19 files changed, 1000 insertions, 1251 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/diagnostics/expr.rs b/crates/hir_ty/src/diagnostics/expr.rs
index d740b7265..66a88e2b6 100644
--- a/crates/hir_ty/src/diagnostics/expr.rs
+++ b/crates/hir_ty/src/diagnostics/expr.rs
@@ -17,7 +17,7 @@ use crate::{
         MissingPatFields, RemoveThisSemicolon,
     },
     utils::variant_data,
-    ApplicationTy, InferenceResult, Ty, TypeCtor,
+    InferenceResult, Ty,
 };
 
 pub(crate) use hir_def::{
@@ -381,14 +381,11 @@ 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::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::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..86fee0050 100644
--- a/crates/hir_ty/src/diagnostics/match_check.rs
+++ b/crates/hir_ty/src/diagnostics/match_check.rs
@@ -227,7 +227,7 @@ use hir_def::{
 use la_arena::Idx;
 use smallvec::{smallvec, SmallVec};
 
-use crate::{db::HirDatabase, ApplicationTy, InferenceResult, Ty, TypeCtor};
+use crate::{db::HirDatabase, 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::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..f3a4333cb 100644
--- a/crates/hir_ty/src/display.rs
+++ b/crates/hir_ty/src/display.rs
@@ -3,8 +3,9 @@
 use std::{borrow::Cow, fmt};
 
 use crate::{
-    db::HirDatabase, utils::generics, ApplicationTy, CallableDefId, FnSig, GenericPredicate,
-    Lifetime, Obligation, OpaqueTy, OpaqueTyId, ProjectionTy, Substs, TraitRef, Ty, TypeCtor,
+    db::HirDatabase, primitive, utils::generics, AliasTy, CallableDefId, CallableSig,
+    GenericPredicate, Lifetime, Obligation, OpaqueTy, OpaqueTyId, ProjectionTy, Scalar, Substs,
+    TraitRef, Ty,
 };
 use arrayvec::ArrayVec;
 use hir_def::{
@@ -234,36 +235,62 @@ 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);
+        }
+
+        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.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();
+        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(_)) {
+                if matches!(self, Ty::Raw(..)) {
                     write!(f, "*{}", m.as_keyword_for_ptr())?;
                 } else {
                     write!(f, "&{}", m.as_keyword_for_ref())?;
@@ -274,10 +301,10 @@ 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 +331,24 @@ 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 +358,7 @@ 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 +366,7 @@ 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, ">")?;
                     }
                 }
@@ -359,10 +385,10 @@ impl HirDisplay for ApplicationTy {
                     write!(f, " -> {}", ret_display)?;
                 }
             }
-            TypeCtor::Adt(def_id) => {
+            Ty::Adt(def_id, parameters) => {
                 match f.display_target {
                     DisplayTarget::Diagnostics | DisplayTarget::Test => {
-                        let name = match def_id {
+                        let name = match *def_id {
                             AdtId::StructId(it) => f.db.struct_data(it).name.clone(),
                             AdtId::UnionId(it) => f.db.union_data(it).name.clone(),
                             AdtId::EnumId(it) => f.db.enum_data(it).name.clone(),
@@ -372,7 +398,7 @@ impl HirDisplay for ApplicationTy {
                     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 +410,18 @@ 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 +429,18 @@ 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 +449,54 @@ 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 +519,6 @@ 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 +537,12 @@ 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 +566,13 @@ 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(), ", ")?;
diff --git a/crates/hir_ty/src/infer.rs b/crates/hir_ty/src/infer.rs
index 4b683c5a7..18a4f5e8a 100644
--- a/crates/hir_ty/src/infer.rs
+++ b/crates/hir_ty/src/infer.rs
@@ -36,25 +36,15 @@ 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;
@@ -405,7 +395,7 @@ 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 +654,17 @@ 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..c33d8c61e 100644
--- a/crates/hir_ty/src/infer/coerce.rs
+++ b/crates/hir_ty/src/infer/coerce.rs
@@ -4,12 +4,13 @@
 //!
 //! See: https://doc.rust-lang.org/nomicon/coercions.html
 
+use chalk_ir::TyVariableKind;
 use hir_def::{lang_item::LangItemTarget, type_ref::Mutability};
 use test_utils::mark;
 
-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
@@ -33,7 +34,7 @@ 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) {
+            if let (Ty::FnDef(..), Ty::FnDef(..)) = (ty1, ty2) {
                 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
@@ -53,12 +54,11 @@ 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 +71,33 @@ 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::Shared, ..))
+            | (Ty::Ref(m1, ..), Ty::Ref(m2 @ Mutability::Shared, ..)) => {
+                *m1 = *m2;
+            }
+            // `&T` -> `*const T`
+            // `&mut T` -> `*mut T`/`*const T`
+            (Ty::Ref(.., substs), &Ty::Raw(m2 @ Mutability::Shared, ..))
+            | (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::Shared, ..), Ty::Raw(Mutability::Mut, ..))
+            | (Ty::Ref(Mutability::Shared, ..), 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 +110,7 @@ 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 +171,17 @@ 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..7852b3d23 100644
--- a/crates/hir_ty/src/infer/expr.rs
+++ b/crates/hir_ty/src/infer/expr.rs
@@ -3,8 +3,8 @@
 use std::iter::{repeat, repeat_with};
 use std::{mem, sync::Arc};
 
+use chalk_ir::TyVariableKind;
 use hir_def::{
-    builtin_type::Signedness,
     expr::{Array, BinaryOp, Expr, ExprId, Literal, Statement, UnaryOp},
     path::{GenericArg, GenericArgs},
     resolver::resolver_for_expr,
@@ -16,10 +16,11 @@ use test_utils::mark;
 
 use crate::{
     autoderef, 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,
+    Binders, CallableDefId, FnPointer, FnSig, Mutability, Obligation, OpaqueTyId, Rawness, Scalar,
+    Substs, TraitRef, Ty,
 };
 
 use super::{
@@ -82,10 +83,7 @@ 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 +118,7 @@ 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 +173,7 @@ 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 +191,7 @@ 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 +201,7 @@ 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 +248,12 @@ 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 +304,8 @@ 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 +316,7 @@ 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 +334,7 @@ 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 +359,7 @@ impl<'a> InferenceContext<'a> {
                         expr: tgt_expr,
                     });
                 }
-
-                Ty::simple(TypeCtor::Never)
+                Ty::Never
             }
             Expr::Return { expr } => {
                 if let Some(expr) = expr {
@@ -374,14 +368,14 @@ 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 +385,7 @@ 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 +424,23 @@ 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::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::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);
@@ -491,19 +478,24 @@ 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(box_, sb.build())
                 } else {
                     Ty::Unknown
                 }
@@ -533,13 +525,11 @@ 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 +538,10 @@ 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 +552,7 @@ 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);
@@ -592,31 +583,31 @@ 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(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(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(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(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(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(adt, Substs::single(ty)),
                         None => Ty::Unknown,
                     },
                     (RangeOp::Inclusive, _, None) => Ty::Unknown,
@@ -650,7 +641,7 @@ 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 +654,11 @@ 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 +675,38 @@ 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::Shared, 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::Shared, 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 +762,7 @@ 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 +819,7 @@ 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 +896,26 @@ 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..a318e47f3 100644
--- a/crates/hir_ty/src/infer/pat.rs
+++ b/crates/hir_ty/src/infer/pat.rs
@@ -13,7 +13,7 @@ use hir_expand::name::Name;
 use test_utils::mark;
 
 use super::{BindingMode, Expectation, InferenceContext};
-use crate::{utils::variant_data, Substs, Ty, TypeCtor};
+use crate::{utils::variant_data, Substs, Ty};
 
 impl<'a> InferenceContext<'a> {
     fn infer_tuple_struct_pat(
@@ -32,7 +32,7 @@ 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 +71,7 @@ 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 {
@@ -138,10 +138,7 @@ 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() {
@@ -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(box_adt, Substs::single(inner_ty))
                 }
                 None => Ty::Unknown,
             },
diff --git a/crates/hir_ty/src/infer/unify.rs b/crates/hir_ty/src/infer/unify.rs
index 76984242e..99a89a7f3 100644
--- a/crates/hir_ty/src/infer/unify.rs
+++ b/crates/hir_ty/src/infer/unify.rs
@@ -2,14 +2,15 @@
 
 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 +27,7 @@ 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 +37,14 @@ 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 +52,11 @@ 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 +67,8 @@ 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 +78,7 @@ 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 +110,10 @@ 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 +133,18 @@ 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 +168,7 @@ 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 +179,73 @@ 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 +280,14 @@ 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 +306,46 @@ 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
             }
 
@@ -350,7 +390,7 @@ impl InferenceTable {
                 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 +413,12 @@ 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);
                     // 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 +440,12 @@ 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);
                     // 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 +456,7 @@ impl InferenceTable {
                     tv_stack.pop();
                     result
                 } else {
-                    tv.fallback_value()
+                    self.type_variable_table.fallback_value(tv, kind)
                 }
             }
             _ => ty,
@@ -426,7 +466,7 @@ 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 +487,7 @@ 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..9bcaf6fa7 100644
--- a/crates/hir_ty/src/lib.rs
+++ b/crates/hir_ty/src/lib.rs
@@ -25,7 +25,7 @@ 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,
@@ -38,19 +38,18 @@ 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::{BoundVar, DebruijnIndex, Scalar, TyVariableKind};
 
 #[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, 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_substs(substs: &Substs, is_varargs: bool) -> FnSig {
-        FnSig { params_and_return: Arc::clone(&substs.0), 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_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 +600,42 @@ 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 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 {
-        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()),
-        })
+        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,
@@ -773,7 +645,7 @@ 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();
         }
 
@@ -782,30 +654,60 @@ impl Ty {
 
     pub fn as_adt(&self) -> Option<(AdtId, &Substs)> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::Adt(adt_def), parameters }) => {
-                Some((*adt_def, parameters))
-            }
+            Ty::Adt(adt_def, parameters) => Some((*adt_def, parameters)),
             _ => None,
         }
     }
 
     pub fn as_tuple(&self) -> Option<&Substs> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::Tuple { .. }, parameters }) => {
-                Some(parameters)
-            }
+            Ty::Tuple(_, substs) => Some(substs),
+            _ => None,
+        }
+    }
+
+    pub fn as_generic_def(&self) -> Option<GenericDefId> {
+        match *self {
+            Ty::Adt(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 +726,30 @@ 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 +758,66 @@ impl Ty {
     /// the `Substs` for these type parameters with the given ones. (So e.g. if
     /// `self` is `Option<_>` and the substs contain `u32`, we'll have
     /// `Option<u32>` afterwards.)
-    pub fn apply_substs(self, substs: Substs) -> Ty {
-        match self {
-            Ty::Apply(ApplicationTy { ctor, parameters: previous_substs }) => {
-                assert_eq!(previous_substs.len(), substs.len());
-                Ty::Apply(ApplicationTy { ctor, parameters: substs })
+    pub fn apply_substs(mut self, new_substs: Substs) -> Ty {
+        match &mut self {
+            Ty::Adt(_, substs)
+            | Ty::Slice(substs)
+            | Ty::Array(substs)
+            | Ty::Raw(_, substs)
+            | Ty::Ref(_, substs)
+            | Ty::FnDef(_, substs)
+            | Ty::Function(FnPointer { substs, .. })
+            | Ty::Tuple(_, substs)
+            | Ty::OpaqueType(_, substs)
+            | Ty::AssociatedType(_, substs)
+            | Ty::Closure(.., substs) => {
+                assert_eq!(substs.len(), new_substs.len());
+                *substs = new_substs;
             }
-            _ => self,
+            _ => (),
         }
+        self
     }
 
     /// Returns the type parameters of this type if it has some (i.e. is an ADT
     /// or function); so if `self` is `Option<u32>`, this returns the `u32`.
-    pub fn substs(&self) -> Option<Substs> {
+    pub fn substs(&self) -> Option<&Substs> {
         match self {
-            Ty::Apply(ApplicationTy { parameters, .. }) => Some(parameters.clone()),
+            Ty::Adt(_, substs)
+            | Ty::Slice(substs)
+            | Ty::Array(substs)
+            | Ty::Raw(_, substs)
+            | Ty::Ref(_, substs)
+            | Ty::FnDef(_, substs)
+            | Ty::Function(FnPointer { substs, .. })
+            | Ty::Tuple(_, substs)
+            | Ty::OpaqueType(_, substs)
+            | Ty::AssociatedType(_, substs)
+            | Ty::Closure(.., substs) => Some(substs),
+            _ => None,
+        }
+    }
+
+    pub fn substs_mut(&mut self) -> Option<&mut Substs> {
+        match self {
+            Ty::Adt(_, substs)
+            | Ty::Slice(substs)
+            | Ty::Array(substs)
+            | Ty::Raw(_, substs)
+            | Ty::Ref(_, substs)
+            | Ty::FnDef(_, substs)
+            | Ty::Function(FnPointer { substs, .. })
+            | Ty::Tuple(_, substs)
+            | Ty::OpaqueType(_, substs)
+            | Ty::AssociatedType(_, substs)
+            | Ty::Closure(.., substs) => Some(substs),
             _ => None,
         }
     }
 
     pub fn impl_trait_bounds(&self, db: &dyn HirDatabase) -> Option<Vec<GenericPredicate>> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::OpaqueType(opaque_ty_id), .. }) => {
+            Ty::OpaqueType(opaque_ty_id, ..) => {
                 match opaque_ty_id {
                     OpaqueTyId::AsyncBlockTypeImplTrait(def, _expr) => {
                         let krate = def.module(db.upcast()).krate();
@@ -911,7 +840,7 @@ impl Ty {
                     OpaqueTyId::ReturnTypeImplTrait(..) => None,
                 }
             }
-            Ty::Opaque(opaque_ty) => {
+            Ty::Alias(AliasTy::Opaque(opaque_ty)) => {
                 let predicates = match opaque_ty.opaque_ty_id {
                     OpaqueTyId::ReturnTypeImplTrait(func, idx) => {
                         db.return_type_impl_traits(func).map(|it| {
@@ -949,13 +878,13 @@ impl Ty {
 
     pub fn associated_type_parent_trait(&self, db: &dyn HirDatabase) -> Option<TraitId> {
         match self {
-            Ty::Apply(ApplicationTy { ctor: TypeCtor::AssociatedType(type_alias_id), .. }) => {
+            Ty::AssociatedType(type_alias_id, ..) => {
                 match type_alias_id.lookup(db.upcast()).container {
                     AssocContainerId::TraitId(trait_id) => Some(trait_id),
                     _ => None,
                 }
             }
-            Ty::Projection(projection_ty) => {
+            Ty::Alias(AliasTy::Projection(projection_ty)) => {
                 match projection_ty.associated_ty.lookup(db.upcast()).container {
                     AssocContainerId::TraitId(trait_id) => Some(trait_id),
                     _ => None,
@@ -1033,7 +962,7 @@ pub trait TypeWalk {
     {
         self.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 = substs.0[bound.index].clone().shift_bound_vars(binders);
                     }
@@ -1051,8 +980,8 @@ pub trait TypeWalk {
     {
         self.fold_binders(
             &mut |ty, binders| match ty {
-                Ty::Bound(bound) if bound.debruijn >= binders => {
-                    Ty::Bound(bound.shifted_in_from(n))
+                Ty::BoundVar(bound) if bound.debruijn >= binders => {
+                    Ty::BoundVar(bound.shifted_in_from(n))
                 }
                 ty => ty,
             },
@@ -1064,13 +993,13 @@ pub trait TypeWalk {
 impl TypeWalk for Ty {
     fn walk(&self, f: &mut impl FnMut(&Ty)) {
         match self {
-            Ty::Apply(a_ty) => {
-                for t in a_ty.parameters.iter() {
+            Ty::Alias(AliasTy::Projection(p_ty)) => {
+                for t in p_ty.parameters.iter() {
                     t.walk(f);
                 }
             }
-            Ty::Projection(p_ty) => {
-                for t in p_ty.parameters.iter() {
+            Ty::Alias(AliasTy::Opaque(o_ty)) => {
+                for t in o_ty.parameters.iter() {
                     t.walk(f);
                 }
             }
@@ -1079,12 +1008,13 @@ impl TypeWalk for Ty {
                     p.walk(f);
                 }
             }
-            Ty::Opaque(o_ty) => {
-                for t in o_ty.parameters.iter() {
-                    t.walk(f);
+            _ => {
+                if let Some(substs) = self.substs() {
+                    for t in substs.iter() {
+                        t.walk(f);
+                    }
                 }
             }
-            Ty::Placeholder { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
         }
         f(self);
     }
@@ -1095,10 +1025,7 @@ impl TypeWalk for Ty {
         binders: DebruijnIndex,
     ) {
         match self {
-            Ty::Apply(a_ty) => {
-                a_ty.parameters.walk_mut_binders(f, binders);
-            }
-            Ty::Projection(p_ty) => {
+            Ty::Alias(AliasTy::Projection(p_ty)) => {
                 p_ty.parameters.walk_mut_binders(f, binders);
             }
             Ty::Dyn(predicates) => {
@@ -1106,10 +1033,14 @@ impl TypeWalk for Ty {
                     p.walk_mut_binders(f, binders.shifted_in());
                 }
             }
-            Ty::Opaque(o_ty) => {
+            Ty::Alias(AliasTy::Opaque(o_ty)) => {
                 o_ty.parameters.walk_mut_binders(f, binders);
             }
-            Ty::Placeholder { .. } | Ty::Bound(_) | Ty::Infer(_) | Ty::Unknown => {}
+            _ => {
+                if let Some(substs) = self.substs_mut() {
+                    substs.walk_mut_binders(f, binders);
+                }
+            }
         }
         f(self, binders);
     }
diff --git a/crates/hir_ty/src/lower.rs b/crates/hir_ty/src/lower.rs
index 99b0ecf3b..ca06c9fe2 100644
--- a/crates/hir_ty/src/lower.rs
+++ b/crates/hir_ty/src/lower.rs
@@ -31,9 +31,9 @@ use crate::{
         all_super_trait_refs, associated_type_by_name_including_super_traits, generics,
         make_mut_slice, variant_data,
     },
-    Binders, BoundVar, DebruijnIndex, FnSig, GenericPredicate, OpaqueTy, OpaqueTyId, PolyFnSig,
-    ProjectionPredicate, ProjectionTy, ReturnTypeImplTrait, ReturnTypeImplTraits, Substs,
-    TraitEnvironment, TraitRef, Ty, TypeCtor, TypeWalk,
+    AliasTy, Binders, BoundVar, CallableSig, DebruijnIndex, FnPointer, FnSig, GenericPredicate,
+    OpaqueTy, OpaqueTyId, PolyFnSig, ProjectionPredicate, ProjectionTy, ReturnTypeImplTrait,
+    ReturnTypeImplTraits, Substs, TraitEnvironment, TraitRef, Ty, TypeWalk,
 };
 
 #[derive(Debug)]
@@ -145,13 +145,10 @@ impl Ty {
     pub fn from_hir_ext(ctx: &TyLoweringContext<'_>, type_ref: &TypeRef) -> (Self, Option<TypeNs>) {
         let mut res = None;
         let ty = match type_ref {
-            TypeRef::Never => Ty::simple(TypeCtor::Never),
+            TypeRef::Never => Ty::Never,
             TypeRef::Tuple(inner) => {
                 let inner_tys: Arc<[Ty]> = inner.iter().map(|tr| Ty::from_hir(ctx, tr)).collect();
-                Ty::apply(
-                    TypeCtor::Tuple { cardinality: inner_tys.len() as u16 },
-                    Substs(inner_tys),
-                )
+                Ty::Tuple(inner_tys.len(), Substs(inner_tys))
             }
             TypeRef::Path(path) => {
                 let (ty, res_) = Ty::from_hir_path(ctx, path);
@@ -160,30 +157,31 @@ impl Ty {
             }
             TypeRef::RawPtr(inner, mutability) => {
                 let inner_ty = Ty::from_hir(ctx, inner);
-                Ty::apply_one(TypeCtor::RawPtr(*mutability), inner_ty)
+                Ty::Raw(*mutability, Substs::single(inner_ty))
             }
             TypeRef::Array(inner) => {
                 let inner_ty = Ty::from_hir(ctx, inner);
-                Ty::apply_one(TypeCtor::Array, inner_ty)
+                Ty::Array(Substs::single(inner_ty))
             }
             TypeRef::Slice(inner) => {
                 let inner_ty = Ty::from_hir(ctx, inner);
-                Ty::apply_one(TypeCtor::Slice, inner_ty)
+                Ty::Slice(Substs::single(inner_ty))
             }
             TypeRef::Reference(inner, _, mutability) => {
                 let inner_ty = Ty::from_hir(ctx, inner);
-                Ty::apply_one(TypeCtor::Ref(*mutability), inner_ty)
+                Ty::Ref(*mutability, Substs::single(inner_ty))
             }
             TypeRef::Placeholder => Ty::Unknown,
             TypeRef::Fn(params, is_varargs) => {
-                let sig = Substs(params.iter().map(|tr| Ty::from_hir(ctx, tr)).collect());
-                Ty::apply(
-                    TypeCtor::FnPtr { num_args: sig.len() as u16 - 1, is_varargs: *is_varargs },
-                    sig,
-                )
+                let substs = Substs(params.iter().map(|tr| Ty::from_hir(ctx, tr)).collect());
+                Ty::Function(FnPointer {
+                    num_args: substs.len() - 1,
+                    sig: FnSig { variadic: *is_varargs },
+                    substs,
+                })
             }
             TypeRef::DynTrait(bounds) => {
-                let self_ty = Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, 0));
+                let self_ty = Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, 0));
                 let predicates = ctx.with_shifted_in(DebruijnIndex::ONE, |ctx| {
                     bounds
                         .iter()
@@ -227,7 +225,10 @@ impl Ty {
                         let impl_trait_id = OpaqueTyId::ReturnTypeImplTrait(func, idx);
                         let generics = generics(ctx.db.upcast(), func.into());
                         let parameters = Substs::bound_vars(&generics, ctx.in_binders);
-                        Ty::Opaque(OpaqueTy { opaque_ty_id: impl_trait_id, parameters })
+                        Ty::Alias(AliasTy::Opaque(OpaqueTy {
+                            opaque_ty_id: impl_trait_id,
+                            parameters,
+                        }))
                     }
                     ImplTraitLoweringMode::Param => {
                         let idx = ctx.impl_trait_counter.get();
@@ -258,7 +259,7 @@ impl Ty {
                             } else {
                                 (0, 0, 0, 0)
                             };
-                        Ty::Bound(BoundVar::new(
+                        Ty::BoundVar(BoundVar::new(
                             ctx.in_binders,
                             idx as usize + parent_params + self_params + list_params,
                         ))
@@ -330,7 +331,7 @@ impl Ty {
             TypeNs::TraitId(trait_) => {
                 // if this is a bare dyn Trait, we'll directly put the required ^0 for the self type in there
                 let self_ty = if remaining_segments.len() == 0 {
-                    Some(Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, 0)))
+                    Some(Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, 0)))
                 } else {
                     None
                 };
@@ -346,10 +347,10 @@ impl Ty {
                     match found {
                         Some((super_trait_ref, associated_ty)) => {
                             // FIXME handle type parameters on the segment
-                            Ty::Projection(ProjectionTy {
+                            Ty::Alias(AliasTy::Projection(ProjectionTy {
                                 associated_ty,
                                 parameters: super_trait_ref.substs,
-                            })
+                            }))
                         }
                         None => {
                             // FIXME: report error (associated type not found)
@@ -373,7 +374,7 @@ impl Ty {
                     TypeParamLoweringMode::Placeholder => Ty::Placeholder(param_id),
                     TypeParamLoweringMode::Variable => {
                         let idx = generics.param_idx(param_id).expect("matching generics");
-                        Ty::Bound(BoundVar::new(ctx.in_binders, idx))
+                        Ty::BoundVar(BoundVar::new(ctx.in_binders, idx))
                     }
                 }
             }
@@ -414,7 +415,6 @@ impl Ty {
             // FIXME: report error
             TypeNs::EnumVariantId(_) => return (Ty::Unknown, None),
         };
-
         Ty::from_type_relative_path(ctx, ty, Some(resolution), remaining_segments)
     }
 
@@ -472,10 +472,10 @@ impl Ty {
                         // associated_type_shorthand_candidates does not do that
                         let substs = substs.shift_bound_vars(ctx.in_binders);
                         // FIXME handle type parameters on the segment
-                        return Some(Ty::Projection(ProjectionTy {
+                        return Some(Ty::Alias(AliasTy::Projection(ProjectionTy {
                             associated_ty,
                             parameters: substs,
-                        }));
+                        })));
                     }
 
                     None
@@ -676,7 +676,7 @@ impl GenericPredicate {
                             TypeParamLoweringMode::Placeholder => Ty::Placeholder(param_id),
                             TypeParamLoweringMode::Variable => {
                                 let idx = generics.param_idx(param_id).expect("matching generics");
-                                Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, idx))
+                                Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, idx))
                             }
                         }
                     }
@@ -750,7 +750,7 @@ fn assoc_type_bindings_from_type_bound<'a>(
                 preds.extend(GenericPredicate::from_type_bound(
                     ctx,
                     bound,
-                    Ty::Projection(projection_ty.clone()),
+                    Ty::Alias(AliasTy::Projection(projection_ty.clone())),
                 ));
             }
             preds
@@ -760,7 +760,7 @@ fn assoc_type_bindings_from_type_bound<'a>(
 impl ReturnTypeImplTrait {
     fn from_hir(ctx: &TyLoweringContext, bounds: &[TypeBound]) -> Self {
         mark::hit!(lower_rpit);
-        let self_ty = Ty::Bound(BoundVar::new(DebruijnIndex::INNERMOST, 0));
+        let self_ty = Ty::BoundVar(BoundVar::new(DebruijnIndex::INNERMOST, 0));
         let predicates = ctx.with_shifted_in(DebruijnIndex::ONE, |ctx| {
             bounds
                 .iter()
@@ -984,7 +984,7 @@ pub(crate) fn generic_defaults_query(
             // Each default can only refer to previous parameters.
             ty.walk_mut_binders(
                 &mut |ty, binders| match ty {
-                    Ty::Bound(BoundVar { debruijn, index }) if *debruijn == binders => {
+                    Ty::BoundVar(BoundVar { debruijn, index }) if *debruijn == binders => {
                         if *index >= idx {
                             // type variable default referring to parameter coming
                             // after it. This is forbidden (FIXME: report
@@ -1017,7 +1017,7 @@ fn fn_sig_for_fn(db: &dyn HirDatabase, def: FunctionId) -> PolyFnSig {
     let ret = Ty::from_hir(&ctx_ret, &data.ret_type);
     let generics = generics(db.upcast(), def.into());
     let num_binders = generics.len();
-    Binders::new(num_binders, FnSig::from_params_and_return(params, ret, data.is_varargs))
+    Binders::new(num_binders, CallableSig::from_params_and_return(params, ret, data.is_varargs))
 }
 
 /// Build the declared type of a function. This should not need to look at the
@@ -1025,7 +1025,7 @@ fn fn_sig_for_fn(db: &dyn HirDatabase, def: FunctionId) -> PolyFnSig {
 fn type_for_fn(db: &dyn HirDatabase, def: FunctionId) -> Binders<Ty> {
     let generics = generics(db.upcast(), def.into());
     let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
-    Binders::new(substs.len(), Ty::apply(TypeCtor::FnDef(def.into()), substs))
+    Binders::new(substs.len(), Ty::FnDef(def.into(), substs))
 }
 
 /// Build the declared type of a const.
@@ -1057,7 +1057,7 @@ fn fn_sig_for_struct_constructor(db: &dyn HirDatabase, def: StructId) -> PolyFnS
     let params =
         fields.iter().map(|(_, field)| Ty::from_hir(&ctx, &field.type_ref)).collect::<Vec<_>>();
     let ret = type_for_adt(db, def.into());
-    Binders::new(ret.num_binders, FnSig::from_params_and_return(params, ret.value, false))
+    Binders::new(ret.num_binders, CallableSig::from_params_and_return(params, ret.value, false))
 }
 
 /// Build the type of a tuple struct constructor.
@@ -1068,7 +1068,7 @@ fn type_for_struct_constructor(db: &dyn HirDatabase, def: StructId) -> Binders<T
     }
     let generics = generics(db.upcast(), def.into());
     let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
-    Binders::new(substs.len(), Ty::apply(TypeCtor::FnDef(def.into()), substs))
+    Binders::new(substs.len(), Ty::FnDef(def.into(), substs))
 }
 
 fn fn_sig_for_enum_variant_constructor(db: &dyn HirDatabase, def: EnumVariantId) -> PolyFnSig {
@@ -1081,7 +1081,7 @@ fn fn_sig_for_enum_variant_constructor(db: &dyn HirDatabase, def: EnumVariantId)
     let params =
         fields.iter().map(|(_, field)| Ty::from_hir(&ctx, &field.type_ref)).collect::<Vec<_>>();
     let ret = type_for_adt(db, def.parent.into());
-    Binders::new(ret.num_binders, FnSig::from_params_and_return(params, ret.value, false))
+    Binders::new(ret.num_binders, CallableSig::from_params_and_return(params, ret.value, false))
 }
 
 /// Build the type of a tuple enum variant constructor.
@@ -1093,13 +1093,13 @@ fn type_for_enum_variant_constructor(db: &dyn HirDatabase, def: EnumVariantId) -
     }
     let generics = generics(db.upcast(), def.parent.into());
     let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
-    Binders::new(substs.len(), Ty::apply(TypeCtor::FnDef(def.into()), substs))
+    Binders::new(substs.len(), Ty::FnDef(def.into(), substs))
 }
 
 fn type_for_adt(db: &dyn HirDatabase, adt: AdtId) -> Binders<Ty> {
     let generics = generics(db.upcast(), adt.into());
     let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
-    Binders::new(substs.len(), Ty::apply(TypeCtor::Adt(adt), substs))
+    Binders::new(substs.len(), Ty::Adt(adt, substs))
 }
 
 fn type_for_type_alias(db: &dyn HirDatabase, t: TypeAliasId) -> Binders<Ty> {
@@ -1107,10 +1107,10 @@ fn type_for_type_alias(db: &dyn HirDatabase, t: TypeAliasId) -> Binders<Ty> {
     let resolver = t.resolver(db.upcast());
     let ctx =
         TyLoweringContext::new(db, &resolver).with_type_param_mode(TypeParamLoweringMode::Variable);
-    let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
     if db.type_alias_data(t).is_extern {
-        Binders::new(substs.len(), Ty::apply(TypeCtor::ForeignType(t), substs))
+        Binders::new(0, Ty::ForeignType(t))
     } else {
+        let substs = Substs::bound_vars(&generics, DebruijnIndex::INNERMOST);
         let type_ref = &db.type_alias_data(t).type_ref;
         let inner = Ty::from_hir(&ctx, type_ref.as_ref().unwrap_or(&TypeRef::Error));
         Binders::new(substs.len(), inner)
diff --git a/crates/hir_ty/src/method_resolution.rs b/crates/hir_ty/src/method_resolution.rs
index b3d1fe9a4..dd5109d4e 100644
--- a/crates/hir_ty/src/method_resolution.rs
+++ b/crates/hir_ty/src/method_resolution.rs
@@ -7,11 +7,8 @@ use std::{iter, sync::Arc};
 use arrayvec::ArrayVec;
 use base_db::CrateId;
 use hir_def::{
-    builtin_type::{IntBitness, Signedness},
-    lang_item::LangItemTarget,
-    type_ref::Mutability,
-    AssocContainerId, AssocItemId, FunctionId, GenericDefId, HasModule, ImplId, Lookup, ModuleId,
-    TraitId,
+    lang_item::LangItemTarget, type_ref::Mutability, AdtId, AssocContainerId, AssocItemId,
+    FunctionId, GenericDefId, HasModule, ImplId, Lookup, ModuleId, TraitId, TypeAliasId,
 };
 use hir_expand::name::Name;
 use rustc_hash::{FxHashMap, FxHashSet};
@@ -19,17 +16,26 @@ use rustc_hash::{FxHashMap, FxHashSet};
 use crate::{
     autoderef,
     db::HirDatabase,
-    primitive::{FloatBitness, FloatTy, IntTy},
+    primitive::{self, FloatTy, IntTy, UintTy},
     utils::all_super_traits,
-    ApplicationTy, Canonical, DebruijnIndex, InEnvironment, Substs, TraitEnvironment, TraitRef, Ty,
-    TyKind, TypeCtor, TypeWalk,
+    Canonical, DebruijnIndex, FnPointer, FnSig, InEnvironment, Scalar, Substs, TraitEnvironment,
+    TraitRef, Ty, TypeWalk,
 };
 
 /// This is used as a key for indexing impls.
 #[derive(Debug, Copy, Clone, PartialEq, Eq, Hash)]
 pub enum TyFingerprint {
-    Apply(TypeCtor),
+    Str,
+    Slice,
+    Array,
+    Never,
+    RawPtr(Mutability),
+    Scalar(Scalar),
+    Adt(AdtId),
     Dyn(TraitId),
+    Tuple(usize),
+    ForeignType(TypeAliasId),
+    FnPtr(usize, FnSig),
 }
 
 impl TyFingerprint {
@@ -37,68 +43,42 @@ impl TyFingerprint {
     /// have impls: if we have some `struct S`, we can have an `impl S`, but not
     /// `impl &S`. Hence, this will return `None` for reference types and such.
     pub(crate) fn for_impl(ty: &Ty) -> Option<TyFingerprint> {
-        match ty {
-            Ty::Apply(a_ty) => Some(TyFingerprint::Apply(a_ty.ctor)),
-            Ty::Dyn(_) => ty.dyn_trait().map(|trait_| TyFingerprint::Dyn(trait_)),
-            _ => None,
-        }
+        let fp = match ty {
+            &Ty::Str => TyFingerprint::Str,
+            &Ty::Never => TyFingerprint::Never,
+            &Ty::Slice(..) => TyFingerprint::Slice,
+            &Ty::Array(..) => TyFingerprint::Array,
+            &Ty::Scalar(scalar) => TyFingerprint::Scalar(scalar),
+            &Ty::Adt(adt, _) => TyFingerprint::Adt(adt),
+            &Ty::Tuple(cardinality, _) => TyFingerprint::Tuple(cardinality),
+            &Ty::Raw(mutability, ..) => TyFingerprint::RawPtr(mutability),
+            &Ty::ForeignType(alias_id, ..) => TyFingerprint::ForeignType(alias_id),
+            &Ty::Function(FnPointer { num_args, sig, .. }) => TyFingerprint::FnPtr(num_args, sig),
+            Ty::Dyn(_) => ty.dyn_trait().map(|trait_| TyFingerprint::Dyn(trait_))?,
+            _ => return None,
+        };
+        Some(fp)
     }
 }
 
 pub(crate) const ALL_INT_FPS: [TyFingerprint; 12] = [
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::X8,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::X16,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::X32,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::X64,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::X128,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Unsigned,
-        bitness: IntBitness::Xsize,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::X8,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::X16,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::X32,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::X64,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::X128,
-    })),
-    TyFingerprint::Apply(TypeCtor::Int(IntTy {
-        signedness: Signedness::Signed,
-        bitness: IntBitness::Xsize,
-    })),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::I8)),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::I16)),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::I32)),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::I64)),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::I128)),
+    TyFingerprint::Scalar(Scalar::Int(IntTy::Isize)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::U8)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::U16)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::U32)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::U64)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::U128)),
+    TyFingerprint::Scalar(Scalar::Uint(UintTy::Usize)),
 ];
 
 pub(crate) const ALL_FLOAT_FPS: [TyFingerprint; 2] = [
-    TyFingerprint::Apply(TypeCtor::Float(FloatTy { bitness: FloatBitness::X32 })),
-    TyFingerprint::Apply(TypeCtor::Float(FloatTy { bitness: FloatBitness::X64 })),
+    TyFingerprint::Scalar(Scalar::Float(FloatTy::F32)),
+    TyFingerprint::Scalar(Scalar::Float(FloatTy::F64)),
 ];
 
 /// Trait impls defined or available in some crate.
@@ -250,27 +230,29 @@ impl Ty {
         let mod_to_crate_ids = |module: ModuleId| Some(std::iter::once(module.krate()).collect());
 
         let lang_item_targets = match self {
-            Ty::Apply(a_ty) => match a_ty.ctor {
-                TypeCtor::Adt(def_id) => {
-                    return mod_to_crate_ids(def_id.module(db.upcast()));
-                }
-                TypeCtor::ForeignType(type_alias_id) => {
-                    return mod_to_crate_ids(type_alias_id.lookup(db.upcast()).module(db.upcast()));
-                }
-                TypeCtor::Bool => lang_item_crate!("bool"),
-                TypeCtor::Char => lang_item_crate!("char"),
-                TypeCtor::Float(f) => match f.bitness {
-                    // There are two lang items: one in libcore (fXX) and one in libstd (fXX_runtime)
-                    FloatBitness::X32 => lang_item_crate!("f32", "f32_runtime"),
-                    FloatBitness::X64 => lang_item_crate!("f64", "f64_runtime"),
-                },
-                TypeCtor::Int(i) => lang_item_crate!(i.ty_to_string()),
-                TypeCtor::Str => lang_item_crate!("str_alloc", "str"),
-                TypeCtor::Slice => lang_item_crate!("slice_alloc", "slice"),
-                TypeCtor::RawPtr(Mutability::Shared) => lang_item_crate!("const_ptr"),
-                TypeCtor::RawPtr(Mutability::Mut) => lang_item_crate!("mut_ptr"),
-                _ => return None,
+            Ty::Adt(def_id, _) => {
+                return mod_to_crate_ids(def_id.module(db.upcast()));
+            }
+            Ty::ForeignType(type_alias_id) => {
+                return mod_to_crate_ids(type_alias_id.lookup(db.upcast()).module(db.upcast()));
+            }
+            Ty::Scalar(Scalar::Bool) => lang_item_crate!("bool"),
+            Ty::Scalar(Scalar::Char) => lang_item_crate!("char"),
+            Ty::Scalar(Scalar::Float(f)) => match f {
+                // There are two lang items: one in libcore (fXX) and one in libstd (fXX_runtime)
+                FloatTy::F32 => lang_item_crate!("f32", "f32_runtime"),
+                FloatTy::F64 => lang_item_crate!("f64", "f64_runtime"),
             },
+            &Ty::Scalar(Scalar::Int(t)) => {
+                lang_item_crate!(primitive::int_ty_to_string(t))
+            }
+            &Ty::Scalar(Scalar::Uint(t)) => {
+                lang_item_crate!(primitive::uint_ty_to_string(t))
+            }
+            Ty::Str => lang_item_crate!("str_alloc", "str"),
+            Ty::Slice(_) => lang_item_crate!("slice_alloc", "slice"),
+            Ty::Raw(Mutability::Shared, _) => lang_item_crate!("const_ptr"),
+            Ty::Raw(Mutability::Mut, _) => lang_item_crate!("mut_ptr"),
             Ty::Dyn(_) => {
                 return self.dyn_trait().and_then(|trait_| {
                     mod_to_crate_ids(GenericDefId::TraitId(trait_).module(db.upcast()))
@@ -447,7 +429,7 @@ fn iterate_method_candidates_with_autoref(
     }
     let refed = Canonical {
         kinds: deref_chain[0].kinds.clone(),
-        value: Ty::apply_one(TypeCtor::Ref(Mutability::Shared), deref_chain[0].value.clone()),
+        value: Ty::Ref(Mutability::Shared, Substs::single(deref_chain[0].value.clone())),
     };
     if iterate_method_candidates_by_receiver(
         &refed,
@@ -463,7 +445,7 @@ fn iterate_method_candidates_with_autoref(
     }
     let ref_muted = Canonical {
         kinds: deref_chain[0].kinds.clone(),
-        value: Ty::apply_one(TypeCtor::Ref(Mutability::Mut), deref_chain[0].value.clone()),
+        value: Ty::Ref(Mutability::Mut, Substs::single(deref_chain[0].value.clone())),
     };
     if iterate_method_candidates_by_receiver(
         &ref_muted,
@@ -685,7 +667,7 @@ pub(crate) fn inherent_impl_substs(
         .build();
     let self_ty_with_vars = db.impl_self_ty(impl_id).subst(&vars);
     let mut kinds = self_ty.kinds.to_vec();
-    kinds.extend(iter::repeat(TyKind::General).take(vars.len()));
+    kinds.extend(iter::repeat(chalk_ir::TyVariableKind::General).take(vars.len()));
     let tys = Canonical { kinds: kinds.into(), value: (self_ty_with_vars, self_ty.value.clone()) };
     let substs = super::infer::unify(&tys);
     // We only want the substs for the vars we added, not the ones from self_ty.
@@ -701,7 +683,7 @@ pub(crate) fn inherent_impl_substs(
 fn fallback_bound_vars(s: Substs, num_vars_to_keep: usize) -> Substs {
     s.fold_binders(
         &mut |ty, binders| {
-            if let Ty::Bound(bound) = &ty {
+            if let Ty::BoundVar(bound) = &ty {
                 if bound.index >= num_vars_to_keep && bound.debruijn >= binders {
                     Ty::Unknown
                 } else {
@@ -777,7 +759,7 @@ fn generic_implements_goal(
         .push(self_ty.value)
         .fill_with_bound_vars(DebruijnIndex::INNERMOST, kinds.len())
         .build();
-    kinds.extend(iter::repeat(TyKind::General).take(substs.len() - 1));
+    kinds.extend(iter::repeat(chalk_ir::TyVariableKind::General).take(substs.len() - 1));
     let trait_ref = TraitRef { trait_, substs };
     let obligation = super::Obligation::Trait(trait_ref);
     Canonical { kinds: kinds.into(), value: InEnvironment::new(env, obligation) }
@@ -790,11 +772,9 @@ fn autoderef_method_receiver(
 ) -> Vec<Canonical<Ty>> {
     let mut deref_chain: Vec<_> = autoderef::autoderef(db, Some(krate), ty).collect();
     // As a last step, we can do array unsizing (that's the only unsizing that rustc does for method receivers!)
-    if let Some(Ty::Apply(ApplicationTy { ctor: TypeCtor::Array, parameters })) =
-        deref_chain.last().map(|ty| &ty.value)
-    {
+    if let Some(Ty::Array(parameters)) = deref_chain.last().map(|ty| &ty.value) {
         let kinds = deref_chain.last().unwrap().kinds.clone();
-        let unsized_ty = Ty::apply(TypeCtor::Slice, parameters.clone());
+        let unsized_ty = Ty::Slice(parameters.clone());
         deref_chain.push(Canonical { value: unsized_ty, kinds })
     }
     deref_chain
diff --git a/crates/hir_ty/src/op.rs b/crates/hir_ty/src/op.rs
index 0870874fc..bb9b8bbfc 100644
--- a/crates/hir_ty/src/op.rs
+++ b/crates/hir_ty/src/op.rs
@@ -1,27 +1,27 @@
 //! Helper functions for binary operator type inference.
+use chalk_ir::TyVariableKind;
 use hir_def::expr::{ArithOp, BinaryOp, CmpOp};
 
-use super::{InferTy, Ty, TypeCtor};
-use crate::ApplicationTy;
+use crate::{Scalar, Ty};
 
 pub(super) fn binary_op_return_ty(op: BinaryOp, lhs_ty: Ty, rhs_ty: Ty) -> Ty {
     match op {
-        BinaryOp::LogicOp(_) | BinaryOp::CmpOp(_) => Ty::simple(TypeCtor::Bool),
+        BinaryOp::LogicOp(_) | BinaryOp::CmpOp(_) => Ty::Scalar(Scalar::Bool),
         BinaryOp::Assignment { .. } => Ty::unit(),
         BinaryOp::ArithOp(ArithOp::Shl) | BinaryOp::ArithOp(ArithOp::Shr) => match lhs_ty {
-            Ty::Apply(ApplicationTy { ctor, .. }) => match ctor {
-                TypeCtor::Int(..) | TypeCtor::Float(..) => lhs_ty,
-                _ => Ty::Unknown,
-            },
-            Ty::Infer(InferTy::IntVar(..)) | Ty::Infer(InferTy::FloatVar(..)) => lhs_ty,
+            Ty::Scalar(Scalar::Int(_))
+            | Ty::Scalar(Scalar::Uint(_))
+            | Ty::Scalar(Scalar::Float(_)) => lhs_ty,
+            Ty::InferenceVar(_, TyVariableKind::Integer)
+            | Ty::InferenceVar(_, TyVariableKind::Float) => lhs_ty,
             _ => Ty::Unknown,
         },
         BinaryOp::ArithOp(_) => match rhs_ty {
-            Ty::Apply(ApplicationTy { ctor, .. }) => match ctor {
-                TypeCtor::Int(..) | TypeCtor::Float(..) => rhs_ty,
-                _ => Ty::Unknown,
-            },
-            Ty::Infer(InferTy::IntVar(..)) | Ty::Infer(InferTy::FloatVar(..)) => rhs_ty,
+            Ty::Scalar(Scalar::Int(_))
+            | Ty::Scalar(Scalar::Uint(_))
+            | Ty::Scalar(Scalar::Float(_)) => rhs_ty,
+            Ty::InferenceVar(_, TyVariableKind::Integer)
+            | Ty::InferenceVar(_, TyVariableKind::Float) => rhs_ty,
             _ => Ty::Unknown,
         },
     }
@@ -29,29 +29,23 @@ pub(super) fn binary_op_return_ty(op: BinaryOp, lhs_ty: Ty, rhs_ty: Ty) -> Ty {
 
 pub(super) fn binary_op_rhs_expectation(op: BinaryOp, lhs_ty: Ty) -> Ty {
     match op {
-        BinaryOp::LogicOp(..) => Ty::simple(TypeCtor::Bool),
+        BinaryOp::LogicOp(..) => Ty::Scalar(Scalar::Bool),
         BinaryOp::Assignment { op: None } => lhs_ty,
         BinaryOp::CmpOp(CmpOp::Eq { .. }) => match lhs_ty {
-            Ty::Apply(ApplicationTy { ctor, .. }) => match ctor {
-                TypeCtor::Int(..)
-                | TypeCtor::Float(..)
-                | TypeCtor::Str
-                | TypeCtor::Char
-                | TypeCtor::Bool => lhs_ty,
-                _ => Ty::Unknown,
-            },
-            Ty::Infer(InferTy::IntVar(..)) | Ty::Infer(InferTy::FloatVar(..)) => lhs_ty,
+            Ty::Scalar(_) | Ty::Str => lhs_ty,
+            Ty::InferenceVar(_, TyVariableKind::Integer)
+            | Ty::InferenceVar(_, TyVariableKind::Float) => lhs_ty,
             _ => Ty::Unknown,
         },
         BinaryOp::ArithOp(ArithOp::Shl) | BinaryOp::ArithOp(ArithOp::Shr) => Ty::Unknown,
         BinaryOp::CmpOp(CmpOp::Ord { .. })
         | BinaryOp::Assignment { op: Some(_) }
         | BinaryOp::ArithOp(_) => match lhs_ty {
-            Ty::Apply(ApplicationTy { ctor, .. }) => match ctor {
-                TypeCtor::Int(..) | TypeCtor::Float(..) => lhs_ty,
-                _ => Ty::Unknown,
-            },
-            Ty::Infer(InferTy::IntVar(..)) | Ty::Infer(InferTy::FloatVar(..)) => lhs_ty,
+            Ty::Scalar(Scalar::Int(_))
+            | Ty::Scalar(Scalar::Uint(_))
+            | Ty::Scalar(Scalar::Float(_)) => lhs_ty,
+            Ty::InferenceVar(_, TyVariableKind::Integer)
+            | Ty::InferenceVar(_, TyVariableKind::Float) => lhs_ty,
             _ => Ty::Unknown,
         },
     }
diff --git a/crates/hir_ty/src/primitive.rs b/crates/hir_ty/src/primitive.rs
index 37966b709..2449addfb 100644
--- a/crates/hir_ty/src/primitive.rs
+++ b/crates/hir_ty/src/primitive.rs
@@ -3,137 +3,63 @@
 //! * during type inference, they can be uncertain (ie, `let x = 92;`)
 //! * they don't belong to any particular crate.
 
-use std::fmt;
-
-pub use hir_def::builtin_type::{BuiltinFloat, BuiltinInt, FloatBitness, IntBitness, Signedness};
-
-#[derive(Copy, Clone, Eq, PartialEq, Hash)]
-pub struct IntTy {
-    pub signedness: Signedness,
-    pub bitness: IntBitness,
-}
-
-impl fmt::Debug for IntTy {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        fmt::Display::fmt(self, f)
-    }
-}
-
-impl fmt::Display for IntTy {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "{}", self.ty_to_string())
-    }
-}
-
-impl IntTy {
-    pub fn isize() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::Xsize }
-    }
-
-    pub fn i8() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::X8 }
-    }
-
-    pub fn i16() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::X16 }
-    }
-
-    pub fn i32() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::X32 }
-    }
-
-    pub fn i64() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::X64 }
-    }
-
-    pub fn i128() -> IntTy {
-        IntTy { signedness: Signedness::Signed, bitness: IntBitness::X128 }
+pub use chalk_ir::{FloatTy, IntTy, UintTy};
+pub use hir_def::builtin_type::{BuiltinFloat, BuiltinInt, BuiltinUint};
+
+pub fn int_ty_to_string(ty: IntTy) -> &'static str {
+    match ty {
+        IntTy::Isize => "isize",
+        IntTy::I8 => "i8",
+        IntTy::I16 => "i16",
+        IntTy::I32 => "i32",
+        IntTy::I64 => "i64",
+        IntTy::I128 => "i128",
     }
-
-    pub fn usize() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::Xsize }
-    }
-
-    pub fn u8() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::X8 }
-    }
-
-    pub fn u16() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::X16 }
-    }
-
-    pub fn u32() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::X32 }
-    }
-
-    pub fn u64() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::X64 }
-    }
-
-    pub fn u128() -> IntTy {
-        IntTy { signedness: Signedness::Unsigned, bitness: IntBitness::X128 }
-    }
-
-    pub fn ty_to_string(self) -> &'static str {
-        match (self.signedness, self.bitness) {
-            (Signedness::Signed, IntBitness::Xsize) => "isize",
-            (Signedness::Signed, IntBitness::X8) => "i8",
-            (Signedness::Signed, IntBitness::X16) => "i16",
-            (Signedness::Signed, IntBitness::X32) => "i32",
-            (Signedness::Signed, IntBitness::X64) => "i64",
-            (Signedness::Signed, IntBitness::X128) => "i128",
-            (Signedness::Unsigned, IntBitness::Xsize) => "usize",
-            (Signedness::Unsigned, IntBitness::X8) => "u8",
-            (Signedness::Unsigned, IntBitness::X16) => "u16",
-            (Signedness::Unsigned, IntBitness::X32) => "u32",
-            (Signedness::Unsigned, IntBitness::X64) => "u64",
-            (Signedness::Unsigned, IntBitness::X128) => "u128",
-        }
-    }
-}
-
-#[derive(Copy, Clone, PartialEq, Eq, Hash)]
-pub struct FloatTy {
-    pub bitness: FloatBitness,
 }
 
-impl fmt::Debug for FloatTy {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        fmt::Display::fmt(self, f)
+pub fn uint_ty_to_string(ty: UintTy) -> &'static str {
+    match ty {
+        UintTy::Usize => "usize",
+        UintTy::U8 => "u8",
+        UintTy::U16 => "u16",
+        UintTy::U32 => "u32",
+        UintTy::U64 => "u64",
+        UintTy::U128 => "u128",
     }
 }
 
-impl fmt::Display for FloatTy {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "{}", self.ty_to_string())
+pub fn float_ty_to_string(ty: FloatTy) -> &'static str {
+    match ty {
+        FloatTy::F32 => "f32",
+        FloatTy::F64 => "f64",
     }
 }
 
-impl FloatTy {
-    pub fn f32() -> FloatTy {
-        FloatTy { bitness: FloatBitness::X32 }
-    }
-
-    pub fn f64() -> FloatTy {
-        FloatTy { bitness: FloatBitness::X64 }
-    }
-
-    pub fn ty_to_string(self) -> &'static str {
-        match self.bitness {
-            FloatBitness::X32 => "f32",
-            FloatBitness::X64 => "f64",
-        }
+pub(super) fn int_ty_from_builtin(t: BuiltinInt) -> IntTy {
+    match t {
+        BuiltinInt::Isize => IntTy::Isize,
+        BuiltinInt::I8 => IntTy::I8,
+        BuiltinInt::I16 => IntTy::I16,
+        BuiltinInt::I32 => IntTy::I32,
+        BuiltinInt::I64 => IntTy::I64,
+        BuiltinInt::I128 => IntTy::I128,
     }
 }
 
-impl From<BuiltinInt> for IntTy {
-    fn from(t: BuiltinInt) -> Self {
-        IntTy { signedness: t.signedness, bitness: t.bitness }
+pub(super) fn uint_ty_from_builtin(t: BuiltinUint) -> UintTy {
+    match t {
+        BuiltinUint::Usize => UintTy::Usize,
+        BuiltinUint::U8 => UintTy::U8,
+        BuiltinUint::U16 => UintTy::U16,
+        BuiltinUint::U32 => UintTy::U32,
+        BuiltinUint::U64 => UintTy::U64,
+        BuiltinUint::U128 => UintTy::U128,
     }
 }
 
-impl From<BuiltinFloat> for FloatTy {
-    fn from(t: BuiltinFloat) -> Self {
-        FloatTy { bitness: t.bitness }
+pub(super) fn float_ty_from_builtin(t: BuiltinFloat) -> FloatTy {
+    match t {
+        BuiltinFloat::F32 => FloatTy::F32,
+        BuiltinFloat::F64 => FloatTy::F64,
     }
 }
diff --git a/crates/hir_ty/src/tests/simple.rs b/crates/hir_ty/src/tests/simple.rs
index 12ec4657b..2947857a5 100644
--- a/crates/hir_ty/src/tests/simple.rs
+++ b/crates/hir_ty/src/tests/simple.rs
@@ -2491,3 +2491,58 @@ fn inner_use_enum_rename() {
         "#]],
     )
 }
+
+#[test]
+fn box_into_vec() {
+    check_infer(
+        r#"
+#[lang = "sized"]
+pub trait Sized {}
+
+#[lang = "unsize"]
+pub trait Unsize<T: ?Sized> {}
+
+#[lang = "coerce_unsized"]
+pub trait CoerceUnsized<T> {}
+
+pub unsafe trait Allocator {}
+
+pub struct Global;
+unsafe impl Allocator for Global {}
+
+#[lang = "owned_box"]
+#[fundamental]
+pub struct Box<T: ?Sized, A: Allocator = Global>;
+
+impl<T: ?Sized + Unsize<U>, U: ?Sized, A: Allocator> CoerceUnsized<Box<U, A>> for Box<T, A> {}
+
+pub struct Vec<T, A: Allocator = Global> {}
+
+#[lang = "slice"]
+impl<T> [T] {}
+
+#[lang = "slice_alloc"]
+impl<T> [T] {
+    pub fn into_vec<A: Allocator>(self: Box<Self, A>) -> Vec<T, A> {
+        unimplemented!()
+    }
+}
+
+fn test() {
+    let vec = <[_]>::into_vec(box [1i32]);
+}
+"#,
+        expect![[r#"
+            569..573 'self': Box<[T], A>
+            602..634 '{     ...     }': Vec<T, A>
+            612..628 'unimpl...ted!()': Vec<T, A>
+            648..694 '{     ...2]); }': ()
+            658..661 'vec': Vec<i32, Global>
+            664..679 '<[_]>::into_vec': fn into_vec<i32, Global>(Box<[i32], Global>) -> Vec<i32, Global>
+            664..691 '<[_]>:...1i32])': Vec<i32, Global>
+            680..690 'box [1i32]': Box<[i32; _], Global>
+            684..690 '[1i32]': [i32; _]
+            685..689 '1i32': i32
+        "#]],
+    )
+}
diff --git a/crates/hir_ty/src/traits.rs b/crates/hir_ty/src/traits.rs
index dfa51896b..e4cdb6d53 100644
--- a/crates/hir_ty/src/traits.rs
+++ b/crates/hir_ty/src/traits.rs
@@ -129,7 +129,7 @@ pub(crate) fn trait_solve_query(
     log::info!("trait_solve_query({})", goal.value.value.display(db));
 
     if let Obligation::Projection(pred) = &goal.value.value {
-        if let Ty::Bound(_) = &pred.projection_ty.parameters[0] {
+        if let Ty::BoundVar(_) = &pred.projection_ty.parameters[0] {
             // Hack: don't ask Chalk to normalize with an unknown self type, it'll say that's impossible
             return Some(Solution::Ambig(Guidance::Unknown));
         }
diff --git a/crates/hir_ty/src/traits/chalk.rs b/crates/hir_ty/src/traits/chalk.rs
index d74c83737..e513fa8f4 100644
--- a/crates/hir_ty/src/traits/chalk.rs
+++ b/crates/hir_ty/src/traits/chalk.rs
@@ -19,8 +19,8 @@ use crate::{
     display::HirDisplay,
     method_resolution::{TyFingerprint, ALL_FLOAT_FPS, ALL_INT_FPS},
     utils::generics,
-    BoundVar, CallableDefId, DebruijnIndex, FnSig, GenericPredicate, ProjectionPredicate,
-    ProjectionTy, Substs, TraitRef, Ty, TypeCtor,
+    BoundVar, CallableDefId, CallableSig, DebruijnIndex, GenericPredicate, ProjectionPredicate,
+    ProjectionTy, Substs, TraitRef, Ty,
 };
 use mapping::{
     convert_where_clauses, generic_predicate_to_inline_bound, make_binders, TypeAliasAsAssocType,
@@ -90,7 +90,7 @@ impl<'a> chalk_solve::RustIrDatabase<Interner> for ChalkContext<'a> {
             ty: &Ty,
             binders: &CanonicalVarKinds<Interner>,
         ) -> Option<chalk_ir::TyVariableKind> {
-            if let Ty::Bound(bv) = ty {
+            if let Ty::BoundVar(bv) = ty {
                 let binders = binders.as_slice(&Interner);
                 if bv.debruijn == DebruijnIndex::INNERMOST {
                     if let chalk_ir::VariableKind::Ty(tk) = binders[bv.index].kind {
@@ -220,18 +220,18 @@ impl<'a> chalk_solve::RustIrDatabase<Interner> for ChalkContext<'a> {
                     let impl_bound = GenericPredicate::Implemented(TraitRef {
                         trait_: future_trait,
                         // Self type as the first parameter.
-                        substs: Substs::single(Ty::Bound(BoundVar {
+                        substs: Substs::single(Ty::BoundVar(BoundVar {
                             debruijn: DebruijnIndex::INNERMOST,
                             index: 0,
                         })),
                     });
                     let proj_bound = GenericPredicate::Projection(ProjectionPredicate {
                         // The parameter of the opaque type.
-                        ty: Ty::Bound(BoundVar { debruijn: DebruijnIndex::ONE, index: 0 }),
+                        ty: Ty::BoundVar(BoundVar { debruijn: DebruijnIndex::ONE, index: 0 }),
                         projection_ty: ProjectionTy {
                             associated_ty: future_output,
                             // Self type as the first parameter.
-                            parameters: Substs::single(Ty::Bound(BoundVar::new(
+                            parameters: Substs::single(Ty::BoundVar(BoundVar::new(
                                 DebruijnIndex::INNERMOST,
                                 0,
                             ))),
@@ -286,9 +286,8 @@ impl<'a> chalk_solve::RustIrDatabase<Interner> for ChalkContext<'a> {
     ) -> chalk_ir::Binders<rust_ir::FnDefInputsAndOutputDatum<Interner>> {
         let sig_ty: Ty =
             from_chalk(self.db, substs.at(&Interner, 0).assert_ty_ref(&Interner).clone());
-        let sig = FnSig::from_fn_ptr_substs(
+        let sig = CallableSig::from_substs(
             &sig_ty.substs().expect("first closure param should be fn ptr"),
-            false,
         );
         let io = rust_ir::FnDefInputsAndOutputDatum {
             argument_types: sig.params().iter().map(|ty| ty.clone().to_chalk(self.db)).collect(),
@@ -393,7 +392,7 @@ pub(crate) fn associated_ty_data_query(
     let resolver = hir_def::resolver::HasResolver::resolver(type_alias, db.upcast());
     let ctx = crate::TyLoweringContext::new(db, &resolver)
         .with_type_param_mode(crate::lower::TypeParamLoweringMode::Variable);
-    let self_ty = Ty::Bound(crate::BoundVar::new(crate::DebruijnIndex::INNERMOST, 0));
+    let self_ty = Ty::BoundVar(crate::BoundVar::new(crate::DebruijnIndex::INNERMOST, 0));
     let bounds = type_alias_data
         .bounds
         .iter()
@@ -489,10 +488,11 @@ pub(crate) fn struct_datum_query(
     struct_id: AdtId,
 ) -> Arc<StructDatum> {
     debug!("struct_datum {:?}", struct_id);
-    let type_ctor = TypeCtor::Adt(from_chalk(db, struct_id));
+    let adt_id = from_chalk(db, struct_id);
+    let type_ctor = Ty::Adt(adt_id, Substs::empty());
     debug!("struct {:?} = {:?}", struct_id, type_ctor);
-    let num_params = type_ctor.num_ty_params(db);
-    let upstream = type_ctor.krate(db) != Some(krate);
+    let num_params = generics(db.upcast(), adt_id.into()).len();
+    let upstream = adt_id.module(db.upcast()).krate() != krate;
     let where_clauses = type_ctor
         .as_generic_def()
         .map(|generic_def| {
diff --git a/crates/hir_ty/src/traits/chalk/mapping.rs b/crates/hir_ty/src/traits/chalk/mapping.rs
index 8700d664e..6e6055d80 100644
--- a/crates/hir_ty/src/traits/chalk/mapping.rs
+++ b/crates/hir_ty/src/traits/chalk/mapping.rs
@@ -4,7 +4,7 @@
 //! conversions.
 
 use chalk_ir::{
-    cast::Cast, fold::shift::Shift, interner::HasInterner, LifetimeData, PlaceholderIndex, Scalar,
+    cast::Cast, fold::shift::Shift, interner::HasInterner, LifetimeData, PlaceholderIndex,
     UniverseIndex,
 };
 use chalk_solve::rust_ir;
@@ -14,10 +14,10 @@ use hir_def::{type_ref::Mutability, AssocContainerId, GenericDefId, Lookup, Type
 
 use crate::{
     db::HirDatabase,
-    primitive::{FloatBitness, FloatTy, IntBitness, IntTy, Signedness},
+    primitive::UintTy,
     traits::{Canonical, Obligation},
-    ApplicationTy, CallableDefId, GenericPredicate, InEnvironment, OpaqueTy, OpaqueTyId,
-    ProjectionPredicate, ProjectionTy, Substs, TraitEnvironment, TraitRef, Ty, TyKind, TypeCtor,
+    AliasTy, CallableDefId, FnPointer, FnSig, GenericPredicate, InEnvironment, OpaqueTy,
+    OpaqueTyId, ProjectionPredicate, ProjectionTy, Scalar, Substs, TraitEnvironment, TraitRef, Ty,
 };
 
 use super::interner::*;
@@ -27,88 +27,68 @@ impl ToChalk for Ty {
     type Chalk = chalk_ir::Ty<Interner>;
     fn to_chalk(self, db: &dyn HirDatabase) -> chalk_ir::Ty<Interner> {
         match self {
-            Ty::Apply(apply_ty) => match apply_ty.ctor {
-                TypeCtor::Ref(m) => ref_to_chalk(db, m, apply_ty.parameters),
-                TypeCtor::Array => array_to_chalk(db, apply_ty.parameters),
-                TypeCtor::FnPtr { num_args: _, is_varargs } => {
-                    let substitution =
-                        chalk_ir::FnSubst(apply_ty.parameters.to_chalk(db).shifted_in(&Interner));
-                    chalk_ir::TyKind::Function(chalk_ir::FnPointer {
-                        num_binders: 0,
-                        sig: chalk_ir::FnSig {
-                            abi: (),
-                            safety: chalk_ir::Safety::Safe,
-                            variadic: is_varargs,
-                        },
-                        substitution,
-                    })
-                    .intern(&Interner)
-                }
-                TypeCtor::AssociatedType(type_alias) => {
-                    let assoc_type = TypeAliasAsAssocType(type_alias);
-                    let assoc_type_id = assoc_type.to_chalk(db);
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::AssociatedType(assoc_type_id, substitution).intern(&Interner)
-                }
+            Ty::Ref(m, parameters) => ref_to_chalk(db, m, parameters),
+            Ty::Array(parameters) => array_to_chalk(db, parameters),
+            Ty::Function(FnPointer { sig: FnSig { variadic }, substs, .. }) => {
+                let substitution = chalk_ir::FnSubst(substs.to_chalk(db).shifted_in(&Interner));
+                chalk_ir::TyKind::Function(chalk_ir::FnPointer {
+                    num_binders: 0,
+                    sig: chalk_ir::FnSig { abi: (), safety: chalk_ir::Safety::Safe, variadic },
+                    substitution,
+                })
+                .intern(&Interner)
+            }
+            Ty::AssociatedType(type_alias, substs) => {
+                let assoc_type = TypeAliasAsAssocType(type_alias);
+                let assoc_type_id = assoc_type.to_chalk(db);
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::AssociatedType(assoc_type_id, substitution).intern(&Interner)
+            }
 
-                TypeCtor::OpaqueType(impl_trait_id) => {
-                    let id = impl_trait_id.to_chalk(db);
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::OpaqueType(id, substitution).intern(&Interner)
-                }
+            Ty::OpaqueType(impl_trait_id, substs) => {
+                let id = impl_trait_id.to_chalk(db);
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::OpaqueType(id, substitution).intern(&Interner)
+            }
 
-                TypeCtor::ForeignType(type_alias) => {
-                    let foreign_type = TypeAliasAsForeignType(type_alias);
-                    let foreign_type_id = foreign_type.to_chalk(db);
-                    chalk_ir::TyKind::Foreign(foreign_type_id).intern(&Interner)
-                }
+            Ty::ForeignType(type_alias) => {
+                let foreign_type = TypeAliasAsForeignType(type_alias);
+                let foreign_type_id = foreign_type.to_chalk(db);
+                chalk_ir::TyKind::Foreign(foreign_type_id).intern(&Interner)
+            }
 
-                TypeCtor::Bool => chalk_ir::TyKind::Scalar(Scalar::Bool).intern(&Interner),
-                TypeCtor::Char => chalk_ir::TyKind::Scalar(Scalar::Char).intern(&Interner),
-                TypeCtor::Int(int_ty) => {
-                    chalk_ir::TyKind::Scalar(int_ty_to_chalk(int_ty)).intern(&Interner)
-                }
-                TypeCtor::Float(FloatTy { bitness: FloatBitness::X32 }) => {
-                    chalk_ir::TyKind::Scalar(Scalar::Float(chalk_ir::FloatTy::F32))
-                        .intern(&Interner)
-                }
-                TypeCtor::Float(FloatTy { bitness: FloatBitness::X64 }) => {
-                    chalk_ir::TyKind::Scalar(Scalar::Float(chalk_ir::FloatTy::F64))
-                        .intern(&Interner)
-                }
+            Ty::Scalar(scalar) => chalk_ir::TyKind::Scalar(scalar).intern(&Interner),
 
-                TypeCtor::Tuple { cardinality } => {
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::Tuple(cardinality.into(), substitution).intern(&Interner)
-                }
-                TypeCtor::RawPtr(mutability) => {
-                    let ty = apply_ty.parameters[0].clone().to_chalk(db);
-                    chalk_ir::TyKind::Raw(mutability.to_chalk(db), ty).intern(&Interner)
-                }
-                TypeCtor::Slice => {
-                    chalk_ir::TyKind::Slice(apply_ty.parameters[0].clone().to_chalk(db))
-                        .intern(&Interner)
-                }
-                TypeCtor::Str => chalk_ir::TyKind::Str.intern(&Interner),
-                TypeCtor::FnDef(callable_def) => {
-                    let id = callable_def.to_chalk(db);
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::FnDef(id, substitution).intern(&Interner)
-                }
-                TypeCtor::Never => chalk_ir::TyKind::Never.intern(&Interner),
+            Ty::Tuple(cardinality, substs) => {
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::Tuple(cardinality.into(), substitution).intern(&Interner)
+            }
+            Ty::Raw(mutability, substs) => {
+                let ty = substs[0].clone().to_chalk(db);
+                chalk_ir::TyKind::Raw(mutability.to_chalk(db), ty).intern(&Interner)
+            }
+            Ty::Slice(substs) => {
+                chalk_ir::TyKind::Slice(substs[0].clone().to_chalk(db)).intern(&Interner)
+            }
+            Ty::Str => chalk_ir::TyKind::Str.intern(&Interner),
+            Ty::FnDef(callable_def, substs) => {
+                let id = callable_def.to_chalk(db);
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::FnDef(id, substitution).intern(&Interner)
+            }
+            Ty::Never => chalk_ir::TyKind::Never.intern(&Interner),
 
-                TypeCtor::Closure { def, expr } => {
-                    let closure_id = db.intern_closure((def, expr));
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::Closure(closure_id.into(), substitution).intern(&Interner)
-                }
+            Ty::Closure(def, expr, substs) => {
+                let closure_id = db.intern_closure((def, expr));
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::Closure(closure_id.into(), substitution).intern(&Interner)
+            }
 
-                TypeCtor::Adt(adt_id) => {
-                    let substitution = apply_ty.parameters.to_chalk(db);
-                    chalk_ir::TyKind::Adt(chalk_ir::AdtId(adt_id), substitution).intern(&Interner)
-                }
-            },
-            Ty::Projection(proj_ty) => {
+            Ty::Adt(adt_id, substs) => {
+                let substitution = substs.to_chalk(db);
+                chalk_ir::TyKind::Adt(chalk_ir::AdtId(adt_id), substitution).intern(&Interner)
+            }
+            Ty::Alias(AliasTy::Projection(proj_ty)) => {
                 let associated_ty_id = TypeAliasAsAssocType(proj_ty.associated_ty).to_chalk(db);
                 let substitution = proj_ty.parameters.to_chalk(db);
                 chalk_ir::AliasTy::Projection(chalk_ir::ProjectionTy {
@@ -126,8 +106,8 @@ impl ToChalk for Ty {
                 }
                 .to_ty::<Interner>(&Interner)
             }
-            Ty::Bound(idx) => chalk_ir::TyKind::BoundVar(idx).intern(&Interner),
-            Ty::Infer(_infer_ty) => panic!("uncanonicalized infer ty"),
+            Ty::BoundVar(idx) => chalk_ir::TyKind::BoundVar(idx).intern(&Interner),
+            Ty::InferenceVar(..) => panic!("uncanonicalized infer ty"),
             Ty::Dyn(predicates) => {
                 let where_clauses = chalk_ir::QuantifiedWhereClauses::from_iter(
                     &Interner,
@@ -139,7 +119,7 @@ impl ToChalk for Ty {
                 };
                 chalk_ir::TyKind::Dyn(bounded_ty).intern(&Interner)
             }
-            Ty::Opaque(opaque_ty) => {
+            Ty::Alias(AliasTy::Opaque(opaque_ty)) => {
                 let opaque_ty_id = opaque_ty.opaque_ty_id.to_chalk(db);
                 let substitution = opaque_ty.parameters.to_chalk(db);
                 chalk_ir::TyKind::Alias(chalk_ir::AliasTy::Opaque(chalk_ir::OpaqueTy {
@@ -154,9 +134,7 @@ impl ToChalk for Ty {
     fn from_chalk(db: &dyn HirDatabase, chalk: chalk_ir::Ty<Interner>) -> Self {
         match chalk.data(&Interner).kind.clone() {
             chalk_ir::TyKind::Error => Ty::Unknown,
-            chalk_ir::TyKind::Array(ty, _size) => {
-                Ty::apply(TypeCtor::Array, Substs::single(from_chalk(db, ty)))
-            }
+            chalk_ir::TyKind::Array(ty, _size) => Ty::Array(Substs::single(from_chalk(db, ty))),
             chalk_ir::TyKind::Placeholder(idx) => {
                 assert_eq!(idx.ui, UniverseIndex::ROOT);
                 let interned_id = crate::db::GlobalTypeParamId::from_intern_id(
@@ -168,12 +146,12 @@ impl ToChalk for Ty {
                 let associated_ty =
                     from_chalk::<TypeAliasAsAssocType, _>(db, proj.associated_ty_id).0;
                 let parameters = from_chalk(db, proj.substitution);
-                Ty::Projection(ProjectionTy { associated_ty, parameters })
+                Ty::Alias(AliasTy::Projection(ProjectionTy { associated_ty, parameters }))
             }
             chalk_ir::TyKind::Alias(chalk_ir::AliasTy::Opaque(opaque_ty)) => {
                 let impl_trait_id = from_chalk(db, opaque_ty.opaque_ty_id);
                 let parameters = from_chalk(db, opaque_ty.substitution);
-                Ty::Opaque(OpaqueTy { opaque_ty_id: impl_trait_id, parameters })
+                Ty::Alias(AliasTy::Opaque(OpaqueTy { opaque_ty_id: impl_trait_id, parameters }))
             }
             chalk_ir::TyKind::Function(chalk_ir::FnPointer {
                 num_binders,
@@ -182,19 +160,17 @@ impl ToChalk for Ty {
                 ..
             }) => {
                 assert_eq!(num_binders, 0);
-                let parameters: Substs = from_chalk(
+                let substs: Substs = from_chalk(
                     db,
                     substitution.0.shifted_out(&Interner).expect("fn ptr should have no binders"),
                 );
-                Ty::Apply(ApplicationTy {
-                    ctor: TypeCtor::FnPtr {
-                        num_args: (parameters.len() - 1) as u16,
-                        is_varargs: variadic,
-                    },
-                    parameters,
+                Ty::Function(FnPointer {
+                    num_args: (substs.len() - 1),
+                    sig: FnSig { variadic },
+                    substs,
                 })
             }
-            chalk_ir::TyKind::BoundVar(idx) => Ty::Bound(idx),
+            chalk_ir::TyKind::BoundVar(idx) => Ty::BoundVar(idx),
             chalk_ir::TyKind::InferenceVar(_iv, _kind) => Ty::Unknown,
             chalk_ir::TyKind::Dyn(where_clauses) => {
                 assert_eq!(where_clauses.bounds.binders.len(&Interner), 1);
@@ -207,75 +183,49 @@ impl ToChalk for Ty {
                 Ty::Dyn(predicates)
             }
 
-            chalk_ir::TyKind::Adt(struct_id, subst) => {
-                apply_ty_from_chalk(db, TypeCtor::Adt(struct_id.0), subst)
-            }
-            chalk_ir::TyKind::AssociatedType(type_id, subst) => apply_ty_from_chalk(
-                db,
-                TypeCtor::AssociatedType(from_chalk::<TypeAliasAsAssocType, _>(db, type_id).0),
-                subst,
+            chalk_ir::TyKind::Adt(struct_id, subst) => Ty::Adt(struct_id.0, from_chalk(db, subst)),
+            chalk_ir::TyKind::AssociatedType(type_id, subst) => Ty::AssociatedType(
+                from_chalk::<TypeAliasAsAssocType, _>(db, type_id).0,
+                from_chalk(db, subst),
             ),
+
             chalk_ir::TyKind::OpaqueType(opaque_type_id, subst) => {
-                apply_ty_from_chalk(db, TypeCtor::OpaqueType(from_chalk(db, opaque_type_id)), subst)
+                Ty::OpaqueType(from_chalk(db, opaque_type_id), from_chalk(db, subst))
             }
 
-            chalk_ir::TyKind::Scalar(Scalar::Bool) => Ty::simple(TypeCtor::Bool),
-            chalk_ir::TyKind::Scalar(Scalar::Char) => Ty::simple(TypeCtor::Char),
-            chalk_ir::TyKind::Scalar(Scalar::Int(int_ty)) => Ty::simple(TypeCtor::Int(IntTy {
-                signedness: Signedness::Signed,
-                bitness: bitness_from_chalk_int(int_ty),
-            })),
-            chalk_ir::TyKind::Scalar(Scalar::Uint(uint_ty)) => Ty::simple(TypeCtor::Int(IntTy {
-                signedness: Signedness::Unsigned,
-                bitness: bitness_from_chalk_uint(uint_ty),
-            })),
-            chalk_ir::TyKind::Scalar(Scalar::Float(chalk_ir::FloatTy::F32)) => {
-                Ty::simple(TypeCtor::Float(FloatTy { bitness: FloatBitness::X32 }))
-            }
-            chalk_ir::TyKind::Scalar(Scalar::Float(chalk_ir::FloatTy::F64)) => {
-                Ty::simple(TypeCtor::Float(FloatTy { bitness: FloatBitness::X64 }))
-            }
+            chalk_ir::TyKind::Scalar(scalar) => Ty::Scalar(scalar),
             chalk_ir::TyKind::Tuple(cardinality, subst) => {
-                apply_ty_from_chalk(db, TypeCtor::Tuple { cardinality: cardinality as u16 }, subst)
+                Ty::Tuple(cardinality, from_chalk(db, subst))
             }
             chalk_ir::TyKind::Raw(mutability, ty) => {
-                Ty::apply_one(TypeCtor::RawPtr(from_chalk(db, mutability)), from_chalk(db, ty))
+                Ty::Raw(from_chalk(db, mutability), Substs::single(from_chalk(db, ty)))
             }
-            chalk_ir::TyKind::Slice(ty) => Ty::apply_one(TypeCtor::Slice, from_chalk(db, ty)),
+            chalk_ir::TyKind::Slice(ty) => Ty::Slice(Substs::single(from_chalk(db, ty))),
             chalk_ir::TyKind::Ref(mutability, _lifetime, ty) => {
-                Ty::apply_one(TypeCtor::Ref(from_chalk(db, mutability)), from_chalk(db, ty))
+                Ty::Ref(from_chalk(db, mutability), Substs::single(from_chalk(db, ty)))
             }
-            chalk_ir::TyKind::Str => Ty::simple(TypeCtor::Str),
-            chalk_ir::TyKind::Never => Ty::simple(TypeCtor::Never),
+            chalk_ir::TyKind::Str => Ty::Str,
+            chalk_ir::TyKind::Never => Ty::Never,
 
             chalk_ir::TyKind::FnDef(fn_def_id, subst) => {
-                let callable_def = from_chalk(db, fn_def_id);
-                apply_ty_from_chalk(db, TypeCtor::FnDef(callable_def), subst)
+                Ty::FnDef(from_chalk(db, fn_def_id), from_chalk(db, subst))
             }
 
             chalk_ir::TyKind::Closure(id, subst) => {
                 let id: crate::db::ClosureId = id.into();
                 let (def, expr) = db.lookup_intern_closure(id);
-                apply_ty_from_chalk(db, TypeCtor::Closure { def, expr }, subst)
+                Ty::Closure(def, expr, from_chalk(db, subst))
             }
 
-            chalk_ir::TyKind::Foreign(foreign_def_id) => Ty::simple(TypeCtor::ForeignType(
-                from_chalk::<TypeAliasAsForeignType, _>(db, foreign_def_id).0,
-            )),
+            chalk_ir::TyKind::Foreign(foreign_def_id) => {
+                Ty::ForeignType(from_chalk::<TypeAliasAsForeignType, _>(db, foreign_def_id).0)
+            }
             chalk_ir::TyKind::Generator(_, _) => unimplemented!(), // FIXME
             chalk_ir::TyKind::GeneratorWitness(_, _) => unimplemented!(), // FIXME
         }
     }
 }
 
-fn apply_ty_from_chalk(
-    db: &dyn HirDatabase,
-    ctor: TypeCtor,
-    subst: chalk_ir::Substitution<Interner>,
-) -> Ty {
-    Ty::Apply(ApplicationTy { ctor, parameters: from_chalk(db, subst) })
-}
-
 /// We currently don't model lifetimes, but Chalk does. So, we have to insert a
 /// fake lifetime here, because Chalks built-in logic may expect it to be there.
 fn ref_to_chalk(
@@ -292,8 +242,7 @@ fn ref_to_chalk(
 /// fake constant here, because Chalks built-in logic may expect it to be there.
 fn array_to_chalk(db: &dyn HirDatabase, subst: Substs) -> chalk_ir::Ty<Interner> {
     let arg = subst[0].clone().to_chalk(db);
-    let usize_ty =
-        chalk_ir::TyKind::Scalar(Scalar::Uint(chalk_ir::UintTy::Usize)).intern(&Interner);
+    let usize_ty = chalk_ir::TyKind::Scalar(Scalar::Uint(UintTy::Usize)).intern(&Interner);
     let const_ = chalk_ir::ConstData {
         ty: usize_ty,
         value: chalk_ir::ConstValue::Concrete(chalk_ir::ConcreteConst { interned: () }),
@@ -364,55 +313,6 @@ impl ToChalk for OpaqueTyId {
     }
 }
 
-fn bitness_from_chalk_uint(uint_ty: chalk_ir::UintTy) -> IntBitness {
-    use chalk_ir::UintTy;
-
-    match uint_ty {
-        UintTy::Usize => IntBitness::Xsize,
-        UintTy::U8 => IntBitness::X8,
-        UintTy::U16 => IntBitness::X16,
-        UintTy::U32 => IntBitness::X32,
-        UintTy::U64 => IntBitness::X64,
-        UintTy::U128 => IntBitness::X128,
-    }
-}
-
-fn bitness_from_chalk_int(int_ty: chalk_ir::IntTy) -> IntBitness {
-    use chalk_ir::IntTy;
-
-    match int_ty {
-        IntTy::Isize => IntBitness::Xsize,
-        IntTy::I8 => IntBitness::X8,
-        IntTy::I16 => IntBitness::X16,
-        IntTy::I32 => IntBitness::X32,
-        IntTy::I64 => IntBitness::X64,
-        IntTy::I128 => IntBitness::X128,
-    }
-}
-
-fn int_ty_to_chalk(int_ty: IntTy) -> Scalar {
-    use chalk_ir::{IntTy, UintTy};
-
-    match int_ty.signedness {
-        Signedness::Signed => Scalar::Int(match int_ty.bitness {
-            IntBitness::Xsize => IntTy::Isize,
-            IntBitness::X8 => IntTy::I8,
-            IntBitness::X16 => IntTy::I16,
-            IntBitness::X32 => IntTy::I32,
-            IntBitness::X64 => IntTy::I64,
-            IntBitness::X128 => IntTy::I128,
-        }),
-        Signedness::Unsigned => Scalar::Uint(match int_ty.bitness {
-            IntBitness::Xsize => UintTy::Usize,
-            IntBitness::X8 => UintTy::U8,
-            IntBitness::X16 => UintTy::U16,
-            IntBitness::X32 => UintTy::U32,
-            IntBitness::X64 => UintTy::U64,
-            IntBitness::X128 => UintTy::U128,
-        }),
-    }
-}
-
 impl ToChalk for Mutability {
     type Chalk = chalk_ir::Mutability;
     fn to_chalk(self, _db: &dyn HirDatabase) -> Self::Chalk {
@@ -632,20 +532,12 @@ where
     type Chalk = chalk_ir::Canonical<T::Chalk>;
 
     fn to_chalk(self, db: &dyn HirDatabase) -> chalk_ir::Canonical<T::Chalk> {
-        let kinds = self
-            .kinds
-            .iter()
-            .map(|k| match k {
-                TyKind::General => chalk_ir::TyVariableKind::General,
-                TyKind::Integer => chalk_ir::TyVariableKind::Integer,
-                TyKind::Float => chalk_ir::TyVariableKind::Float,
-            })
-            .map(|tk| {
-                chalk_ir::CanonicalVarKind::new(
-                    chalk_ir::VariableKind::Ty(tk),
-                    chalk_ir::UniverseIndex::ROOT,
-                )
-            });
+        let kinds = self.kinds.iter().map(|&tk| {
+            chalk_ir::CanonicalVarKind::new(
+                chalk_ir::VariableKind::Ty(tk),
+                chalk_ir::UniverseIndex::ROOT,
+            )
+        });
         let value = self.value.to_chalk(db);
         chalk_ir::Canonical {
             value,
@@ -658,17 +550,13 @@ where
             .binders
             .iter(&Interner)
             .map(|k| match k.kind {
-                chalk_ir::VariableKind::Ty(tk) => match tk {
-                    chalk_ir::TyVariableKind::General => TyKind::General,
-                    chalk_ir::TyVariableKind::Integer => TyKind::Integer,
-                    chalk_ir::TyVariableKind::Float => TyKind::Float,
-                },
+                chalk_ir::VariableKind::Ty(tk) => tk,
                 // HACK: Chalk can sometimes return new lifetime variables. We
                 // want to just skip them, but to not mess up the indices of
                 // other variables, we'll just create a new type variable in
                 // their place instead. This should not matter (we never see the
                 // actual *uses* of the lifetime variable).
-                chalk_ir::VariableKind::Lifetime => TyKind::General,
+                chalk_ir::VariableKind::Lifetime => chalk_ir::TyVariableKind::General,
                 chalk_ir::VariableKind::Const(_) => panic!("unexpected const from Chalk"),
             })
             .collect();