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| <h1 id="constraint-propagation"><a class="header" href="#constraint-propagation">Constraint propagation</a></h1> |
| <p>The main work of the region inference is <strong>constraint propagation</strong>, |
| which is done in the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#method.propagate_constraints"><code>propagate_constraints</code></a> function. There are |
| three sorts of constraints that are used in NLL, and we'll explain how |
| <code>propagate_constraints</code> works by "layering" those sorts of constraints |
| on one at a time (each of them is fairly independent from the others):</p> |
| <ul> |
| <li>liveness constraints (<code>R live at E</code>), which arise from liveness;</li> |
| <li>outlives constraints (<code>R1: R2</code>), which arise from subtyping;</li> |
| <li><a href="./member_constraints.html">member constraints</a> (<code>member R_m of [R_c...]</code>), which arise from impl Trait.</li> |
| </ul> |
| <p>In this chapter, we'll explain the "heart" of constraint propagation, |
| covering both liveness and outlives constraints.</p> |
| <h2 id="notation-and-high-level-concepts"><a class="header" href="#notation-and-high-level-concepts">Notation and high-level concepts</a></h2> |
| <p>Conceptually, region inference is a "fixed-point" computation. It is |
| given some set of constraints <code>{C}</code> and it computes a set of values |
| <code>Values: R -> {E}</code> that maps each region <code>R</code> to a set of elements |
| <code>{E}</code> (see <a href="../region_inference.html#region-variables">here</a> for more notes on region elements):</p> |
| <ul> |
| <li>Initially, each region is mapped to an empty set, so <code>Values(R) = {}</code> for all regions <code>R</code>.</li> |
| <li>Next, we process the constraints repeatedly until a fixed-point is reached: |
| <ul> |
| <li>For each constraint C: |
| <ul> |
| <li>Update <code>Values</code> as needed to satisfy the constraint</li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <p>As a simple example, if we have a liveness constraint <code>R live at E</code>, |
| then we can apply <code>Values(R) = Values(R) union {E}</code> to make the |
| constraint be satisfied. Similarly, if we have an outlives constraints |
| <code>R1: R2</code>, we can apply <code>Values(R1) = Values(R1) union Values(R2)</code>. |
| (Member constraints are more complex and we discuss them <a href="./member_constraints.html">in this section</a>.)</p> |
| <p>In practice, however, we are a bit more clever. Instead of applying |
| the constraints in a loop, we can analyze the constraints and figure |
| out the correct order to apply them, so that we only have to apply |
| each constraint once in order to find the final result.</p> |
| <p>Similarly, in the implementation, the <code>Values</code> set is stored in the |
| <code>scc_values</code> field, but they are indexed not by a <em>region</em> but by a |
| <em>strongly connected component</em> (SCC). SCCs are an optimization that |
| avoids a lot of redundant storage and computation. They are explained |
| in the section on outlives constraints.</p> |
| <h2 id="liveness-constraints"><a class="header" href="#liveness-constraints">Liveness constraints</a></h2> |
| <p>A <strong>liveness constraint</strong> arises when some variable whose type |
| includes a region R is live at some <a href="../../appendix/glossary.html#point">point</a> P. This simply means that |
| the value of R must include the point P. Liveness constraints are |
| computed by the MIR type checker.</p> |
| <p>A liveness constraint <code>R live at E</code> is satisfied if <code>E</code> is a member of |
| <code>Values(R)</code>. So to "apply" such a constraint to <code>Values</code>, we just have |
| to compute <code>Values(R) = Values(R) union {E}</code>.</p> |
| <p>The liveness values are computed in the type-check and passed to the |
| region inference upon creation in the <code>liveness_constraints</code> argument. |
| These are not represented as individual constraints like <code>R live at E</code> |
| though; instead, we store a (sparse) bitset per region variable (of |
| type <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/values/struct.LivenessValues.html"><code>LivenessValues</code></a>). This way we only need a single bit for each |
| liveness constraint.</p> |
| <p>One thing that is worth mentioning: All lifetime parameters are always |
| considered to be live over the entire function body. This is because |
| they correspond to some portion of the <em>caller's</em> execution, and that |
| execution clearly includes the time spent in this function, since the |
| caller is waiting for us to return.</p> |
| <h2 id="outlives-constraints"><a class="header" href="#outlives-constraints">Outlives constraints</a></h2> |
| <p>An outlives constraint <code>'a: 'b</code> indicates that the value of <code>'a</code> must |
| be a <strong>superset</strong> of the value of <code>'b</code>. That is, an outlives |
| constraint <code>R1: R2</code> is satisfied if <code>Values(R1)</code> is a superset of |
| <code>Values(R2)</code>. So to "apply" such a constraint to <code>Values</code>, we just |
| have to compute <code>Values(R1) = Values(R1) union Values(R2)</code>.</p> |
| <p>One observation that follows from this is that if you have <code>R1: R2</code> |
| and <code>R2: R1</code>, then <code>R1 = R2</code> must be true. Similarly, if you have:</p> |
| <pre><code class="language-txt">R1: R2 |
| R2: R3 |
| R3: R4 |
| R4: R1 |
| </code></pre> |
| <p>then <code>R1 = R2 = R3 = R4</code> follows. We take advantage of this to make things |
| much faster, as described shortly.</p> |
| <p>In the code, the set of outlives constraints is given to the region |
| inference context on creation in a parameter of type |
| <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/constraints/struct.OutlivesConstraintSet.html"><code>OutlivesConstraintSet</code></a>. The constraint set is basically just a list of <code>'a: 'b</code> constraints.</p> |
| <h3 id="the-outlives-constraint-graph-and-sccs"><a class="header" href="#the-outlives-constraint-graph-and-sccs">The outlives constraint graph and SCCs</a></h3> |
| <p>In order to work more efficiently with outlives constraints, they are |
| <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/constraints/struct.OutlivesConstraintSet.html#method.graph">converted into the form of a graph</a>, where the nodes of the |
| graph are region variables (<code>'a</code>, <code>'b</code>) and each constraint <code>'a: 'b</code> |
| induces an edge <code>'a -> 'b</code>. This conversion happens in the |
| <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#method.new"><code>RegionInferenceContext::new</code></a> function that creates the inference |
| context.</p> |
| <p>When using a graph representation, we can detect regions that must be equal |
| by looking for cycles. That is, if you have a constraint like</p> |
| <pre><code class="language-txt">'a: 'b |
| 'b: 'c |
| 'c: 'd |
| 'd: 'a |
| </code></pre> |
| <p>then this will correspond to a cycle in the graph containing the |
| elements <code>'a...'d</code>.</p> |
| <p>Therefore, one of the first things that we do in propagating region |
| values is to compute the <strong>strongly connected components</strong> (SCCs) in |
| the constraint graph. The result is stored in the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#structfield.constraint_sccs"><code>constraint_sccs</code></a> |
| field. You can then easily find the SCC that a region <code>r</code> is a part of |
| by invoking <code>constraint_sccs.scc(r)</code>.</p> |
| <p>Working in terms of SCCs allows us to be more efficient: if we have a |
| set of regions <code>'a...'d</code> that are part of a single SCC, we don't have |
| to compute/store their values separately. We can just store one value |
| <strong>for the SCC</strong>, since they must all be equal.</p> |
| <p>If you look over the region inference code, you will see that a number |
| of fields are defined in terms of SCCs. For example, the |
| <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#structfield.scc_values"><code>scc_values</code></a> field stores the values of each SCC. To get the value |
| of a specific region <code>'a</code> then, we first figure out the SCC that the |
| region is a part of, and then find the value of that SCC.</p> |
| <p>When we compute SCCs, we not only figure out which regions are a |
| member of each SCC, we also figure out the edges between them. So for example |
| consider this set of outlives constraints:</p> |
| <pre><code class="language-txt">'a: 'b |
| 'b: 'a |
| |
| 'a: 'c |
| |
| 'c: 'd |
| 'd: 'c |
| </code></pre> |
| <p>Here we have two SCCs: S0 contains <code>'a</code> and <code>'b</code>, and S1 contains <code>'c</code> |
| and <code>'d</code>. But these SCCs are not independent: because <code>'a: 'c</code>, that |
| means that <code>S0: S1</code> as well. That is -- the value of <code>S0</code> must be a |
| superset of the value of <code>S1</code>. One crucial thing is that this graph of |
| SCCs is always a DAG -- that is, it never has cycles. This is because |
| all the cycles have been removed to form the SCCs themselves.</p> |
| <h3 id="applying-liveness-constraints-to-sccs"><a class="header" href="#applying-liveness-constraints-to-sccs">Applying liveness constraints to SCCs</a></h3> |
| <p>The liveness constraints that come in from the type-checker are |
| expressed in terms of regions -- that is, we have a map like |
| <code>Liveness: R -> {E}</code>. But we want our final result to be expressed |
| in terms of SCCs -- we can integrate these liveness constraints very |
| easily just by taking the union:</p> |
| <pre><code class="language-txt">for each region R: |
| let S be the SCC that contains R |
| Values(S) = Values(S) union Liveness(R) |
| </code></pre> |
| <p>In the region inferencer, this step is done in <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#method.new"><code>RegionInferenceContext::new</code></a>.</p> |
| <h3 id="applying-outlives-constraints"><a class="header" href="#applying-outlives-constraints">Applying outlives constraints</a></h3> |
| <p>Once we have computed the DAG of SCCs, we use that to structure out |
| entire computation. If we have an edge <code>S1 -> S2</code> between two SCCs, |
| that means that <code>Values(S1) >= Values(S2)</code> must hold. So, to compute |
| the value of <code>S1</code>, we first compute the values of each successor <code>S2</code>. |
| Then we simply union all of those values together. To use a |
| quasi-iterator-like notation:</p> |
| <pre><code class="language-txt">Values(S1) = |
| s1.successors() |
| .map(|s2| Values(s2)) |
| .union() |
| </code></pre> |
| <p>In the code, this work starts in the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#method.propagate_constraints"><code>propagate_constraints</code></a> |
| function, which iterates over all the SCCs. For each SCC <code>S1</code>, we |
| compute its value by first computing the value of its |
| successors. Since SCCs form a DAG, we don't have to be concerned about |
| cycles, though we do need to keep a set around to track whether we |
| have already processed a given SCC or not. For each successor <code>S2</code>, once |
| we have computed <code>S2</code>'s value, we can union those elements into the |
| value for <code>S1</code>. (Although we have to be careful in this process to |
| properly handle <a href="./placeholders_and_universes.html">higher-ranked |
| placeholders</a>. Note that the value |
| for <code>S1</code> already contains the liveness constraints, since they were |
| added in <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_borrowck/region_infer/struct.RegionInferenceContext.html#method.new"><code>RegionInferenceContext::new</code></a>.</p> |
| <p>Once that process is done, we now have the "minimal value" for <code>S1</code>, |
| taking into account all of the liveness and outlives |
| constraints. However, in order to complete the process, we must also |
| consider <a href="./member_constraints.html">member constraints</a>, which are described in <a href="./member_constraints.html">a later |
| section</a>.</p> |
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