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<main>
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<h1 id="higher-ranked-trait-bounds"><a class="header" href="#higher-ranked-trait-bounds">Higher-ranked trait bounds</a></h1>
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<p>One of the more subtle concepts in trait resolution is <em>higher-ranked trait
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bounds</em>. An example of such a bound is <code>for<'a> MyTrait<&'a isize></code>.
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Let's walk through how selection on higher-ranked trait references
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works.</p>
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<h2 id="basic-matching-and-placeholder-leaks"><a class="header" href="#basic-matching-and-placeholder-leaks">Basic matching and placeholder leaks</a></h2>
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<p>Suppose we have a trait <code>Foo</code>:</p>
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<pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
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</span><span class="boring">fn main() {
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</span>trait Foo<X> {
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fn foo(&self, x: X) { }
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}
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<span class="boring">}</span></code></pre></pre>
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<p>Let's say we have a function <code>want_hrtb</code> that wants a type which
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implements <code>Foo<&'a isize></code> for any <code>'a</code>:</p>
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<pre><code class="language-rust ignore">fn want_hrtb<T>() where T : for<'a> Foo<&'a isize> { ... }</code></pre>
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<p>Now we have a struct <code>AnyInt</code> that implements <code>Foo<&'a isize></code> for any
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<code>'a</code>:</p>
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<pre><code class="language-rust ignore">struct AnyInt;
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impl<'a> Foo<&'a isize> for AnyInt { }</code></pre>
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<p>And the question is, does <code>AnyInt : for<'a> Foo<&'a isize></code>? We want the
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answer to be yes. The algorithm for figuring it out is closely related
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to the subtyping for higher-ranked types (which is described <a href="./hrtb.html">here</a>
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and also in a <a href="https://www.microsoft.com/en-us/research/publication/practical-type-inference-for-arbitrary-rank-types">paper by SPJ</a>. If you wish to understand higher-ranked
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subtyping, we recommend you read the paper). There are a few parts:</p>
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<ol>
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<li>Replace bound regions in the obligation with placeholders.</li>
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<li>Match the impl against the <a href="../appendix/glossary.html#placeholder">placeholder</a> obligation.</li>
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<li>Check for <em>placeholder leaks</em>.</li>
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</ol>
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<p>So let's work through our example.</p>
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<ol>
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<li>
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<p>The first thing we would do is to
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replace the bound region in the obligation with a placeholder, yielding
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<code>AnyInt : Foo<&'0 isize></code> (here <code>'0</code> represents placeholder region #0).
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Note that we now have no quantifiers;
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in terms of the compiler type, this changes from a <code>ty::PolyTraitRef</code>
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to a <code>TraitRef</code>. We would then create the <code>TraitRef</code> from the impl,
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using fresh variables for it's bound regions (and thus getting
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<code>Foo<&'$a isize></code>, where <code>'$a</code> is the inference variable for <code>'a</code>).</p>
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</li>
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<li>
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<p>Next
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we relate the two trait refs, yielding a graph with the constraint
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that <code>'0 == '$a</code>.</p>
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</li>
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<li>
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<p>Finally, we check for placeholder "leaks" – a
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leak is basically any attempt to relate a placeholder region to another
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placeholder region, or to any region that pre-existed the impl match.
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The leak check is done by searching from the placeholder region to find
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the set of regions that it is related to in any way. This is called
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the "taint" set. To pass the check, that set must consist <em>solely</em> of
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itself and region variables from the impl. If the taint set includes
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any other region, then the match is a failure. In this case, the taint
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set for <code>'0</code> is <code>{'0, '$a}</code>, and hence the check will succeed.</p>
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</li>
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</ol>
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<p>Let's consider a failure case. Imagine we also have a struct</p>
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<pre><code class="language-rust ignore">struct StaticInt;
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impl Foo<&'static isize> for StaticInt;</code></pre>
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<p>We want the obligation <code>StaticInt : for<'a> Foo<&'a isize></code> to be
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considered unsatisfied. The check begins just as before. <code>'a</code> is
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replaced with a placeholder <code>'0</code> and the impl trait reference is instantiated to
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<code>Foo<&'static isize></code>. When we relate those two, we get a constraint
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like <code>'static == '0</code>. This means that the taint set for <code>'0</code> is <code>{'0, 'static}</code>, which fails the leak check.</p>
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<p><strong>TODO</strong>: This is because <code>'static</code> is not a region variable but is in the
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taint set, right?</p>
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<h2 id="higher-ranked-trait-obligations"><a class="header" href="#higher-ranked-trait-obligations">Higher-ranked trait obligations</a></h2>
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<p>Once the basic matching is done, we get to another interesting topic:
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how to deal with impl obligations. I'll work through a simple example
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here. Imagine we have the traits <code>Foo</code> and <code>Bar</code> and an associated impl:</p>
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<pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
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</span><span class="boring">fn main() {
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</span>trait Foo<X> {
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fn foo(&self, x: X) { }
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}
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trait Bar<X> {
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fn bar(&self, x: X) { }
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}
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impl<X,F> Foo<X> for F
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where F : Bar<X>
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{
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}
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<span class="boring">}</span></code></pre></pre>
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<p>Now let's say we have an obligation <code>Baz: for<'a> Foo<&'a isize></code> and we match
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this impl. What obligation is generated as a result? We want to get
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<code>Baz: for<'a> Bar<&'a isize></code>, but how does that happen?</p>
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<p>After the matching, we are in a position where we have a placeholder
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substitution like <code>X => &'0 isize</code>. If we apply this substitution to the
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impl obligations, we get <code>F : Bar<&'0 isize></code>. Obviously this is not
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directly usable because the placeholder region <code>'0</code> cannot leak out of
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our computation.</p>
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<p>What we do is to create an inverse mapping from the taint set of <code>'0</code>
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back to the original bound region (<code>'a</code>, here) that <code>'0</code> resulted
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from. (This is done in <code>higher_ranked::plug_leaks</code>). We know that the
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leak check passed, so this taint set consists solely of the placeholder
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region itself plus various intermediate region variables. We then walk
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the trait-reference and convert every region in that taint set back to
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a late-bound region, so in this case we'd wind up with
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<code>Baz: for<'a> Bar<&'a isize></code>.</p>
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