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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> |
| <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/~yannis/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 id="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 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> |
| <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> |
| |
| </main> |
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