1 files changed, 1132 insertions, 2 deletions

diff --git a/crates/ra_hir_ty/src/lib.rs b/crates/ra_hir_ty/src/lib.rs
index 28859ba63..f25846326 100644
--- a/crates/ra_hir_ty/src/lib.rs
+++ b/crates/ra_hir_ty/src/lib.rs
@@ -1,4 +1,1134 @@
-//! Work in Progress: everything related to types, type inference and trait
-//! solving.
+//! The type system. We currently use this to infer types for completion, hover
+//! information and various assists.
 
+macro_rules! impl_froms {
+    ($e:ident: $($v:ident $(($($sv:ident),*))?),*) => {
+        $(
+            impl From<$v> for $e {
+                fn from(it: $v) -> $e {
+                    $e::$v(it)
+                }
+            }
+            $($(
+                impl From<$sv> for $e {
+                    fn from(it: $sv) -> $e {
+                        $e::$v($v::$sv(it))
+                    }
+                }
+            )*)?
+        )*
+    }
+}
+
+mod autoderef;
 pub mod primitive;
+pub mod traits;
+pub mod method_resolution;
+mod op;
+mod lower;
+mod infer;
+pub mod display;
+pub(crate) mod utils;
+pub mod db;
+pub mod diagnostics;
+pub mod expr;
+
+#[cfg(test)]
+mod tests;
+#[cfg(test)]
+mod test_db;
+mod marks;
+
+use std::ops::Deref;
+use std::sync::Arc;
+use std::{fmt, iter, mem};
+
+use hir_def::{
+    expr::ExprId, generics::GenericParams, type_ref::Mutability, AdtId, ContainerId, DefWithBodyId,
+    GenericDefId, HasModule, Lookup, TraitId, TypeAliasId,
+};
+use hir_expand::name::Name;
+use ra_db::{impl_intern_key, salsa, CrateId};
+
+use crate::{
+    db::HirDatabase,
+    primitive::{FloatTy, IntTy, Uncertain},
+    utils::make_mut_slice,
+};
+use display::{HirDisplay, HirFormatter};
+
+pub use autoderef::autoderef;
+pub use infer::{infer_query, InferTy, InferenceResult};
+pub use lower::CallableDef;
+pub use lower::{callable_item_sig, TyDefId, ValueTyDefId};
+pub use traits::{InEnvironment, Obligation, ProjectionPredicate, TraitEnvironment};
+
+/// 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(Uncertain<IntTy>),
+
+    /// A primitive floating-point type. For example, `f64`.
+    Float(Uncertain<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(CallableDef),
+
+    /// 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;
+    /// ```
+    FnPtr { num_args: u16 },
+
+    /// 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),
+
+    /// 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 },
+}
+
+/// This exists just for Chalk, because Chalk just has a single `StructId` where
+/// we have different kinds of ADTs, primitive types and special type
+/// constructors like tuples and function pointers.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub struct TypeCtorId(salsa::InternId);
+impl_intern_key!(TypeCtorId);
+
+impl TypeCtor {
+    pub fn num_ty_params(self, db: &impl 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 = db.generic_params(AdtId::from(adt).into());
+                generic_params.count_params_including_parent()
+            }
+            TypeCtor::FnDef(callable) => {
+                let generic_params = db.generic_params(callable.into());
+                generic_params.count_params_including_parent()
+            }
+            TypeCtor::AssociatedType(type_alias) => {
+                let generic_params = db.generic_params(type_alias.into());
+                generic_params.count_params_including_parent()
+            }
+            TypeCtor::FnPtr { num_args } => num_args as usize + 1,
+            TypeCtor::Tuple { cardinality } => cardinality as usize,
+        }
+    }
+
+    pub fn krate(self, db: &impl 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).krate),
+            TypeCtor::FnDef(callable) => Some(callable.krate(db)),
+            TypeCtor::AssociatedType(type_alias) => Some(type_alias.lookup(db).module(db).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()),
+        }
+    }
+}
+
+/// 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,
+}
+
+/// 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: &impl HirDatabase) -> TraitRef {
+        TraitRef { trait_: self.trait_(db).into(), substs: self.parameters.clone() }
+    }
+
+    fn trait_(&self, db: &impl HirDatabase) -> TraitId {
+        match self.associated_ty.lookup(db).container {
+            ContainerId::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, usize), binders: usize) {
+        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),
+
+    /// A type parameter; for example, `T` in `fn f<T>(x: T) {}
+    Param {
+        /// The index of the parameter (starting with parameters from the
+        /// surrounding impl, then the current function).
+        idx: u32,
+        /// The name of the parameter, for displaying.
+        // FIXME get rid of this
+        name: Name,
+    },
+
+    /// A bound type variable. Used during trait resolution to represent Chalk
+    /// variables, and in `Dyn` and `Opaque` bounds to represent the `Self` type.
+    Bound(u32),
+
+    /// A type variable used during type checking. Not to be confused with a
+    /// type parameter.
+    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]>),
+
+    /// An opaque type (`impl Trait`).
+    ///
+    /// The predicates are quantified over the `Self` type; see `Ty::Dyn` for
+    /// more.
+    Opaque(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, usize), binders: usize) {
+        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 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 fn identity(generic_params: &GenericParams) -> Substs {
+        Substs(
+            generic_params
+                .params_including_parent()
+                .into_iter()
+                .map(|p| Ty::Param { idx: p.idx, name: p.name.clone() })
+                .collect(),
+        )
+    }
+
+    /// Return Substs that replace each parameter by a bound variable.
+    pub fn bound_vars(generic_params: &GenericParams) -> Substs {
+        Substs(
+            generic_params
+                .params_including_parent()
+                .into_iter()
+                .map(|p| Ty::Bound(p.idx))
+                .collect(),
+        )
+    }
+
+    pub fn build_for_def(db: &impl HirDatabase, def: impl Into<GenericDefId>) -> SubstsBuilder {
+        let def = def.into();
+        let params = db.generic_params(def);
+        let param_count = params.count_params_including_parent();
+        Substs::builder(param_count)
+    }
+
+    pub fn build_for_generics(generic_params: &GenericParams) -> SubstsBuilder {
+        Substs::builder(generic_params.count_params_including_parent())
+    }
+
+    pub fn build_for_type_ctor(db: &impl 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 }
+    }
+}
+
+#[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, starting_from: u32) -> Self {
+        self.fill((starting_from..).map(Ty::Bound))
+    }
+
+    pub fn fill_with_params(self) -> Self {
+        let start = self.vec.len() as u32;
+        self.fill((start..).map(|idx| Ty::Param { idx, name: Name::missing() }))
+    }
+
+    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
+    }
+}
+
+/// 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, usize), binders: usize) {
+        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 {
+        match self {
+            GenericPredicate::Error => true,
+            _ => false,
+        }
+    }
+
+    pub fn is_implemented(&self) -> bool {
+        match self {
+            GenericPredicate::Implemented(_) => true,
+            _ => false,
+        }
+    }
+
+    pub fn trait_ref(&self, db: &impl 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, usize), binders: usize) {
+        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 `num_vars` tells us how
+/// many there are. 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 num_vars: usize,
+}
+
+/// 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]>,
+}
+
+impl FnSig {
+    pub fn from_params_and_return(mut params: Vec<Ty>, ret: Ty) -> FnSig {
+        params.push(ret);
+        FnSig { params_and_return: params.into() }
+    }
+
+    pub fn from_fn_ptr_substs(substs: &Substs) -> FnSig {
+        FnSig { params_and_return: Arc::clone(&substs.0) }
+    }
+
+    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, usize), binders: usize) {
+        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 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_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 as_callable(&self) -> Option<(CallableDef, &Substs)> {
+        match self {
+            Ty::Apply(ApplicationTy { ctor: TypeCtor::FnDef(callable_def), parameters }) => {
+                Some((*callable_def, parameters))
+            }
+            _ => None,
+        }
+    }
+
+    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,
+        }
+    }
+
+    fn callable_sig(&self, db: &impl HirDatabase) -> Option<FnSig> {
+        match self {
+            Ty::Apply(a_ty) => match a_ty.ctor {
+                TypeCtor::FnPtr { .. } => Some(FnSig::from_fn_ptr_substs(&a_ty.parameters)),
+                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,
+        }
+    }
+
+    /// If this is an `impl Trait` or `dyn Trait`, returns that trait.
+    pub fn inherent_trait(&self) -> Option<TraitId> {
+        match self {
+            Ty::Dyn(predicates) | Ty::Opaque(predicates) => {
+                predicates.iter().find_map(|pred| match pred {
+                    GenericPredicate::Implemented(tr) => Some(tr.trait_),
+                    _ => 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), 0);
+    }
+    /// 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, usize), binders: usize);
+
+    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
+    }
+
+    /// Replaces type parameters in this type using the given `Substs`. (So e.g.
+    /// if `self` is `&[T]`, where type parameter T has index 0, and the
+    /// `Substs` contain `u32` at index 0, we'll have `&[u32]` afterwards.)
+    fn subst(self, substs: &Substs) -> Self
+    where
+        Self: Sized,
+    {
+        self.fold(&mut |ty| match ty {
+            Ty::Param { idx, name } => {
+                substs.get(idx as usize).cloned().unwrap_or(Ty::Param { idx, name })
+            }
+            ty => ty,
+        })
+    }
+
+    /// Substitutes `Ty::Bound` vars (as opposed to type parameters).
+    fn subst_bound_vars(mut self, substs: &Substs) -> Self
+    where
+        Self: Sized,
+    {
+        self.walk_mut_binders(
+            &mut |ty, binders| match ty {
+                &mut Ty::Bound(idx) => {
+                    if idx as usize >= binders && (idx as usize - binders) < substs.len() {
+                        *ty = substs.0[idx as usize - binders].clone();
+                    }
+                }
+                _ => {}
+            },
+            0,
+        );
+        self
+    }
+
+    /// Shifts up `Ty::Bound` vars by `n`.
+    fn shift_bound_vars(self, n: i32) -> Self
+    where
+        Self: Sized,
+    {
+        self.fold(&mut |ty| match ty {
+            Ty::Bound(idx) => {
+                assert!(idx as i32 >= -n);
+                Ty::Bound((idx as i32 + n) as u32)
+            }
+            ty => ty,
+        })
+    }
+}
+
+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) | Ty::Opaque(predicates) => {
+                for p in predicates.iter() {
+                    p.walk(f);
+                }
+            }
+            Ty::Param { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
+        }
+        f(self);
+    }
+
+    fn walk_mut_binders(&mut self, f: &mut impl FnMut(&mut Ty, usize), binders: usize) {
+        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) | Ty::Opaque(predicates) => {
+                for p in make_mut_slice(predicates) {
+                    p.walk_mut_binders(f, binders + 1);
+                }
+            }
+            Ty::Param { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
+        }
+        f(self, binders);
+    }
+}
+
+impl HirDisplay for &Ty {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        HirDisplay::hir_fmt(*self, f)
+    }
+}
+
+impl HirDisplay for ApplicationTy {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        if f.should_truncate() {
+            return write!(f, "…");
+        }
+
+        match self.ctor {
+            TypeCtor::Bool => write!(f, "bool")?,
+            TypeCtor::Char => write!(f, "char")?,
+            TypeCtor::Int(t) => write!(f, "{}", t)?,
+            TypeCtor::Float(t) => write!(f, "{}", t)?,
+            TypeCtor::Str => write!(f, "str")?,
+            TypeCtor::Slice => {
+                let t = self.parameters.as_single();
+                write!(f, "[{}]", t.display(f.db))?;
+            }
+            TypeCtor::Array => {
+                let t = self.parameters.as_single();
+                write!(f, "[{};_]", t.display(f.db))?;
+            }
+            TypeCtor::RawPtr(m) => {
+                let t = self.parameters.as_single();
+                write!(f, "*{}{}", m.as_keyword_for_ptr(), t.display(f.db))?;
+            }
+            TypeCtor::Ref(m) => {
+                let t = self.parameters.as_single();
+                write!(f, "&{}{}", m.as_keyword_for_ref(), t.display(f.db))?;
+            }
+            TypeCtor::Never => write!(f, "!")?,
+            TypeCtor::Tuple { .. } => {
+                let ts = &self.parameters;
+                if ts.len() == 1 {
+                    write!(f, "({},)", ts[0].display(f.db))?;
+                } else {
+                    write!(f, "(")?;
+                    f.write_joined(&*ts.0, ", ")?;
+                    write!(f, ")")?;
+                }
+            }
+            TypeCtor::FnPtr { .. } => {
+                let sig = FnSig::from_fn_ptr_substs(&self.parameters);
+                write!(f, "fn(")?;
+                f.write_joined(sig.params(), ", ")?;
+                write!(f, ") -> {}", sig.ret().display(f.db))?;
+            }
+            TypeCtor::FnDef(def) => {
+                let sig = f.db.callable_item_signature(def);
+                let name = match def {
+                    CallableDef::FunctionId(ff) => f.db.function_data(ff).name.clone(),
+                    CallableDef::StructId(s) => {
+                        f.db.struct_data(s).name.clone().unwrap_or_else(Name::missing)
+                    }
+                    CallableDef::EnumVariantId(e) => {
+                        let enum_data = f.db.enum_data(e.parent);
+                        enum_data.variants[e.local_id].name.clone().unwrap_or_else(Name::missing)
+                    }
+                };
+                match def {
+                    CallableDef::FunctionId(_) => write!(f, "fn {}", name)?,
+                    CallableDef::StructId(_) | CallableDef::EnumVariantId(_) => {
+                        write!(f, "{}", name)?
+                    }
+                }
+                if self.parameters.len() > 0 {
+                    write!(f, "<")?;
+                    f.write_joined(&*self.parameters.0, ", ")?;
+                    write!(f, ">")?;
+                }
+                write!(f, "(")?;
+                f.write_joined(sig.params(), ", ")?;
+                write!(f, ") -> {}", sig.ret().display(f.db))?;
+            }
+            TypeCtor::Adt(def_id) => {
+                let name = match def_id {
+                    AdtId::StructId(it) => f.db.struct_data(it).name.clone(),
+                    AdtId::UnionId(it) => f.db.union_data(it).name.clone(),
+                    AdtId::EnumId(it) => f.db.enum_data(it).name.clone(),
+                }
+                .unwrap_or_else(Name::missing);
+                write!(f, "{}", name)?;
+                if self.parameters.len() > 0 {
+                    write!(f, "<")?;
+                    f.write_joined(&*self.parameters.0, ", ")?;
+                    write!(f, ">")?;
+                }
+            }
+            TypeCtor::AssociatedType(type_alias) => {
+                let trait_ = match type_alias.lookup(f.db).container {
+                    ContainerId::TraitId(it) => it,
+                    _ => panic!("not an associated type"),
+                };
+                let trait_name = f.db.trait_data(trait_).name.clone().unwrap_or_else(Name::missing);
+                let name = f.db.type_alias_data(type_alias).name.clone();
+                write!(f, "{}::{}", trait_name, name)?;
+                if self.parameters.len() > 0 {
+                    write!(f, "<")?;
+                    f.write_joined(&*self.parameters.0, ", ")?;
+                    write!(f, ">")?;
+                }
+            }
+            TypeCtor::Closure { .. } => {
+                let sig = self.parameters[0]
+                    .callable_sig(f.db)
+                    .expect("first closure parameter should contain signature");
+                write!(f, "|")?;
+                f.write_joined(sig.params(), ", ")?;
+                write!(f, "| -> {}", sig.ret().display(f.db))?;
+            }
+        }
+        Ok(())
+    }
+}
+
+impl HirDisplay for ProjectionTy {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        if f.should_truncate() {
+            return write!(f, "…");
+        }
+
+        let trait_name =
+            f.db.trait_data(self.trait_(f.db)).name.clone().unwrap_or_else(Name::missing);
+        write!(f, "<{} as {}", self.parameters[0].display(f.db), trait_name,)?;
+        if self.parameters.len() > 1 {
+            write!(f, "<")?;
+            f.write_joined(&self.parameters[1..], ", ")?;
+            write!(f, ">")?;
+        }
+        write!(f, ">::{}", f.db.type_alias_data(self.associated_ty).name)?;
+        Ok(())
+    }
+}
+
+impl HirDisplay for Ty {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        if f.should_truncate() {
+            return write!(f, "…");
+        }
+
+        match self {
+            Ty::Apply(a_ty) => a_ty.hir_fmt(f)?,
+            Ty::Projection(p_ty) => p_ty.hir_fmt(f)?,
+            Ty::Param { name, .. } => write!(f, "{}", name)?,
+            Ty::Bound(idx) => write!(f, "?{}", idx)?,
+            Ty::Dyn(predicates) | Ty::Opaque(predicates) => {
+                match self {
+                    Ty::Dyn(_) => write!(f, "dyn ")?,
+                    Ty::Opaque(_) => write!(f, "impl ")?,
+                    _ => unreachable!(),
+                };
+                // Note: This code is written to produce nice results (i.e.
+                // corresponding to surface Rust) for types that can occur in
+                // actual Rust. It will have weird results if the predicates
+                // aren't as expected (i.e. self types = $0, projection
+                // predicates for a certain trait come after the Implemented
+                // predicate for that trait).
+                let mut first = true;
+                let mut angle_open = false;
+                for p in predicates.iter() {
+                    match p {
+                        GenericPredicate::Implemented(trait_ref) => {
+                            if angle_open {
+                                write!(f, ">")?;
+                            }
+                            if !first {
+                                write!(f, " + ")?;
+                            }
+                            // We assume that the self type is $0 (i.e. the
+                            // existential) here, which is the only thing that's
+                            // possible in actual Rust, and hence don't print it
+                            write!(
+                                f,
+                                "{}",
+                                f.db.trait_data(trait_ref.trait_)
+                                    .name
+                                    .clone()
+                                    .unwrap_or_else(Name::missing)
+                            )?;
+                            if trait_ref.substs.len() > 1 {
+                                write!(f, "<")?;
+                                f.write_joined(&trait_ref.substs[1..], ", ")?;
+                                // there might be assoc type bindings, so we leave the angle brackets open
+                                angle_open = true;
+                            }
+                        }
+                        GenericPredicate::Projection(projection_pred) => {
+                            // in types in actual Rust, these will always come
+                            // after the corresponding Implemented predicate
+                            if angle_open {
+                                write!(f, ", ")?;
+                            } else {
+                                write!(f, "<")?;
+                                angle_open = true;
+                            }
+                            let name =
+                                f.db.type_alias_data(projection_pred.projection_ty.associated_ty)
+                                    .name
+                                    .clone();
+                            write!(f, "{} = ", name)?;
+                            projection_pred.ty.hir_fmt(f)?;
+                        }
+                        GenericPredicate::Error => {
+                            if angle_open {
+                                // impl Trait<X, {error}>
+                                write!(f, ", ")?;
+                            } else if !first {
+                                // impl Trait + {error}
+                                write!(f, " + ")?;
+                            }
+                            p.hir_fmt(f)?;
+                        }
+                    }
+                    first = false;
+                }
+                if angle_open {
+                    write!(f, ">")?;
+                }
+            }
+            Ty::Unknown => write!(f, "{{unknown}}")?,
+            Ty::Infer(..) => write!(f, "_")?,
+        }
+        Ok(())
+    }
+}
+
+impl TraitRef {
+    fn hir_fmt_ext(&self, f: &mut HirFormatter<impl HirDatabase>, use_as: bool) -> fmt::Result {
+        if f.should_truncate() {
+            return write!(f, "…");
+        }
+
+        self.substs[0].hir_fmt(f)?;
+        if use_as {
+            write!(f, " as ")?;
+        } else {
+            write!(f, ": ")?;
+        }
+        write!(f, "{}", f.db.trait_data(self.trait_).name.clone().unwrap_or_else(Name::missing))?;
+        if self.substs.len() > 1 {
+            write!(f, "<")?;
+            f.write_joined(&self.substs[1..], ", ")?;
+            write!(f, ">")?;
+        }
+        Ok(())
+    }
+}
+
+impl HirDisplay for TraitRef {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        self.hir_fmt_ext(f, false)
+    }
+}
+
+impl HirDisplay for &GenericPredicate {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        HirDisplay::hir_fmt(*self, f)
+    }
+}
+
+impl HirDisplay for GenericPredicate {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        if f.should_truncate() {
+            return write!(f, "…");
+        }
+
+        match self {
+            GenericPredicate::Implemented(trait_ref) => trait_ref.hir_fmt(f)?,
+            GenericPredicate::Projection(projection_pred) => {
+                write!(f, "<")?;
+                projection_pred.projection_ty.trait_ref(f.db).hir_fmt_ext(f, true)?;
+                write!(
+                    f,
+                    ">::{} = {}",
+                    f.db.type_alias_data(projection_pred.projection_ty.associated_ty).name,
+                    projection_pred.ty.display(f.db)
+                )?;
+            }
+            GenericPredicate::Error => write!(f, "{{error}}")?,
+        }
+        Ok(())
+    }
+}
+
+impl HirDisplay for Obligation {
+    fn hir_fmt(&self, f: &mut HirFormatter<impl HirDatabase>) -> fmt::Result {
+        match self {
+            Obligation::Trait(tr) => write!(f, "Implements({})", tr.display(f.db)),
+            Obligation::Projection(proj) => write!(
+                f,
+                "Normalize({} => {})",
+                proj.projection_ty.display(f.db),
+                proj.ty.display(f.db)
+            ),
+        }
+    }
+}