1 files changed, 1078 insertions, 0 deletions

diff --git a/crates/hir_ty/src/lib.rs b/crates/hir_ty/src/lib.rs
new file mode 100644
index 000000000..1e748476a
--- /dev/null
+++ b/crates/hir_ty/src/lib.rs
@@ -0,0 +1,1078 @@
+//! The type system. We currently use this to infer types for completion, hover
+//! information and various assists.
+
+#[allow(unused)]
+macro_rules! eprintln {
+    ($($tt:tt)*) => { stdx::eprintln!($($tt)*) };
+}
+
+mod autoderef;
+pub mod primitive;
+pub mod traits;
+pub mod method_resolution;
+mod op;
+mod lower;
+pub(crate) mod infer;
+pub(crate) mod utils;
+
+pub mod display;
+pub mod db;
+pub mod diagnostics;
+
+#[cfg(test)]
+mod tests;
+#[cfg(test)]
+mod test_db;
+
+use std::{iter, mem, ops::Deref, sync::Arc};
+
+use base_db::{salsa, CrateId};
+use hir_def::{
+    expr::ExprId,
+    type_ref::{Mutability, Rawness},
+    AdtId, AssocContainerId, DefWithBodyId, GenericDefId, HasModule, Lookup, TraitId, TypeAliasId,
+    TypeParamId,
+};
+use itertools::Itertools;
+
+use crate::{
+    db::HirDatabase,
+    display::HirDisplay,
+    primitive::{FloatTy, IntTy},
+    utils::{generics, make_mut_slice, Generics},
+};
+
+pub use autoderef::autoderef;
+pub use infer::{InferTy, InferenceResult};
+pub use lower::CallableDefId;
+pub use lower::{
+    associated_type_shorthand_candidates, callable_item_sig, ImplTraitLoweringMode, TyDefId,
+    TyLoweringContext, ValueTyDefId,
+};
+pub use traits::{InEnvironment, Obligation, ProjectionPredicate, TraitEnvironment};
+
+pub use chalk_ir::{BoundVar, DebruijnIndex};
+
+/// A type constructor or type name: this might be something like the primitive
+/// type `bool`, a struct like `Vec`, or things like function pointers or
+/// tuples.
+#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
+pub enum TypeCtor {
+    /// The primitive boolean type. Written as `bool`.
+    Bool,
+
+    /// The primitive character type; holds a Unicode scalar value
+    /// (a non-surrogate code point). Written as `char`.
+    Char,
+
+    /// A primitive integer type. For example, `i32`.
+    Int(IntTy),
+
+    /// A primitive floating-point type. For example, `f64`.
+    Float(FloatTy),
+
+    /// Structures, enumerations and unions.
+    Adt(AdtId),
+
+    /// The pointee of a string slice. Written as `str`.
+    Str,
+
+    /// The pointee of an array slice.  Written as `[T]`.
+    Slice,
+
+    /// An array with the given length. Written as `[T; n]`.
+    Array,
+
+    /// A raw pointer. Written as `*mut T` or `*const T`
+    RawPtr(Mutability),
+
+    /// A reference; a pointer with an associated lifetime. Written as
+    /// `&'a mut T` or `&'a T`.
+    Ref(Mutability),
+
+    /// The anonymous type of a function declaration/definition. Each
+    /// function has a unique type, which is output (for a function
+    /// named `foo` returning an `i32`) as `fn() -> i32 {foo}`.
+    ///
+    /// This includes tuple struct / enum variant constructors as well.
+    ///
+    /// For example the type of `bar` here:
+    ///
+    /// ```
+    /// fn foo() -> i32 { 1 }
+    /// let bar = foo; // bar: fn() -> i32 {foo}
+    /// ```
+    FnDef(CallableDefId),
+
+    /// A pointer to a function.  Written as `fn() -> i32`.
+    ///
+    /// For example the type of `bar` here:
+    ///
+    /// ```
+    /// fn foo() -> i32 { 1 }
+    /// let bar: fn() -> i32 = foo;
+    /// ```
+    // FIXME make this a Ty variant like in Chalk
+    FnPtr { num_args: u16, is_varargs: bool },
+
+    /// The never type `!`.
+    Never,
+
+    /// A tuple type.  For example, `(i32, bool)`.
+    Tuple { cardinality: u16 },
+
+    /// Represents an associated item like `Iterator::Item`.  This is used
+    /// when we have tried to normalize a projection like `T::Item` but
+    /// couldn't find a better representation.  In that case, we generate
+    /// an **application type** like `(Iterator::Item)<T>`.
+    AssociatedType(TypeAliasId),
+
+    /// This represents a placeholder for an opaque type in situations where we
+    /// don't know the hidden type (i.e. currently almost always). This is
+    /// analogous to the `AssociatedType` type constructor. As with that one,
+    /// these are only produced by Chalk.
+    OpaqueType(OpaqueTyId),
+
+    /// The type of a specific closure.
+    ///
+    /// The closure signature is stored in a `FnPtr` type in the first type
+    /// parameter.
+    Closure { def: DefWithBodyId, expr: ExprId },
+}
+
+impl TypeCtor {
+    pub fn num_ty_params(self, db: &dyn HirDatabase) -> usize {
+        match self {
+            TypeCtor::Bool
+            | TypeCtor::Char
+            | TypeCtor::Int(_)
+            | TypeCtor::Float(_)
+            | TypeCtor::Str
+            | TypeCtor::Never => 0,
+            TypeCtor::Slice
+            | TypeCtor::Array
+            | TypeCtor::RawPtr(_)
+            | TypeCtor::Ref(_)
+            | TypeCtor::Closure { .. } // 1 param representing the signature of the closure
+            => 1,
+            TypeCtor::Adt(adt) => {
+                let generic_params = generics(db.upcast(), adt.into());
+                generic_params.len()
+            }
+            TypeCtor::FnDef(callable) => {
+                let generic_params = generics(db.upcast(), callable.into());
+                generic_params.len()
+            }
+            TypeCtor::AssociatedType(type_alias) => {
+                let generic_params = generics(db.upcast(), type_alias.into());
+                generic_params.len()
+            }
+            TypeCtor::OpaqueType(opaque_ty_id) => {
+                match opaque_ty_id {
+                    OpaqueTyId::ReturnTypeImplTrait(func, _) => {
+                        let generic_params = generics(db.upcast(), func.into());
+                        generic_params.len()
+                    }
+                }
+            }
+            TypeCtor::FnPtr { num_args, is_varargs: _ } => num_args as usize + 1,
+            TypeCtor::Tuple { cardinality } => cardinality as usize,
+        }
+    }
+
+    pub fn krate(self, db: &dyn HirDatabase) -> Option<CrateId> {
+        match self {
+            TypeCtor::Bool
+            | TypeCtor::Char
+            | TypeCtor::Int(_)
+            | TypeCtor::Float(_)
+            | TypeCtor::Str
+            | TypeCtor::Never
+            | TypeCtor::Slice
+            | TypeCtor::Array
+            | TypeCtor::RawPtr(_)
+            | TypeCtor::Ref(_)
+            | TypeCtor::FnPtr { .. }
+            | TypeCtor::Tuple { .. } => None,
+            // Closure's krate is irrelevant for coherence I would think?
+            TypeCtor::Closure { .. } => None,
+            TypeCtor::Adt(adt) => Some(adt.module(db.upcast()).krate),
+            TypeCtor::FnDef(callable) => Some(callable.krate(db)),
+            TypeCtor::AssociatedType(type_alias) => {
+                Some(type_alias.lookup(db.upcast()).module(db.upcast()).krate)
+            }
+            TypeCtor::OpaqueType(opaque_ty_id) => match opaque_ty_id {
+                OpaqueTyId::ReturnTypeImplTrait(func, _) => {
+                    Some(func.lookup(db.upcast()).module(db.upcast()).krate)
+                }
+            },
+        }
+    }
+
+    pub fn as_generic_def(self) -> Option<GenericDefId> {
+        match self {
+            TypeCtor::Bool
+            | TypeCtor::Char
+            | TypeCtor::Int(_)
+            | TypeCtor::Float(_)
+            | TypeCtor::Str
+            | TypeCtor::Never
+            | TypeCtor::Slice
+            | TypeCtor::Array
+            | TypeCtor::RawPtr(_)
+            | TypeCtor::Ref(_)
+            | TypeCtor::FnPtr { .. }
+            | TypeCtor::Tuple { .. }
+            | TypeCtor::Closure { .. } => None,
+            TypeCtor::Adt(adt) => Some(adt.into()),
+            TypeCtor::FnDef(callable) => Some(callable.into()),
+            TypeCtor::AssociatedType(type_alias) => Some(type_alias.into()),
+            TypeCtor::OpaqueType(_impl_trait_id) => None,
+        }
+    }
+}
+
+/// A nominal type with (maybe 0) type parameters. This might be a primitive
+/// type like `bool`, a struct, tuple, function pointer, reference or
+/// several other things.
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct ApplicationTy {
+    pub ctor: TypeCtor,
+    pub parameters: Substs,
+}
+
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct OpaqueTy {
+    pub opaque_ty_id: OpaqueTyId,
+    pub parameters: Substs,
+}
+
+/// A "projection" type corresponds to an (unnormalized)
+/// projection like `<P0 as Trait<P1..Pn>>::Foo`. Note that the
+/// trait and all its parameters are fully known.
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct ProjectionTy {
+    pub associated_ty: TypeAliasId,
+    pub parameters: Substs,
+}
+
+impl ProjectionTy {
+    pub fn trait_ref(&self, db: &dyn HirDatabase) -> TraitRef {
+        TraitRef { trait_: self.trait_(db), substs: self.parameters.clone() }
+    }
+
+    fn trait_(&self, db: &dyn HirDatabase) -> TraitId {
+        match self.associated_ty.lookup(db.upcast()).container {
+            AssocContainerId::TraitId(it) => it,
+            _ => panic!("projection ty without parent trait"),
+        }
+    }
+}
+
+impl TypeWalk for ProjectionTy {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        self.parameters.walk(f);
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        self.parameters.walk_mut_binders(f, binders);
+    }
+}
+
+/// A type.
+///
+/// See also the `TyKind` enum in rustc (librustc/ty/sty.rs), which represents
+/// the same thing (but in a different way).
+///
+/// This should be cheap to clone.
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub enum Ty {
+    /// A nominal type with (maybe 0) type parameters. This might be a primitive
+    /// type like `bool`, a struct, tuple, function pointer, reference or
+    /// several other things.
+    Apply(ApplicationTy),
+
+    /// A "projection" type corresponds to an (unnormalized)
+    /// projection like `<P0 as Trait<P1..Pn>>::Foo`. Note that the
+    /// trait and all its parameters are fully known.
+    Projection(ProjectionTy),
+
+    /// An opaque type (`impl Trait`).
+    ///
+    /// This is currently only used for return type impl trait; each instance of
+    /// `impl Trait` in a return type gets its own ID.
+    Opaque(OpaqueTy),
+
+    /// A placeholder for a type parameter; for example, `T` in `fn f<T>(x: T)
+    /// {}` when we're type-checking the body of that function. In this
+    /// situation, we know this stands for *some* type, but don't know the exact
+    /// type.
+    Placeholder(TypeParamId),
+
+    /// A bound type variable. This is used in various places: when representing
+    /// some polymorphic type like the type of function `fn f<T>`, the type
+    /// parameters get turned into variables; during trait resolution, inference
+    /// variables get turned into bound variables and back; and in `Dyn` the
+    /// `Self` type is represented with a bound variable as well.
+    Bound(BoundVar),
+
+    /// A type variable used during type checking.
+    Infer(InferTy),
+
+    /// A trait object (`dyn Trait` or bare `Trait` in pre-2018 Rust).
+    ///
+    /// The predicates are quantified over the `Self` type, i.e. `Ty::Bound(0)`
+    /// represents the `Self` type inside the bounds. This is currently
+    /// implicit; Chalk has the `Binders` struct to make it explicit, but it
+    /// didn't seem worth the overhead yet.
+    Dyn(Arc<[GenericPredicate]>),
+
+    /// A placeholder for a type which could not be computed; this is propagated
+    /// to avoid useless error messages. Doubles as a placeholder where type
+    /// variables are inserted before type checking, since we want to try to
+    /// infer a better type here anyway -- for the IDE use case, we want to try
+    /// to infer as much as possible even in the presence of type errors.
+    Unknown,
+}
+
+/// A list of substitutions for generic parameters.
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct Substs(Arc<[Ty]>);
+
+impl TypeWalk for Substs {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        for t in self.0.iter() {
+            t.walk(f);
+        }
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        for t in make_mut_slice(&mut self.0) {
+            t.walk_mut_binders(f, binders);
+        }
+    }
+}
+
+impl Substs {
+    pub fn empty() -> Substs {
+        Substs(Arc::new([]))
+    }
+
+    pub fn single(ty: Ty) -> Substs {
+        Substs(Arc::new([ty]))
+    }
+
+    pub fn prefix(&self, n: usize) -> Substs {
+        Substs(self.0[..std::cmp::min(self.0.len(), n)].into())
+    }
+
+    pub fn suffix(&self, n: usize) -> Substs {
+        Substs(self.0[self.0.len() - std::cmp::min(self.0.len(), n)..].into())
+    }
+
+    pub fn as_single(&self) -> &Ty {
+        if self.0.len() != 1 {
+            panic!("expected substs of len 1, got {:?}", self);
+        }
+        &self.0[0]
+    }
+
+    /// Return Substs that replace each parameter by itself (i.e. `Ty::Param`).
+    pub(crate) fn type_params_for_generics(generic_params: &Generics) -> Substs {
+        Substs(generic_params.iter().map(|(id, _)| Ty::Placeholder(id)).collect())
+    }
+
+    /// Return Substs that replace each parameter by itself (i.e. `Ty::Param`).
+    pub fn type_params(db: &dyn HirDatabase, def: impl Into<GenericDefId>) -> Substs {
+        let params = generics(db.upcast(), def.into());
+        Substs::type_params_for_generics(&params)
+    }
+
+    /// Return Substs that replace each parameter by a bound variable.
+    pub(crate) fn bound_vars(generic_params: &Generics, debruijn: DebruijnIndex) -> Substs {
+        Substs(
+            generic_params
+                .iter()
+                .enumerate()
+                .map(|(idx, _)| Ty::Bound(BoundVar::new(debruijn, idx)))
+                .collect(),
+        )
+    }
+
+    pub fn build_for_def(db: &dyn HirDatabase, def: impl Into<GenericDefId>) -> SubstsBuilder {
+        let def = def.into();
+        let params = generics(db.upcast(), def);
+        let param_count = params.len();
+        Substs::builder(param_count)
+    }
+
+    pub(crate) fn build_for_generics(generic_params: &Generics) -> SubstsBuilder {
+        Substs::builder(generic_params.len())
+    }
+
+    pub fn build_for_type_ctor(db: &dyn HirDatabase, type_ctor: TypeCtor) -> SubstsBuilder {
+        Substs::builder(type_ctor.num_ty_params(db))
+    }
+
+    fn builder(param_count: usize) -> SubstsBuilder {
+        SubstsBuilder { vec: Vec::with_capacity(param_count), param_count }
+    }
+}
+
+/// Return an index of a parameter in the generic type parameter list by it's id.
+pub fn param_idx(db: &dyn HirDatabase, id: TypeParamId) -> Option<usize> {
+    generics(db.upcast(), id.parent).param_idx(id)
+}
+
+#[derive(Debug, Clone)]
+pub struct SubstsBuilder {
+    vec: Vec<Ty>,
+    param_count: usize,
+}
+
+impl SubstsBuilder {
+    pub fn build(self) -> Substs {
+        assert_eq!(self.vec.len(), self.param_count);
+        Substs(self.vec.into())
+    }
+
+    pub fn push(mut self, ty: Ty) -> Self {
+        self.vec.push(ty);
+        self
+    }
+
+    fn remaining(&self) -> usize {
+        self.param_count - self.vec.len()
+    }
+
+    pub fn fill_with_bound_vars(self, debruijn: DebruijnIndex, starting_from: usize) -> Self {
+        self.fill((starting_from..).map(|idx| Ty::Bound(BoundVar::new(debruijn, idx))))
+    }
+
+    pub fn fill_with_unknown(self) -> Self {
+        self.fill(iter::repeat(Ty::Unknown))
+    }
+
+    pub fn fill(mut self, filler: impl Iterator<Item = Ty>) -> Self {
+        self.vec.extend(filler.take(self.remaining()));
+        assert_eq!(self.remaining(), 0);
+        self
+    }
+
+    pub fn use_parent_substs(mut self, parent_substs: &Substs) -> Self {
+        assert!(self.vec.is_empty());
+        assert!(parent_substs.len() <= self.param_count);
+        self.vec.extend(parent_substs.iter().cloned());
+        self
+    }
+}
+
+impl Deref for Substs {
+    type Target = [Ty];
+
+    fn deref(&self) -> &[Ty] {
+        &self.0
+    }
+}
+
+#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
+pub struct Binders<T> {
+    pub num_binders: usize,
+    pub value: T,
+}
+
+impl<T> Binders<T> {
+    pub fn new(num_binders: usize, value: T) -> Self {
+        Self { num_binders, value }
+    }
+
+    pub fn as_ref(&self) -> Binders<&T> {
+        Binders { num_binders: self.num_binders, value: &self.value }
+    }
+
+    pub fn map<U>(self, f: impl FnOnce(T) -> U) -> Binders<U> {
+        Binders { num_binders: self.num_binders, value: f(self.value) }
+    }
+
+    pub fn filter_map<U>(self, f: impl FnOnce(T) -> Option<U>) -> Option<Binders<U>> {
+        Some(Binders { num_binders: self.num_binders, value: f(self.value)? })
+    }
+}
+
+impl<T: Clone> Binders<&T> {
+    pub fn cloned(&self) -> Binders<T> {
+        Binders { num_binders: self.num_binders, value: self.value.clone() }
+    }
+}
+
+impl<T: TypeWalk> Binders<T> {
+    /// Substitutes all variables.
+    pub fn subst(self, subst: &Substs) -> T {
+        assert_eq!(subst.len(), self.num_binders);
+        self.value.subst_bound_vars(subst)
+    }
+
+    /// Substitutes just a prefix of the variables (shifting the rest).
+    pub fn subst_prefix(self, subst: &Substs) -> Binders<T> {
+        assert!(subst.len() < self.num_binders);
+        Binders::new(self.num_binders - subst.len(), self.value.subst_bound_vars(subst))
+    }
+}
+
+impl<T: TypeWalk> TypeWalk for Binders<T> {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        self.value.walk(f);
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        self.value.walk_mut_binders(f, binders.shifted_in())
+    }
+}
+
+/// A trait with type parameters. This includes the `Self`, so this represents a concrete type implementing the trait.
+/// Name to be bikeshedded: TraitBound? TraitImplements?
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct TraitRef {
+    /// FIXME name?
+    pub trait_: TraitId,
+    pub substs: Substs,
+}
+
+impl TraitRef {
+    pub fn self_ty(&self) -> &Ty {
+        &self.substs[0]
+    }
+}
+
+impl TypeWalk for TraitRef {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        self.substs.walk(f);
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        self.substs.walk_mut_binders(f, binders);
+    }
+}
+
+/// Like `generics::WherePredicate`, but with resolved types: A condition on the
+/// parameters of a generic item.
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
+pub enum GenericPredicate {
+    /// The given trait needs to be implemented for its type parameters.
+    Implemented(TraitRef),
+    /// An associated type bindings like in `Iterator<Item = T>`.
+    Projection(ProjectionPredicate),
+    /// We couldn't resolve the trait reference. (If some type parameters can't
+    /// be resolved, they will just be Unknown).
+    Error,
+}
+
+impl GenericPredicate {
+    pub fn is_error(&self) -> bool {
+        matches!(self, GenericPredicate::Error)
+    }
+
+    pub fn is_implemented(&self) -> bool {
+        matches!(self, GenericPredicate::Implemented(_))
+    }
+
+    pub fn trait_ref(&self, db: &dyn HirDatabase) -> Option<TraitRef> {
+        match self {
+            GenericPredicate::Implemented(tr) => Some(tr.clone()),
+            GenericPredicate::Projection(proj) => Some(proj.projection_ty.trait_ref(db)),
+            GenericPredicate::Error => None,
+        }
+    }
+}
+
+impl TypeWalk for GenericPredicate {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        match self {
+            GenericPredicate::Implemented(trait_ref) => trait_ref.walk(f),
+            GenericPredicate::Projection(projection_pred) => projection_pred.walk(f),
+            GenericPredicate::Error => {}
+        }
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        match self {
+            GenericPredicate::Implemented(trait_ref) => trait_ref.walk_mut_binders(f, binders),
+            GenericPredicate::Projection(projection_pred) => {
+                projection_pred.walk_mut_binders(f, binders)
+            }
+            GenericPredicate::Error => {}
+        }
+    }
+}
+
+/// Basically a claim (currently not validated / checked) that the contained
+/// type / trait ref contains no inference variables; any inference variables it
+/// contained have been replaced by bound variables, and `kinds` tells us how
+/// many there are and whether they were normal or float/int variables. This is
+/// used to erase irrelevant differences between types before using them in
+/// queries.
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
+pub struct Canonical<T> {
+    pub value: T,
+    pub kinds: Arc<[TyKind]>,
+}
+
+impl<T> Canonical<T> {
+    pub fn new(value: T, kinds: impl IntoIterator<Item = TyKind>) -> Self {
+        Self { value, kinds: kinds.into_iter().collect() }
+    }
+}
+
+#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
+pub enum TyKind {
+    General,
+    Integer,
+    Float,
+}
+
+/// A function signature as seen by type inference: Several parameter types and
+/// one return type.
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct FnSig {
+    params_and_return: Arc<[Ty]>,
+    is_varargs: bool,
+}
+
+/// A polymorphic function signature.
+pub type PolyFnSig = Binders<FnSig>;
+
+impl FnSig {
+    pub fn from_params_and_return(mut params: Vec<Ty>, ret: Ty, is_varargs: bool) -> FnSig {
+        params.push(ret);
+        FnSig { params_and_return: params.into(), is_varargs }
+    }
+
+    pub fn from_fn_ptr_substs(substs: &Substs, is_varargs: bool) -> FnSig {
+        FnSig { params_and_return: Arc::clone(&substs.0), is_varargs }
+    }
+
+    pub fn params(&self) -> &[Ty] {
+        &self.params_and_return[0..self.params_and_return.len() - 1]
+    }
+
+    pub fn ret(&self) -> &Ty {
+        &self.params_and_return[self.params_and_return.len() - 1]
+    }
+}
+
+impl TypeWalk for FnSig {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        for t in self.params_and_return.iter() {
+            t.walk(f);
+        }
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        for t in make_mut_slice(&mut self.params_and_return) {
+            t.walk_mut_binders(f, binders);
+        }
+    }
+}
+
+impl Ty {
+    pub fn simple(ctor: TypeCtor) -> Ty {
+        Ty::Apply(ApplicationTy { ctor, parameters: Substs::empty() })
+    }
+    pub fn apply_one(ctor: TypeCtor, param: Ty) -> Ty {
+        Ty::Apply(ApplicationTy { ctor, parameters: Substs::single(param) })
+    }
+    pub fn apply(ctor: TypeCtor, parameters: Substs) -> Ty {
+        Ty::Apply(ApplicationTy { ctor, parameters })
+    }
+    pub fn unit() -> Self {
+        Ty::apply(TypeCtor::Tuple { cardinality: 0 }, Substs::empty())
+    }
+    pub fn fn_ptr(sig: FnSig) -> Self {
+        Ty::apply(
+            TypeCtor::FnPtr { num_args: sig.params().len() as u16, is_varargs: sig.is_varargs },
+            Substs(sig.params_and_return),
+        )
+    }
+
+    pub fn as_reference(&self) -> Option<(&Ty, Mutability)> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::Ref(mutability), parameters }) => {
+                Some((parameters.as_single(), *mutability))
+            }
+            _ => None,
+        }
+    }
+
+    pub fn as_reference_or_ptr(&self) -> Option<(&Ty, Rawness, Mutability)> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::Ref(mutability), parameters }) => {
+                Some((parameters.as_single(), Rawness::Ref, *mutability))
+            }
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::RawPtr(mutability), parameters }) => {
+                Some((parameters.as_single(), Rawness::RawPtr, *mutability))
+            }
+            _ => None,
+        }
+    }
+
+    pub fn strip_references(&self) -> &Ty {
+        let mut t: &Ty = self;
+
+        while let Ty::Apply(ApplicationTy { ctor: TypeCtor::Ref(_mutability), parameters }) = t {
+            t = parameters.as_single();
+        }
+
+        t
+    }
+
+    pub fn as_adt(&self) -> Option<(AdtId, &Substs)> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::Adt(adt_def), parameters }) => {
+                Some((*adt_def, parameters))
+            }
+            _ => None,
+        }
+    }
+
+    pub fn as_tuple(&self) -> Option<&Substs> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::Tuple { .. }, parameters }) => {
+                Some(parameters)
+            }
+            _ => None,
+        }
+    }
+
+    pub fn is_never(&self) -> bool {
+        matches!(self, Ty::Apply(ApplicationTy { ctor: TypeCtor::Never, .. }))
+    }
+
+    /// If this is a `dyn Trait` type, this returns the `Trait` part.
+    pub fn dyn_trait_ref(&self) -> Option<&TraitRef> {
+        match self {
+            Ty::Dyn(bounds) => bounds.get(0).and_then(|b| match b {
+                GenericPredicate::Implemented(trait_ref) => Some(trait_ref),
+                _ => None,
+            }),
+            _ => None,
+        }
+    }
+
+    /// If this is a `dyn Trait`, returns that trait.
+    pub fn dyn_trait(&self) -> Option<TraitId> {
+        self.dyn_trait_ref().map(|it| it.trait_)
+    }
+
+    fn builtin_deref(&self) -> Option<Ty> {
+        match self {
+            Ty::Apply(a_ty) => match a_ty.ctor {
+                TypeCtor::Ref(..) => Some(Ty::clone(a_ty.parameters.as_single())),
+                TypeCtor::RawPtr(..) => Some(Ty::clone(a_ty.parameters.as_single())),
+                _ => None,
+            },
+            _ => None,
+        }
+    }
+
+    pub fn callable_sig(&self, db: &dyn HirDatabase) -> Option<FnSig> {
+        match self {
+            Ty::Apply(a_ty) => match a_ty.ctor {
+                TypeCtor::FnPtr { is_varargs, .. } => {
+                    Some(FnSig::from_fn_ptr_substs(&a_ty.parameters, is_varargs))
+                }
+                TypeCtor::FnDef(def) => {
+                    let sig = db.callable_item_signature(def);
+                    Some(sig.subst(&a_ty.parameters))
+                }
+                TypeCtor::Closure { .. } => {
+                    let sig_param = &a_ty.parameters[0];
+                    sig_param.callable_sig(db)
+                }
+                _ => None,
+            },
+            _ => None,
+        }
+    }
+
+    /// If this is a type with type parameters (an ADT or function), replaces
+    /// the `Substs` for these type parameters with the given ones. (So e.g. if
+    /// `self` is `Option<_>` and the substs contain `u32`, we'll have
+    /// `Option<u32>` afterwards.)
+    pub fn apply_substs(self, substs: Substs) -> Ty {
+        match self {
+            Ty::Apply(ApplicationTy { ctor, parameters: previous_substs }) => {
+                assert_eq!(previous_substs.len(), substs.len());
+                Ty::Apply(ApplicationTy { ctor, parameters: substs })
+            }
+            _ => self,
+        }
+    }
+
+    /// Returns the type parameters of this type if it has some (i.e. is an ADT
+    /// or function); so if `self` is `Option<u32>`, this returns the `u32`.
+    pub fn substs(&self) -> Option<Substs> {
+        match self {
+            Ty::Apply(ApplicationTy { parameters, .. }) => Some(parameters.clone()),
+            _ => None,
+        }
+    }
+
+    pub fn impl_trait_bounds(&self, db: &dyn HirDatabase) -> Option<Vec<GenericPredicate>> {
+        match self {
+            Ty::Opaque(opaque_ty) => {
+                let predicates = match opaque_ty.opaque_ty_id {
+                    OpaqueTyId::ReturnTypeImplTrait(func, idx) => {
+                        db.return_type_impl_traits(func).map(|it| {
+                            let data = (*it)
+                                .as_ref()
+                                .map(|rpit| rpit.impl_traits[idx as usize].bounds.clone());
+                            data.subst(&opaque_ty.parameters)
+                        })
+                    }
+                };
+
+                predicates.map(|it| it.value)
+            }
+            Ty::Placeholder(id) => {
+                let generic_params = db.generic_params(id.parent);
+                let param_data = &generic_params.types[id.local_id];
+                match param_data.provenance {
+                    hir_def::generics::TypeParamProvenance::ArgumentImplTrait => {
+                        let predicates = db
+                            .generic_predicates_for_param(*id)
+                            .into_iter()
+                            .map(|pred| pred.value.clone())
+                            .collect_vec();
+
+                        Some(predicates)
+                    }
+                    _ => None,
+                }
+            }
+            _ => None,
+        }
+    }
+
+    pub fn associated_type_parent_trait(&self, db: &dyn HirDatabase) -> Option<TraitId> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::AssociatedType(type_alias_id), .. }) => {
+                match type_alias_id.lookup(db.upcast()).container {
+                    AssocContainerId::TraitId(trait_id) => Some(trait_id),
+                    _ => None,
+                }
+            }
+            Ty::Projection(projection_ty) => {
+                match projection_ty.associated_ty.lookup(db.upcast()).container {
+                    AssocContainerId::TraitId(trait_id) => Some(trait_id),
+                    _ => None,
+                }
+            }
+            _ => None,
+        }
+    }
+}
+
+/// This allows walking structures that contain types to do something with those
+/// types, similar to Chalk's `Fold` trait.
+pub trait TypeWalk {
+    fn walk(&self, f: &mut impl FnMut(&Ty));
+    fn walk_mut(&mut self, f: &mut impl FnMut(&mut Ty)) {
+        self.walk_mut_binders(&mut |ty, _binders| f(ty), DebruijnIndex::INNERMOST);
+    }
+    /// Walk the type, counting entered binders.
+    ///
+    /// `Ty::Bound` variables use DeBruijn indexing, which means that 0 refers
+    /// to the innermost binder, 1 to the next, etc.. So when we want to
+    /// substitute a certain bound variable, we can't just walk the whole type
+    /// and blindly replace each instance of a certain index; when we 'enter'
+    /// things that introduce new bound variables, we have to keep track of
+    /// that. Currently, the only thing that introduces bound variables on our
+    /// side are `Ty::Dyn` and `Ty::Opaque`, which each introduce a bound
+    /// variable for the self type.
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    );
+
+    fn fold_binders(
+        mut self,
+        f: &mut impl FnMut(Ty, DebruijnIndex) -> Ty,
+        binders: DebruijnIndex,
+    ) -> Self
+    where
+        Self: Sized,
+    {
+        self.walk_mut_binders(
+            &mut |ty_mut, binders| {
+                let ty = mem::replace(ty_mut, Ty::Unknown);
+                *ty_mut = f(ty, binders);
+            },
+            binders,
+        );
+        self
+    }
+
+    fn fold(mut self, f: &mut impl FnMut(Ty) -> Ty) -> Self
+    where
+        Self: Sized,
+    {
+        self.walk_mut(&mut |ty_mut| {
+            let ty = mem::replace(ty_mut, Ty::Unknown);
+            *ty_mut = f(ty);
+        });
+        self
+    }
+
+    /// Substitutes `Ty::Bound` vars with the given substitution.
+    fn subst_bound_vars(self, substs: &Substs) -> Self
+    where
+        Self: Sized,
+    {
+        self.subst_bound_vars_at_depth(substs, DebruijnIndex::INNERMOST)
+    }
+
+    /// Substitutes `Ty::Bound` vars with the given substitution.
+    fn subst_bound_vars_at_depth(mut self, substs: &Substs, depth: DebruijnIndex) -> Self
+    where
+        Self: Sized,
+    {
+        self.walk_mut_binders(
+            &mut |ty, binders| {
+                if let &mut Ty::Bound(bound) = ty {
+                    if bound.debruijn >= binders {
+                        *ty = substs.0[bound.index].clone().shift_bound_vars(binders);
+                    }
+                }
+            },
+            depth,
+        );
+        self
+    }
+
+    /// Shifts up debruijn indices of `Ty::Bound` vars by `n`.
+    fn shift_bound_vars(self, n: DebruijnIndex) -> Self
+    where
+        Self: Sized,
+    {
+        self.fold_binders(
+            &mut |ty, binders| match ty {
+                Ty::Bound(bound) if bound.debruijn >= binders => {
+                    Ty::Bound(bound.shifted_in_from(n))
+                }
+                ty => ty,
+            },
+            DebruijnIndex::INNERMOST,
+        )
+    }
+}
+
+impl TypeWalk for Ty {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        match self {
+            Ty::Apply(a_ty) => {
+                for t in a_ty.parameters.iter() {
+                    t.walk(f);
+                }
+            }
+            Ty::Projection(p_ty) => {
+                for t in p_ty.parameters.iter() {
+                    t.walk(f);
+                }
+            }
+            Ty::Dyn(predicates) => {
+                for p in predicates.iter() {
+                    p.walk(f);
+                }
+            }
+            Ty::Opaque(o_ty) => {
+                for t in o_ty.parameters.iter() {
+                    t.walk(f);
+                }
+            }
+            Ty::Placeholder { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
+        }
+        f(self);
+    }
+
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        match self {
+            Ty::Apply(a_ty) => {
+                a_ty.parameters.walk_mut_binders(f, binders);
+            }
+            Ty::Projection(p_ty) => {
+                p_ty.parameters.walk_mut_binders(f, binders);
+            }
+            Ty::Dyn(predicates) => {
+                for p in make_mut_slice(predicates) {
+                    p.walk_mut_binders(f, binders.shifted_in());
+                }
+            }
+            Ty::Opaque(o_ty) => {
+                o_ty.parameters.walk_mut_binders(f, binders);
+            }
+            Ty::Placeholder { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
+        }
+        f(self, binders);
+    }
+}
+
+impl<T: TypeWalk> TypeWalk for Vec<T> {
+    fn walk(&self, f: &mut impl FnMut(&Ty)) {
+        for t in self {
+            t.walk(f);
+        }
+    }
+    fn walk_mut_binders(
+        &mut self,
+        f: &mut impl FnMut(&mut Ty, DebruijnIndex),
+        binders: DebruijnIndex,
+    ) {
+        for t in self {
+            t.walk_mut_binders(f, binders);
+        }
+    }
+}
+
+#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
+pub enum OpaqueTyId {
+    ReturnTypeImplTrait(hir_def::FunctionId, u16),
+}
+
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub struct ReturnTypeImplTraits {
+    pub(crate) impl_traits: Vec<ReturnTypeImplTrait>,
+}
+
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub(crate) struct ReturnTypeImplTrait {
+    pub bounds: Binders<Vec<GenericPredicate>>,
+}