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| <ol class="chapter"><li class="chapter-item affix "><a href="../about-this-guide.html">About this guide</a></li><li class="chapter-item affix "><a href="../getting-started.html">Getting Started</a></li><li class="spacer"></li><li class="chapter-item affix "><li class="part-title">Building and debugging rustc</li><li class="chapter-item "><a href="../building/how-to-build-and-run.html"><strong aria-hidden="true">1.</strong> How to Build and Run the Compiler</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../building/prerequisites.html"><strong aria-hidden="true">1.1.</strong> Prerequisites</a></li><li class="chapter-item "><a href="../building/suggested.html"><strong aria-hidden="true">1.2.</strong> Suggested Workflows</a></li><li class="chapter-item "><a href="../building/build-install-distribution-artifacts.html"><strong aria-hidden="true">1.3.</strong> Distribution artifacts</a></li><li class="chapter-item "><a href="../building/compiler-documenting.html"><strong aria-hidden="true">1.4.</strong> Documenting Compiler</a></li><li class="chapter-item "><a href="../rustdoc.html"><strong aria-hidden="true">1.5.</strong> Rustdoc overview</a></li><li class="chapter-item "><a href="../building/new-target.html"><strong aria-hidden="true">1.6.</strong> Adding a new target</a></li></ol></li><li class="chapter-item "><a href="../tests/intro.html"><strong aria-hidden="true">2.</strong> The compiler testing framework</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../tests/running.html"><strong aria-hidden="true">2.1.</strong> Running tests</a></li><li class="chapter-item "><a href="../tests/adding.html"><strong aria-hidden="true">2.2.</strong> Adding new tests</a></li><li class="chapter-item "><a href="../compiletest.html"><strong aria-hidden="true">2.3.</strong> Using compiletest commands to control test execution</a></li></ol></li><li class="chapter-item "><a href="../compiler-debugging.html"><strong aria-hidden="true">3.</strong> Debugging the Compiler</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../tracing.html"><strong aria-hidden="true">3.1.</strong> Using the tracing/logging instrumentation</a></li></ol></li><li class="chapter-item "><a href="../profiling.html"><strong aria-hidden="true">4.</strong> Profiling the compiler</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../profiling/with_perf.html"><strong aria-hidden="true">4.1.</strong> with the linux perf tool</a></li><li class="chapter-item "><a href="../profiling/wpa_profiling.html"><strong aria-hidden="true">4.2.</strong> with Windows Performance Analyzer</a></li></ol></li><li class="chapter-item "><a href="../crates-io.html"><strong aria-hidden="true">5.</strong> crates.io Dependencies</a></li><li class="chapter-item affix "><li class="part-title">Contributing to Rust</li><li class="chapter-item "><a href="../contributing.html"><strong aria-hidden="true">6.</strong> Introduction</a></li><li class="chapter-item "><a href="../compiler-team.html"><strong aria-hidden="true">7.</strong> About the compiler team</a></li><li class="chapter-item "><a href="../git.html"><strong aria-hidden="true">8.</strong> Using Git</a></li><li class="chapter-item "><a href="../rustbot.html"><strong aria-hidden="true">9.</strong> Mastering @rustbot</a></li><li class="chapter-item "><a href="../walkthrough.html"><strong aria-hidden="true">10.</strong> Walkthrough: a typical contribution</a></li><li class="chapter-item "><a href="../bug-fix-procedure.html"><strong aria-hidden="true">11.</strong> Bug Fix Procedure</a></li><li class="chapter-item "><a href="../implementing_new_features.html"><strong aria-hidden="true">12.</strong> Implementing new features</a></li><li class="chapter-item "><a href="../stability.html"><strong aria-hidden="true">13.</strong> Stability attributes</a></li><li class="chapter-item "><a href="../stabilization_guide.html"><strong aria-hidden="true">14.</strong> Stabilizing Features</a></li><li class="chapter-item "><a href="../feature-gates.html"><strong aria-hidden="true">15.</strong> Feature Gates</a></li><li class="chapter-item "><a href="../conventions.html"><strong aria-hidden="true">16.</strong> Coding conventions</a></li><li class="chapter-item "><a href="../notification-groups/about.html"><strong aria-hidden="true">17.</strong> Notification groups</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../notification-groups/arm.html"><strong aria-hidden="true">17.1.</strong> ARM</a></li><li class="chapter-item "><a href="../notification-groups/cleanup-crew.html"><strong aria-hidden="true">17.2.</strong> Cleanup Crew</a></li><li class="chapter-item "><a href="../notification-groups/llvm.html"><strong aria-hidden="true">17.3.</strong> LLVM</a></li><li class="chapter-item "><a href="../notification-groups/risc-v.html"><strong aria-hidden="true">17.4.</strong> RISC-V</a></li><li class="chapter-item "><a href="../notification-groups/windows.html"><strong aria-hidden="true">17.5.</strong> Windows</a></li></ol></li><li class="chapter-item "><a href="../licenses.html"><strong aria-hidden="true">18.</strong> Licenses</a></li><li class="chapter-item affix "><li class="part-title">High-level Compiler Architecture</li><li class="chapter-item "><a href="../part-2-intro.html"><strong aria-hidden="true">19.</strong> Prologue</a></li><li class="chapter-item "><a href="../overview.html"><strong aria-hidden="true">20.</strong> Overview of the Compiler</a></li><li class="chapter-item "><a href="../compiler-src.html"><strong aria-hidden="true">21.</strong> The compiler source code</a></li><li class="chapter-item "><a href="../building/bootstrapping.html"><strong aria-hidden="true">22.</strong> Bootstrapping</a></li><li class="chapter-item "><a href="../query.html"><strong aria-hidden="true">23.</strong> Queries: demand-driven compilation</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../queries/query-evaluation-model-in-detail.html"><strong aria-hidden="true">23.1.</strong> The Query Evaluation Model in Detail</a></li><li class="chapter-item "><a href="../queries/incremental-compilation.html"><strong aria-hidden="true">23.2.</strong> Incremental compilation</a></li><li class="chapter-item "><a href="../queries/incremental-compilation-in-detail.html"><strong aria-hidden="true">23.3.</strong> Incremental compilation In Detail</a></li><li class="chapter-item "><a href="../incrcomp-debugging.html"><strong aria-hidden="true">23.4.</strong> Debugging and Testing</a></li><li class="chapter-item "><a href="../salsa.html"><strong aria-hidden="true">23.5.</strong> Salsa</a></li></ol></li><li class="chapter-item "><a href="../memory.html"><strong aria-hidden="true">24.</strong> Memory Management in Rustc</a></li><li class="chapter-item "><a href="../serialization.html"><strong aria-hidden="true">25.</strong> Serialization in Rustc</a></li><li class="chapter-item "><a href="../parallel-rustc.html"><strong aria-hidden="true">26.</strong> Parallel Compilation</a></li><li class="chapter-item "><a href="../rustdoc-internals.html"><strong aria-hidden="true">27.</strong> Rustdoc internals</a></li><li class="chapter-item affix "><li class="part-title">Source Code Representation</li><li class="chapter-item "><a href="../part-3-intro.html"><strong aria-hidden="true">28.</strong> Prologue</a></li><li class="chapter-item "><a href="../cli.html"><strong aria-hidden="true">29.</strong> Command-line arguments</a></li><li class="chapter-item "><a href="../rustc-driver.html"><strong aria-hidden="true">30.</strong> The Rustc Driver and Interface</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../rustc-driver-interacting-with-the-ast.html"><strong aria-hidden="true">30.1.</strong> Ex: Type checking through rustc_interface</a></li><li class="chapter-item "><a href="../rustc-driver-getting-diagnostics.html"><strong aria-hidden="true">30.2.</strong> Ex: Getting diagnostics through rustc_interface</a></li></ol></li><li class="chapter-item "><a href="../syntax-intro.html"><strong aria-hidden="true">31.</strong> Syntax and the AST</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../the-parser.html"><strong aria-hidden="true">31.1.</strong> Lexing and Parsing</a></li><li class="chapter-item "><a href="../macro-expansion.html"><strong aria-hidden="true">31.2.</strong> Macro expansion</a></li><li class="chapter-item "><a href="../name-resolution.html"><strong aria-hidden="true">31.3.</strong> Name resolution</a></li><li class="chapter-item "><a href="../test-implementation.html"><strong aria-hidden="true">31.4.</strong> #[test] Implementation</a></li><li class="chapter-item "><a href="../panic-implementation.html"><strong aria-hidden="true">31.5.</strong> Panic Implementation</a></li><li class="chapter-item "><a href="../ast-validation.html"><strong aria-hidden="true">31.6.</strong> AST Validation</a></li><li class="chapter-item "><a href="../feature-gate-ck.html"><strong aria-hidden="true">31.7.</strong> Feature Gate Checking</a></li><li class="chapter-item "><a href="../lang-items.html"><strong aria-hidden="true">31.8.</strong> Lang Items</a></li></ol></li><li class="chapter-item "><a href="../hir.html"><strong aria-hidden="true">32.</strong> The HIR (High-level IR)</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../lowering.html"><strong aria-hidden="true">32.1.</strong> Lowering AST to HIR</a></li><li class="chapter-item "><a href="../hir-debugging.html"><strong aria-hidden="true">32.2.</strong> Debugging</a></li></ol></li><li class="chapter-item "><a href="../thir.html"><strong aria-hidden="true">33.</strong> The THIR (Typed High-level IR)</a></li><li class="chapter-item "><a href="../mir/index.html"><strong aria-hidden="true">34.</strong> The MIR (Mid-level IR)</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../mir/construction.html"><strong aria-hidden="true">34.1.</strong> MIR construction</a></li><li class="chapter-item "><a href="../mir/visitor.html"><strong aria-hidden="true">34.2.</strong> MIR visitor and traversal</a></li><li class="chapter-item "><a href="../mir/passes.html"><strong aria-hidden="true">34.3.</strong> MIR passes: getting the MIR for a function</a></li></ol></li><li class="chapter-item "><a href="../identifiers.html"><strong aria-hidden="true">35.</strong> Identifiers in the Compiler</a></li><li class="chapter-item "><a href="../closure.html"><strong aria-hidden="true">36.</strong> Closure expansion</a></li><li class="chapter-item affix "><li class="part-title">Analysis</li><li class="chapter-item "><a href="../part-4-intro.html"><strong aria-hidden="true">37.</strong> Prologue</a></li><li class="chapter-item "><a href="../ty.html"><strong aria-hidden="true">38.</strong> The ty module: representing types</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../generics.html"><strong aria-hidden="true">38.1.</strong> Generics and substitutions</a></li><li class="chapter-item "><a href="../ty-fold.html"><strong aria-hidden="true">38.2.</strong> TypeFolder and TypeFoldable</a></li><li class="chapter-item "><a href="../generic_arguments.html"><strong aria-hidden="true">38.3.</strong> Generic arguments</a></li><li class="chapter-item "><a href="../constants.html"><strong aria-hidden="true">38.4.</strong> Constants in the type system</a></li></ol></li><li class="chapter-item "><a href="../type-inference.html"><strong aria-hidden="true">39.</strong> Type inference</a></li><li class="chapter-item "><a href="../traits/resolution.html"><strong aria-hidden="true">40.</strong> Trait solving</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../early-late-bound.html"><strong aria-hidden="true">40.1.</strong> Early and Late Bound Parameters</a></li><li class="chapter-item "><a href="../traits/hrtb.html"><strong aria-hidden="true">40.2.</strong> Higher-ranked trait bounds</a></li><li class="chapter-item "><a href="../traits/caching.html"><strong aria-hidden="true">40.3.</strong> Caching subtleties</a></li><li class="chapter-item "><a href="../traits/specialization.html"><strong aria-hidden="true">40.4.</strong> Specialization</a></li><li class="chapter-item "><a href="../traits/chalk.html"><strong aria-hidden="true">40.5.</strong> Chalk-based trait solving</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../traits/lowering-to-logic.html"><strong aria-hidden="true">40.5.1.</strong> Lowering to logic</a></li><li class="chapter-item "><a href="../traits/goals-and-clauses.html"><strong aria-hidden="true">40.5.2.</strong> Goals and clauses</a></li><li class="chapter-item "><a href="../traits/canonical-queries.html"><strong aria-hidden="true">40.5.3.</strong> Canonical queries</a></li></ol></li></ol></li><li class="chapter-item "><a href="../type-checking.html"><strong aria-hidden="true">41.</strong> Type checking</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../method-lookup.html"><strong aria-hidden="true">41.1.</strong> Method Lookup</a></li><li class="chapter-item "><a href="../variance.html"><strong aria-hidden="true">41.2.</strong> Variance</a></li><li class="chapter-item "><a href="../opaque-types-type-alias-impl-trait.html"><strong aria-hidden="true">41.3.</strong> Opaque Types</a></li></ol></li><li class="chapter-item "><a href="../pat-exhaustive-checking.html"><strong aria-hidden="true">42.</strong> Pattern and Exhaustiveness Checking</a></li><li class="chapter-item "><a href="../mir/dataflow.html"><strong aria-hidden="true">43.</strong> MIR dataflow</a></li><li class="chapter-item "><a href="../borrow_check.html"><strong aria-hidden="true">44.</strong> The borrow checker</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../borrow_check/moves_and_initialization.html"><strong aria-hidden="true">44.1.</strong> Tracking moves and initialization</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../borrow_check/moves_and_initialization/move_paths.html"><strong aria-hidden="true">44.1.1.</strong> Move paths</a></li></ol></li><li class="chapter-item "><a href="../borrow_check/type_check.html"><strong aria-hidden="true">44.2.</strong> MIR type checker</a></li><li class="chapter-item "><a href="../borrow_check/region_inference.html"><strong aria-hidden="true">44.3.</strong> Region inference</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../borrow_check/region_inference/constraint_propagation.html"><strong aria-hidden="true">44.3.1.</strong> Constraint propagation</a></li><li class="chapter-item "><a href="../borrow_check/region_inference/lifetime_parameters.html"><strong aria-hidden="true">44.3.2.</strong> Lifetime parameters</a></li><li class="chapter-item "><a href="../borrow_check/region_inference/member_constraints.html"><strong aria-hidden="true">44.3.3.</strong> Member constraints</a></li><li class="chapter-item "><a href="../borrow_check/region_inference/placeholders_and_universes.html"><strong aria-hidden="true">44.3.4.</strong> Placeholders and universes</a></li><li class="chapter-item "><a href="../borrow_check/region_inference/closure_constraints.html"><strong aria-hidden="true">44.3.5.</strong> Closure constraints</a></li><li class="chapter-item "><a href="../borrow_check/region_inference/error_reporting.html"><strong aria-hidden="true">44.3.6.</strong> Error reporting</a></li></ol></li><li class="chapter-item "><a href="../borrow_check/two_phase_borrows.html"><strong aria-hidden="true">44.4.</strong> Two-phase-borrows</a></li></ol></li><li class="chapter-item "><a href="../param_env.html"><strong aria-hidden="true">45.</strong> Parameter Environments</a></li><li class="chapter-item "><a href="../diagnostics.html"><strong aria-hidden="true">46.</strong> Errors and Lints</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../diagnostics/sessiondiagnostic.html"><strong aria-hidden="true">46.1.</strong> Creating Errors With SessionDiagnostic</a></li><li class="chapter-item "><a href="../diagnostics/lintstore.html"><strong aria-hidden="true">46.2.</strong> LintStore</a></li><li class="chapter-item "><a href="../diagnostics/diagnostic-codes.html"><strong aria-hidden="true">46.3.</strong> Diagnostic Codes</a></li><li class="chapter-item "><a href="../diagnostics/diagnostic-items.html"><strong aria-hidden="true">46.4.</strong> Diagnostic Items</a></li></ol></li><li class="chapter-item "><li class="part-title">MIR to Binaries</li><li class="chapter-item "><a href="../part-5-intro.html"><strong aria-hidden="true">47.</strong> Prologue</a></li><li class="chapter-item "><a href="../mir/optimizations.html"><strong aria-hidden="true">48.</strong> MIR optimizations</a></li><li class="chapter-item "><a href="../mir/debugging.html"><strong aria-hidden="true">49.</strong> Debugging</a></li><li class="chapter-item "><a href="../const-eval.html"><strong aria-hidden="true">50.</strong> Constant evaluation</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../miri.html"><strong aria-hidden="true">50.1.</strong> miri const evaluator</a></li></ol></li><li class="chapter-item "><a href="../backend/monomorph.html"><strong aria-hidden="true">51.</strong> Monomorphization</a></li><li class="chapter-item "><a href="../backend/lowering-mir.html"><strong aria-hidden="true">52.</strong> Lowering MIR</a></li><li class="chapter-item "><a href="../backend/codegen.html"><strong aria-hidden="true">53.</strong> Code Generation</a><a class="toggle"><div>❱</div></a></li><li><ol class="section"><li class="chapter-item "><a href="../backend/updating-llvm.html"><strong aria-hidden="true">53.1.</strong> Updating LLVM</a></li><li class="chapter-item "><a href="../backend/debugging.html"><strong aria-hidden="true">53.2.</strong> Debugging LLVM</a></li><li class="chapter-item "><a href="../backend/backend-agnostic.html"><strong aria-hidden="true">53.3.</strong> Backend Agnostic Codegen</a></li><li class="chapter-item "><a href="../backend/implicit-caller-location.html"><strong aria-hidden="true">53.4.</strong> Implicit Caller Location</a></li></ol></li><li class="chapter-item "><a href="../backend/libs-and-metadata.html"><strong aria-hidden="true">54.</strong> Libraries and Metadata</a></li><li class="chapter-item "><a href="../profile-guided-optimization.html"><strong aria-hidden="true">55.</strong> Profile-guided Optimization</a></li><li class="chapter-item "><a href="../llvm-coverage-instrumentation.html"><strong aria-hidden="true">56.</strong> LLVM Source-Based Code Coverage</a></li><li class="chapter-item "><a href="../sanitizers.html"><strong aria-hidden="true">57.</strong> Sanitizers Support</a></li><li class="chapter-item "><a href="../debugging-support-in-rustc.html"><strong aria-hidden="true">58.</strong> Debugging Support in the Rust Compiler</a></li><li class="spacer"></li><li class="chapter-item affix "><a href="../appendix/background.html" class="active">Appendix A: Background topics</a></li><li class="chapter-item affix "><a href="../appendix/glossary.html">Appendix B: Glossary</a></li><li 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| <main> |
| <h1 id="background-topics"><a class="header" href="#background-topics">Background topics</a></h1> |
| <p>This section covers a numbers of common compiler terms that arise in |
| this guide. We try to give the general definition while providing some |
| Rust-specific context.</p> |
| <p><a name="cfg"></a></p> |
| <h2 id="what-is-a-control-flow-graph"><a class="header" href="#what-is-a-control-flow-graph">What is a control-flow graph?</a></h2> |
| <p>A control-flow graph (CFG) is a common term from compilers. If you've ever |
| used a flow-chart, then the concept of a control-flow graph will be |
| pretty familiar to you. It's a representation of your program that |
| clearly exposes the underlying control flow.</p> |
| <p>A control-flow graph is structured as a set of <strong>basic blocks</strong> |
| connected by edges. The key idea of a basic block is that it is a set |
| of statements that execute "together" – that is, whenever you branch |
| to a basic block, you start at the first statement and then execute |
| all the remainder. Only at the end of the block is there the |
| possibility of branching to more than one place (in MIR, we call that |
| final statement the <strong>terminator</strong>):</p> |
| <pre><code class="language-mir">bb0: { |
| statement0; |
| statement1; |
| statement2; |
| ... |
| terminator; |
| } |
| </code></pre> |
| <p>Many expressions that you are used to in Rust compile down to multiple |
| basic blocks. For example, consider an if statement:</p> |
| <pre><code class="language-rust ignore">a = 1; |
| if some_variable { |
| b = 1; |
| } else { |
| c = 1; |
| } |
| d = 1; |
| </code></pre> |
| <p>This would compile into four basic blocks in MIR. In textual form, it looks like |
| this:</p> |
| <pre><code class="language-mir">BB0: { |
| a = 1; |
| if some_variable { |
| goto BB1; |
| } else { |
| goto BB2; |
| } |
| } |
| |
| BB1: { |
| b = 1; |
| goto BB3; |
| } |
| |
| BB2: { |
| c = 1; |
| goto BB3; |
| } |
| |
| BB3: { |
| d = 1; |
| ... |
| } |
| </code></pre> |
| <p>In graphical form, it looks like this:</p> |
| <pre><code> BB0 |
| +--------------------+ |
| | a = 1; | |
| +--------------------+ |
| / \ |
| if some_variable else |
| / \ |
| BB1 / \ BB2 |
| +-----------+ +-----------+ |
| | b = 1; | | c = 1; | |
| +-----------+ +-----------+ |
| \ / |
| \ / |
| \ BB3 / |
| +----------+ |
| | d = 1; | |
| | ... | |
| +----------+ |
| </code></pre> |
| <p>When using a control-flow graph, a loop simply appears as a cycle in |
| the graph, and the <code>break</code> keyword translates into a path out of that |
| cycle.</p> |
| <p><a name="dataflow"></a></p> |
| <h2 id="what-is-a-dataflow-analysis"><a class="header" href="#what-is-a-dataflow-analysis">What is a dataflow analysis?</a></h2> |
| <p><a href="https://cs.au.dk/%7Eamoeller/spa/"><em>Static Program Analysis</em></a> by Anders Møller |
| and Michael I. Schwartzbach is an incredible resource!</p> |
| <p><em>Dataflow analysis</em> is a type of static analysis that is common in many |
| compilers. It describes a general technique, rather than a particular analysis.</p> |
| <p>The basic idea is that we can walk over a <a href="#cfg">control-flow graph (CFG)</a> and |
| keep track of what some value could be. At the end of the walk, we might have |
| shown that some claim is true or not necessarily true (e.g. "this variable must |
| be initialized"). <code>rustc</code> tends to do dataflow analyses over the MIR, since MIR |
| is already a CFG.</p> |
| <p>For example, suppose we want to check that <code>x</code> is initialized before it is used |
| in this snippet:</p> |
| <pre><code class="language-rust ignore">fn foo() { |
| let mut x; |
| |
| if some_cond { |
| x = 1; |
| } |
| |
| dbg!(x); |
| } |
| </code></pre> |
| <p>A CFG for this code might look like this:</p> |
| <pre><code class="language-txt"> +------+ |
| | Init | (A) |
| +------+ |
| | \ |
| | if some_cond |
| else \ +-------+ |
| | \| x = 1 | (B) |
| | +-------+ |
| | / |
| +---------+ |
| | dbg!(x) | (C) |
| +---------+ |
| </code></pre> |
| <p>We can do the dataflow analysis as follows: we will start off with a flag <code>init</code> |
| which indicates if we know <code>x</code> is initialized. As we walk the CFG, we will |
| update the flag. At the end, we can check its value.</p> |
| <p>So first, in block (A), the variable <code>x</code> is declared but not initialized, so |
| <code>init = false</code>. In block (B), we initialize the value, so we know that <code>x</code> is |
| initialized. So at the end of (B), <code>init = true</code>.</p> |
| <p>Block (C) is where things get interesting. Notice that there are two incoming |
| edges, one from (A) and one from (B), corresponding to whether <code>some_cond</code> is true or not. |
| But we cannot know that! It could be the case the <code>some_cond</code> is always true, |
| so that <code>x</code> is actually always initialized. It could also be the case that |
| <code>some_cond</code> depends on something random (e.g. the time), so <code>x</code> may not be |
| initialized. In general, we cannot know statically (due to <a href="https://en.wikipedia.org/wiki/Rice%27s_theorem">Rice's |
| Theorem</a>). So what should the value of <code>init</code> be in block (C)?</p> |
| <p>Generally, in dataflow analyses, if a block has multiple parents (like (C) in |
| our example), its dataflow value will be some function of all its parents (and |
| of course, what happens in (C)). Which function we use depends on the analysis |
| we are doing.</p> |
| <p>In this case, we want to be able to prove definitively that <code>x</code> must be |
| initialized before use. This forces us to be conservative and assume that |
| <code>some_cond</code> might be false sometimes. So our "merging function" is "and". That |
| is, <code>init = true</code> in (C) if <code>init = true</code> in (A) <em>and</em> in (B) (or if <code>x</code> is |
| initialized in (C)). But this is not the case; in particular, <code>init = false</code> in |
| (A), and <code>x</code> is not initialized in (C). Thus, <code>init = false</code> in (C); we can |
| report an error that "<code>x</code> may not be initialized before use".</p> |
| <p>There is definitely a lot more that can be said about dataflow analyses. There is an |
| extensive body of research literature on the topic, including a lot of theory. |
| We only discussed a forwards analysis, but backwards dataflow analysis is also |
| useful. For example, rather than starting from block (A) and moving forwards, |
| we might have started with the usage of <code>x</code> and moved backwards to try to find |
| its initialization.</p> |
| <p><a name="quantified"></a></p> |
| <h2 id="what-is-universally-quantified-what-about-existentially-quantified"><a class="header" href="#what-is-universally-quantified-what-about-existentially-quantified">What is "universally quantified"? What about "existentially quantified"?</a></h2> |
| <p>In math, a predicate may be <em>universally quantified</em> or <em>existentially |
| quantified</em>:</p> |
| <ul> |
| <li><em>Universal</em> quantification: |
| <ul> |
| <li>the predicate holds if it is true for all possible inputs.</li> |
| <li>Traditional notation: ∀x: P(x). Read as "for all x, P(x) holds".</li> |
| </ul> |
| </li> |
| <li><em>Existential</em> quantification: |
| <ul> |
| <li>the predicate holds if there is any input where it is true, i.e., there |
| only has to be a single input.</li> |
| <li>Traditional notation: ∃x: P(x). Read as "there exists x such that P(x) holds".</li> |
| </ul> |
| </li> |
| </ul> |
| <p>In Rust, they come up in type checking and trait solving. For example,</p> |
| <pre><code class="language-rust ignore">fn foo<T>() |
| </code></pre> |
| <p>This function claims that the function is well-typed for all types <code>T</code>: <code>∀ T: well_typed(foo)</code>.</p> |
| <p>Another example:</p> |
| <pre><code class="language-rust ignore">fn foo<'a>(_: &'a usize) |
| </code></pre> |
| <p>This function claims that for any lifetime <code>'a</code> (determined by the |
| caller), it is well-typed: <code>∀ 'a: well_typed(foo)</code>.</p> |
| <p>Another example:</p> |
| <pre><code class="language-rust ignore">fn foo<F>() |
| where for<'a> F: Fn(&'a u8) |
| </code></pre> |
| <p>This function claims that it is well-typed for all types <code>F</code> such that for all |
| lifetimes <code>'a</code>, <code>F: Fn(&'a u8)</code>: <code>∀ F: ∀ 'a: (F: Fn(&'a u8)) => well_typed(foo)</code>.</p> |
| <p>One more example:</p> |
| <pre><code class="language-rust ignore">fn foo(_: dyn Debug) |
| </code></pre> |
| <p>This function claims that there exists some type <code>T</code> that implements <code>Debug</code> |
| such that the function is well-typed: <code>∃ T: (T: Debug) and well_typed(foo)</code>.</p> |
| <p><a name="variance"></a></p> |
| <h2 id="what-is-a-de-bruijn-index"><a class="header" href="#what-is-a-de-bruijn-index">What is a de Bruijn Index?</a></h2> |
| <p><a href="https://en.wikipedia.org/wiki/De_Bruijn_index">De Bruijn indices</a> are a way of representing, using only integers, |
| which variables are bound in which binders. They were originally invented for |
| use in lambda calculus evaluation (see <a href="https://en.wikipedia.org/wiki/De_Bruijn_index">this Wikipedia article</a> for |
| more). In <code>rustc</code>, we use de Bruijn indices to <a href="../generics.html">represent generic types</a>.</p> |
| <p>Here is a basic example of how de Bruijn indices might be used for closures (we |
| don't actually do this in <code>rustc</code> though!):</p> |
| <pre><code class="language-rust ignore">|x| { |
| f(x) // de Bruijn index of `x` is 1 because `x` is bound 1 level up |
| |
| |y| { |
| g(x, y) // index of `x` is 2 because it is bound 2 levels up |
| // index of `y` is 1 because it is bound 1 level up |
| } |
| } |
| </code></pre> |
| <h2 id="what-are-co--and-contra-variance"><a class="header" href="#what-are-co--and-contra-variance">What are co- and contra-variance?</a></h2> |
| <p>Check out the subtyping chapter from the |
| <a href="https://doc.rust-lang.org/nomicon/subtyping.html">Rust Nomicon</a>.</p> |
| <p>See the <a href="../variance.html">variance</a> chapter of this guide for more info on how |
| the type checker handles variance.</p> |
| <p><a name="free-vs-bound"></a></p> |
| <h2 id="what-is-a-free-region-or-a-free-variable-what-about-bound-region"><a class="header" href="#what-is-a-free-region-or-a-free-variable-what-about-bound-region">What is a "free region" or a "free variable"? What about "bound region"?</a></h2> |
| <p>Let's describe the concepts of free vs bound in terms of program |
| variables, since that's the thing we're most familiar with.</p> |
| <ul> |
| <li>Consider this expression, which creates a closure: <code>|a, b| a + b</code>. |
| Here, the <code>a</code> and <code>b</code> in <code>a + b</code> refer to the arguments that the closure will |
| be given when it is called. We say that the <code>a</code> and <code>b</code> there are <strong>bound</strong> to |
| the closure, and that the closure signature <code>|a, b|</code> is a <strong>binder</strong> for the |
| names <code>a</code> and <code>b</code> (because any references to <code>a</code> or <code>b</code> within refer to the |
| variables that it introduces).</li> |
| <li>Consider this expression: <code>a + b</code>. In this expression, <code>a</code> and <code>b</code> refer to |
| local variables that are defined <em>outside</em> of the expression. We say that |
| those variables <strong>appear free</strong> in the expression (i.e., they are <strong>free</strong>, |
| not <strong>bound</strong> (tied up)).</li> |
| </ul> |
| <p>So there you have it: a variable "appears free" in some |
| expression/statement/whatever if it refers to something defined |
| outside of that expressions/statement/whatever. Equivalently, we can |
| then refer to the "free variables" of an expression – which is just |
| the set of variables that "appear free".</p> |
| <p>So what does this have to do with regions? Well, we can apply the |
| analogous concept to type and regions. For example, in the type <code>&'a u32</code>, <code>'a</code> appears free. But in the type <code>for<'a> fn(&'a u32)</code>, it |
| does not.</p> |
| <h1 id="further-reading-about-compilers"><a class="header" href="#further-reading-about-compilers">Further Reading About Compilers</a></h1> |
| <blockquote> |
| <p>Thanks to <code>mem</code>, <code>scottmcm</code>, and <code>Levi</code> on the official Discord for the |
| recommendations, and to <code>tinaun</code> for posting a link to a <a href="https://twitter.com/graydon_pub/status/1039615569132118016">twitter thread from |
| Graydon Hoare</a> |
| which had some more recommendations!</p> |
| <p>Other sources: https://gcc.gnu.org/wiki/ListOfCompilerBooks</p> |
| <p>If you have other suggestions, please feel free to open an issue or PR.</p> |
| </blockquote> |
| <h2 id="books"><a class="header" href="#books">Books</a></h2> |
| <ul> |
| <li><a href="https://www.cis.upenn.edu/%7Ebcpierce/tapl/">Types and Programming Languages</a></li> |
| <li><a href="https://www.cs.rochester.edu/%7Escott/pragmatics/">Programming Language Pragmatics</a></li> |
| <li><a href="https://www.cs.cmu.edu/%7Erwh/pfpl/2nded.pdf">Practical Foundations for Programming Languages</a></li> |
| <li><a href="https://www.pearson.com/us/higher-education/program/Aho-Compilers-Principles-Techniques-and-Tools-2nd-Edition/PGM167067.html">Compilers: Principles, Techniques, and Tools, 2nd Edition</a></li> |
| <li><a href="https://www.cs.kent.ac.uk/people/staff/rej/gcbook/">Garbage Collection: Algorithms for Automatic Dynamic Memory Management</a></li> |
| <li><a href="https://www.amazon.com/Linkers-Kaufmann-Software-Engineering-Programming/dp/1558604960">Linkers and Loaders</a> (There are also free versions of this, but the version we had linked seems to be offline at the moment.)</li> |
| <li><a href="https://www.goodreads.com/book/show/887908.Advanced_Compiler_Design_and_Implementation">Advanced Compiler Design and Implementation</a></li> |
| <li><a href="https://www.goodreads.com/book/show/2063103.Building_an_Optimizing_Compiler">Building an Optimizing Compiler</a></li> |
| <li><a href="http://www.craftinginterpreters.com/">Crafting Interpreters</a></li> |
| </ul> |
| <h2 id="courses"><a class="header" href="#courses">Courses</a></h2> |
| <ul> |
| <li><a href="https://www.cs.uoregon.edu/research/summerschool/archives.html">University of Oregon Programming Languages Summer School archive</a></li> |
| </ul> |
| <h2 id="wikis"><a class="header" href="#wikis">Wikis</a></h2> |
| <ul> |
| <li><a href="https://en.wikipedia.org/wiki/List_of_programming_languages_by_type">Wikipedia</a></li> |
| <li><a href="https://esolangs.org/wiki/Main_Page">Esoteric Programming Languages</a></li> |
| <li><a href="https://plato.stanford.edu/index.html">Stanford Encyclopedia of Philosophy</a></li> |
| <li><a href="https://ncatlab.org/nlab/show/HomePage">nLab</a></li> |
| </ul> |
| <h2 id="misc-papers-and-blog-posts"><a class="header" href="#misc-papers-and-blog-posts">Misc Papers and Blog Posts</a></h2> |
| <ul> |
| <li><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.6683&rep=rep1&type=pdf">Programming in Martin-Löf's Type Theory</a></li> |
| <li><a href="https://dl.acm.org/doi/10.1145/3093333.3009882">Polymorphism, Subtyping, and Type Inference in MLsub</a></li> |
| </ul> |
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