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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 expanded "><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 expanded "><a href="variance.html" class="active"><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">Appendix A: Background topics</a></li><li class="chapter-item affix "><a href="appendix/glossary.html">Appendix B: Glossary</a></li><li class="chapter-item affix "><a href="appendix/code-index.html">Appendix C: Code Index</a></li><li class="chapter-item affix "><a href="appendix/compiler-lecture.html">Appendix D: Compiler Lecture Series</a></li><li class="chapter-item affix "><a href="appendix/bibliography.html">Appendix E: Bibliography</a></li><li class="chapter-item affix "><a href="appendix/humorust.html">Appendix Z: HumorRust</a></li><li class="spacer"></li></ol> |
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| <h1 id="variance-of-type-and-lifetime-parameters"><a class="header" href="#variance-of-type-and-lifetime-parameters">Variance of type and lifetime parameters</a></h1> |
| <ul> |
| <li><a href="#the-algorithm">The algorithm</a></li> |
| <li><a href="#constraints">Constraints</a> |
| <ul> |
| <li><a href="#dependency-graph-management">Dependency graph management</a></li> |
| </ul> |
| </li> |
| <li><a href="#addendum-variance-on-traits">Addendum: Variance on traits</a> |
| <ul> |
| <li><a href="#variance-and-object-types">Variance and object types</a></li> |
| <li><a href="#trait-variance-and-vtable-resolution">Trait variance and vtable resolution</a></li> |
| <li><a href="#variance-and-associated-types">Variance and associated types</a></li> |
| </ul> |
| </li> |
| </ul> |
| <p>For a more general background on variance, see the <a href="./appendix/background.html">background</a> appendix.</p> |
| <p>During type checking we must infer the variance of type and lifetime |
| parameters. The algorithm is taken from Section 4 of the paper <a href="https://people.cs.umass.edu/%7Eyannis/variance-extended2011.pdf">"Taming the |
| Wildcards: Combining Definition- and Use-Site Variance"</a> published in |
| PLDI'11 and written by Altidor et al., and hereafter referred to as The Paper.</p> |
| <p>This inference is explicitly designed <em>not</em> to consider the uses of |
| types within code. To determine the variance of type parameters |
| defined on type <code>X</code>, we only consider the definition of the type <code>X</code> |
| and the definitions of any types it references.</p> |
| <p>We only infer variance for type parameters found on <em>data types</em> |
| like structs and enums. In these cases, there is a fairly straightforward |
| explanation for what variance means. The variance of the type |
| or lifetime parameters defines whether <code>T<A></code> is a subtype of <code>T<B></code> |
| (resp. <code>T<'a></code> and <code>T<'b></code>) based on the relationship of <code>A</code> and <code>B</code> |
| (resp. <code>'a</code> and <code>'b</code>).</p> |
| <p>We do not infer variance for type parameters found on traits, functions, |
| or impls. Variance on trait parameters can indeed make sense |
| (and we used to compute it) but it is actually rather subtle in |
| meaning and not that useful in practice, so we removed it. See the |
| <a href="#addendum">addendum</a> for some details. Variances on function/impl parameters, on the |
| other hand, doesn't make sense because these parameters are instantiated and |
| then forgotten, they don't persist in types or compiled byproducts.</p> |
| <blockquote> |
| <p><strong>Notation</strong></p> |
| <p>We use the notation of The Paper throughout this chapter:</p> |
| <ul> |
| <li><code>+</code> is <em>covariance</em>.</li> |
| <li><code>-</code> is <em>contravariance</em>.</li> |
| <li><code>*</code> is <em>bivariance</em>.</li> |
| <li><code>o</code> is <em>invariance</em>.</li> |
| </ul> |
| </blockquote> |
| <h2 id="the-algorithm"><a class="header" href="#the-algorithm">The algorithm</a></h2> |
| <p>The basic idea is quite straightforward. We iterate over the types |
| defined and, for each use of a type parameter <code>X</code>, accumulate a |
| constraint indicating that the variance of <code>X</code> must be valid for the |
| variance of that use site. We then iteratively refine the variance of |
| <code>X</code> until all constraints are met. There is <em>always</em> a solution, because at |
| the limit we can declare all type parameters to be invariant and all |
| constraints will be satisfied.</p> |
| <p>As a simple example, consider:</p> |
| <pre><code class="language-rust ignore">enum Option<A> { Some(A), None } |
| enum OptionalFn<B> { Some(|B|), None } |
| enum OptionalMap<C> { Some(|C| -> C), None } |
| </code></pre> |
| <p>Here, we will generate the constraints:</p> |
| <pre><code class="language-text">1. V(A) <= + |
| 2. V(B) <= - |
| 3. V(C) <= + |
| 4. V(C) <= - |
| </code></pre> |
| <p>These indicate that (1) the variance of A must be at most covariant; |
| (2) the variance of B must be at most contravariant; and (3, 4) the |
| variance of C must be at most covariant <em>and</em> contravariant. All of these |
| results are based on a variance lattice defined as follows:</p> |
| <pre><code class="language-text"> * Top (bivariant) |
| - + |
| o Bottom (invariant) |
| </code></pre> |
| <p>Based on this lattice, the solution <code>V(A)=+</code>, <code>V(B)=-</code>, <code>V(C)=o</code> is the |
| optimal solution. Note that there is always a naive solution which |
| just declares all variables to be invariant.</p> |
| <p>You may be wondering why fixed-point iteration is required. The reason |
| is that the variance of a use site may itself be a function of the |
| variance of other type parameters. In full generality, our constraints |
| take the form:</p> |
| <pre><code class="language-text">V(X) <= Term |
| Term := + | - | * | o | V(X) | Term x Term |
| </code></pre> |
| <p>Here the notation <code>V(X)</code> indicates the variance of a type/region |
| parameter <code>X</code> with respect to its defining class. <code>Term x Term</code> |
| represents the "variance transform" as defined in the paper:</p> |
| <blockquote> |
| <p>If the variance of a type variable <code>X</code> in type expression <code>E</code> is <code>V2</code> |
| and the definition-site variance of the corresponding type parameter |
| of a class <code>C</code> is <code>V1</code>, then the variance of <code>X</code> in the type expression |
| <code>C<E></code> is <code>V3 = V1.xform(V2)</code>.</p> |
| </blockquote> |
| <h2 id="constraints"><a class="header" href="#constraints">Constraints</a></h2> |
| <p>If I have a struct or enum with where clauses:</p> |
| <pre><code class="language-rust ignore">struct Foo<T: Bar> { ... } |
| </code></pre> |
| <p>you might wonder whether the variance of <code>T</code> with respect to <code>Bar</code> affects the |
| variance <code>T</code> with respect to <code>Foo</code>. I claim no. The reason: assume that <code>T</code> is |
| invariant with respect to <code>Bar</code> but covariant with respect to <code>Foo</code>. And then |
| we have a <code>Foo<X></code> that is upcast to <code>Foo<Y></code>, where <code>X <: Y</code>. However, while |
| <code>X : Bar</code>, <code>Y : Bar</code> does not hold. In that case, the upcast will be illegal, |
| but not because of a variance failure, but rather because the target type |
| <code>Foo<Y></code> is itself just not well-formed. Basically we get to assume |
| well-formedness of all types involved before considering variance.</p> |
| <h3 id="dependency-graph-management"><a class="header" href="#dependency-graph-management">Dependency graph management</a></h3> |
| <p>Because variance is a whole-crate inference, its dependency graph |
| can become quite muddled if we are not careful. To resolve this, we refactor |
| into two queries:</p> |
| <ul> |
| <li><code>crate_variances</code> computes the variance for all items in the current crate.</li> |
| <li><code>variances_of</code> accesses the variance for an individual reading; it |
| works by requesting <code>crate_variances</code> and extracting the relevant data.</li> |
| </ul> |
| <p>If you limit yourself to reading <code>variances_of</code>, your code will only |
| depend then on the inference of that particular item.</p> |
| <p>Ultimately, this setup relies on the <a href="./queries/incremental-compilation.html">red-green algorithm</a>. In particular, |
| every variance query effectively depends on all type definitions in the entire |
| crate (through <code>crate_variances</code>), but since most changes will not result in a |
| change to the actual results from variance inference, the <code>variances_of</code> query |
| will wind up being considered green after it is re-evaluated.</p> |
| <p><a name="addendum"></a></p> |
| <h2 id="addendum-variance-on-traits"><a class="header" href="#addendum-variance-on-traits">Addendum: Variance on traits</a></h2> |
| <p>As mentioned above, we used to permit variance on traits. This was |
| computed based on the appearance of trait type parameters in |
| method signatures and was used to represent the compatibility of |
| vtables in trait objects (and also "virtual" vtables or dictionary |
| in trait bounds). One complication was that variance for |
| associated types is less obvious, since they can be projected out |
| and put to myriad uses, so it's not clear when it is safe to allow |
| <code>X<A>::Bar</code> to vary (or indeed just what that means). Moreover (as |
| covered below) all inputs on any trait with an associated type had |
| to be invariant, limiting the applicability. Finally, the |
| annotations (<code>MarkerTrait</code>, <code>PhantomFn</code>) needed to ensure that all |
| trait type parameters had a variance were confusing and annoying |
| for little benefit.</p> |
| <p>Just for historical reference, I am going to preserve some text indicating how |
| one could interpret variance and trait matching.</p> |
| <h3 id="variance-and-object-types"><a class="header" href="#variance-and-object-types">Variance and object types</a></h3> |
| <p>Just as with structs and enums, we can decide the subtyping |
| relationship between two object types <code>&Trait<A></code> and <code>&Trait<B></code> |
| based on the relationship of <code>A</code> and <code>B</code>. Note that for object |
| types we ignore the <code>Self</code> type parameter – it is unknown, and |
| the nature of dynamic dispatch ensures that we will always call a |
| function that is expected the appropriate <code>Self</code> type. However, we |
| must be careful with the other type parameters, or else we could |
| end up calling a function that is expecting one type but provided |
| another.</p> |
| <p>To see what I mean, consider a trait like so:</p> |
| <pre><pre class="playground"><code class="language-rust"> |
| <span class="boring">#![allow(unused)] |
| </span><span class="boring">fn main() { |
| </span>trait ConvertTo<A> { |
| fn convertTo(&self) -> A; |
| } |
| <span class="boring">} |
| </span></code></pre></pre> |
| <p>Intuitively, If we had one object <code>O=&ConvertTo<Object></code> and another |
| <code>S=&ConvertTo<String></code>, then <code>S <: O</code> because <code>String <: Object</code> |
| (presuming Java-like "string" and "object" types, my go to examples |
| for subtyping). The actual algorithm would be to compare the |
| (explicit) type parameters pairwise respecting their variance: here, |
| the type parameter A is covariant (it appears only in a return |
| position), and hence we require that <code>String <: Object</code>.</p> |
| <p>You'll note though that we did not consider the binding for the |
| (implicit) <code>Self</code> type parameter: in fact, it is unknown, so that's |
| good. The reason we can ignore that parameter is precisely because we |
| don't need to know its value until a call occurs, and at that time (as |
| you said) the dynamic nature of virtual dispatch means the code we run |
| will be correct for whatever value <code>Self</code> happens to be bound to for |
| the particular object whose method we called. <code>Self</code> is thus different |
| from <code>A</code>, because the caller requires that <code>A</code> be known in order to |
| know the return type of the method <code>convertTo()</code>. (As an aside, we |
| have rules preventing methods where <code>Self</code> appears outside of the |
| receiver position from being called via an object.)</p> |
| <h3 id="trait-variance-and-vtable-resolution"><a class="header" href="#trait-variance-and-vtable-resolution">Trait variance and vtable resolution</a></h3> |
| <p>But traits aren't only used with objects. They're also used when |
| deciding whether a given impl satisfies a given trait bound. To set the |
| scene here, imagine I had a function:</p> |
| <pre><code class="language-rust ignore">fn convertAll<A,T:ConvertTo<A>>(v: &[T]) { ... } |
| </code></pre> |
| <p>Now imagine that I have an implementation of <code>ConvertTo</code> for <code>Object</code>:</p> |
| <pre><code class="language-rust ignore">impl ConvertTo<i32> for Object { ... } |
| </code></pre> |
| <p>And I want to call <code>convertAll</code> on an array of strings. Suppose |
| further that for whatever reason I specifically supply the value of |
| <code>String</code> for the type parameter <code>T</code>:</p> |
| <pre><code class="language-rust ignore">let mut vector = vec!["string", ...]; |
| convertAll::<i32, String>(vector); |
| </code></pre> |
| <p>Is this legal? To put another way, can we apply the <code>impl</code> for |
| <code>Object</code> to the type <code>String</code>? The answer is yes, but to see why |
| we have to expand out what will happen:</p> |
| <ul> |
| <li> |
| <p><code>convertAll</code> will create a pointer to one of the entries in the |
| vector, which will have type <code>&String</code></p> |
| </li> |
| <li> |
| <p>It will then call the impl of <code>convertTo()</code> that is intended |
| for use with objects. This has the type <code>fn(self: &Object) -> i32</code>.</p> |
| <p>It is OK to provide a value for <code>self</code> of type <code>&String</code> because |
| <code>&String <: &Object</code>.</p> |
| </li> |
| </ul> |
| <p>OK, so intuitively we want this to be legal, so let's bring this back |
| to variance and see whether we are computing the correct result. We |
| must first figure out how to phrase the question "is an impl for |
| <code>Object,i32</code> usable where an impl for <code>String,i32</code> is expected?"</p> |
| <p>Maybe it's helpful to think of a dictionary-passing implementation of |
| type classes. In that case, <code>convertAll()</code> takes an implicit parameter |
| representing the impl. In short, we <em>have</em> an impl of type:</p> |
| <pre><code class="language-text">V_O = ConvertTo<i32> for Object |
| </code></pre> |
| <p>and the function prototype expects an impl of type:</p> |
| <pre><code class="language-text">V_S = ConvertTo<i32> for String |
| </code></pre> |
| <p>As with any argument, this is legal if the type of the value given |
| (<code>V_O</code>) is a subtype of the type expected (<code>V_S</code>). So is <code>V_O <: V_S</code>? |
| The answer will depend on the variance of the various parameters. In |
| this case, because the <code>Self</code> parameter is contravariant and <code>A</code> is |
| covariant, it means that:</p> |
| <pre><code class="language-text">V_O <: V_S iff |
| i32 <: i32 |
| String <: Object |
| </code></pre> |
| <p>These conditions are satisfied and so we are happy.</p> |
| <h3 id="variance-and-associated-types"><a class="header" href="#variance-and-associated-types">Variance and associated types</a></h3> |
| <p>Traits with associated types – or at minimum projection |
| expressions – must be invariant with respect to all of their |
| inputs. To see why this makes sense, consider what subtyping for a |
| trait reference means:</p> |
| <pre><code class="language-text"><T as Trait> <: <U as Trait> |
| </code></pre> |
| <p>means that if I know that <code>T as Trait</code>, I also know that <code>U as Trait</code>. Moreover, if you think of it as dictionary passing style, |
| it means that a dictionary for <code><T as Trait></code> is safe to use where |
| a dictionary for <code><U as Trait></code> is expected.</p> |
| <p>The problem is that when you can project types out from <code><T as Trait></code>, the relationship to types projected out of <code><U as Trait></code> |
| is completely unknown unless <code>T==U</code> (see #21726 for more |
| details). Making <code>Trait</code> invariant ensures that this is true.</p> |
| <p>Another related reason is that if we didn't make traits with |
| associated types invariant, then projection is no longer a |
| function with a single result. Consider:</p> |
| <pre><code class="language-rust ignore">trait Identity { type Out; fn foo(&self); } |
| impl<T> Identity for T { type Out = T; ... } |
| </code></pre> |
| <p>Now if I have <code><&'static () as Identity>::Out</code>, this can be |
| validly derived as <code>&'a ()</code> for any <code>'a</code>:</p> |
| <pre><code class="language-text"><&'a () as Identity> <: <&'static () as Identity> |
| if &'static () < : &'a () -- Identity is contravariant in Self |
| if 'static : 'a -- Subtyping rules for relations |
| </code></pre> |
| <p>This change otoh means that <code><'static () as Identity>::Out</code> is |
| always <code>&'static ()</code> (which might then be upcast to <code>'a ()</code>, |
| separately). This was helpful in solving #21750.</p> |
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