Give overview of MIR dataflow framework

src/SUMMARY.md

@@ -110,6 +110,7 @@
     - [Variance](./variance.md)
     - [Opaque Types](./opaque-types-type-alias-impl-trait.md)
 - [Pattern and Exhaustiveness Checking](./pat-exhaustive-checking.md)
+- [MIR dataflow](./mir/dataflow.md)
 - [The borrow checker](./borrow_check.md)
     - [Tracking moves and initialization](./borrow_check/moves_and_initialization.md)
         - [Move paths](./borrow_check/moves_and_initialization/move_paths.md)

src/mir/dataflow.md

@@ -0,0 +1,165 @@
+# Dataflow Analysis
+
+If you work on the MIR, you will frequently come across various flavors of
+[dataflow analysis][wiki]. For example, `rustc` uses dataflow to find
+uninitialized variables, determine what variables are live across a generator
+`yield` statement, and compute which `Place`s are borrowed at a given point in
+the control-flow graph. Dataflow analysis is a fundamental concept in modern
+compilers, and knowledge of the subject will be helpful to prospective
+contributors.
+
+However, this documentation is not a general introduction to dataflow analysis.
+It is merely a description of the framework used to define these analyses in
+`rustc`. It assumes that the reader is familiar with some basic terminology,
+such as "transfer function", "fixpoint" and "lattice". If you're unfamiliar
+with these terms, or if you want a quick refresher, [*Static Program Analysis*]
+by Anders Møller and Michael I. Schwartzbach is an excellent, freely available
+textbook.  For those who prefer audiovisual learning, the Goethe University
+Frankfurt has published a series of short [youtube lectures][goethe] in English
+that are very approachable.
+
+## Defining a Dataflow Analysis
+
+The interface for dataflow analyses is split into three traits. The first is
+[`AnalysisDomain`], which must be implemented by *all* analyses. In addition to
+the type of the dataflow state, this trait defines the initial value of that
+state at entry to each block, as well as the direction of the analysis, either
+forward or backward. The domain of your dataflow analysis must be a [lattice][]
+(strictly speaking a join-semilattice) with a well-behaved `join` operator. See
+documentation for the [`lattice`] module, as well as the [`JoinSemiLattice`]
+trait, for more information.
+
+You must then provide *either* a direct implementation of the [`Analysis`] trait
+*or* an implementation of the proxy trait [`GenKillAnalysis`]. The latter is for
+so-called ["gen-kill" problems], which have a simple class of transfer function
+that can be applied very efficiently. Analyses whose domain is not a `BitSet`
+of some index type, or whose transfer functions cannot be expressed through
+"gen" and "kill" operations, must implement `Analysis` directly, and will run
+slower as a result. All implementers of `GenKillAnalysis` also implement
+`Analysis` automatically via a default `impl`.
+
+
+```text
+ AnalysisDomain
+       ^
+       |          | = has as a supertrait
+       |          . = provides a default impl for
+       |
+   Analysis
+     ^   ^
+     |   .
+     |   .
+     |   .
+ GenKillAnalysis
+
+```
+
+### Transfer Functions and Effects
+
+The dataflow framework in `rustc` allows each statement inside a basic block as
+well as the terminator to define its own transfer function. For brevity, these
+individual transfer functions are known as "effects". Each effect is applied
+successively in dataflow order, and together they define the transfer function
+for the entire basic block. It's also possible to define an effect for
+particular outgoing edges of some terminators (e.g.
+[`apply_call_return_effect`] for the `success` edge of a `Call`
+terminator). Collectively, these are known as per-edge effects.
+
+The only meaningful difference (besides the "apply" prefix) between the methods
+of the `GenKillAnalysis` trait and the `Analysis` trait is that an `Analysis`
+has direct, mutable access to the dataflow state, whereas a `GenKillAnalysis`
+only sees an implementer of the `GenKill` trait, which only allows the `gen`
+and `kill` operations for mutation.
+
+Observant readers of the documentation for these traits may notice that there
+are actually *two* possible effects for each statement and terminator, the
+"before" effect and the unprefixed (or "primary") effect. The "before" effects
+are applied immediately before the unprefixed effect **regardless of whether
+the analysis is backward or forward**. The vast majority of analyses should use
+only the unprefixed effects: Having multiple effects for each statement makes
+it difficult for consumers to know where they should be looking. However, the
+"before" variants can be useful in some scenarios, such as when the effect of
+the right-hand side of an assignment statement must be considered separately
+from the left-hand side.
+
+### Convergence
+
+TODO
+
+## Inspecting the Results of a Dataflow Analysis
+
+Once you have constructed an analysis, you must pass it to an [`Engine`], which
+is responsible for finding the steady-state solution to your dataflow problem.
+You should use the [`into_engine`] method defined on the `Analysis` trait for
+this, since it will use the more efficient `Engine::new_gen_kill` constructor
+when possible.
+
+Calling `iterate_to_fixpoint` on your `Engine` will return a `Results`, which
+contains the dataflow state at fixpoint upon entry of each block. Once you have
+a `Results`, you can can inspect the dataflow state at fixpoint at any point in
+the CFG. If you only need the state at a few locations (e.g., each `Drop`
+terminator) use a [`ResultsCursor`]. If you need the state at *every* location,
+a [`ResultsVisitor`] will be more efficient.
+
+```text
+                         Analysis
+                            |
+                            | into_engine(…)
+                            |
+                          Engine
+                            |
+                            | iterate_to_fixpoint()
+                            |
+                         Results
+                         /     \
+ into_results_cursor(…) /       \  visit_with(…)
+                       /         \
+               ResultsCursor  ResultsVisitor
+```
+
+For example, the following code uses a [`ResultsVisitor`]...
+
+
+```rust,ignore
+// Assuming `MyVisitor` implements `ResultsVisitor<FlowState = MyAnalysis::Domain>`...
+let my_visitor = MyVisitor::new();
+
+// inspect the fixpoint state for every location within every block in RPO.
+let results = MyAnalysis()
+    .into_engine(tcx, body, def_id)
+    .iterate_to_fixpoint()
+    .visit_with(body, traversal::reverse_postorder(body), &mut my_visitor);
+```
+
+whereas this code uses [`ResultsCursor`]:
+
+```rust,ignore
+let mut results = MyAnalysis()
+    .into_engine(tcx, body, def_id)
+    .iterate_to_fixpoint()
+    .into_results_cursor(body);
+
+// Inspect the fixpoint state immediately before each `Drop` terminator.
+for (bb, block) in body.basic_blocks().iter_enumerated() {
+    if let TerminatorKind::Drop { .. } = block.terminator().kind {
+        results.seek_before_primary_effect(body.terminator_loc(bb));
+        let state = results.get();
+        println!("state before drop: {:#?}", state);
+    }
+}
+```
+
+["gen-kill" problems]: https://en.wikipedia.org/wiki/Data-flow_analysis#Bit_vector_problems
+[*Static Program Analysis*]: https://cs.au.dk/~amoeller/spa/
+[`AnalysisDomain`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.AnalysisDomain.html
+[`Analysis`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.Analysis.html
+[`GenKillAnalysis`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.GenKillAnalysis.html
+[`JoinSemiLattice`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/lattice/trait.JoinSemiLattice.html
+[`ResultsCursor`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/struct.ResultsCursor.html
+[`ResultsVisitor`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.ResultsVisitor.html
+[`apply_call_return_effect`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.Analysis.html#tymethod.apply_call_return_effect
+[`into_engine`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/trait.Analysis.html#method.into_engine
+[`lattice`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir/dataflow/lattice/index.html
+[goethe]: https://www.youtube.com/watch?v=NVBQSR_HdL0&list=PL_sGR8T76Y58l3Gck3ZwIIHLWEmXrOLV_&index=2
+[lattice]: https://en.wikipedia.org/wiki/Lattice_(order)
+[wiki]: https://en.wikipedia.org/wiki/Data-flow_analysis#Basic_principles