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                         <h1 id="invariants-of-the-type-system"><a class="header" href="#invariants-of-the-type-system">Invariants of the type system</a></h1>
 <p>FIXME: This file talks about invariants of the type system as a whole, not only the solver</p>
 <p>There are a lot of invariants - things the type system guarantees to be true at all times -
 which are desirable or expected from other languages and type systems. Unfortunately, quite
 a few of them do not hold in Rust right now. This is either a fundamental to its design or
 caused by bugs and something that may change in the future.</p>
 <p>It is important to know about the things you can assume while working on - and with - the
 type system, so here's an incomplete and unofficial list of invariants of
 the core type system:</p>
 <ul>
 <li>✅: this invariant mostly holds, with some weird exceptions, you can rely on it outside
 of these cases</li>
 <li>❌: this invariant does not hold, either due to bugs or by design, you must not rely on
 it for soundness or have to be incredibly careful when doing so</li>
 </ul>
 <h3 id="wfx-implies-wfnormalizex-"><a class="header" href="#wfx-implies-wfnormalizex-"><code>wf(X)</code> implies <code>wf(normalize(X))</code> ✅</a></h3>
 <p>If a type containing aliases is well-formed, it should also be
 well-formed after normalizing said aliases. We rely on this as
 otherwise we would have to re-check for well-formedness for these
 types.</p>
 <h3 id="structural-equality-modulo-regions-implies-semantic-equality-"><a class="header" href="#structural-equality-modulo-regions-implies-semantic-equality-">Structural equality modulo regions implies semantic equality ✅</a></h3>
 <p>If you have a some type and equate it to itself after replacing any regions with unique
 inference variables in both the lhs and rhs, the now potentially structurally different
 types should still be equal to each other.</p>
 <p>Needed to prevent goals from succeeding in HIR typeck and then failing in MIR borrowck.
 If this invariant is broken MIR typeck ends up failing with an ICE.</p>
 <h3 id="applying-inference-results-from-a-goal-does-not-change-its-result-"><a class="header" href="#applying-inference-results-from-a-goal-does-not-change-its-result-">Applying inference results from a goal does not change its result ❌</a></h3>
 <p>TODO: this invariant is formulated in a weird way and needs to be elaborated.
 Pretty much: I would like this check to only fail if there's a solver bug:
 https://github.com/rust-lang/rust/blob/2ffeb4636b4ae376f716dc4378a7efb37632dc2d/compiler/rustc_trait_selection/src/solve/eval_ctxt.rs#L391-L407</p>
 <p>If we prove some goal/equate types/whatever, apply the resulting inference constraints,
 and then redo the original action, the result should be the same.</p>
 <p>This unfortunately does not hold - at least in the new solver - due to a few annoying reasons.</p>
 <h3 id="the-trait-solver-has-to-be-locally-sound-"><a class="header" href="#the-trait-solver-has-to-be-locally-sound-">The trait solver has to be <em>locally sound</em> ✅</a></h3>
 <p>This means that we must never return <em>success</em> for goals for which no <code>impl</code> exists. That would
 mean we assume a trait is implemented even though it is not, which is very likely to result in
 actual unsoundness. When using <code>where</code>-bounds to prove a goal, the <code>impl</code> will be provided by the
 user of the item.</p>
 <p>This invariant only holds if we check region constraints. As we do not check region constraints
 during implicit negative overlap check in coherence, this invariant is broken there. As this check
 relies on <em>completeness</em> of the trait solver, it is not able to use the current region constraints
 check - <code>InferCtxt::resolve_regions</code> - as its handling of type outlives goals is incomplete.</p>
 <h3 id="normalization-of-semantically-equal-aliases-in-empty-environments-results-in-a-unique-type-"><a class="header" href="#normalization-of-semantically-equal-aliases-in-empty-environments-results-in-a-unique-type-">Normalization of semantically equal aliases in empty environments results in a unique type ✅</a></h3>
 <p>Normalization for alias types/consts has to have a unique result. Otherwise we can easily
 implement transmute in safe code. Given the following function, we have to make sure that
 the input and output types always get normalized to the same concrete type.</p>
 <pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
 </span><span class="boring">fn main() {
 </span>fn foo&lt;T: Trait&gt;(
     x: &lt;T as Trait&gt;::Assoc
 ) -&gt; &lt;T as Trait&gt;::Assoc {
     x
 }
 <span class="boring">}</span></code></pre></pre>
 <p>Many of the currently known unsound issues end up relying on this invariant being broken.
 It is however very difficult to imagine a sound type system without this invariant, so
 the issue is that the invariant is broken, not that we incorrectly rely on it.</p>
 <h3 id="generic-goals-and-their-instantiations-have-the-same-result-"><a class="header" href="#generic-goals-and-their-instantiations-have-the-same-result-">Generic goals and their instantiations have the same result ✅</a></h3>
 <p>Pretty much: If we successfully typecheck a generic function concrete instantiations
 of that function should also typeck. We should not get errors post-monomorphization.
 We can however get overflow errors at that point.</p>
 <p>TODO: example for overflow error post-monomorphization</p>
 <p>This invariant is relied on to allow the normalization of generic aliases. Breaking
 it can easily result in unsoundness, e.g. <a href="https://github.com/rust-lang/rust/issues/57893">#57893</a></p>
 <h3 id="trait-goals-in-empty-environments-are-proven-by-a-unique-impl-"><a class="header" href="#trait-goals-in-empty-environments-are-proven-by-a-unique-impl-">Trait goals in empty environments are proven by a unique impl ✅</a></h3>
 <p>If a trait goal holds with an empty environment, there should be a unique <code>impl</code>,
 either user-defined or builtin, which is used to prove that goal. This is
 necessary to select a unique method.</p>
 <p>We do however break this invariant in few cases, some of which are due to bugs,
 some by design:</p>
 <ul>
 <li><em>marker traits</em> are allowed to overlap as they do not have associated items</li>
 <li><em>specialization</em> allows specializing impls to overlap with their parent</li>
 <li>the builtin trait object trait implementation can overlap with a user-defined impl:
 <a href="https://github.com/rust-lang/rust/issues/57893">#57893</a></li>
 </ul>
 <h3 id="the-type-system-is-complete-"><a class="header" href="#the-type-system-is-complete-">The type system is complete ❌</a></h3>
 <p>The type system is not complete, it often adds unnecessary inference constraints, and errors
 even though the goal could hold.</p>
 <ul>
 <li>method selection</li>
 <li>opaque type inference</li>
 <li>handling type outlives constraints</li>
 <li>preferring <code>ParamEnv</code> candidates over <code>Impl</code> candidates during candidate selection
 in the trait solver</li>
 </ul>
 <h4 id="the-type-system-is-complete-during-the-implicit-negative-overlap-check-in-coherence-"><a class="header" href="#the-type-system-is-complete-during-the-implicit-negative-overlap-check-in-coherence-">The type system is complete during the implicit negative overlap check in coherence ✅</a></h4>
 <p>For more on overlap checking: <a href="../coherence.html">coherence</a></p>
 <p>During the implicit negative overlap check in coherence we must never return <em>error</em> for
 goals which can be proven. This would allow for overlapping impls with potentially different
 associated items, breaking a bunch of other invariants.</p>
 <p>This invariant is currently broken in many different ways while actually something we rely on.
 We have to be careful as it is quite easy to break:</p>
 <ul>
 <li>generalization of aliases</li>
 <li>generalization during subtyping binders (luckily not exploitable in coherence)</li>
 </ul>
 <h3 id="trait-solving-must-be-free-lifetime-agnostic-"><a class="header" href="#trait-solving-must-be-free-lifetime-agnostic-">Trait solving must be (free) lifetime agnostic ✅</a></h3>
 <p>Trait solving during codegen should have the same result as during typeck. As we erase
 all free regions during codegen we must not rely on them during typeck. A noteworthy example
 is special behavior for <code>'static</code>.</p>
 <p>We also have to be careful with relying on equality of regions in the trait solver.
 This is fine for codegen, as we treat all erased regions as equal. We can however
 lose equality information from HIR to MIR typeck.</p>
 <p>The new solver "uniquifies regions" during canonicalization, canonicalizing <code>u32: Trait&lt;'x, 'x&gt;</code>
 as <code>exists&lt;'0, '1&gt; u32: Trait&lt;'0, '1&gt;</code>, to make it harder to rely on this property.</p>
 <h3 id="removing-ambiguity-makes-strictly-more-things-compile-"><a class="header" href="#removing-ambiguity-makes-strictly-more-things-compile-">Removing ambiguity makes strictly more things compile ❌</a></h3>
 <p>Ideally we <em>should</em> not rely on ambiguity for things to compile.
 Not doing that will cause future improvements to be breaking changes.</p>
 <p>Due to <em>incompleteness</em> this is not the case and improving inference can result in inference
 changes, breaking existing projects.</p>
 <h3 id="semantic-equality-implies-structural-equality-"><a class="header" href="#semantic-equality-implies-structural-equality-">Semantic equality implies structural equality ✅</a></h3>
 <p>Two types being equal in the type system must mean that they have the
 same <code>TypeId</code> after instantiating their generic parameters with concrete
 arguments. This currently does not hold: <a href="https://github.com/rust-lang/rust/issues/97156">#97156</a>.</p>

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	<h1 id="invariants-of-the-type-system"><a class="header" href="#invariants-of-the-type-system">Invariants of the type system</a></h1>
	<p>FIXME: This file talks about invariants of the type system as a whole, not only the solver</p>
	<p>There are a lot of invariants - things the type system guarantees to be true at all times -
	which are desirable or expected from other languages and type systems. Unfortunately, quite
	a few of them do not hold in Rust right now. This is either a fundamental to its design or
	caused by bugs and something that may change in the future.</p>
	<p>It is important to know about the things you can assume while working on - and with - the
	type system, so here's an incomplete and unofficial list of invariants of
	the core type system:</p>
	<ul>
	<li>✅: this invariant mostly holds, with some weird exceptions, you can rely on it outside
	of these cases</li>
	<li>❌: this invariant does not hold, either due to bugs or by design, you must not rely on
	it for soundness or have to be incredibly careful when doing so</li>
	</ul>
	<h3 id="wfx-implies-wfnormalizex-"><a class="header" href="#wfx-implies-wfnormalizex-"><code>wf(X)</code> implies <code>wf(normalize(X))</code> ✅</a></h3>
	<p>If a type containing aliases is well-formed, it should also be
	well-formed after normalizing said aliases. We rely on this as
	otherwise we would have to re-check for well-formedness for these
	types.</p>
	<h3 id="structural-equality-modulo-regions-implies-semantic-equality-"><a class="header" href="#structural-equality-modulo-regions-implies-semantic-equality-">Structural equality modulo regions implies semantic equality ✅</a></h3>
	<p>If you have a some type and equate it to itself after replacing any regions with unique
	inference variables in both the lhs and rhs, the now potentially structurally different
	types should still be equal to each other.</p>
	<p>Needed to prevent goals from succeeding in HIR typeck and then failing in MIR borrowck.
	If this invariant is broken MIR typeck ends up failing with an ICE.</p>
	<h3 id="applying-inference-results-from-a-goal-does-not-change-its-result-"><a class="header" href="#applying-inference-results-from-a-goal-does-not-change-its-result-">Applying inference results from a goal does not change its result ❌</a></h3>
	<p>TODO: this invariant is formulated in a weird way and needs to be elaborated.
	Pretty much: I would like this check to only fail if there's a solver bug:
	https://github.com/rust-lang/rust/blob/2ffeb4636b4ae376f716dc4378a7efb37632dc2d/compiler/rustc_trait_selection/src/solve/eval_ctxt.rs#L391-L407</p>
	<p>If we prove some goal/equate types/whatever, apply the resulting inference constraints,
	and then redo the original action, the result should be the same.</p>
	<p>This unfortunately does not hold - at least in the new solver - due to a few annoying reasons.</p>
	<h3 id="the-trait-solver-has-to-be-locally-sound-"><a class="header" href="#the-trait-solver-has-to-be-locally-sound-">The trait solver has to be <em>locally sound</em> ✅</a></h3>
	<p>This means that we must never return <em>success</em> for goals for which no <code>impl</code> exists. That would
	mean we assume a trait is implemented even though it is not, which is very likely to result in
	actual unsoundness. When using <code>where</code>-bounds to prove a goal, the <code>impl</code> will be provided by the
	user of the item.</p>
	<p>This invariant only holds if we check region constraints. As we do not check region constraints
	during implicit negative overlap check in coherence, this invariant is broken there. As this check
	relies on <em>completeness</em> of the trait solver, it is not able to use the current region constraints
	check - <code>InferCtxt::resolve_regions</code> - as its handling of type outlives goals is incomplete.</p>
	<h3 id="normalization-of-semantically-equal-aliases-in-empty-environments-results-in-a-unique-type-"><a class="header" href="#normalization-of-semantically-equal-aliases-in-empty-environments-results-in-a-unique-type-">Normalization of semantically equal aliases in empty environments results in a unique type ✅</a></h3>
	<p>Normalization for alias types/consts has to have a unique result. Otherwise we can easily
	implement transmute in safe code. Given the following function, we have to make sure that
	the input and output types always get normalized to the same concrete type.</p>
	<pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
	</span><span class="boring">fn main() {
	</span>fn foo<T: Trait>(
	x: <T as Trait>::Assoc
	) -> <T as Trait>::Assoc {
	x
	}
	<span class="boring">}</span></code></pre></pre>
	<p>Many of the currently known unsound issues end up relying on this invariant being broken.
	It is however very difficult to imagine a sound type system without this invariant, so
	the issue is that the invariant is broken, not that we incorrectly rely on it.</p>
	<h3 id="generic-goals-and-their-instantiations-have-the-same-result-"><a class="header" href="#generic-goals-and-their-instantiations-have-the-same-result-">Generic goals and their instantiations have the same result ✅</a></h3>
	<p>Pretty much: If we successfully typecheck a generic function concrete instantiations
	of that function should also typeck. We should not get errors post-monomorphization.
	We can however get overflow errors at that point.</p>
	<p>TODO: example for overflow error post-monomorphization</p>
	<p>This invariant is relied on to allow the normalization of generic aliases. Breaking
	it can easily result in unsoundness, e.g. <a href="https://github.com/rust-lang/rust/issues/57893">#57893</a></p>
	<h3 id="trait-goals-in-empty-environments-are-proven-by-a-unique-impl-"><a class="header" href="#trait-goals-in-empty-environments-are-proven-by-a-unique-impl-">Trait goals in empty environments are proven by a unique impl ✅</a></h3>
	<p>If a trait goal holds with an empty environment, there should be a unique <code>impl</code>,
	either user-defined or builtin, which is used to prove that goal. This is
	necessary to select a unique method.</p>
	<p>We do however break this invariant in few cases, some of which are due to bugs,
	some by design:</p>
	<ul>
	<li><em>marker traits</em> are allowed to overlap as they do not have associated items</li>
	<li><em>specialization</em> allows specializing impls to overlap with their parent</li>
	<li>the builtin trait object trait implementation can overlap with a user-defined impl:
	<a href="https://github.com/rust-lang/rust/issues/57893">#57893</a></li>
	</ul>
	<h3 id="the-type-system-is-complete-"><a class="header" href="#the-type-system-is-complete-">The type system is complete ❌</a></h3>
	<p>The type system is not complete, it often adds unnecessary inference constraints, and errors
	even though the goal could hold.</p>
	<ul>
	<li>method selection</li>
	<li>opaque type inference</li>
	<li>handling type outlives constraints</li>
	<li>preferring <code>ParamEnv</code> candidates over <code>Impl</code> candidates during candidate selection
	in the trait solver</li>
	</ul>
	<h4 id="the-type-system-is-complete-during-the-implicit-negative-overlap-check-in-coherence-"><a class="header" href="#the-type-system-is-complete-during-the-implicit-negative-overlap-check-in-coherence-">The type system is complete during the implicit negative overlap check in coherence ✅</a></h4>
	<p>For more on overlap checking: <a href="../coherence.html">coherence</a></p>
	<p>During the implicit negative overlap check in coherence we must never return <em>error</em> for
	goals which can be proven. This would allow for overlapping impls with potentially different
	associated items, breaking a bunch of other invariants.</p>
	<p>This invariant is currently broken in many different ways while actually something we rely on.
	We have to be careful as it is quite easy to break:</p>
	<ul>
	<li>generalization of aliases</li>
	<li>generalization during subtyping binders (luckily not exploitable in coherence)</li>
	</ul>
	<h3 id="trait-solving-must-be-free-lifetime-agnostic-"><a class="header" href="#trait-solving-must-be-free-lifetime-agnostic-">Trait solving must be (free) lifetime agnostic ✅</a></h3>
	<p>Trait solving during codegen should have the same result as during typeck. As we erase
	all free regions during codegen we must not rely on them during typeck. A noteworthy example
	is special behavior for <code>'static</code>.</p>
	<p>We also have to be careful with relying on equality of regions in the trait solver.
	This is fine for codegen, as we treat all erased regions as equal. We can however
	lose equality information from HIR to MIR typeck.</p>
	<p>The new solver "uniquifies regions" during canonicalization, canonicalizing <code>u32: Trait<'x, 'x></code>
	as <code>exists<'0, '1> u32: Trait<'0, '1></code>, to make it harder to rely on this property.</p>
	<h3 id="removing-ambiguity-makes-strictly-more-things-compile-"><a class="header" href="#removing-ambiguity-makes-strictly-more-things-compile-">Removing ambiguity makes strictly more things compile ❌</a></h3>
	<p>Ideally we <em>should</em> not rely on ambiguity for things to compile.
	Not doing that will cause future improvements to be breaking changes.</p>
	<p>Due to <em>incompleteness</em> this is not the case and improving inference can result in inference
	changes, breaking existing projects.</p>
	<h3 id="semantic-equality-implies-structural-equality-"><a class="header" href="#semantic-equality-implies-structural-equality-">Semantic equality implies structural equality ✅</a></h3>
	<p>Two types being equal in the type system must mean that they have the
	same <code>TypeId</code> after instantiating their generic parameters with concrete
	arguments. This currently does not hold: <a href="https://github.com/rust-lang/rust/issues/97156">#97156</a>.</p>

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