30 files changed, 1239 insertions, 1441 deletions

diff --git a/crates/hir_ty/src/autoderef.rs b/crates/hir_ty/src/autoderef.rs
index ece68183e..be1fd1f13 100644
--- a/crates/hir_ty/src/autoderef.rs
+++ b/crates/hir_ty/src/autoderef.rs
@@ -81,7 +81,7 @@ fn deref_by_trait(
 
     // Now do the assoc type projection
     let projection = super::traits::ProjectionPredicate {
-        ty: Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, ty.value.kinds.len())),
+        ty: Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, ty.value.kinds.len())),
         projection_ty: super::ProjectionTy { associated_ty: target, parameters },
     };
 
@@ -89,8 +89,10 @@ fn deref_by_trait(
 
     let in_env = InEnvironment { value: obligation, environment: ty.environment };
 
-    let canonical =
-        Canonical::new(in_env, ty.value.kinds.iter().copied().chain(Some(super::TyKind::General)));
+    let canonical = Canonical::new(
+        in_env,
+        ty.value.kinds.iter().copied().chain(Some(chalk_ir::TyVariableKind::General)),
+    );
 
     let solution = db.trait_solve(krate, canonical)?;
 
@@ -112,7 +114,8 @@ fn deref_by_trait(
             // new variables in that case
 
             for i in 1..vars.0.kinds.len() {
-                if vars.0.value[i - 1] != Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, i - 1))
+                if vars.0.value[i - 1]
+                    != Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, i - 1))
                 {
                     warn!("complex solution for derefing {:?}: {:?}, ignoring", ty.value, solution);
                     return None;
diff --git a/crates/hir_ty/src/db.rs b/crates/hir_ty/src/db.rs
index b3af82444..06714409f 100644
--- a/crates/hir_ty/src/db.rs
+++ b/crates/hir_ty/src/db.rs
@@ -130,7 +130,7 @@ pub trait HirDatabase: DefDatabase + Upcast<dyn DefDatabase> {
     ) -> chalk_ir::ProgramClauses<chalk::Interner>;
 }
 
-fn infer_wait(db: &impl HirDatabase, def: DefWithBodyId) -> Arc<InferenceResult> {
+fn infer_wait(db: &dyn HirDatabase, def: DefWithBodyId) -> Arc<InferenceResult> {
     let _p = profile::span("infer:wait").detail(|| match def {
         DefWithBodyId::FunctionId(it) => db.function_data(it).name.to_string(),
         DefWithBodyId::StaticId(it) => {
diff --git a/crates/hir_ty/src/diagnostics.rs b/crates/hir_ty/src/diagnostics.rs
index 6bca7aa0d..86f937e1d 100644
--- a/crates/hir_ty/src/diagnostics.rs
+++ b/crates/hir_ty/src/diagnostics.rs
@@ -706,6 +706,35 @@ fn x(a: S) {
     }
 
     #[test]
+    fn import_extern_crate_clash_with_inner_item() {
+        // This is more of a resolver test, but doesn't really work with the hir_def testsuite.
+
+        check_diagnostics(
+            r#"
+//- /lib.rs crate:lib deps:jwt
+mod permissions;
+
+use permissions::jwt;
+
+fn f() {
+    fn inner() {}
+    jwt::Claims {}; // should resolve to the local one with 0 fields, and not get a diagnostic
+}
+
+//- /permissions.rs
+pub mod jwt  {
+    pub struct Claims {}
+}
+
+//- /jwt/lib.rs crate:jwt
+pub struct Claims {
+    field: u8,
+}
+        "#,
+        );
+    }
+
+    #[test]
     fn break_outside_of_loop() {
         check_diagnostics(
             r#"
diff --git a/crates/hir_ty/src/diagnostics/decl_check.rs b/crates/hir_ty/src/diagnostics/decl_check.rs
index 6773ddea3..3605ca581 100644
--- a/crates/hir_ty/src/diagnostics/decl_check.rs
+++ b/crates/hir_ty/src/diagnostics/decl_check.rs
@@ -28,7 +28,6 @@ use syntax::{
     ast::{self, NameOwner},
     AstNode, AstPtr,
 };
-use test_utils::mark;
 
 use crate::{
     db::HirDatabase,
@@ -93,16 +92,21 @@ impl<'a, 'b> DeclValidator<'a, 'b> {
     fn validate_func(&mut self, func: FunctionId) {
         let data = self.db.function_data(func);
         if data.is_extern {
-            mark::hit!(extern_func_incorrect_case_ignored);
+            cov_mark::hit!(extern_func_incorrect_case_ignored);
             return;
         }
 
         let body = self.db.body(func.into());
 
         // Recursively validate inner scope items, such as static variables and constants.
-        for (item_id, _) in body.item_scope.values() {
-            let mut validator = DeclValidator::new(self.db, self.krate, self.sink);
-            validator.validate_item(item_id);
+        let db = self.db;
+        for block_def_map in body.block_scopes.iter().filter_map(|block| db.block_def_map(*block)) {
+            for (_, module) in block_def_map.modules() {
+                for (def_id, _) in module.scope.values() {
+                    let mut validator = DeclValidator::new(self.db, self.krate, self.sink);
+                    validator.validate_item(def_id);
+                }
+            }
         }
 
         // Check whether non-snake case identifiers are allowed for this function.
@@ -625,7 +629,7 @@ impl<'a, 'b> DeclValidator<'a, 'b> {
     fn validate_static(&mut self, static_id: StaticId) {
         let data = self.db.static_data(static_id);
         if data.is_extern {
-            mark::hit!(extern_static_incorrect_case_ignored);
+            cov_mark::hit!(extern_static_incorrect_case_ignored);
             return;
         }
 
@@ -673,8 +677,6 @@ impl<'a, 'b> DeclValidator<'a, 'b> {
 
 #[cfg(test)]
 mod tests {
-    use test_utils::mark;
-
     use crate::diagnostics::tests::check_diagnostics;
 
     #[test]
@@ -889,8 +891,8 @@ fn main() {
 
     #[test]
     fn ignores_extern_items() {
-        mark::check!(extern_func_incorrect_case_ignored);
-        mark::check!(extern_static_incorrect_case_ignored);
+        cov_mark::check!(extern_func_incorrect_case_ignored);
+        cov_mark::check!(extern_static_incorrect_case_ignored);
         check_diagnostics(
             r#"
 extern {
diff --git a/crates/hir_ty/src/diagnostics/expr.rs b/crates/hir_ty/src/diagnostics/expr.rs
index d740b7265..2751cd304 100644
--- a/crates/hir_ty/src/diagnostics/expr.rs
+++ b/crates/hir_ty/src/diagnostics/expr.rs
@@ -2,9 +2,7 @@
 
 use std::sync::Arc;
 
-use hir_def::{
-    expr::Statement, path::path, resolver::HasResolver, AdtId, AssocItemId, DefWithBodyId,
-};
+use hir_def::{expr::Statement, path::path, resolver::HasResolver, AssocItemId, DefWithBodyId};
 use hir_expand::{diagnostics::DiagnosticSink, name};
 use rustc_hash::FxHashSet;
 use syntax::{ast, AstPtr};
@@ -17,7 +15,7 @@ use crate::{
         MissingPatFields, RemoveThisSemicolon,
     },
     utils::variant_data,
-    ApplicationTy, InferenceResult, Ty, TypeCtor,
+    AdtId, InferenceResult, Ty,
 };
 
 pub(crate) use hir_def::{
@@ -381,14 +379,15 @@ impl<'a, 'b> ExprValidator<'a, 'b> {
             _ => return,
         };
 
-        let core_result_ctor = TypeCtor::Adt(AdtId::EnumId(core_result_enum));
-        let core_option_ctor = TypeCtor::Adt(AdtId::EnumId(core_option_enum));
-
-        let (params, required) = match &mismatch.expected {
-            Ty::Apply(ApplicationTy { ctor, parameters }) if ctor == &core_result_ctor => {
+        let (params, required) = match mismatch.expected {
+            Ty::Adt(AdtId(hir_def::AdtId::EnumId(enum_id)), ref parameters)
+                if enum_id == core_result_enum =>
+            {
                 (parameters, "Ok".to_string())
             }
-            Ty::Apply(ApplicationTy { ctor, parameters }) if ctor == &core_option_ctor => {
+            Ty::Adt(AdtId(hir_def::AdtId::EnumId(enum_id)), ref parameters)
+                if enum_id == core_option_enum =>
+            {
                 (parameters, "Some".to_string())
             }
             _ => return,
diff --git a/crates/hir_ty/src/diagnostics/match_check.rs b/crates/hir_ty/src/diagnostics/match_check.rs
index 1c1423fbf..04d39c571 100644
--- a/crates/hir_ty/src/diagnostics/match_check.rs
+++ b/crates/hir_ty/src/diagnostics/match_check.rs
@@ -222,12 +222,12 @@ use hir_def::{
     adt::VariantData,
     body::Body,
     expr::{Expr, Literal, Pat, PatId},
-    AdtId, EnumVariantId, StructId, VariantId,
+    EnumVariantId, StructId, VariantId,
 };
 use la_arena::Idx;
 use smallvec::{smallvec, SmallVec};
 
-use crate::{db::HirDatabase, ApplicationTy, InferenceResult, Ty, TypeCtor};
+use crate::{db::HirDatabase, AdtId, InferenceResult, Ty};
 
 #[derive(Debug, Clone, Copy)]
 /// Either a pattern from the source code being analyzed, represented as
@@ -627,14 +627,12 @@ pub(super) fn is_useful(
     // - `!` type
     // In those cases, no match arm is useful.
     match cx.infer[cx.match_expr].strip_references() {
-        Ty::Apply(ApplicationTy { ctor: TypeCtor::Adt(AdtId::EnumId(enum_id)), .. }) => {
+        Ty::Adt(AdtId(hir_def::AdtId::EnumId(enum_id)), ..) => {
             if cx.db.enum_data(*enum_id).variants.is_empty() {
                 return Ok(Usefulness::NotUseful);
             }
         }
-        Ty::Apply(ApplicationTy { ctor: TypeCtor::Never, .. }) => {
-            return Ok(Usefulness::NotUseful);
-        }
+        Ty::Never => return Ok(Usefulness::NotUseful),
         _ => (),
     }
 
diff --git a/crates/hir_ty/src/diagnostics/unsafe_check.rs b/crates/hir_ty/src/diagnostics/unsafe_check.rs
index 9c506112d..e77a20fea 100644
--- a/crates/hir_ty/src/diagnostics/unsafe_check.rs
+++ b/crates/hir_ty/src/diagnostics/unsafe_check.rs
@@ -11,9 +11,7 @@ use hir_def::{
 };
 use hir_expand::diagnostics::DiagnosticSink;
 
-use crate::{
-    db::HirDatabase, diagnostics::MissingUnsafe, ApplicationTy, InferenceResult, Ty, TypeCtor,
-};
+use crate::{db::HirDatabase, diagnostics::MissingUnsafe, InferenceResult, Ty};
 
 pub(super) struct UnsafeValidator<'a, 'b: 'a> {
     owner: DefWithBodyId,
@@ -112,7 +110,7 @@ fn walk_unsafe(
             }
         }
         Expr::UnaryOp { expr, op: UnaryOp::Deref } => {
-            if let Ty::Apply(ApplicationTy { ctor: TypeCtor::RawPtr(..), .. }) = &infer[*expr] {
+            if let Ty::Raw(..) = &infer[*expr] {
                 unsafe_exprs.push(UnsafeExpr { expr: current, inside_unsafe_block });
             }
         }
diff --git a/crates/hir_ty/src/display.rs b/crates/hir_ty/src/display.rs
index 271fcbfaf..ab51cb0a6 100644
--- a/crates/hir_ty/src/display.rs
+++ b/crates/hir_ty/src/display.rs
@@ -2,17 +2,20 @@
 
 use std::{borrow::Cow, fmt};
 
-use crate::{
-    db::HirDatabase, utils::generics, ApplicationTy, CallableDefId, FnSig, GenericPredicate,
-    Lifetime, Obligation, OpaqueTy, OpaqueTyId, ProjectionTy, Substs, TraitRef, Ty, TypeCtor,
-};
 use arrayvec::ArrayVec;
+use chalk_ir::Mutability;
 use hir_def::{
-    db::DefDatabase, find_path, generics::TypeParamProvenance, item_scope::ItemInNs, AdtId,
-    AssocContainerId, HasModule, Lookup, ModuleId, TraitId,
+    db::DefDatabase, find_path, generics::TypeParamProvenance, item_scope::ItemInNs,
+    AssocContainerId, Lookup, ModuleId, TraitId,
 };
 use hir_expand::name::Name;
 
+use crate::{
+    db::HirDatabase, primitive, utils::generics, AdtId, AliasTy, CallableDefId, CallableSig,
+    GenericPredicate, Lifetime, Obligation, OpaqueTy, OpaqueTyId, ProjectionTy, Scalar, Substs,
+    TraitRef, Ty,
+};
+
 pub struct HirFormatter<'a> {
     pub db: &'a dyn HirDatabase,
     fmt: &'a mut dyn fmt::Write,
@@ -234,39 +237,79 @@ impl HirDisplay for &Ty {
     }
 }
 
-impl HirDisplay for ApplicationTy {
+impl HirDisplay for ProjectionTy {
     fn hir_fmt(&self, f: &mut HirFormatter) -> Result<(), HirDisplayError> {
         if f.should_truncate() {
             return write!(f, "{}", TYPE_HINT_TRUNCATION);
         }
 
-        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();
+        let trait_ = f.db.trait_data(self.trait_(f.db));
+        let first_parameter = self.parameters[0].into_displayable(
+            f.db,
+            f.max_size,
+            f.omit_verbose_types,
+            f.display_target,
+        );
+        write!(f, "<{} as {}", first_parameter, 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) -> Result<(), HirDisplayError> {
+        if f.should_truncate() {
+            return write!(f, "{}", TYPE_HINT_TRUNCATION);
+        }
+
+        match self {
+            Ty::Never => write!(f, "!")?,
+            Ty::Str => write!(f, "str")?,
+            Ty::Scalar(Scalar::Bool) => write!(f, "bool")?,
+            Ty::Scalar(Scalar::Char) => write!(f, "char")?,
+            &Ty::Scalar(Scalar::Float(t)) => write!(f, "{}", primitive::float_ty_to_string(t))?,
+            &Ty::Scalar(Scalar::Int(t)) => write!(f, "{}", primitive::int_ty_to_string(t))?,
+            &Ty::Scalar(Scalar::Uint(t)) => write!(f, "{}", primitive::uint_ty_to_string(t))?,
+            Ty::Slice(parameters) => {
+                let t = parameters.as_single();
                 write!(f, "[")?;
                 t.hir_fmt(f)?;
                 write!(f, "]")?;
             }
-            TypeCtor::Array => {
-                let t = self.parameters.as_single();
+            Ty::Array(parameters) => {
+                let t = parameters.as_single();
                 write!(f, "[")?;
                 t.hir_fmt(f)?;
                 write!(f, "; _]")?;
             }
-            TypeCtor::RawPtr(m) | TypeCtor::Ref(m) => {
-                let t = self.parameters.as_single();
+            Ty::Raw(m, parameters) | Ty::Ref(m, parameters) => {
+                let t = parameters.as_single();
                 let ty_display =
                     t.into_displayable(f.db, f.max_size, f.omit_verbose_types, f.display_target);
 
-                if matches!(self.ctor, TypeCtor::RawPtr(_)) {
-                    write!(f, "*{}", m.as_keyword_for_ptr())?;
+                if matches!(self, Ty::Raw(..)) {
+                    write!(
+                        f,
+                        "*{}",
+                        match m {
+                            Mutability::Not => "const ",
+                            Mutability::Mut => "mut ",
+                        }
+                    )?;
                 } else {
-                    write!(f, "&{}", m.as_keyword_for_ref())?;
+                    write!(
+                        f,
+                        "&{}",
+                        match m {
+                            Mutability::Not => "",
+                            Mutability::Mut => "mut ",
+                        }
+                    )?;
                 }
 
                 let datas;
@@ -274,10 +317,10 @@ impl HirDisplay for ApplicationTy {
                     Ty::Dyn(predicates) if predicates.len() > 1 => {
                         Cow::Borrowed(predicates.as_ref())
                     }
-                    &Ty::Opaque(OpaqueTy {
+                    &Ty::Alias(AliasTy::Opaque(OpaqueTy {
                         opaque_ty_id: OpaqueTyId::ReturnTypeImplTrait(func, idx),
                         ref parameters,
-                    }) => {
+                    })) => {
                         datas =
                             f.db.return_type_impl_traits(func).expect("impl trait id without data");
                         let data = (*datas)
@@ -304,25 +347,24 @@ impl HirDisplay for ApplicationTy {
                     write!(f, "{}", ty_display)?;
                 }
             }
-            TypeCtor::Never => write!(f, "!")?,
-            TypeCtor::Tuple { .. } => {
-                let ts = &self.parameters;
-                if ts.len() == 1 {
+            Ty::Tuple(_, substs) => {
+                if substs.len() == 1 {
                     write!(f, "(")?;
-                    ts[0].hir_fmt(f)?;
+                    substs[0].hir_fmt(f)?;
                     write!(f, ",)")?;
                 } else {
                     write!(f, "(")?;
-                    f.write_joined(&*ts.0, ", ")?;
+                    f.write_joined(&*substs.0, ", ")?;
                     write!(f, ")")?;
                 }
             }
-            TypeCtor::FnPtr { is_varargs, .. } => {
-                let sig = FnSig::from_fn_ptr_substs(&self.parameters, is_varargs);
+            Ty::Function(fn_ptr) => {
+                let sig = CallableSig::from_fn_ptr(fn_ptr);
                 sig.hir_fmt(f)?;
             }
-            TypeCtor::FnDef(def) => {
-                let sig = f.db.callable_item_signature(def).subst(&self.parameters);
+            Ty::FnDef(def, parameters) => {
+                let def = *def;
+                let sig = f.db.callable_item_signature(def).subst(parameters);
                 match def {
                     CallableDefId::FunctionId(ff) => {
                         write!(f, "fn {}", f.db.function_data(ff).name)?
@@ -332,7 +374,7 @@ impl HirDisplay for ApplicationTy {
                         write!(f, "{}", f.db.enum_data(e.parent).variants[e.local_id].name)?
                     }
                 };
-                if self.parameters.len() > 0 {
+                if parameters.len() > 0 {
                     let generics = generics(f.db.upcast(), def.into());
                     let (parent_params, self_param, type_params, _impl_trait_params) =
                         generics.provenance_split();
@@ -340,7 +382,7 @@ impl HirDisplay for ApplicationTy {
                     // We print all params except implicit impl Trait params. Still a bit weird; should we leave out parent and self?
                     if total_len > 0 {
                         write!(f, "<")?;
-                        f.write_joined(&self.parameters.0[..total_len], ", ")?;
+                        f.write_joined(&parameters.0[..total_len], ", ")?;
                         write!(f, ">")?;
                     }
                 }
@@ -359,20 +401,20 @@ impl HirDisplay for ApplicationTy {
                     write!(f, " -> {}", ret_display)?;
                 }
             }
-            TypeCtor::Adt(def_id) => {
+            Ty::Adt(AdtId(def_id), parameters) => {
                 match f.display_target {
                     DisplayTarget::Diagnostics | DisplayTarget::Test => {
-                        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(),
+                        let name = match *def_id {
+                            hir_def::AdtId::StructId(it) => f.db.struct_data(it).name.clone(),
+                            hir_def::AdtId::UnionId(it) => f.db.union_data(it).name.clone(),
+                            hir_def::AdtId::EnumId(it) => f.db.enum_data(it).name.clone(),
                         };
                         write!(f, "{}", name)?;
                     }
                     DisplayTarget::SourceCode { module_id } => {
                         if let Some(path) = find_path::find_path(
                             f.db.upcast(),
-                            ItemInNs::Types(def_id.into()),
+                            ItemInNs::Types((*def_id).into()),
                             module_id,
                         ) {
                             write!(f, "{}", path)?;
@@ -384,19 +426,18 @@ impl HirDisplay for ApplicationTy {
                     }
                 }
 
-                if self.parameters.len() > 0 {
+                if parameters.len() > 0 {
                     let parameters_to_write =
                         if f.display_target.is_source_code() || f.omit_verbose_types() {
                             match self
-                                .ctor
                                 .as_generic_def()
                                 .map(|generic_def_id| f.db.generic_defaults(generic_def_id))
                                 .filter(|defaults| !defaults.is_empty())
                             {
-                                None => self.parameters.0.as_ref(),
+                                None => parameters.0.as_ref(),
                                 Some(default_parameters) => {
                                     let mut default_from = 0;
-                                    for (i, parameter) in self.parameters.iter().enumerate() {
+                                    for (i, parameter) in parameters.iter().enumerate() {
                                         match (parameter, default_parameters.get(i)) {
                                             (&Ty::Unknown, _) | (_, None) => {
                                                 default_from = i + 1;
@@ -404,18 +445,18 @@ impl HirDisplay for ApplicationTy {
                                             (_, Some(default_parameter)) => {
                                                 let actual_default = default_parameter
                                                     .clone()
-                                                    .subst(&self.parameters.prefix(i));
+                                                    .subst(&parameters.prefix(i));
                                                 if parameter != &actual_default {
                                                     default_from = i + 1;
                                                 }
                                             }
                                         }
                                     }
-                                    &self.parameters.0[0..default_from]
+                                    &parameters.0[0..default_from]
                                 }
                             }
                         } else {
-                            self.parameters.0.as_ref()
+                            parameters.0.as_ref()
                         };
                     if !parameters_to_write.is_empty() {
                         write!(f, "<")?;
@@ -424,61 +465,54 @@ impl HirDisplay for ApplicationTy {
                     }
                 }
             }
-            TypeCtor::AssociatedType(type_alias) => {
+            Ty::AssociatedType(type_alias, parameters) => {
                 let trait_ = match type_alias.lookup(f.db.upcast()).container {
                     AssocContainerId::TraitId(it) => it,
                     _ => panic!("not an associated type"),
                 };
                 let trait_ = f.db.trait_data(trait_);
-                let type_alias_data = f.db.type_alias_data(type_alias);
+                let type_alias_data = f.db.type_alias_data(*type_alias);
 
                 // Use placeholder associated types when the target is test (https://rust-lang.github.io/chalk/book/clauses/type_equality.html#placeholder-associated-types)
                 if f.display_target.is_test() {
                     write!(f, "{}::{}", trait_.name, type_alias_data.name)?;
-                    if self.parameters.len() > 0 {
+                    if parameters.len() > 0 {
                         write!(f, "<")?;
-                        f.write_joined(&*self.parameters.0, ", ")?;
+                        f.write_joined(&*parameters.0, ", ")?;
                         write!(f, ">")?;
                     }
                 } else {
-                    let projection_ty = ProjectionTy {
-                        associated_ty: type_alias,
-                        parameters: self.parameters.clone(),
-                    };
+                    let projection_ty =
+                        ProjectionTy { associated_ty: *type_alias, parameters: parameters.clone() };
 
                     projection_ty.hir_fmt(f)?;
                 }
             }
-            TypeCtor::ForeignType(type_alias) => {
-                let type_alias = f.db.type_alias_data(type_alias);
+            Ty::ForeignType(type_alias) => {
+                let type_alias = f.db.type_alias_data(*type_alias);
                 write!(f, "{}", type_alias.name)?;
-                if self.parameters.len() > 0 {
-                    write!(f, "<")?;
-                    f.write_joined(&*self.parameters.0, ", ")?;
-                    write!(f, ">")?;
-                }
             }
-            TypeCtor::OpaqueType(opaque_ty_id) => {
+            Ty::OpaqueType(opaque_ty_id, parameters) => {
                 match opaque_ty_id {
-                    OpaqueTyId::ReturnTypeImplTrait(func, idx) => {
+                    &OpaqueTyId::ReturnTypeImplTrait(func, idx) => {
                         let datas =
                             f.db.return_type_impl_traits(func).expect("impl trait id without data");
                         let data = (*datas)
                             .as_ref()
                             .map(|rpit| rpit.impl_traits[idx as usize].bounds.clone());
-                        let bounds = data.subst(&self.parameters);
+                        let bounds = data.subst(&parameters);
                         write_bounds_like_dyn_trait_with_prefix("impl", &bounds.value, f)?;
                         // FIXME: it would maybe be good to distinguish this from the alias type (when debug printing), and to show the substitution
                     }
                     OpaqueTyId::AsyncBlockTypeImplTrait(..) => {
                         write!(f, "impl Future<Output = ")?;
-                        self.parameters[0].hir_fmt(f)?;
+                        parameters[0].hir_fmt(f)?;
                         write!(f, ">")?;
                     }
                 }
             }
-            TypeCtor::Closure { .. } => {
-                let sig = self.parameters[0].callable_sig(f.db);
+            Ty::Closure(.., substs) => {
+                let sig = substs[0].callable_sig(f.db);
                 if let Some(sig) = sig {
                     if sig.params().is_empty() {
                         write!(f, "||")?;
@@ -501,44 +535,6 @@ impl HirDisplay for ApplicationTy {
                     write!(f, "{{closure}}")?;
                 }
             }
-        }
-        Ok(())
-    }
-}
-
-impl HirDisplay for ProjectionTy {
-    fn hir_fmt(&self, f: &mut HirFormatter) -> Result<(), HirDisplayError> {
-        if f.should_truncate() {
-            return write!(f, "{}", TYPE_HINT_TRUNCATION);
-        }
-
-        let trait_ = f.db.trait_data(self.trait_(f.db));
-        let first_parameter = self.parameters[0].into_displayable(
-            f.db,
-            f.max_size,
-            f.omit_verbose_types,
-            f.display_target,
-        );
-        write!(f, "<{} as {}", first_parameter, 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) -> Result<(), HirDisplayError> {
-        if f.should_truncate() {
-            return write!(f, "{}", TYPE_HINT_TRUNCATION);
-        }
-
-        match self {
-            Ty::Apply(a_ty) => a_ty.hir_fmt(f)?,
-            Ty::Projection(p_ty) => p_ty.hir_fmt(f)?,
             Ty::Placeholder(id) => {
                 let generics = generics(f.db.upcast(), id.parent);
                 let param_data = &generics.params.types[id.local_id];
@@ -557,11 +553,12 @@ impl HirDisplay for Ty {
                     }
                 }
             }
-            Ty::Bound(idx) => write!(f, "?{}.{}", idx.debruijn.depth(), idx.index)?,
+            Ty::BoundVar(idx) => write!(f, "?{}.{}", idx.debruijn.depth(), idx.index)?,
             Ty::Dyn(predicates) => {
                 write_bounds_like_dyn_trait_with_prefix("dyn", predicates, f)?;
             }
-            Ty::Opaque(opaque_ty) => {
+            Ty::Alias(AliasTy::Projection(p_ty)) => p_ty.hir_fmt(f)?,
+            Ty::Alias(AliasTy::Opaque(opaque_ty)) => {
                 match opaque_ty.opaque_ty_id {
                     OpaqueTyId::ReturnTypeImplTrait(func, idx) => {
                         let datas =
@@ -585,13 +582,13 @@ impl HirDisplay for Ty {
                 }
                 write!(f, "{{unknown}}")?;
             }
-            Ty::Infer(..) => write!(f, "_")?,
+            Ty::InferenceVar(..) => write!(f, "_")?,
         }
         Ok(())
     }
 }
 
-impl HirDisplay for FnSig {
+impl HirDisplay for CallableSig {
     fn hir_fmt(&self, f: &mut HirFormatter) -> Result<(), HirDisplayError> {
         write!(f, "fn(")?;
         f.write_joined(self.params(), ", ")?;
@@ -614,7 +611,7 @@ impl HirDisplay for FnSig {
 }
 
 fn fn_traits(db: &dyn DefDatabase, trait_: TraitId) -> impl Iterator<Item = TraitId> {
-    let krate = trait_.lookup(db).container.module(db).krate();
+    let krate = trait_.lookup(db).container.krate();
     let fn_traits = [
         db.lang_item(krate, "fn".into()),
         db.lang_item(krate, "fn_mut".into()),
diff --git a/crates/hir_ty/src/infer.rs b/crates/hir_ty/src/infer.rs
index 4b683c5a7..4d771a91e 100644
--- a/crates/hir_ty/src/infer.rs
+++ b/crates/hir_ty/src/infer.rs
@@ -18,6 +18,7 @@ use std::mem;
 use std::ops::Index;
 use std::sync::Arc;
 
+use chalk_ir::Mutability;
 use hir_def::{
     body::Body,
     data::{ConstData, FunctionData, StaticData},
@@ -25,7 +26,7 @@ use hir_def::{
     lang_item::LangItemTarget,
     path::{path, Path},
     resolver::{HasResolver, Resolver, TypeNs},
-    type_ref::{Mutability, TypeRef},
+    type_ref::TypeRef,
     AdtId, AssocItemId, DefWithBodyId, EnumVariantId, FieldId, FunctionId, Lookup, TraitId,
     TypeAliasId, VariantId,
 };
@@ -36,25 +37,15 @@ use stdx::impl_from;
 use syntax::SmolStr;
 
 use super::{
-    primitive::{FloatTy, IntTy},
     traits::{Guidance, Obligation, ProjectionPredicate, Solution},
-    InEnvironment, ProjectionTy, Substs, TraitEnvironment, TraitRef, Ty, TypeCtor, TypeWalk,
+    InEnvironment, ProjectionTy, Substs, TraitEnvironment, TraitRef, Ty, TypeWalk,
 };
 use crate::{
-    db::HirDatabase, infer::diagnostics::InferenceDiagnostic, lower::ImplTraitLoweringMode,
+    db::HirDatabase, infer::diagnostics::InferenceDiagnostic, lower::ImplTraitLoweringMode, AliasTy,
 };
 
 pub(crate) use unify::unify;
 
-macro_rules! ty_app {
-    ($ctor:pat, $param:pat) => {
-        crate::Ty::Apply(crate::ApplicationTy { ctor: $ctor, parameters: $param })
-    };
-    ($ctor:pat) => {
-        ty_app!($ctor, _)
-    };
-}
-
 mod unify;
 mod path;
 mod expr;
@@ -97,7 +88,7 @@ impl BindingMode {
     fn convert(annotation: BindingAnnotation) -> BindingMode {
         match annotation {
             BindingAnnotation::Unannotated | BindingAnnotation::Mutable => BindingMode::Move,
-            BindingAnnotation::Ref => BindingMode::Ref(Mutability::Shared),
+            BindingAnnotation::Ref => BindingMode::Ref(Mutability::Not),
             BindingAnnotation::RefMut => BindingMode::Ref(Mutability::Mut),
         }
     }
@@ -405,7 +396,7 @@ impl<'a> InferenceContext<'a> {
     fn normalize_associated_types_in(&mut self, ty: Ty) -> Ty {
         let ty = self.resolve_ty_as_possible(ty);
         ty.fold(&mut |ty| match ty {
-            Ty::Projection(proj_ty) => self.normalize_projection_ty(proj_ty),
+            Ty::Alias(AliasTy::Projection(proj_ty)) => self.normalize_projection_ty(proj_ty),
             _ => ty,
         })
     }
@@ -664,30 +655,17 @@ impl<'a> InferenceContext<'a> {
 /// two are used for inference of literal values (e.g. `100` could be one of
 /// several integer types).
 #[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
-pub enum InferTy {
-    TypeVar(unify::TypeVarId),
-    IntVar(unify::TypeVarId),
-    FloatVar(unify::TypeVarId),
-    MaybeNeverTypeVar(unify::TypeVarId),
+pub struct InferenceVar {
+    index: u32,
 }
 
-impl InferTy {
+impl InferenceVar {
     fn to_inner(self) -> unify::TypeVarId {
-        match self {
-            InferTy::TypeVar(ty)
-            | InferTy::IntVar(ty)
-            | InferTy::FloatVar(ty)
-            | InferTy::MaybeNeverTypeVar(ty) => ty,
-        }
+        unify::TypeVarId(self.index)
     }
 
-    fn fallback_value(self) -> Ty {
-        match self {
-            InferTy::TypeVar(..) => Ty::Unknown,
-            InferTy::IntVar(..) => Ty::simple(TypeCtor::Int(IntTy::i32())),
-            InferTy::FloatVar(..) => Ty::simple(TypeCtor::Float(FloatTy::f64())),
-            InferTy::MaybeNeverTypeVar(..) => Ty::simple(TypeCtor::Never),
-        }
+    fn from_inner(unify::TypeVarId(index): unify::TypeVarId) -> Self {
+        InferenceVar { index }
     }
 }
 
diff --git a/crates/hir_ty/src/infer/coerce.rs b/crates/hir_ty/src/infer/coerce.rs
index 32c7c57cd..7e8846f27 100644
--- a/crates/hir_ty/src/infer/coerce.rs
+++ b/crates/hir_ty/src/infer/coerce.rs
@@ -4,12 +4,12 @@
 //!
 //! See: https://doc.rust-lang.org/nomicon/coercions.html
 
-use hir_def::{lang_item::LangItemTarget, type_ref::Mutability};
-use test_utils::mark;
+use chalk_ir::{Mutability, TyVariableKind};
+use hir_def::lang_item::LangItemTarget;
 
-use crate::{autoderef, traits::Solution, Obligation, Substs, TraitRef, Ty, TypeCtor};
+use crate::{autoderef, traits::Solution, Obligation, Substs, TraitRef, Ty};
 
-use super::{unify::TypeVarValue, InEnvironment, InferTy, InferenceContext};
+use super::{InEnvironment, InferenceContext};
 
 impl<'a> InferenceContext<'a> {
     /// Unify two types, but may coerce the first one to the second one
@@ -33,8 +33,8 @@ impl<'a> InferenceContext<'a> {
         } else if self.coerce(ty2, ty1) {
             ty1.clone()
         } else {
-            if let (ty_app!(TypeCtor::FnDef(_)), ty_app!(TypeCtor::FnDef(_))) = (ty1, ty2) {
-                mark::hit!(coerce_fn_reification);
+            if let (Ty::FnDef(..), Ty::FnDef(..)) = (ty1, ty2) {
+                cov_mark::hit!(coerce_fn_reification);
                 // Special case: two function types. Try to coerce both to
                 // pointers to have a chance at getting a match. See
                 // https://github.com/rust-lang/rust/blob/7b805396bf46dce972692a6846ce2ad8481c5f85/src/librustc_typeck/check/coercion.rs#L877-L916
@@ -44,7 +44,7 @@ impl<'a> InferenceContext<'a> {
                 let ptr_ty2 = Ty::fn_ptr(sig2);
                 self.coerce_merge_branch(&ptr_ty1, &ptr_ty2)
             } else {
-                mark::hit!(coerce_merge_fail_fallback);
+                cov_mark::hit!(coerce_merge_fail_fallback);
                 ty1.clone()
             }
         }
@@ -53,12 +53,11 @@ impl<'a> InferenceContext<'a> {
     fn coerce_inner(&mut self, mut from_ty: Ty, to_ty: &Ty) -> bool {
         match (&from_ty, to_ty) {
             // Never type will make type variable to fallback to Never Type instead of Unknown.
-            (ty_app!(TypeCtor::Never), Ty::Infer(InferTy::TypeVar(tv))) => {
-                let var = self.table.new_maybe_never_type_var();
-                self.table.var_unification_table.union_value(*tv, TypeVarValue::Known(var));
+            (Ty::Never, Ty::InferenceVar(tv, TyVariableKind::General)) => {
+                self.table.type_variable_table.set_diverging(*tv, true);
                 return true;
             }
-            (ty_app!(TypeCtor::Never), _) => return true,
+            (Ty::Never, _) => return true,
 
             // Trivial cases, this should go after `never` check to
             // avoid infer result type to be never
@@ -71,38 +70,33 @@ impl<'a> InferenceContext<'a> {
 
         // Pointer weakening and function to pointer
         match (&mut from_ty, to_ty) {
-            // `*mut T`, `&mut T, `&T`` -> `*const T`
+            // `*mut T` -> `*const T`
             // `&mut T` -> `&T`
-            // `&mut T` -> `*mut T`
-            (ty_app!(c1@TypeCtor::RawPtr(_)), ty_app!(c2@TypeCtor::RawPtr(Mutability::Shared)))
-            | (ty_app!(c1@TypeCtor::Ref(_)), ty_app!(c2@TypeCtor::RawPtr(Mutability::Shared)))
-            | (ty_app!(c1@TypeCtor::Ref(_)), ty_app!(c2@TypeCtor::Ref(Mutability::Shared)))
-            | (ty_app!(c1@TypeCtor::Ref(Mutability::Mut)), ty_app!(c2@TypeCtor::RawPtr(_))) => {
-                *c1 = *c2;
+            (Ty::Raw(m1, ..), Ty::Raw(m2 @ Mutability::Not, ..))
+            | (Ty::Ref(m1, ..), Ty::Ref(m2 @ Mutability::Not, ..)) => {
+                *m1 = *m2;
+            }
+            // `&T` -> `*const T`
+            // `&mut T` -> `*mut T`/`*const T`
+            (Ty::Ref(.., substs), &Ty::Raw(m2 @ Mutability::Not, ..))
+            | (Ty::Ref(Mutability::Mut, substs), &Ty::Raw(m2, ..)) => {
+                from_ty = Ty::Raw(m2, substs.clone());
             }
 
-            // Illegal mutablity conversion
-            (
-                ty_app!(TypeCtor::RawPtr(Mutability::Shared)),
-                ty_app!(TypeCtor::RawPtr(Mutability::Mut)),
-            )
-            | (
-                ty_app!(TypeCtor::Ref(Mutability::Shared)),
-                ty_app!(TypeCtor::Ref(Mutability::Mut)),
-            ) => return false,
+            // Illegal mutability conversion
+            (Ty::Raw(Mutability::Not, ..), Ty::Raw(Mutability::Mut, ..))
+            | (Ty::Ref(Mutability::Not, ..), Ty::Ref(Mutability::Mut, ..)) => return false,
 
             // `{function_type}` -> `fn()`
-            (ty_app!(TypeCtor::FnDef(_)), ty_app!(TypeCtor::FnPtr { .. })) => {
-                match from_ty.callable_sig(self.db) {
-                    None => return false,
-                    Some(sig) => {
-                        from_ty = Ty::fn_ptr(sig);
-                    }
+            (Ty::FnDef(..), Ty::Function { .. }) => match from_ty.callable_sig(self.db) {
+                None => return false,
+                Some(sig) => {
+                    from_ty = Ty::fn_ptr(sig);
                 }
-            }
+            },
 
-            (ty_app!(TypeCtor::Closure { .. }, params), ty_app!(TypeCtor::FnPtr { .. })) => {
-                from_ty = params[0].clone();
+            (Ty::Closure(.., substs), Ty::Function { .. }) => {
+                from_ty = substs[0].clone();
             }
 
             _ => {}
@@ -115,9 +109,7 @@ impl<'a> InferenceContext<'a> {
         // Auto Deref if cannot coerce
         match (&from_ty, to_ty) {
             // FIXME: DerefMut
-            (ty_app!(TypeCtor::Ref(_), st1), ty_app!(TypeCtor::Ref(_), st2)) => {
-                self.unify_autoderef_behind_ref(&st1[0], &st2[0])
-            }
+            (Ty::Ref(_, st1), Ty::Ref(_, st2)) => self.unify_autoderef_behind_ref(&st1[0], &st2[0]),
 
             // Otherwise, normal unify
             _ => self.unify(&from_ty, to_ty),
@@ -178,17 +170,17 @@ impl<'a> InferenceContext<'a> {
             },
         ) {
             let derefed_ty = canonicalized.decanonicalize_ty(derefed_ty.value);
-            match (&*self.resolve_ty_shallow(&derefed_ty), &*to_ty) {
-                // Stop when constructor matches.
-                (ty_app!(from_ctor, st1), ty_app!(to_ctor, st2)) if from_ctor == to_ctor => {
-                    // It will not recurse to `coerce`.
-                    return self.table.unify_substs(st1, st2, 0);
-                }
-                _ => {
-                    if self.table.unify_inner_trivial(&derefed_ty, &to_ty, 0) {
-                        return true;
-                    }
-                }
+            let from_ty = self.resolve_ty_shallow(&derefed_ty);
+            // Stop when constructor matches.
+            if from_ty.equals_ctor(&to_ty) {
+                // It will not recurse to `coerce`.
+                return match (from_ty.substs(), to_ty.substs()) {
+                    (Some(st1), Some(st2)) => self.table.unify_substs(st1, st2, 0),
+                    (None, None) => true,
+                    _ => false,
+                };
+            } else if self.table.unify_inner_trivial(&derefed_ty, &to_ty, 0) {
+                return true;
             }
         }
 
diff --git a/crates/hir_ty/src/infer/expr.rs b/crates/hir_ty/src/infer/expr.rs
index cb59a6937..262177ffb 100644
--- a/crates/hir_ty/src/infer/expr.rs
+++ b/crates/hir_ty/src/infer/expr.rs
@@ -3,23 +3,25 @@
 use std::iter::{repeat, repeat_with};
 use std::{mem, sync::Arc};
 
+use chalk_ir::{Mutability, TyVariableKind};
 use hir_def::{
-    builtin_type::Signedness,
     expr::{Array, BinaryOp, Expr, ExprId, Literal, Statement, UnaryOp},
     path::{GenericArg, GenericArgs},
     resolver::resolver_for_expr,
-    AdtId, AssocContainerId, FieldId, Lookup,
+    AssocContainerId, FieldId, Lookup,
 };
 use hir_expand::name::{name, Name};
 use syntax::ast::RangeOp;
-use test_utils::mark;
 
 use crate::{
-    autoderef, method_resolution, op,
+    autoderef,
+    lower::lower_to_chalk_mutability,
+    method_resolution, op,
+    primitive::{self, UintTy},
     traits::{FnTrait, InEnvironment},
     utils::{generics, variant_data, Generics},
-    ApplicationTy, Binders, CallableDefId, InferTy, IntTy, Mutability, Obligation, OpaqueTyId,
-    Rawness, Substs, TraitRef, Ty, TypeCtor,
+    AdtId, Binders, CallableDefId, FnPointer, FnSig, Obligation, OpaqueTyId, Rawness, Scalar,
+    Substs, TraitRef, Ty,
 };
 
 use super::{
@@ -82,10 +84,7 @@ impl<'a> InferenceContext<'a> {
             arg_tys.push(arg);
         }
         let parameters = param_builder.build();
-        let arg_ty = Ty::Apply(ApplicationTy {
-            ctor: TypeCtor::Tuple { cardinality: num_args as u16 },
-            parameters,
-        });
+        let arg_ty = Ty::Tuple(num_args, parameters);
         let substs =
             Substs::build_for_generics(&generic_params).push(ty.clone()).push(arg_ty).build();
 
@@ -120,7 +119,7 @@ impl<'a> InferenceContext<'a> {
             Expr::Missing => Ty::Unknown,
             Expr::If { condition, then_branch, else_branch } => {
                 // if let is desugared to match, so this is always simple if
-                self.infer_expr(*condition, &Expectation::has_type(Ty::simple(TypeCtor::Bool)));
+                self.infer_expr(*condition, &Expectation::has_type(Ty::Scalar(Scalar::Bool)));
 
                 let condition_diverges = mem::replace(&mut self.diverges, Diverges::Maybe);
                 let mut both_arms_diverge = Diverges::Always;
@@ -175,7 +174,7 @@ impl<'a> InferenceContext<'a> {
                 // existenail type AsyncBlockImplTrait<InnerType>: Future<Output = InnerType>
                 let inner_ty = self.infer_expr(*body, &Expectation::none());
                 let opaque_ty_id = OpaqueTyId::AsyncBlockTypeImplTrait(self.owner, *body);
-                Ty::apply_one(TypeCtor::OpaqueType(opaque_ty_id), inner_ty)
+                Ty::OpaqueType(opaque_ty_id, Substs::single(inner_ty))
             }
             Expr::Loop { body, label } => {
                 self.breakables.push(BreakableContext {
@@ -193,7 +192,7 @@ impl<'a> InferenceContext<'a> {
                 if ctxt.may_break {
                     ctxt.break_ty
                 } else {
-                    Ty::simple(TypeCtor::Never)
+                    Ty::Never
                 }
             }
             Expr::While { condition, body, label } => {
@@ -203,7 +202,7 @@ impl<'a> InferenceContext<'a> {
                     label: label.map(|label| self.body[label].name.clone()),
                 });
                 // while let is desugared to a match loop, so this is always simple while
-                self.infer_expr(*condition, &Expectation::has_type(Ty::simple(TypeCtor::Bool)));
+                self.infer_expr(*condition, &Expectation::has_type(Ty::Scalar(Scalar::Bool)));
                 self.infer_expr(*body, &Expectation::has_type(Ty::unit()));
                 let _ctxt = self.breakables.pop().expect("breakable stack broken");
                 // the body may not run, so it diverging doesn't mean we diverge
@@ -250,12 +249,12 @@ impl<'a> InferenceContext<'a> {
                     None => self.table.new_type_var(),
                 };
                 sig_tys.push(ret_ty.clone());
-                let sig_ty = Ty::apply(
-                    TypeCtor::FnPtr { num_args: sig_tys.len() as u16 - 1, is_varargs: false },
-                    Substs(sig_tys.clone().into()),
-                );
-                let closure_ty =
-                    Ty::apply_one(TypeCtor::Closure { def: self.owner, expr: tgt_expr }, sig_ty);
+                let sig_ty = Ty::Function(FnPointer {
+                    num_args: sig_tys.len() - 1,
+                    sig: FnSig { variadic: false },
+                    substs: Substs(sig_tys.clone().into()),
+                });
+                let closure_ty = Ty::Closure(self.owner, tgt_expr, Substs::single(sig_ty));
 
                 // Eagerly try to relate the closure type with the expected
                 // type, otherwise we often won't have enough information to
@@ -306,11 +305,8 @@ impl<'a> InferenceContext<'a> {
             Expr::Match { expr, arms } => {
                 let input_ty = self.infer_expr(*expr, &Expectation::none());
 
-                let mut result_ty = if arms.is_empty() {
-                    Ty::simple(TypeCtor::Never)
-                } else {
-                    self.table.new_type_var()
-                };
+                let mut result_ty =
+                    if arms.is_empty() { Ty::Never } else { self.table.new_type_var() };
 
                 let matchee_diverges = self.diverges;
                 let mut all_arms_diverge = Diverges::Always;
@@ -321,7 +317,7 @@ impl<'a> InferenceContext<'a> {
                     if let Some(guard_expr) = arm.guard {
                         self.infer_expr(
                             guard_expr,
-                            &Expectation::has_type(Ty::simple(TypeCtor::Bool)),
+                            &Expectation::has_type(Ty::Scalar(Scalar::Bool)),
                         );
                     }
 
@@ -339,7 +335,7 @@ impl<'a> InferenceContext<'a> {
                 let resolver = resolver_for_expr(self.db.upcast(), self.owner, tgt_expr);
                 self.infer_path(&resolver, p, tgt_expr.into()).unwrap_or(Ty::Unknown)
             }
-            Expr::Continue { .. } => Ty::simple(TypeCtor::Never),
+            Expr::Continue { .. } => Ty::Never,
             Expr::Break { expr, label } => {
                 let val_ty = if let Some(expr) = expr {
                     self.infer_expr(*expr, &Expectation::none())
@@ -364,8 +360,7 @@ impl<'a> InferenceContext<'a> {
                         expr: tgt_expr,
                     });
                 }
-
-                Ty::simple(TypeCtor::Never)
+                Ty::Never
             }
             Expr::Return { expr } => {
                 if let Some(expr) = expr {
@@ -374,14 +369,14 @@ impl<'a> InferenceContext<'a> {
                     let unit = Ty::unit();
                     self.coerce(&unit, &self.return_ty.clone());
                 }
-                Ty::simple(TypeCtor::Never)
+                Ty::Never
             }
             Expr::Yield { expr } => {
                 // FIXME: track yield type for coercion
                 if let Some(expr) = expr {
                     self.infer_expr(*expr, &Expectation::none());
                 }
-                Ty::simple(TypeCtor::Never)
+                Ty::Never
             }
             Expr::RecordLit { path, fields, spread } => {
                 let (ty, def_id) = self.resolve_variant(path.as_ref());
@@ -391,7 +386,7 @@ impl<'a> InferenceContext<'a> {
 
                 self.unify(&ty, &expected.ty);
 
-                let substs = ty.substs().unwrap_or_else(Substs::empty);
+                let substs = ty.substs().cloned().unwrap_or_else(Substs::empty);
                 let field_types = def_id.map(|it| self.db.field_types(it)).unwrap_or_default();
                 let variant_data = def_id.map(|it| variant_data(self.db.upcast(), it));
                 for (field_idx, field) in fields.iter().enumerate() {
@@ -430,30 +425,23 @@ impl<'a> InferenceContext<'a> {
                     },
                 )
                 .find_map(|derefed_ty| match canonicalized.decanonicalize_ty(derefed_ty.value) {
-                    Ty::Apply(a_ty) => match a_ty.ctor {
-                        TypeCtor::Tuple { .. } => name
-                            .as_tuple_index()
-                            .and_then(|idx| a_ty.parameters.0.get(idx).cloned()),
-                        TypeCtor::Adt(AdtId::StructId(s)) => {
-                            self.db.struct_data(s).variant_data.field(name).map(|local_id| {
-                                let field = FieldId { parent: s.into(), local_id };
-                                self.write_field_resolution(tgt_expr, field);
-                                self.db.field_types(s.into())[field.local_id]
-                                    .clone()
-                                    .subst(&a_ty.parameters)
-                            })
-                        }
-                        TypeCtor::Adt(AdtId::UnionId(u)) => {
-                            self.db.union_data(u).variant_data.field(name).map(|local_id| {
-                                let field = FieldId { parent: u.into(), local_id };
-                                self.write_field_resolution(tgt_expr, field);
-                                self.db.field_types(u.into())[field.local_id]
-                                    .clone()
-                                    .subst(&a_ty.parameters)
-                            })
-                        }
-                        _ => None,
-                    },
+                    Ty::Tuple(_, substs) => {
+                        name.as_tuple_index().and_then(|idx| substs.0.get(idx).cloned())
+                    }
+                    Ty::Adt(AdtId(hir_def::AdtId::StructId(s)), parameters) => {
+                        self.db.struct_data(s).variant_data.field(name).map(|local_id| {
+                            let field = FieldId { parent: s.into(), local_id };
+                            self.write_field_resolution(tgt_expr, field);
+                            self.db.field_types(s.into())[field.local_id].clone().subst(&parameters)
+                        })
+                    }
+                    Ty::Adt(AdtId(hir_def::AdtId::UnionId(u)), parameters) => {
+                        self.db.union_data(u).variant_data.field(name).map(|local_id| {
+                            let field = FieldId { parent: u.into(), local_id };
+                            self.write_field_resolution(tgt_expr, field);
+                            self.db.field_types(u.into())[field.local_id].clone().subst(&parameters)
+                        })
+                    }
                     _ => None,
                 })
                 .unwrap_or(Ty::Unknown);
@@ -475,10 +463,11 @@ impl<'a> InferenceContext<'a> {
                 cast_ty
             }
             Expr::Ref { expr, rawness, mutability } => {
+                let mutability = lower_to_chalk_mutability(*mutability);
                 let expectation = if let Some((exp_inner, exp_rawness, exp_mutability)) =
                     &expected.ty.as_reference_or_ptr()
                 {
-                    if *exp_mutability == Mutability::Mut && *mutability == Mutability::Shared {
+                    if *exp_mutability == Mutability::Mut && mutability == Mutability::Not {
                         // FIXME: throw type error - expected mut reference but found shared ref,
                         // which cannot be coerced
                     }
@@ -491,19 +480,24 @@ impl<'a> InferenceContext<'a> {
                     Expectation::none()
                 };
                 let inner_ty = self.infer_expr_inner(*expr, &expectation);
-                let ty = match rawness {
-                    Rawness::RawPtr => TypeCtor::RawPtr(*mutability),
-                    Rawness::Ref => TypeCtor::Ref(*mutability),
-                };
-                Ty::apply_one(ty, inner_ty)
+                match rawness {
+                    Rawness::RawPtr => Ty::Raw(mutability, Substs::single(inner_ty)),
+                    Rawness::Ref => Ty::Ref(mutability, Substs::single(inner_ty)),
+                }
             }
             Expr::Box { expr } => {
                 let inner_ty = self.infer_expr_inner(*expr, &Expectation::none());
                 if let Some(box_) = self.resolve_boxed_box() {
-                    let mut sb = Substs::build_for_type_ctor(self.db, TypeCtor::Adt(box_));
+                    let mut sb = Substs::builder(generics(self.db.upcast(), box_.into()).len());
                     sb = sb.push(inner_ty);
+                    match self.db.generic_defaults(box_.into()).as_ref() {
+                        [_, alloc_ty, ..] if !alloc_ty.value.is_unknown() => {
+                            sb = sb.push(alloc_ty.value.clone());
+                        }
+                        _ => (),
+                    }
                     sb = sb.fill(repeat_with(|| self.table.new_type_var()));
-                    Ty::apply(TypeCtor::Adt(box_), sb.build())
+                    Ty::adt_ty(box_, sb.build())
                 } else {
                     Ty::Unknown
                 }
@@ -533,13 +527,11 @@ impl<'a> InferenceContext<'a> {
                     UnaryOp::Neg => {
                         match &inner_ty {
                             // Fast path for builtins
-                            Ty::Apply(ApplicationTy {
-                                ctor: TypeCtor::Int(IntTy { signedness: Signedness::Signed, .. }),
-                                ..
-                            })
-                            | Ty::Apply(ApplicationTy { ctor: TypeCtor::Float(_), .. })
-                            | Ty::Infer(InferTy::IntVar(..))
-                            | Ty::Infer(InferTy::FloatVar(..)) => inner_ty,
+                            Ty::Scalar(Scalar::Int(_))
+                            | Ty::Scalar(Scalar::Uint(_))
+                            | Ty::Scalar(Scalar::Float(_))
+                            | Ty::InferenceVar(_, TyVariableKind::Integer)
+                            | Ty::InferenceVar(_, TyVariableKind::Float) => inner_ty,
                             // Otherwise we resolve via the std::ops::Neg trait
                             _ => self
                                 .resolve_associated_type(inner_ty, self.resolve_ops_neg_output()),
@@ -548,9 +540,10 @@ impl<'a> InferenceContext<'a> {
                     UnaryOp::Not => {
                         match &inner_ty {
                             // Fast path for builtins
-                            Ty::Apply(ApplicationTy { ctor: TypeCtor::Bool, .. })
-                            | Ty::Apply(ApplicationTy { ctor: TypeCtor::Int(_), .. })
-                            | Ty::Infer(InferTy::IntVar(..)) => inner_ty,
+                            Ty::Scalar(Scalar::Bool)
+                            | Ty::Scalar(Scalar::Int(_))
+                            | Ty::Scalar(Scalar::Uint(_))
+                            | Ty::InferenceVar(_, TyVariableKind::Integer) => inner_ty,
                             // Otherwise we resolve via the std::ops::Not trait
                             _ => self
                                 .resolve_associated_type(inner_ty, self.resolve_ops_not_output()),
@@ -561,7 +554,7 @@ impl<'a> InferenceContext<'a> {
             Expr::BinaryOp { lhs, rhs, op } => match op {
                 Some(op) => {
                     let lhs_expectation = match op {
-                        BinaryOp::LogicOp(..) => Expectation::has_type(Ty::simple(TypeCtor::Bool)),
+                        BinaryOp::LogicOp(..) => Expectation::has_type(Ty::Scalar(Scalar::Bool)),
                         _ => Expectation::none(),
                     };
                     let lhs_ty = self.infer_expr(*lhs, &lhs_expectation);
@@ -571,7 +564,7 @@ impl<'a> InferenceContext<'a> {
                     let ret = op::binary_op_return_ty(*op, lhs_ty.clone(), rhs_ty.clone());
 
                     if ret == Ty::Unknown {
-                        mark::hit!(infer_expr_inner_binary_operator_overload);
+                        cov_mark::hit!(infer_expr_inner_binary_operator_overload);
 
                         self.resolve_associated_type_with_params(
                             lhs_ty,
@@ -592,31 +585,31 @@ impl<'a> InferenceContext<'a> {
                 let rhs_ty = rhs.map(|e| self.infer_expr(e, &rhs_expect));
                 match (range_type, lhs_ty, rhs_ty) {
                     (RangeOp::Exclusive, None, None) => match self.resolve_range_full() {
-                        Some(adt) => Ty::simple(TypeCtor::Adt(adt)),
+                        Some(adt) => Ty::adt_ty(adt, Substs::empty()),
                         None => Ty::Unknown,
                     },
                     (RangeOp::Exclusive, None, Some(ty)) => match self.resolve_range_to() {
-                        Some(adt) => Ty::apply_one(TypeCtor::Adt(adt), ty),
+                        Some(adt) => Ty::adt_ty(adt, Substs::single(ty)),
                         None => Ty::Unknown,
                     },
                     (RangeOp::Inclusive, None, Some(ty)) => {
                         match self.resolve_range_to_inclusive() {
-                            Some(adt) => Ty::apply_one(TypeCtor::Adt(adt), ty),
+                            Some(adt) => Ty::adt_ty(adt, Substs::single(ty)),
                             None => Ty::Unknown,
                         }
                     }
                     (RangeOp::Exclusive, Some(_), Some(ty)) => match self.resolve_range() {
-                        Some(adt) => Ty::apply_one(TypeCtor::Adt(adt), ty),
+                        Some(adt) => Ty::adt_ty(adt, Substs::single(ty)),
                         None => Ty::Unknown,
                     },
                     (RangeOp::Inclusive, Some(_), Some(ty)) => {
                         match self.resolve_range_inclusive() {
-                            Some(adt) => Ty::apply_one(TypeCtor::Adt(adt), ty),
+                            Some(adt) => Ty::adt_ty(adt, Substs::single(ty)),
                             None => Ty::Unknown,
                         }
                     }
                     (RangeOp::Exclusive, Some(ty), None) => match self.resolve_range_from() {
-                        Some(adt) => Ty::apply_one(TypeCtor::Adt(adt), ty),
+                        Some(adt) => Ty::adt_ty(adt, Substs::single(ty)),
                         None => Ty::Unknown,
                     },
                     (RangeOp::Inclusive, _, None) => Ty::Unknown,
@@ -650,7 +643,7 @@ impl<'a> InferenceContext<'a> {
             }
             Expr::Tuple { exprs } => {
                 let mut tys = match &expected.ty {
-                    ty_app!(TypeCtor::Tuple { .. }, st) => st
+                    Ty::Tuple(_, substs) => substs
                         .iter()
                         .cloned()
                         .chain(repeat_with(|| self.table.new_type_var()))
@@ -663,15 +656,11 @@ impl<'a> InferenceContext<'a> {
                     self.infer_expr_coerce(*expr, &Expectation::has_type(ty.clone()));
                 }
 
-                Ty::apply(TypeCtor::Tuple { cardinality: tys.len() as u16 }, Substs(tys.into()))
+                Ty::Tuple(tys.len(), Substs(tys.into()))
             }
             Expr::Array(array) => {
                 let elem_ty = match &expected.ty {
-                    // FIXME: remove when https://github.com/rust-lang/rust/issues/80501 is fixed
-                    #[allow(unreachable_patterns)]
-                    ty_app!(TypeCtor::Array, st) | ty_app!(TypeCtor::Slice, st) => {
-                        st.as_single().clone()
-                    }
+                    Ty::Array(st) | Ty::Slice(st) => st.as_single().clone(),
                     _ => self.table.new_type_var(),
                 };
 
@@ -688,30 +677,38 @@ impl<'a> InferenceContext<'a> {
                         );
                         self.infer_expr(
                             *repeat,
-                            &Expectation::has_type(Ty::simple(TypeCtor::Int(IntTy::usize()))),
+                            &Expectation::has_type(Ty::Scalar(Scalar::Uint(UintTy::Usize))),
                         );
                     }
                 }
 
-                Ty::apply_one(TypeCtor::Array, elem_ty)
+                Ty::Array(Substs::single(elem_ty))
             }
             Expr::Literal(lit) => match lit {
-                Literal::Bool(..) => Ty::simple(TypeCtor::Bool),
-                Literal::String(..) => {
-                    Ty::apply_one(TypeCtor::Ref(Mutability::Shared), Ty::simple(TypeCtor::Str))
-                }
+                Literal::Bool(..) => Ty::Scalar(Scalar::Bool),
+                Literal::String(..) => Ty::Ref(Mutability::Not, Substs::single(Ty::Str)),
                 Literal::ByteString(..) => {
-                    let byte_type = Ty::simple(TypeCtor::Int(IntTy::u8()));
-                    let array_type = Ty::apply_one(TypeCtor::Array, byte_type);
-                    Ty::apply_one(TypeCtor::Ref(Mutability::Shared), array_type)
+                    let byte_type = Ty::Scalar(Scalar::Uint(UintTy::U8));
+                    let array_type = Ty::Array(Substs::single(byte_type));
+                    Ty::Ref(Mutability::Not, Substs::single(array_type))
                 }
-                Literal::Char(..) => Ty::simple(TypeCtor::Char),
+                Literal::Char(..) => Ty::Scalar(Scalar::Char),
                 Literal::Int(_v, ty) => match ty {
-                    Some(int_ty) => Ty::simple(TypeCtor::Int((*int_ty).into())),
+                    Some(int_ty) => {
+                        Ty::Scalar(Scalar::Int(primitive::int_ty_from_builtin(*int_ty)))
+                    }
+                    None => self.table.new_integer_var(),
+                },
+                Literal::Uint(_v, ty) => match ty {
+                    Some(int_ty) => {
+                        Ty::Scalar(Scalar::Uint(primitive::uint_ty_from_builtin(*int_ty)))
+                    }
                     None => self.table.new_integer_var(),
                 },
                 Literal::Float(_v, ty) => match ty {
-                    Some(float_ty) => Ty::simple(TypeCtor::Float((*float_ty).into())),
+                    Some(float_ty) => {
+                        Ty::Scalar(Scalar::Float(primitive::float_ty_from_builtin(*float_ty)))
+                    }
                     None => self.table.new_float_var(),
                 },
             },
@@ -767,7 +764,7 @@ impl<'a> InferenceContext<'a> {
             // `!`).
             if self.diverges.is_always() {
                 // we don't even make an attempt at coercion
-                self.table.new_maybe_never_type_var()
+                self.table.new_maybe_never_var()
             } else {
                 self.coerce(&Ty::unit(), expected.coercion_target());
                 Ty::unit()
@@ -824,7 +821,7 @@ impl<'a> InferenceContext<'a> {
         // Apply autoref so the below unification works correctly
         // FIXME: return correct autorefs from lookup_method
         let actual_receiver_ty = match expected_receiver_ty.as_reference() {
-            Some((_, mutability)) => Ty::apply_one(TypeCtor::Ref(mutability), derefed_receiver_ty),
+            Some((_, mutability)) => Ty::Ref(mutability, Substs::single(derefed_receiver_ty)),
             _ => derefed_receiver_ty,
         };
         self.unify(&expected_receiver_ty, &actual_receiver_ty);
@@ -901,30 +898,26 @@ impl<'a> InferenceContext<'a> {
     }
 
     fn register_obligations_for_call(&mut self, callable_ty: &Ty) {
-        if let Ty::Apply(a_ty) = callable_ty {
-            if let TypeCtor::FnDef(def) = a_ty.ctor {
-                let generic_predicates = self.db.generic_predicates(def.into());
-                for predicate in generic_predicates.iter() {
-                    let predicate = predicate.clone().subst(&a_ty.parameters);
-                    if let Some(obligation) = Obligation::from_predicate(predicate) {
-                        self.obligations.push(obligation);
-                    }
+        if let &Ty::FnDef(def, ref parameters) = callable_ty {
+            let generic_predicates = self.db.generic_predicates(def.into());
+            for predicate in generic_predicates.iter() {
+                let predicate = predicate.clone().subst(parameters);
+                if let Some(obligation) = Obligation::from_predicate(predicate) {
+                    self.obligations.push(obligation);
                 }
-                // add obligation for trait implementation, if this is a trait method
-                match def {
-                    CallableDefId::FunctionId(f) => {
-                        if let AssocContainerId::TraitId(trait_) =
-                            f.lookup(self.db.upcast()).container
-                        {
-                            // construct a TraitDef
-                            let substs = a_ty
-                                .parameters
-                                .prefix(generics(self.db.upcast(), trait_.into()).len());
-                            self.obligations.push(Obligation::Trait(TraitRef { trait_, substs }));
-                        }
+            }
+            // add obligation for trait implementation, if this is a trait method
+            match def {
+                CallableDefId::FunctionId(f) => {
+                    if let AssocContainerId::TraitId(trait_) = f.lookup(self.db.upcast()).container
+                    {
+                        // construct a TraitDef
+                        let substs =
+                            parameters.prefix(generics(self.db.upcast(), trait_.into()).len());
+                        self.obligations.push(Obligation::Trait(TraitRef { trait_, substs }));
                     }
-                    CallableDefId::StructId(_) | CallableDefId::EnumVariantId(_) => {}
                 }
+                CallableDefId::StructId(_) | CallableDefId::EnumVariantId(_) => {}
             }
         }
     }
diff --git a/crates/hir_ty/src/infer/pat.rs b/crates/hir_ty/src/infer/pat.rs
index d974f805b..a0ac8d80f 100644
--- a/crates/hir_ty/src/infer/pat.rs
+++ b/crates/hir_ty/src/infer/pat.rs
@@ -3,17 +3,16 @@
 use std::iter::repeat;
 use std::sync::Arc;
 
+use chalk_ir::Mutability;
 use hir_def::{
     expr::{BindingAnnotation, Expr, Literal, Pat, PatId, RecordFieldPat},
     path::Path,
-    type_ref::Mutability,
     FieldId,
 };
 use hir_expand::name::Name;
-use test_utils::mark;
 
 use super::{BindingMode, Expectation, InferenceContext};
-use crate::{utils::variant_data, Substs, Ty, TypeCtor};
+use crate::{lower::lower_to_chalk_mutability, utils::variant_data, Substs, Ty};
 
 impl<'a> InferenceContext<'a> {
     fn infer_tuple_struct_pat(
@@ -32,7 +31,7 @@ impl<'a> InferenceContext<'a> {
         }
         self.unify(&ty, expected);
 
-        let substs = ty.substs().unwrap_or_else(Substs::empty);
+        let substs = ty.substs().cloned().unwrap_or_else(Substs::empty);
 
         let field_tys = def.map(|it| self.db.field_types(it)).unwrap_or_default();
         let (pre, post) = match ellipsis {
@@ -71,7 +70,7 @@ impl<'a> InferenceContext<'a> {
 
         self.unify(&ty, expected);
 
-        let substs = ty.substs().unwrap_or_else(Substs::empty);
+        let substs = ty.substs().cloned().unwrap_or_else(Substs::empty);
 
         let field_tys = def.map(|it| self.db.field_types(it)).unwrap_or_default();
         for subpat in subpats {
@@ -103,12 +102,12 @@ impl<'a> InferenceContext<'a> {
                 expected = inner;
                 default_bm = match default_bm {
                     BindingMode::Move => BindingMode::Ref(mutability),
-                    BindingMode::Ref(Mutability::Shared) => BindingMode::Ref(Mutability::Shared),
+                    BindingMode::Ref(Mutability::Not) => BindingMode::Ref(Mutability::Not),
                     BindingMode::Ref(Mutability::Mut) => BindingMode::Ref(mutability),
                 }
             }
         } else if let Pat::Ref { .. } = &body[pat] {
-            mark::hit!(match_ergonomics_ref);
+            cov_mark::hit!(match_ergonomics_ref);
             // When you encounter a `&pat` pattern, reset to Move.
             // This is so that `w` is by value: `let (_, &w) = &(1, &2);`
             default_bm = BindingMode::Move;
@@ -138,10 +137,7 @@ impl<'a> InferenceContext<'a> {
                 inner_tys.extend(expectations_iter.by_ref().take(n_uncovered_patterns).cloned());
                 inner_tys.extend(post.iter().zip(expectations_iter).map(infer_pat));
 
-                Ty::apply(
-                    TypeCtor::Tuple { cardinality: inner_tys.len() as u16 },
-                    Substs(inner_tys.into()),
-                )
+                Ty::Tuple(inner_tys.len(), Substs(inner_tys.into()))
             }
             Pat::Or(ref pats) => {
                 if let Some((first_pat, rest)) = pats.split_first() {
@@ -155,9 +151,10 @@ impl<'a> InferenceContext<'a> {
                 }
             }
             Pat::Ref { pat, mutability } => {
+                let mutability = lower_to_chalk_mutability(*mutability);
                 let expectation = match expected.as_reference() {
                     Some((inner_ty, exp_mut)) => {
-                        if *mutability != exp_mut {
+                        if mutability != exp_mut {
                             // FIXME: emit type error?
                         }
                         inner_ty
@@ -165,7 +162,7 @@ impl<'a> InferenceContext<'a> {
                     _ => &Ty::Unknown,
                 };
                 let subty = self.infer_pat(*pat, expectation, default_bm);
-                Ty::apply_one(TypeCtor::Ref(*mutability), subty)
+                Ty::Ref(mutability, Substs::single(subty))
             }
             Pat::TupleStruct { path: p, args: subpats, ellipsis } => self.infer_tuple_struct_pat(
                 p.as_ref(),
@@ -198,7 +195,7 @@ impl<'a> InferenceContext<'a> {
 
                 let bound_ty = match mode {
                     BindingMode::Ref(mutability) => {
-                        Ty::apply_one(TypeCtor::Ref(mutability), inner_ty.clone())
+                        Ty::Ref(mutability, Substs::single(inner_ty.clone()))
                     }
                     BindingMode::Move => inner_ty.clone(),
                 };
@@ -207,17 +204,17 @@ impl<'a> InferenceContext<'a> {
                 return inner_ty;
             }
             Pat::Slice { prefix, slice, suffix } => {
-                let (container_ty, elem_ty) = match &expected {
-                    ty_app!(TypeCtor::Array, st) => (TypeCtor::Array, st.as_single().clone()),
-                    ty_app!(TypeCtor::Slice, st) => (TypeCtor::Slice, st.as_single().clone()),
-                    _ => (TypeCtor::Slice, Ty::Unknown),
+                let (container_ty, elem_ty): (fn(_) -> _, _) = match &expected {
+                    Ty::Array(st) => (Ty::Array, st.as_single().clone()),
+                    Ty::Slice(st) => (Ty::Slice, st.as_single().clone()),
+                    _ => (Ty::Slice, Ty::Unknown),
                 };
 
                 for pat_id in prefix.iter().chain(suffix) {
                     self.infer_pat(*pat_id, &elem_ty, default_bm);
                 }
 
-                let pat_ty = Ty::apply_one(container_ty, elem_ty);
+                let pat_ty = container_ty(Substs::single(elem_ty));
                 if let Some(slice_pat_id) = slice {
                     self.infer_pat(*slice_pat_id, &pat_ty, default_bm);
                 }
@@ -239,7 +236,7 @@ impl<'a> InferenceContext<'a> {
                     };
 
                     let inner_ty = self.infer_pat(*inner, inner_expected, default_bm);
-                    Ty::apply_one(TypeCtor::Adt(box_adt), inner_ty)
+                    Ty::adt_ty(box_adt, Substs::single(inner_ty))
                 }
                 None => Ty::Unknown,
             },
diff --git a/crates/hir_ty/src/infer/path.rs b/crates/hir_ty/src/infer/path.rs
index 5d541104e..ae3554bac 100644
--- a/crates/hir_ty/src/infer/path.rs
+++ b/crates/hir_ty/src/infer/path.rs
@@ -260,7 +260,7 @@ impl<'a> InferenceContext<'a> {
                         }));
                         Some(trait_substs)
                     }
-                    AssocContainerId::ContainerId(_) => None,
+                    AssocContainerId::ModuleId(_) => None,
                 };
 
                 self.write_assoc_resolution(id, item);
diff --git a/crates/hir_ty/src/infer/unify.rs b/crates/hir_ty/src/infer/unify.rs
index 76984242e..54fcfed10 100644
--- a/crates/hir_ty/src/infer/unify.rs
+++ b/crates/hir_ty/src/infer/unify.rs
@@ -2,14 +2,13 @@
 
 use std::borrow::Cow;
 
+use chalk_ir::{FloatTy, IntTy, TyVariableKind};
 use ena::unify::{InPlaceUnificationTable, NoError, UnifyKey, UnifyValue};
 
-use test_utils::mark;
-
 use super::{InferenceContext, Obligation};
 use crate::{
-    BoundVar, Canonical, DebruijnIndex, GenericPredicate, InEnvironment, InferTy, Substs, Ty,
-    TyKind, TypeCtor, TypeWalk,
+    BoundVar, Canonical, DebruijnIndex, GenericPredicate, InEnvironment, InferenceVar, Scalar,
+    Substs, Ty, TypeWalk,
 };
 
 impl<'a> InferenceContext<'a> {
@@ -26,7 +25,7 @@ where
     'a: 'b,
 {
     ctx: &'b mut InferenceContext<'a>,
-    free_vars: Vec<InferTy>,
+    free_vars: Vec<(InferenceVar, TyVariableKind)>,
     /// A stack of type variables that is used to detect recursive types (which
     /// are an error, but we need to protect against them to avoid stack
     /// overflows).
@@ -36,17 +35,14 @@ where
 #[derive(Debug)]
 pub(super) struct Canonicalized<T> {
     pub(super) value: Canonical<T>,
-    free_vars: Vec<InferTy>,
+    free_vars: Vec<(InferenceVar, TyVariableKind)>,
 }
 
-impl<'a, 'b> Canonicalizer<'a, 'b>
-where
-    'a: 'b,
-{
-    fn add(&mut self, free_var: InferTy) -> usize {
-        self.free_vars.iter().position(|&v| v == free_var).unwrap_or_else(|| {
+impl<'a, 'b> Canonicalizer<'a, 'b> {
+    fn add(&mut self, free_var: InferenceVar, kind: TyVariableKind) -> usize {
+        self.free_vars.iter().position(|&(v, _)| v == free_var).unwrap_or_else(|| {
             let next_index = self.free_vars.len();
-            self.free_vars.push(free_var);
+            self.free_vars.push((free_var, kind));
             next_index
         })
     }
@@ -54,11 +50,11 @@ where
     fn do_canonicalize<T: TypeWalk>(&mut self, t: T, binders: DebruijnIndex) -> T {
         t.fold_binders(
             &mut |ty, binders| match ty {
-                Ty::Infer(tv) => {
-                    let inner = tv.to_inner();
+                Ty::InferenceVar(var, kind) => {
+                    let inner = var.to_inner();
                     if self.var_stack.contains(&inner) {
                         // recursive type
-                        return tv.fallback_value();
+                        return self.ctx.table.type_variable_table.fallback_value(var, kind);
                     }
                     if let Some(known_ty) =
                         self.ctx.table.var_unification_table.inlined_probe_value(inner).known()
@@ -69,14 +65,8 @@ where
                         result
                     } else {
                         let root = self.ctx.table.var_unification_table.find(inner);
-                        let free_var = match tv {
-                            InferTy::TypeVar(_) => InferTy::TypeVar(root),
-                            InferTy::IntVar(_) => InferTy::IntVar(root),
-                            InferTy::FloatVar(_) => InferTy::FloatVar(root),
-                            InferTy::MaybeNeverTypeVar(_) => InferTy::MaybeNeverTypeVar(root),
-                        };
-                        let position = self.add(free_var);
-                        Ty::Bound(BoundVar::new(binders, position))
+                        let position = self.add(InferenceVar::from_inner(root), kind);
+                        Ty::BoundVar(BoundVar::new(binders, position))
                     }
                 }
                 _ => ty,
@@ -86,19 +76,7 @@ where
     }
 
     fn into_canonicalized<T>(self, result: T) -> Canonicalized<T> {
-        let kinds = self
-            .free_vars
-            .iter()
-            .map(|v| match v {
-                // mapping MaybeNeverTypeVar to the same kind as general ones
-                // should be fine, because as opposed to int or float type vars,
-                // they don't restrict what kind of type can go into them, they
-                // just affect fallback.
-                InferTy::TypeVar(_) | InferTy::MaybeNeverTypeVar(_) => TyKind::General,
-                InferTy::IntVar(_) => TyKind::Integer,
-                InferTy::FloatVar(_) => TyKind::Float,
-            })
-            .collect();
+        let kinds = self.free_vars.iter().map(|&(_, k)| k).collect();
         Canonicalized { value: Canonical { value: result, kinds }, free_vars: self.free_vars }
     }
 
@@ -130,9 +108,10 @@ impl<T> Canonicalized<T> {
     pub(super) fn decanonicalize_ty(&self, mut ty: Ty) -> Ty {
         ty.walk_mut_binders(
             &mut |ty, binders| {
-                if let &mut Ty::Bound(bound) = ty {
+                if let &mut Ty::BoundVar(bound) = ty {
                     if bound.debruijn >= binders {
-                        *ty = Ty::Infer(self.free_vars[bound.index]);
+                        let (v, k) = self.free_vars[bound.index];
+                        *ty = Ty::InferenceVar(v, k);
                     }
                 }
             },
@@ -152,18 +131,18 @@ impl<T> Canonicalized<T> {
                 .kinds
                 .iter()
                 .map(|k| match k {
-                    TyKind::General => ctx.table.new_type_var(),
-                    TyKind::Integer => ctx.table.new_integer_var(),
-                    TyKind::Float => ctx.table.new_float_var(),
+                    TyVariableKind::General => ctx.table.new_type_var(),
+                    TyVariableKind::Integer => ctx.table.new_integer_var(),
+                    TyVariableKind::Float => ctx.table.new_float_var(),
                 })
                 .collect(),
         );
         for (i, ty) in solution.value.into_iter().enumerate() {
-            let var = self.free_vars[i];
+            let (v, k) = self.free_vars[i];
             // eagerly replace projections in the type; we may be getting types
             // e.g. from where clauses where this hasn't happened yet
             let ty = ctx.normalize_associated_types_in(ty.clone().subst_bound_vars(&new_vars));
-            ctx.table.unify(&Ty::Infer(var), &ty);
+            ctx.table.unify(&Ty::InferenceVar(v, k), &ty);
         }
     }
 }
@@ -187,7 +166,7 @@ pub(crate) fn unify(tys: &Canonical<(Ty, Ty)>) -> Option<Substs> {
     // (kind of hacky)
     for (i, var) in vars.iter().enumerate() {
         if &*table.resolve_ty_shallow(var) == var {
-            table.unify(var, &Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, i)));
+            table.unify(var, &Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, i)));
         }
     }
     Some(
@@ -198,31 +177,73 @@ pub(crate) fn unify(tys: &Canonical<(Ty, Ty)>) -> Option<Substs> {
 }
 
 #[derive(Clone, Debug)]
+pub(super) struct TypeVariableTable {
+    inner: Vec<TypeVariableData>,
+}
+
+impl TypeVariableTable {
+    fn push(&mut self, data: TypeVariableData) {
+        self.inner.push(data);
+    }
+
+    pub(super) fn set_diverging(&mut self, iv: InferenceVar, diverging: bool) {
+        self.inner[iv.to_inner().0 as usize].diverging = diverging;
+    }
+
+    fn is_diverging(&mut self, iv: InferenceVar) -> bool {
+        self.inner[iv.to_inner().0 as usize].diverging
+    }
+
+    fn fallback_value(&self, iv: InferenceVar, kind: TyVariableKind) -> Ty {
+        match kind {
+            _ if self.inner[iv.to_inner().0 as usize].diverging => Ty::Never,
+            TyVariableKind::General => Ty::Unknown,
+            TyVariableKind::Integer => Ty::Scalar(Scalar::Int(IntTy::I32)),
+            TyVariableKind::Float => Ty::Scalar(Scalar::Float(FloatTy::F64)),
+        }
+    }
+}
+
+#[derive(Copy, Clone, Debug)]
+pub(crate) struct TypeVariableData {
+    diverging: bool,
+}
+
+#[derive(Clone, Debug)]
 pub(crate) struct InferenceTable {
     pub(super) var_unification_table: InPlaceUnificationTable<TypeVarId>,
+    pub(super) type_variable_table: TypeVariableTable,
 }
 
 impl InferenceTable {
     pub(crate) fn new() -> Self {
-        InferenceTable { var_unification_table: InPlaceUnificationTable::new() }
+        InferenceTable {
+            var_unification_table: InPlaceUnificationTable::new(),
+            type_variable_table: TypeVariableTable { inner: Vec::new() },
+        }
+    }
+
+    fn new_var(&mut self, kind: TyVariableKind, diverging: bool) -> Ty {
+        self.type_variable_table.push(TypeVariableData { diverging });
+        let key = self.var_unification_table.new_key(TypeVarValue::Unknown);
+        assert_eq!(key.0 as usize, self.type_variable_table.inner.len() - 1);
+        Ty::InferenceVar(InferenceVar::from_inner(key), kind)
     }
 
     pub(crate) fn new_type_var(&mut self) -> Ty {
-        Ty::Infer(InferTy::TypeVar(self.var_unification_table.new_key(TypeVarValue::Unknown)))
+        self.new_var(TyVariableKind::General, false)
     }
 
     pub(crate) fn new_integer_var(&mut self) -> Ty {
-        Ty::Infer(InferTy::IntVar(self.var_unification_table.new_key(TypeVarValue::Unknown)))
+        self.new_var(TyVariableKind::Integer, false)
     }
 
     pub(crate) fn new_float_var(&mut self) -> Ty {
-        Ty::Infer(InferTy::FloatVar(self.var_unification_table.new_key(TypeVarValue::Unknown)))
+        self.new_var(TyVariableKind::Float, false)
     }
 
-    pub(crate) fn new_maybe_never_type_var(&mut self) -> Ty {
-        Ty::Infer(InferTy::MaybeNeverTypeVar(
-            self.var_unification_table.new_key(TypeVarValue::Unknown),
-        ))
+    pub(crate) fn new_maybe_never_var(&mut self) -> Ty {
+        self.new_var(TyVariableKind::General, true)
     }
 
     pub(crate) fn resolve_ty_completely(&mut self, ty: Ty) -> Ty {
@@ -257,12 +278,14 @@ impl InferenceTable {
         // try to resolve type vars first
         let ty1 = self.resolve_ty_shallow(ty1);
         let ty2 = self.resolve_ty_shallow(ty2);
-        match (&*ty1, &*ty2) {
-            (Ty::Apply(a_ty1), Ty::Apply(a_ty2)) if a_ty1.ctor == a_ty2.ctor => {
-                self.unify_substs(&a_ty1.parameters, &a_ty2.parameters, depth + 1)
+        if ty1.equals_ctor(&ty2) {
+            match (ty1.substs(), ty2.substs()) {
+                (Some(st1), Some(st2)) => self.unify_substs(st1, st2, depth + 1),
+                (None, None) => true,
+                _ => false,
             }
-
-            _ => self.unify_inner_trivial(&ty1, &ty2, depth),
+        } else {
+            self.unify_inner_trivial(&ty1, &ty2, depth)
         }
     }
 
@@ -281,31 +304,46 @@ impl InferenceTable {
                 true
             }
 
-            (Ty::Infer(InferTy::TypeVar(tv1)), Ty::Infer(InferTy::TypeVar(tv2)))
-            | (Ty::Infer(InferTy::IntVar(tv1)), Ty::Infer(InferTy::IntVar(tv2)))
-            | (Ty::Infer(InferTy::FloatVar(tv1)), Ty::Infer(InferTy::FloatVar(tv2)))
+            (
+                Ty::InferenceVar(tv1, TyVariableKind::General),
+                Ty::InferenceVar(tv2, TyVariableKind::General),
+            )
             | (
-                Ty::Infer(InferTy::MaybeNeverTypeVar(tv1)),
-                Ty::Infer(InferTy::MaybeNeverTypeVar(tv2)),
-            ) => {
+                Ty::InferenceVar(tv1, TyVariableKind::Integer),
+                Ty::InferenceVar(tv2, TyVariableKind::Integer),
+            )
+            | (
+                Ty::InferenceVar(tv1, TyVariableKind::Float),
+                Ty::InferenceVar(tv2, TyVariableKind::Float),
+            ) if self.type_variable_table.is_diverging(*tv1)
+                == self.type_variable_table.is_diverging(*tv2) =>
+            {
                 // both type vars are unknown since we tried to resolve them
-                self.var_unification_table.union(*tv1, *tv2);
+                self.var_unification_table.union(tv1.to_inner(), tv2.to_inner());
                 true
             }
 
             // The order of MaybeNeverTypeVar matters here.
             // Unifying MaybeNeverTypeVar and TypeVar will let the latter become MaybeNeverTypeVar.
             // Unifying MaybeNeverTypeVar and other concrete type will let the former become it.
-            (Ty::Infer(InferTy::TypeVar(tv)), other)
-            | (other, Ty::Infer(InferTy::TypeVar(tv)))
-            | (Ty::Infer(InferTy::MaybeNeverTypeVar(tv)), other)
-            | (other, Ty::Infer(InferTy::MaybeNeverTypeVar(tv)))
-            | (Ty::Infer(InferTy::IntVar(tv)), other @ ty_app!(TypeCtor::Int(_)))
-            | (other @ ty_app!(TypeCtor::Int(_)), Ty::Infer(InferTy::IntVar(tv)))
-            | (Ty::Infer(InferTy::FloatVar(tv)), other @ ty_app!(TypeCtor::Float(_)))
-            | (other @ ty_app!(TypeCtor::Float(_)), Ty::Infer(InferTy::FloatVar(tv))) => {
+            (Ty::InferenceVar(tv, TyVariableKind::General), other)
+            | (other, Ty::InferenceVar(tv, TyVariableKind::General))
+            | (Ty::InferenceVar(tv, TyVariableKind::Integer), other @ Ty::Scalar(Scalar::Int(_)))
+            | (other @ Ty::Scalar(Scalar::Int(_)), Ty::InferenceVar(tv, TyVariableKind::Integer))
+            | (
+                Ty::InferenceVar(tv, TyVariableKind::Integer),
+                other @ Ty::Scalar(Scalar::Uint(_)),
+            )
+            | (
+                other @ Ty::Scalar(Scalar::Uint(_)),
+                Ty::InferenceVar(tv, TyVariableKind::Integer),
+            )
+            | (Ty::InferenceVar(tv, TyVariableKind::Float), other @ Ty::Scalar(Scalar::Float(_)))
+            | (other @ Ty::Scalar(Scalar::Float(_)), Ty::InferenceVar(tv, TyVariableKind::Float)) =>
+            {
                 // the type var is unknown since we tried to resolve it
-                self.var_unification_table.union_value(*tv, TypeVarValue::Known(other.clone()));
+                self.var_unification_table
+                    .union_value(tv.to_inner(), TypeVarValue::Known(other.clone()));
                 true
             }
 
@@ -347,10 +385,10 @@ impl InferenceTable {
         // more than once
         for i in 0..3 {
             if i > 0 {
-                mark::hit!(type_var_resolves_to_int_var);
+                cov_mark::hit!(type_var_resolves_to_int_var);
             }
             match &*ty {
-                Ty::Infer(tv) => {
+                Ty::InferenceVar(tv, _) => {
                     let inner = tv.to_inner();
                     match self.var_unification_table.inlined_probe_value(inner).known() {
                         Some(known_ty) => {
@@ -373,12 +411,12 @@ impl InferenceTable {
     /// known type.
     fn resolve_ty_as_possible_inner(&mut self, tv_stack: &mut Vec<TypeVarId>, ty: Ty) -> Ty {
         ty.fold(&mut |ty| match ty {
-            Ty::Infer(tv) => {
+            Ty::InferenceVar(tv, kind) => {
                 let inner = tv.to_inner();
                 if tv_stack.contains(&inner) {
-                    mark::hit!(type_var_cycles_resolve_as_possible);
+                    cov_mark::hit!(type_var_cycles_resolve_as_possible);
                     // recursive type
-                    return tv.fallback_value();
+                    return self.type_variable_table.fallback_value(tv, kind);
                 }
                 if let Some(known_ty) =
                     self.var_unification_table.inlined_probe_value(inner).known()
@@ -400,12 +438,12 @@ impl InferenceTable {
     /// replaced by Ty::Unknown.
     fn resolve_ty_completely_inner(&mut self, tv_stack: &mut Vec<TypeVarId>, ty: Ty) -> Ty {
         ty.fold(&mut |ty| match ty {
-            Ty::Infer(tv) => {
+            Ty::InferenceVar(tv, kind) => {
                 let inner = tv.to_inner();
                 if tv_stack.contains(&inner) {
-                    mark::hit!(type_var_cycles_resolve_completely);
+                    cov_mark::hit!(type_var_cycles_resolve_completely);
                     // recursive type
-                    return tv.fallback_value();
+                    return self.type_variable_table.fallback_value(tv, kind);
                 }
                 if let Some(known_ty) =
                     self.var_unification_table.inlined_probe_value(inner).known()
@@ -416,7 +454,7 @@ impl InferenceTable {
                     tv_stack.pop();
                     result
                 } else {
-                    tv.fallback_value()
+                    self.type_variable_table.fallback_value(tv, kind)
                 }
             }
             _ => ty,
@@ -426,7 +464,7 @@ impl InferenceTable {
 
 /// The ID of a type variable.
 #[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
-pub struct TypeVarId(pub(super) u32);
+pub(super) struct TypeVarId(pub(super) u32);
 
 impl UnifyKey for TypeVarId {
     type Value = TypeVarValue;
@@ -447,7 +485,7 @@ impl UnifyKey for TypeVarId {
 /// The value of a type variable: either we already know the type, or we don't
 /// know it yet.
 #[derive(Clone, PartialEq, Eq, Debug)]
-pub enum TypeVarValue {
+pub(super) enum TypeVarValue {
     Known(Ty),
     Unknown,
 }
diff --git a/crates/hir_ty/src/lib.rs b/crates/hir_ty/src/lib.rs
index 50d248674..e77f24e4e 100644
--- a/crates/hir_ty/src/lib.rs
+++ b/crates/hir_ty/src/lib.rs
@@ -25,32 +25,31 @@ mod test_db;
 
 use std::{iter, mem, ops::Deref, sync::Arc};
 
-use base_db::{salsa, CrateId};
+use base_db::salsa;
 use hir_def::{
-    builtin_type::BuiltinType,
-    expr::ExprId,
-    type_ref::{Mutability, Rawness},
-    AdtId, AssocContainerId, DefWithBodyId, FunctionId, GenericDefId, HasModule, LifetimeParamId,
-    Lookup, TraitId, TypeAliasId, TypeParamId,
+    builtin_type::BuiltinType, expr::ExprId, type_ref::Rawness, AssocContainerId, DefWithBodyId,
+    FunctionId, GenericDefId, HasModule, LifetimeParamId, 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 infer::{InferenceResult, InferenceVar};
 pub use lower::{
     associated_type_shorthand_candidates, callable_item_sig, CallableDefId, ImplTraitLoweringMode,
     TyDefId, TyLoweringContext, ValueTyDefId,
 };
 pub use traits::{InEnvironment, Obligation, ProjectionPredicate, TraitEnvironment};
 
-pub use chalk_ir::{BoundVar, DebruijnIndex};
+pub use chalk_ir::{AdtId, BoundVar, DebruijnIndex, Mutability, Scalar, TyVariableKind};
+
+pub(crate) use crate::traits::chalk::Interner;
 
 #[derive(Clone, PartialEq, Eq, Debug, Hash)]
 pub enum Lifetime {
@@ -58,211 +57,6 @@ pub enum Lifetime {
     Static,
 }
 
-/// 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.
-    /// It is also used as the type of async block, with one type parameter
-    /// representing the Future::Output type.
-    OpaqueType(OpaqueTyId),
-
-    /// Represents a foreign type declared in external blocks.
-    ForeignType(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 },
-}
-
-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::ForeignType(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()
-                    }
-                    // 1 param representing Future::Output type.
-                    OpaqueTyId::AsyncBlockTypeImplTrait(..) => 1,
-                }
-            }
-            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::ForeignType(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())
-                }
-                OpaqueTyId::AsyncBlockTypeImplTrait(def, _) => {
-                    Some(def.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::ForeignType(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,
@@ -305,29 +99,118 @@ impl TypeWalk for ProjectionTy {
     }
 }
 
-/// 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, Copy, PartialEq, Eq, Debug, Hash)]
+pub struct FnSig {
+    pub variadic: bool,
+}
+
 #[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),
+pub struct FnPointer {
+    pub num_args: usize,
+    pub sig: FnSig,
+    pub substs: Substs,
+}
 
+#[derive(Clone, PartialEq, Eq, Debug, Hash)]
+pub enum AliasTy {
     /// 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 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 {
+    /// Structures, enumerations and unions.
+    Adt(AdtId<Interner>, Substs),
+
+    /// 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, Substs),
+
+    /// a scalar type like `bool` or `u32`
+    Scalar(Scalar),
+
+    /// A tuple type.  For example, `(i32, bool)`.
+    Tuple(usize, Substs),
+
+    /// An array with the given length. Written as `[T; n]`.
+    Array(Substs),
+
+    /// The pointee of an array slice.  Written as `[T]`.
+    Slice(Substs),
+
+    /// A raw pointer. Written as `*mut T` or `*const T`
+    Raw(Mutability, Substs),
+
+    /// A reference; a pointer with an associated lifetime. Written as
+    /// `&'a mut T` or `&'a T`.
+    Ref(Mutability, Substs),
+
+    /// 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.
+    /// It is also used as the type of async block, with one type parameter
+    /// representing the Future::Output type.
+    OpaqueType(OpaqueTyId, Substs),
+
+    /// 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, Substs),
+
+    /// The pointee of a string slice. Written as `str`.
+    Str,
+
+    /// The never type `!`.
+    Never,
+
+    /// The type of a specific closure.
+    ///
+    /// The closure signature is stored in a `FnPtr` type in the first type
+    /// parameter.
+    Closure(DefWithBodyId, ExprId, Substs),
+
+    /// Represents a foreign type declared in external blocks.
+    ForeignType(TypeAliasId),
+
+    /// 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;
+    /// ```
+    Function(FnPointer),
+
+    /// An "alias" type represents some form of type alias, such as:
+    /// - An associated type projection like `<T as Iterator>::Item`
+    /// - `impl Trait` types
+    /// - Named type aliases like `type Foo<X> = Vec<X>`
+    Alias(AliasTy),
 
     /// 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
@@ -340,10 +223,10 @@ pub enum Ty {
     /// 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),
+    BoundVar(BoundVar),
 
     /// A type variable used during type checking.
-    Infer(InferTy),
+    InferenceVar(InferenceVar, TyVariableKind),
 
     /// A trait object (`dyn Trait` or bare `Trait` in pre-2018 Rust).
     ///
@@ -424,7 +307,7 @@ impl Substs {
             generic_params
                 .iter()
                 .enumerate()
-                .map(|(idx, _)| Ty::Bound(BoundVar::new(debruijn, idx)))
+                .map(|(idx, _)| Ty::BoundVar(BoundVar::new(debruijn, idx)))
                 .collect(),
         )
     }
@@ -440,10 +323,6 @@ impl Substs {
         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 }
     }
@@ -476,7 +355,7 @@ impl SubstsBuilder {
     }
 
     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))))
+        self.fill((starting_from..).map(|idx| Ty::BoundVar(BoundVar::new(debruijn, idx))))
     }
 
     pub fn fill_with_unknown(self) -> Self {
@@ -656,41 +535,41 @@ impl TypeWalk for GenericPredicate {
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub struct Canonical<T> {
     pub value: T,
-    pub kinds: Arc<[TyKind]>,
+    pub kinds: Arc<[TyVariableKind]>,
 }
 
 impl<T> Canonical<T> {
-    pub fn new(value: T, kinds: impl IntoIterator<Item = TyKind>) -> Self {
+    pub fn new(value: T, kinds: impl IntoIterator<Item = TyVariableKind>) -> 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 {
+pub struct CallableSig {
     params_and_return: Arc<[Ty]>,
     is_varargs: bool,
 }
 
 /// A polymorphic function signature.
-pub type PolyFnSig = Binders<FnSig>;
+pub type PolyFnSig = Binders<CallableSig>;
 
-impl FnSig {
-    pub fn from_params_and_return(mut params: Vec<Ty>, ret: Ty, is_varargs: bool) -> FnSig {
+impl CallableSig {
+    pub fn from_params_and_return(mut params: Vec<Ty>, ret: Ty, is_varargs: bool) -> CallableSig {
         params.push(ret);
-        FnSig { params_and_return: params.into(), is_varargs }
+        CallableSig { params_and_return: params.into(), is_varargs }
+    }
+
+    pub fn from_fn_ptr(fn_ptr: &FnPointer) -> CallableSig {
+        CallableSig {
+            params_and_return: Arc::clone(&fn_ptr.substs.0),
+            is_varargs: fn_ptr.sig.variadic,
+        }
     }
 
-    pub fn from_fn_ptr_substs(substs: &Substs, is_varargs: bool) -> FnSig {
-        FnSig { params_and_return: Arc::clone(&substs.0), is_varargs }
+    pub fn from_substs(substs: &Substs) -> CallableSig {
+        CallableSig { params_and_return: Arc::clone(&substs.0), is_varargs: false }
     }
 
     pub fn params(&self) -> &[Ty] {
@@ -702,7 +581,7 @@ impl FnSig {
     }
 }
 
-impl TypeWalk for FnSig {
+impl TypeWalk for CallableSig {
     fn walk(&self, f: &mut impl FnMut(&Ty)) {
         for t in self.params_and_return.iter() {
             t.walk(f);
@@ -721,49 +600,46 @@ impl TypeWalk for FnSig {
 }
 
 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())
+        Ty::Tuple(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 adt_ty(adt: hir_def::AdtId, substs: Substs) -> Ty {
+        Ty::Adt(AdtId(adt), substs)
     }
-    pub fn builtin(builtin: BuiltinType) -> Self {
-        Ty::simple(match builtin {
-            BuiltinType::Char => TypeCtor::Char,
-            BuiltinType::Bool => TypeCtor::Bool,
-            BuiltinType::Str => TypeCtor::Str,
-            BuiltinType::Int(t) => TypeCtor::Int(IntTy::from(t).into()),
-            BuiltinType::Float(t) => TypeCtor::Float(FloatTy::from(t).into()),
+
+    pub fn fn_ptr(sig: CallableSig) -> Self {
+        Ty::Function(FnPointer {
+            num_args: sig.params().len(),
+            sig: FnSig { variadic: sig.is_varargs },
+            substs: Substs(sig.params_and_return),
         })
     }
 
+    pub fn builtin(builtin: BuiltinType) -> Self {
+        match builtin {
+            BuiltinType::Char => Ty::Scalar(Scalar::Char),
+            BuiltinType::Bool => Ty::Scalar(Scalar::Bool),
+            BuiltinType::Str => Ty::Str,
+            BuiltinType::Int(t) => Ty::Scalar(Scalar::Int(primitive::int_ty_from_builtin(t))),
+            BuiltinType::Uint(t) => Ty::Scalar(Scalar::Uint(primitive::uint_ty_from_builtin(t))),
+            BuiltinType::Float(t) => Ty::Scalar(Scalar::Float(primitive::float_ty_from_builtin(t))),
+        }
+    }
+
     pub fn as_reference(&self) -> Option<(&Ty, Mutability)> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::Ref(mutability), parameters }) => {
-                Some((parameters.as_single(), *mutability))
-            }
+            Ty::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 }) => {
+            Ty::Ref(mutability, parameters) => {
                 Some((parameters.as_single(), Rawness::Ref, *mutability))
             }
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::RawPtr(mutability), parameters }) => {
+            Ty::Raw(mutability, parameters) => {
                 Some((parameters.as_single(), Rawness::RawPtr, *mutability))
             }
             _ => None,
@@ -773,39 +649,69 @@ impl Ty {
     pub fn strip_references(&self) -> &Ty {
         let mut t: &Ty = self;
 
-        while let Ty::Apply(ApplicationTy { ctor: TypeCtor::Ref(_mutability), parameters }) = t {
+        while let Ty::Ref(_mutability, parameters) = t {
             t = parameters.as_single();
         }
 
         t
     }
 
-    pub fn as_adt(&self) -> Option<(AdtId, &Substs)> {
+    pub fn as_adt(&self) -> Option<(hir_def::AdtId, &Substs)> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::Adt(adt_def), parameters }) => {
-                Some((*adt_def, parameters))
-            }
+            Ty::Adt(AdtId(adt), parameters) => Some((*adt, parameters)),
             _ => None,
         }
     }
 
     pub fn as_tuple(&self) -> Option<&Substs> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::Tuple { .. }, parameters }) => {
-                Some(parameters)
-            }
+            Ty::Tuple(_, substs) => Some(substs),
+            _ => None,
+        }
+    }
+
+    pub fn as_generic_def(&self) -> Option<GenericDefId> {
+        match *self {
+            Ty::Adt(AdtId(adt), ..) => Some(adt.into()),
+            Ty::FnDef(callable, ..) => Some(callable.into()),
+            Ty::AssociatedType(type_alias, ..) => Some(type_alias.into()),
+            Ty::ForeignType(type_alias, ..) => Some(type_alias.into()),
             _ => None,
         }
     }
 
     pub fn is_never(&self) -> bool {
-        matches!(self, Ty::Apply(ApplicationTy { ctor: TypeCtor::Never, .. }))
+        matches!(self, Ty::Never)
     }
 
     pub fn is_unknown(&self) -> bool {
         matches!(self, Ty::Unknown)
     }
 
+    pub fn equals_ctor(&self, other: &Ty) -> bool {
+        match (self, other) {
+            (Ty::Adt(adt, ..), Ty::Adt(adt2, ..)) => adt == adt2,
+            (Ty::Slice(_), Ty::Slice(_)) | (Ty::Array(_), Ty::Array(_)) => true,
+            (Ty::FnDef(def_id, ..), Ty::FnDef(def_id2, ..)) => def_id == def_id2,
+            (Ty::OpaqueType(ty_id, ..), Ty::OpaqueType(ty_id2, ..)) => ty_id == ty_id2,
+            (Ty::AssociatedType(ty_id, ..), Ty::AssociatedType(ty_id2, ..))
+            | (Ty::ForeignType(ty_id, ..), Ty::ForeignType(ty_id2, ..)) => ty_id == ty_id2,
+            (Ty::Closure(def, expr, _), Ty::Closure(def2, expr2, _)) => {
+                expr == expr2 && def == def2
+            }
+            (Ty::Ref(mutability, ..), Ty::Ref(mutability2, ..))
+            | (Ty::Raw(mutability, ..), Ty::Raw(mutability2, ..)) => mutability == mutability2,
+            (
+                Ty::Function(FnPointer { num_args, sig, .. }),
+                Ty::Function(FnPointer { num_args: num_args2, sig: sig2, .. }),
+            ) => num_args == num_args2 && sig == sig2,
+            (Ty::Tuple(cardinality, _), Ty::Tuple(cardinality2, _)) => cardinality == cardinality2,
+            (Ty::Str, Ty::Str) | (Ty::Never, Ty::Never) => true,
+            (Ty::Scalar(scalar), Ty::Scalar(scalar2)) => scalar == scalar2,
+            _ => false,
+        }
+    }
+
     /// If this is a `dyn Trait` type, this returns the `Trait` part.
     pub fn dyn_trait_ref(&self) -> Option<&TraitRef> {
         match self {
@@ -824,41 +730,30 @@ impl Ty {
 
     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,
-            },
+            Ty::Ref(.., parameters) => Some(Ty::clone(parameters.as_single())),
+            Ty::Raw(.., parameters) => Some(Ty::clone(parameters.as_single())),
             _ => None,
         }
     }
 
     pub fn as_fn_def(&self) -> Option<FunctionId> {
         match self {
-            &Ty::Apply(ApplicationTy {
-                ctor: TypeCtor::FnDef(CallableDefId::FunctionId(func)),
-                ..
-            }) => Some(func),
+            &Ty::FnDef(CallableDefId::FunctionId(func), ..) => Some(func),
             _ => None,
         }
     }
 
-    pub fn callable_sig(&self, db: &dyn HirDatabase) -> Option<FnSig> {
+    pub fn callable_sig(&self, db: &dyn HirDatabase) -> Option<CallableSig> {
         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,
-            },
+            Ty::Function(fn_ptr) => Some(CallableSig::from_fn_ptr(fn_ptr)),
+            Ty::FnDef(def, parameters) => {
+                let sig = db.callable_item_signature(*def);
+                Some(sig.subst(&parameters))
+            }
+            Ty::Closure(.., substs) => {
+                let sig_param = &substs[0];
+                sig_param.callable_sig(db)
+            }
             _ => None,
         }
     }
@@ -867,28 +762,66 @@ impl Ty {