add section for the new trait solver

src/SUMMARY.md

@@ -117,6 +117,10 @@
         - [Lowering to logic](./traits/lowering-to-logic.md)
         - [Goals and clauses](./traits/goals-and-clauses.md)
         - [Canonical queries](./traits/canonical-queries.md)
+    - [Next-gen trait solving](./solve/trait-solving.md)
+        - [The solver](./solve/the-solver.md)
+        - [Canonicalization](./solve/canonicalization.md)
+        - [Coinduction](./solve/coinduction.md)
 - [Type checking](./type-checking.md)
     - [Method Lookup](./method-lookup.md)
     - [Variance](./variance.md)

src/solve/canonicalization.md

@@ -0,0 +1,8 @@
+# Canonicalization
+
+While the exact approach to canonicalization for this solver will differ slightly
+wrt to lifetimes, please visit [the relevant chalk chapter][chalk] for now.
+
+As of the 10th January canonicalization is not yet fully implemented for the solver.
+
+[chalk]: https://rust-lang.github.io/chalk/book/canonical_queries/canonicalization.html#canonicalization

src/solve/coinduction.md

@@ -0,0 +1,201 @@
+# Coinduction
+
+The trait solver may use coinduction when proving goals. Coinduction is fairly subtle so we're giving it its own chapter.
+
+## Coinduction and induction
+
+With induction, we recursively apply proofs until we end up with a finite proof tree. Consider the example of `Vec<Vec<Vec<u32>>>: Debug` which results in the following tree.
+
+- `Vec<Vec<Vec<u32>>>: Debug`
+    - `Vec<Vec<u32>>: Debug`
+        - `Vec<u32>: Debug`
+            - `u32: Debug`
+
+This tree is finite. But not all goals we would want to hold have finite proof trees, consider the following example:
+
+```rust
+struct List<T> {
+    value: T,
+    next: Option<Box<List<T>>>,
+}
+```
+
+For `List<T>: Send` to hold all its fields have to recursively implement `Send` as well. This would result in the following proof tree:
+
+- `List<T>: Send`
+    - `T: Send`
+    - `Option<Box<List<T>>>: Send`
+        - `Box<List<T>>: Send`
+            - `List<T>: Send`
+                - `T: Send`
+                - `Option<Box<List<T>>>: Send`
+                    - `Box<List<T>>: Send`
+                        - ...
+
+This tree would be infinitely large which is exactly what coinduction is about. 
+
+> To **inductively** prove a goal you need to provide a finite proof tree for it.
+> To **coinductively** prove a goal the provided proof tree may be infinite.
+
+## Why is coinduction correct
+
+When checking whether some trait goals holds, we're asking "does there exist an `impl`
+which satisfies this bound". Even if are infinite chains of nested goals, we still have a
+unique `impl` which should be used.
+
+## How to implement coinduction
+
+While our implementation can not check for coninduction by trying to construct an infinite
+tree as that would take infinite ressources, it still makes sense to think of coinduction
+from this perspective.
+
+As we cannot check for infinite trees, we instead search for patterns for which we know that
+they would result in an infinite proof tree. The currently pattern we detect are (canonical)
+cycles. If `T: Send` relies on `T: Send` then it's pretty clear that this will just go on forever.
+
+With cycles we have to be careful with caching. Due to canonicalization of regions and inference
+variables we also have to rerun queries until the provisional result returned when hitting the cycle
+is equal to the final result.
+
+TODO: elaborate here. We use the same approach as chalk for coinductive cycles. Note that the treatment
+for inductive cycles currently differs by simply returning `Overflow`. See [the relevant chapters][chalk]
+in the chalk book.
+
+[chalk]: https://rust-lang.github.io/chalk/book/recursive/inductive_cycles.html
+
+
+## Future work
+
+We currently only consider auto-traits, `Sized`, and `WF`-goals to be coinductive.
+In the future we pretty much intend for all goals to be coinductive.
+Lets first elaborate on why allowing more coinductive proofs is even desirable.
+
+### Recursive data types already rely on coinduction...
+
+...they just tend to avoid them in the trait solver.
+
+```rust
+enum List<T> {
+    Nil,
+    Succ(T, Box<List<T>>),
+}
+
+impl<T: Clone> Clone for List<T> {
+    fn clone(&self) -> Self {
+        match self {
+            List::Nil => List::Nil,
+            List::Succ(head, tail) => List::Succ(head.clone(), tail.clone()),
+        }
+    }
+}
+```
+
+We are using `tail.clone()` in this impl. For this we have to prove `Box<List<T>>: Clone` which requires `List<T>: Clone` but that relies on the currently impl which we are currently checking. By adding that requirement to the `where`-clauses of the impl, which is what we would do with [perfect derive], we move that cycle into the trait solver and [get an error][ex1].
+
+### Recursive data types
+
+We also need coinduction to reason about recursive types containing projections, e.g. the following currently fails to compile even though it should be valid.
+```rust
+use std::borrow::Cow;
+pub struct Foo<'a>(Cow<'a, [Foo<'a>]>);
+```
+This issue has been known since at least 2015, see [#23714](https://github.com/rust-lang/rust/issues/23714) if you want to know more.
+
+### Explicitly checked implied bounds
+
+When checking an impl, we assume that the types in the impl headers are well-formed. This means that when using instantiating the impl we have to prove that's actually the case. [#100051](https://github.com/rust-lang/rust/issues/100051) shows that this is not the case. To fix this, we have to add `WF` predicates for the types in impl headers. Without coinduction for all traits, this even breaks `core`.
+
+```rust
+trait FromResidual<R> {}
+trait Try: FromResidual<<Self as Try>::Residual> {
+    type Residual;
+}
+
+struct Ready<T>(T);
+impl<T> Try for Ready<T> {
+    type Residual = Ready<()>;
+}
+impl<T> FromResidual<<Ready<T> as Try>::Residual> for Ready<T> {}
+```
+
+When checking that the impl of `FromResidual` is well formed we get the following cycle:
+
+The impl is well formed if `<Ready<T> as Try>::Residual` and `Ready<T>` are well formed.
+- `wf(<Ready<T> as Try>::Residual)` requires
+-  `Ready<T>: Try`, which requires because of the super trait
+-  `Ready<T>: FromResidual<Ready<T> as Try>::Residual>`, which has an impl which requires **because of implied bounds**
+-  `wf(<Ready<T> as Try>::Residual)` :tada: **cycle**
+
+### Issues when extending coinduction to more goals
+
+There are some additional issues to keep in mind when extending coinduction.
+The issues here are not relevant for the current solver.
+
+#### Implied super trait bounds
+
+Our trait system currectly treats super traits, e.g. `trait Trait: SuperTrait`, by 1) requiring that `SuperTrait` has to hold for all types which implement `Trait`, and 2) assuming `SuperTrait` holds if `Trait` holds.
+
+Relying on 2) while proving 1) is unsound. This can only be observed in case of coinductive cycles. Without a cycles, whenever we rely on 2) we must have also proven 1) without relying on 2) for the used impl of `Trait`.
+
+```rust
+trait Trait: SuperTrait {}
+
+impl<T: Trait> Trait for T {}
+
+// Keeping the current setup for coinduction
+// would allow this compile. Uff :<
+fn sup<T: SuperTrait>() {}
+fn requires_trait<T: Trait>() { sup::<T>() }
+fn generic<T>() { requires_trait::<T>() }
+```
+This is not really fundamental to coinduction but rather an existing property which is made unsound because of it.
+
+##### Possible solutions
+
+The easiest way to solve this would be to completely remove 2) and always elaborate
+`T: Trait` to `T: Trait` and `T: SuperTrait` outside of the trait solver.
+This would allow us to also remove 1), but as we still have to prove ordinary `where`-bounds on traits,
+that's just additional work.
+
+While one could imagine ways to disable cyclic uses of 2) when checking 1), at least the ideas of myself - @lcnr -
+are all far to complex to be reasonable.
+
+#### `normalizes_to` goals and progress
+
+A `normalizes_to` goal represents the requirement that `<T as Trait>::Assoc` normalizes to some `U`. This is achieved by defacto first normalizing `<T as Trait>::Assoc` and then equating the resulting type with `U`. It should be a mapping as each projection should normalize to exactly one type. By simply allowing infinite proof trees, we would get the following behavior:
+
+```rust
+trait Trait {
+    type Assoc;
+}
+
+impl Trait for () {
+    type Assoc = <() as Trait>::Assoc;
+}
+```
+
+If we now compute `normalizes_to(<() as Trait>::Assoc, Vec<u32>)`, we would resolve the impl and get the associated type `<() as Trait>::Assoc`. We then equate that with the expected type, causing us to check `normalizes_to(<() as Trait>::Assoc, Vec<u32>)` again. This just goes on forever, resulting in an infinite proof tree.
+
+This means that `<() as Trait>::Assoc` would be equal to any other type which is unsound.
+
+##### How to solve this
+
+**WARNING: THIS IS SUBTLE AND MIGHT BE WRONG**
+
+Unlike trait goals, `normalizes_to` has to be *productive*[^1]. A `normalizes_to` goal is productive once the projection normalizes to a rigid type constructor, so `<() as Trait>::Assoc` normalizing to `Vec<<() as Trait>::Assoc>` would be productive.
+
+A `normalizes_to` goal has two kinds of nested goals. Nested requirements needed to actually normalize the projection, and the equality between the normalized projection and the expected type. Only the equality has to be productive. A branch in the proof tree is productive if it is either finite, or contains at least one `normalizes_to` where the alias is resolved to a rigid type constructor.
+
+Alternatively, we could simply always treat the equate branch of `normalizes_to` as inductive. Any cycles should result in infinite types, which aren't supported anyways and would only result in overflow when deeply normalizing for codegen.
+
+experimentation and examples: https://hackmd.io/-8p0AHnzSq2VAE6HE_wX-w?view
+
+Another attempt at a summary.
+- in projection eq, we must make progress with constraining the rhs
+- a cycle is only ok if while equating we have a rigid ty on the lhs after norm at least once
+- cycles outside of the recursive `eq` call of `normalizes_to` are always fine
+
+[^1]: related: https://coq.inria.fr/refman/language/core/coinductive.html#top-level-definitions-of-corecursive-functions
+
+[perfect derive]: https://smallcultfollowing.com/babysteps/blog/2022/04/12/implied-bounds-and-perfect-derive
+[ex1]: https://play.rust-lang.org/?version=stable&mode=debug&edition=2021&gist=0a9c3830b93a2380e6978d6328df8f72

src/solve/the-solver.md

@@ -0,0 +1,16 @@
+# The solver
+
+Also consider reading the documentation for [the recursive solver in chalk][chalk]
+as it is very similar to this implementation and also talks about limitations of this
+approach.
+
+[chalk]: https://rust-lang.github.io/chalk/book/recursive.html
+
+The basic structure of the solver is a pure function
+`fn evaluate_goal(goal: Goal<'tcx>) -> Response`.
+While the actual solver is not fully pure to deal with overflow and cycles, we are
+going to defer that for now.
+
+To deal with inference variables and to improve caching, we use [canonicalization](/canonicalization.html).
+
+TODO: write the remaining code for this as well.

src/solve/trait-solving.md

@@ -0,0 +1,99 @@
+# Trait solving (new)
+
+This chapter describes how trait solving works with the new WIP solver located in
+[`rustc_trait_selection/solve`][solve]. Feel free to also look at the docs for
+[the current solver](../traits/resolution.hmtl) and [the chalk solver](./chalk.html)
+can be found separately.
+
+## Core concepts
+
+The goal of the trait system is to check whether a given trait bound is satisfied.
+Most notably when typechecking the body of - potentially generic - functions.
+For example:
+
+```rust
+fn uses_vec_clone<T: Clone>(x: Vec<T>) -> (Vec<T>, Vec<T>) {
+    (x.clone(), x)
+}
+```
+Here the call to `x.clone()` requires us to prove that `Vec<T>` implements `Clone` given
+the assumption that `T: Clone` is true. We can assume `T: Clone` as that will be proven by
+callers of this function.
+
+The concept of "prove the `Vec<T>: Clone` with the assumption `T: Clone`" is called a [`Goal`].
+Both `Vec<T>: Clone` and `T: Clone` are represented using [`Predicate`]. There are other
+predicates, most notably equality bounds on associated items: `<Vec<T> as IntoIterator>::Item == T`.
+See the `PredicateKind` enum for an exhaustive list. A `Goal` is represented as the `predicate` we
+have to prove and the `param_env` in which this predicate has to hold.
+
+We prove goals by checking whether each possible [`Candidate`] applies for the given goal by
+recursively proving its nested goals. For a list of possible candidates with examples, look at
+[`CandidateSource`]. The most important candidates are `Impl` candidates, i.e. trait implementations
+written by the user,  and `ParamEnv` candidates, i.e. assumptions in our current environment.
+
+Looking at the above example, to prove `Vec<T>: Clone` we first use `impl<T: Clone> Clone for Vec<T>`.
+To use this impl we have to prove the nested goal that `T: Clone` holds. This can use the
+assumption `T: Clone` from the `ParamEnv` which does not have any nested goals.
+Therefore `Vec<T>: Clone` holds.
+
+The trait solver can either return success, ambiguity or an error as a [`CanonicalResponse`].
+For success and ambiguity it also returns constraints inference and region constraints.
+
+## Requirements
+
+Before we dive into the new solver lets first take the time to go through all of our requirements
+on the trait system. We can then use these to guide our design later on.
+
+TODO: elaborate on these rules and get more precise about their meaning.
+Also add issues where each of these rules have been broken in the past
+(or still are).
+
+### 1. The trait solver has to be *sound*
+
+This means that we must never return *success* for goals for which no `impl` exists. That would
+simply be unsound by assuming a trait is implemented even though it is not.
+
+### 2. If type checker solves generic goal concrete instantiations of that goal have the same result
+
+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.
+
+### 3. Trait goals in empty environments are proven by a unique impl.
+
+If a trait goal holds with an empty environment, there is a unique `impl`,
+either user-defined or builtin, which is used to prove that goal.
+
+This is necessary for codegen to select a unique method.
+An exception here are *marker traits* which are allowed to overlap.
+
+### 4. Normalization in empty environments results in a unique type
+
+Normalization for alias types/consts has a unique result. Otherwise we can easily implement
+transmute in safe code.
+
+### 5. During coherence trait solving has to be complete
+
+During coherence we never return *error* for goals which can be proven. This allows overlapping
+impls which would break rule 3.
+
+### 6. Trait solving must be (free) lifetime agnostic
+
+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 `'static`.
+
+### 7. Removing ambiguity makes strictly more things compile
+
+We *should* not rely on ambiguity for things to compile. Not doing that will cause future improvements to be breaking changes.
+
+### 8. semantic equality implies structural equality
+
+Two types being equal in the type system must mean that they have the same `TypeId`.
+
+
+[solve]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_trait_selection/solve/index.html
+[`Goal`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_trait_selection/solve/struct.Goal.html
+[`Predicate`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_middle/ty/struct.Predicate.html
+[`Candidate`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_trait_selection/solve/assembly/struct.Candidate.html
+[`CandidateSource`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_trait_selection/solve/trait_goals/enum.CandidateSource.html
+[`CanonicalResponse`]: https://doc.rust-lang.org/nightly/nightly-rustc/rustc_trait_selection/solve/type.CanonicalResponse.html