2?, …"]; + {rank=same; PTR_PERSON; PTR_S1; PTR_MORE; PTR_NULL;} + {rank=same; PTR_ANY; PTR_PERSON_NIL; PTR_S1_NIL; PTR_MORE_NIL;} + PTR_PERSON -> PTR_S1 -> PTR_MORE -> PTR_NULL [style=invis]; + PTR_ANY -> PTR_PERSON_NIL -> PTR_S1_NIL -> PTR_MORE_NIL [style=invis]; + PTR_TOP -> {PTR_PERSON PTR_S1 PTR_MORE PTR_NULL}; + {PTR_PERSON PTR_S1 PTR_MORE} -> PTR_ANY; + PTR_PERSON -> PTR_PERSON_NIL; + PTR_S1 -> PTR_S1_NIL; + PTR_MORE -> PTR_MORE_NIL; + PTR_NULL -> {PTR_PERSON_NIL PTR_S1_NIL PTR_MORE_NIL}; + {PTR_ANY PTR_PERSON_NIL PTR_S1_NIL PTR_MORE_NIL} -> PTR_BOT; + } + + subgraph cluster_struct { + label="Struct\nnamed collection of named scalar types"; + fontname="Arial"; color="#cccccc"; + node [fillcolor="#90ee90"]; + STRUCT_TOP [label="⊤:struct\n[struct top]"]; + STRUCT_BOT [label="⊥:struct\n[struct bottom]"]; + STRUCT_PERSON [label="Person\nage: int", shape=box]; + STRUCT_S1 [label="s1\nx: int", shape=box]; + STRUCT_S2 [label="s2\nx: int, y: int", 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 PTR_TOP STRUCT_TOP MEM_TOP TUPLE_TOP}; + {CTRL INT_BOT PTR_BOT STRUCT_BOT MEM_BOT TUPLE_BOT} -> BOT; + {rank=same; XCTRL; INT_TOP; PTR_TOP; STRUCT_TOP; MEM_TOP; TUPLE_TOP;} + {rank=same; CTRL; INT_BOT; PTR_BOT; STRUCT_BOT; MEM_BOT; TUPLE_BOT;} + XCTRL -> INT_TOP -> PTR_TOP -> STRUCT_TOP -> MEM_TOP -> TUPLE_TOP [style=invis]; +} diff --git a/docs/chapter11/lattice.svg b/docs/chapter11/lattice.svg new file mode 100644 index 00000000..8d2e2875 --- /dev/null +++ b/docs/chapter11/lattice.svg @@ -0,0 +1,644 @@ + + + + + + +Lattice + + +cluster_control + +Control + + +cluster_integer + +Integer + + +cluster_pointer + +Pointer = nullability × struct type + + +cluster_struct + +Struct +named collection of named scalar types + + +cluster_memory + +Memory +precise alias slices + + +cluster_tuple + +Tuple +collection of types + + + +TOP + +⊤ + + + +XCTRL + +⊤:ctrl + + + +TOP->XCTRL + + + + + +INT_TOP + +⊤:int + + + +TOP->INT_TOP + + + + + +PTR_TOP + +⊤:ptr +[*⊤:struct] + + + +TOP->PTR_TOP + + + + + +STRUCT_TOP + +⊤:struct +[struct top] + + + +TOP->STRUCT_TOP + + + + + +MEM_TOP + +⊤:mem + + + +TOP->MEM_TOP + + + + + +TUPLE_TOP + +⊤:tuple + + + +TOP->TUPLE_TOP + + + + + +BOT + +⊥ + + + +CTRL + +⊥:ctrl + + + +XCTRL->CTRL + + + + + + +CTRL->BOT + + + + + +INT_NEG + +… −2, −1 + + + +INT_TOP->INT_NEG + + + + + +INT_ZERO + +0 + + + +INT_TOP->INT_ZERO + + + + + +INT_POS + +1, 2, … + + + +INT_TOP->INT_POS + + + + + + +INT_BOT + +⊥:int + + + +INT_BOT->BOT + + + + + +INT_NEG->INT_BOT + + + + + + +INT_ZERO->INT_BOT + + + + + + +INT_POS->INT_BOT + + + + + +PTR_NULL + +null + + + +PTR_TOP->PTR_NULL + + + + + +PTR_PERSON + +*Person + + + +PTR_TOP->PTR_PERSON + + + + + +PTR_S1 + +*s1 + + + +PTR_TOP->PTR_S1 + + + + + +PTR_MORE + +*s2, … + + + +PTR_TOP->PTR_MORE + + + + + + +PTR_BOT + +⊥:ptr +[*⊥:struct?] + + + +PTR_BOT->BOT + + + + + +PTR_PERSON_NIL + +*Person? + + + +PTR_NULL->PTR_PERSON_NIL + + + + + +PTR_S1_NIL + +*s1? + + + +PTR_NULL->PTR_S1_NIL + + + + + +PTR_MORE_NIL + +*s2?, … + + + +PTR_NULL->PTR_MORE_NIL + + + + + +PTR_ANY + +*⊥:struct +[ptr any struct] + + + +PTR_ANY->PTR_BOT + + + + + + +PTR_PERSON->PTR_ANY + + + + + + +PTR_PERSON->PTR_PERSON_NIL + + + + + +PTR_S1->PTR_ANY + + + + + + +PTR_S1->PTR_S1_NIL + + + + + + +PTR_MORE->PTR_ANY + + + + + +PTR_MORE->PTR_MORE_NIL + + + + + +PTR_PERSON_NIL->PTR_BOT + + + + + + +PTR_S1_NIL->PTR_BOT + + + + + + +PTR_MORE_NIL->PTR_BOT + + + + + +STRUCT_PERSON + +Person +age: int + + + +STRUCT_TOP->STRUCT_PERSON + + + + + +STRUCT_S1 + +s1 +x: int + + + +STRUCT_TOP->STRUCT_S1 + + + + + +STRUCT_S2 + +s2 +x: int, y: int + + + +STRUCT_TOP->STRUCT_S2 + + + + + +STRUCT_MORE + +… + + + +STRUCT_TOP->STRUCT_MORE + + + + + + +STRUCT_BOT + +⊥:struct +[struct bottom] + + + +STRUCT_BOT->BOT + + + + + +STRUCT_PERSON->STRUCT_BOT + + + + + + +STRUCT_S1->STRUCT_BOT + + + + + + +STRUCT_S2->STRUCT_BOT + + + + + + +STRUCT_MORE->STRUCT_BOT + + + + + +MEM_ALIAS2 + +MEM#2 + + + +MEM_TOP->MEM_ALIAS2 + + + + + +MEM_ALIAS3 + +MEM#3 + + + +MEM_TOP->MEM_ALIAS3 + + + + + +MEM_MORE + +… + + + +MEM_TOP->MEM_MORE + + + + + + +MEM_BOT + +⊥:mem + + + +MEM_BOT->BOT + + + + + +MEM_ALIAS2->MEM_BOT + + + + + + +MEM_ALIAS3->MEM_BOT + + + + + + +MEM_MORE->MEM_BOT + + + + + +TUPLE1 + + + +tuple + + +type + + + +TUPLE_TOP->TUPLE1 + + + + + +TUPLE2 + + + +tuple + + +type + + +type + + + +TUPLE_TOP->TUPLE2 + + + + + +TUPLEN + + + +tuple + + +type + + +… + + +type + + + +TUPLE_TOP->TUPLEN + + + + + +TUPLE_BOT + +⊥:tuple + + + +TUPLE_BOT->BOT + + + + + +TUPLE1->TUPLE_BOT + + + + + + +TUPLE2->TUPLE_BOT + + + + + + +TUPLEN->TUPLE_BOT + + + + + -- cgit v1.2.3