diff --git a/Cargo.lock b/Cargo.lock
index 1d7f93c789a..03a075b345c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -4303,6 +4303,13 @@ dependencies = [
  "tracing",
 ]
 
+[[package]]
+name = "rustc_next_trait_solver"
+version = "0.0.0"
+dependencies = [
+ "rustc_type_ir",
+]
+
 [[package]]
 name = "rustc_parse"
 version = "0.0.0"
@@ -4571,6 +4578,7 @@ dependencies = [
  "rustc_infer",
  "rustc_macros",
  "rustc_middle",
+ "rustc_next_trait_solver",
  "rustc_parse_format",
  "rustc_query_system",
  "rustc_session",
diff --git a/compiler/rustc_infer/src/infer/mod.rs b/compiler/rustc_infer/src/infer/mod.rs
index 32c09e491c7..3a71251e73d 100644
--- a/compiler/rustc_infer/src/infer/mod.rs
+++ b/compiler/rustc_infer/src/infer/mod.rs
@@ -345,37 +345,61 @@ pub struct InferCtxt<'tcx> {
 impl<'tcx> ty::InferCtxtLike for InferCtxt<'tcx> {
     type Interner = TyCtxt<'tcx>;
 
-    fn universe_of_ty(&self, ty: ty::InferTy) -> Option<ty::UniverseIndex> {
-        use InferTy::*;
-        match ty {
-            // FIXME(BoxyUwU): this is kind of jank and means that printing unresolved
-            // ty infers will give you the universe of the var it resolved to not the universe
-            // it actually had. It also means that if you have a `?0.1` and infer it to `u8` then
-            // try to print out `?0.1` it will just print `?0`.
-            TyVar(ty_vid) => match self.probe_ty_var(ty_vid) {
-                Err(universe) => Some(universe),
-                Ok(_) => None,
-            },
-            IntVar(_) | FloatVar(_) | FreshTy(_) | FreshIntTy(_) | FreshFloatTy(_) => None,
+    fn interner(&self) -> TyCtxt<'tcx> {
+        self.tcx
+    }
+
+    fn universe_of_ty(&self, vid: TyVid) -> Option<ty::UniverseIndex> {
+        // FIXME(BoxyUwU): this is kind of jank and means that printing unresolved
+        // ty infers will give you the universe of the var it resolved to not the universe
+        // it actually had. It also means that if you have a `?0.1` and infer it to `u8` then
+        // try to print out `?0.1` it will just print `?0`.
+        match self.probe_ty_var(vid) {
+            Err(universe) => Some(universe),
+            Ok(_) => None,
         }
     }
 
-    fn universe_of_ct(&self, ct: ty::InferConst) -> Option<ty::UniverseIndex> {
-        use ty::InferConst::*;
-        match ct {
-            // Same issue as with `universe_of_ty`
-            Var(ct_vid) => match self.probe_const_var(ct_vid) {
-                Err(universe) => Some(universe),
-                Ok(_) => None,
-            },
-            EffectVar(_) => None,
-            Fresh(_) => None,
+    fn universe_of_ct(&self, ct: ConstVid) -> Option<ty::UniverseIndex> {
+        // Same issue as with `universe_of_ty`
+        match self.probe_const_var(ct) {
+            Err(universe) => Some(universe),
+            Ok(_) => None,
         }
     }
 
     fn universe_of_lt(&self, lt: ty::RegionVid) -> Option<ty::UniverseIndex> {
         Some(self.universe_of_region_vid(lt))
     }
+
+    fn root_ty_var(&self, vid: TyVid) -> TyVid {
+        self.root_var(vid)
+    }
+
+    fn probe_ty_var(&self, vid: TyVid) -> Option<Ty<'tcx>> {
+        self.probe_ty_var(vid).ok()
+    }
+
+    fn root_lt_var(&self, vid: ty::RegionVid) -> ty::RegionVid {
+        self.root_region_var(vid)
+    }
+
+    fn probe_lt_var(&self, vid: ty::RegionVid) -> Option<ty::Region<'tcx>> {
+        let re = self
+            .inner
+            .borrow_mut()
+            .unwrap_region_constraints()
+            .opportunistic_resolve_var(self.tcx, vid);
+        if re.is_var() { None } else { Some(re) }
+    }
+
+    fn root_ct_var(&self, vid: ConstVid) -> ConstVid {
+        self.root_const_var(vid)
+    }
+
+    fn probe_ct_var(&self, vid: ConstVid) -> Option<ty::Const<'tcx>> {
+        self.probe_const_var(vid).ok()
+    }
 }
 
 /// See the `error_reporting` module for more details.
@@ -1347,6 +1371,10 @@ impl<'tcx> InferCtxt<'tcx> {
         self.inner.borrow_mut().type_variables().root_var(var)
     }
 
+    pub fn root_region_var(&self, var: ty::RegionVid) -> ty::RegionVid {
+        self.inner.borrow_mut().unwrap_region_constraints().root_var(var)
+    }
+
     pub fn root_const_var(&self, var: ty::ConstVid) -> ty::ConstVid {
         self.inner.borrow_mut().const_unification_table().find(var).vid
     }
diff --git a/compiler/rustc_infer/src/infer/region_constraints/mod.rs b/compiler/rustc_infer/src/infer/region_constraints/mod.rs
index cbd8040c9f1..5c043b1d3dd 100644
--- a/compiler/rustc_infer/src/infer/region_constraints/mod.rs
+++ b/compiler/rustc_infer/src/infer/region_constraints/mod.rs
@@ -623,6 +623,11 @@ impl<'tcx> RegionConstraintCollector<'_, 'tcx> {
         }
     }
 
+    pub fn root_var(&mut self, vid: ty::RegionVid) -> ty::RegionVid {
+        let mut ut = self.unification_table_mut(); // FIXME(rust-lang/ena#42): unnecessary mut
+        ut.find(vid).vid
+    }
+
     fn combine_map(&mut self, t: CombineMapType) -> &mut CombineMap<'tcx> {
         match t {
             Glb => &mut self.glbs,
diff --git a/compiler/rustc_middle/src/ty/consts.rs b/compiler/rustc_middle/src/ty/consts.rs
index e48840fac20..78cc2f91796 100644
--- a/compiler/rustc_middle/src/ty/consts.rs
+++ b/compiler/rustc_middle/src/ty/consts.rs
@@ -7,7 +7,7 @@ use rustc_hir as hir;
 use rustc_hir::def::{DefKind, Res};
 use rustc_hir::def_id::LocalDefId;
 use rustc_macros::HashStable;
-use rustc_type_ir::{TypeFlags, WithCachedTypeInfo};
+use rustc_type_ir::{ConstTy, IntoKind, TypeFlags, WithCachedTypeInfo};
 
 mod int;
 mod kind;
@@ -26,6 +26,20 @@ use super::sty::ConstKind;
 #[rustc_pass_by_value]
 pub struct Const<'tcx>(pub(super) Interned<'tcx, WithCachedTypeInfo<ConstData<'tcx>>>);
 
+impl<'tcx> IntoKind for Const<'tcx> {
+    type Kind = ConstKind<'tcx>;
+
+    fn kind(&self) -> ConstKind<'tcx> {
+        (*self).kind().clone()
+    }
+}
+
+impl<'tcx> ConstTy<TyCtxt<'tcx>> for Const<'tcx> {
+    fn ty(&self) -> Ty<'tcx> {
+        (*self).ty()
+    }
+}
+
 /// Typed constant value.
 #[derive(PartialEq, Eq, PartialOrd, Ord, Hash, HashStable, TyEncodable, TyDecodable)]
 pub struct ConstData<'tcx> {
diff --git a/compiler/rustc_middle/src/ty/context.rs b/compiler/rustc_middle/src/ty/context.rs
index 3012434ad3f..a39acc9859f 100644
--- a/compiler/rustc_middle/src/ty/context.rs
+++ b/compiler/rustc_middle/src/ty/context.rs
@@ -131,6 +131,42 @@ impl<'tcx> Interner for TyCtxt<'tcx> {
     ) -> (Self::Ty, ty::Mutability) {
         (ty, mutbl)
     }
+
+    fn mk_canonical_var_infos(
+        &self,
+        infos: &[rustc_type_ir::CanonicalVarInfo<Self>],
+    ) -> Self::CanonicalVars {
+        (*self).mk_canonical_var_infos(infos)
+    }
+
+    fn mk_bound_ty(
+        &self,
+        debruijn: rustc_type_ir::DebruijnIndex,
+        var: rustc_type_ir::BoundVar,
+    ) -> Self::Ty {
+        Ty::new_bound(*self, debruijn, ty::BoundTy { var, kind: ty::BoundTyKind::Anon })
+    }
+
+    fn mk_bound_region(
+        &self,
+        debruijn: rustc_type_ir::DebruijnIndex,
+        var: rustc_type_ir::BoundVar,
+    ) -> Self::Region {
+        Region::new_bound(
+            *self,
+            debruijn,
+            ty::BoundRegion { var, kind: ty::BoundRegionKind::BrAnon },
+        )
+    }
+
+    fn mk_bound_const(
+        &self,
+        debruijn: rustc_type_ir::DebruijnIndex,
+        var: rustc_type_ir::BoundVar,
+        ty: Self::Ty,
+    ) -> Self::Const {
+        Const::new_bound(*self, debruijn, var, ty)
+    }
 }
 
 type InternedSet<'tcx, T> = ShardedHashMap<InternedInSet<'tcx, T>, ()>;
diff --git a/compiler/rustc_middle/src/ty/mod.rs b/compiler/rustc_middle/src/ty/mod.rs
index 203c9eb65df..6aaa363eb01 100644
--- a/compiler/rustc_middle/src/ty/mod.rs
+++ b/compiler/rustc_middle/src/ty/mod.rs
@@ -474,6 +474,14 @@ pub struct CReaderCacheKey {
 #[rustc_pass_by_value]
 pub struct Ty<'tcx>(Interned<'tcx, WithCachedTypeInfo<TyKind<'tcx>>>);
 
+impl<'tcx> IntoKind for Ty<'tcx> {
+    type Kind = TyKind<'tcx>;
+
+    fn kind(&self) -> TyKind<'tcx> {
+        (*self).kind().clone()
+    }
+}
+
 impl EarlyParamRegion {
     /// Does this early bound region have a name? Early bound regions normally
     /// always have names except when using anonymous lifetimes (`'_`).
@@ -1554,8 +1562,12 @@ impl rustc_type_ir::Placeholder for PlaceholderRegion {
         self.bound.var
     }
 
-    fn with_updated_universe(self, ui: UniverseIndex) -> Self {
-        Placeholder { universe: ui, ..self }
+    fn with_updated_universe(&self, ui: UniverseIndex) -> Self {
+        Placeholder { universe: ui, ..*self }
+    }
+
+    fn new(ui: UniverseIndex, var: BoundVar) -> Self {
+        Placeholder { universe: ui, bound: BoundRegion { var, kind: BoundRegionKind::BrAnon } }
     }
 }
 
@@ -1570,8 +1582,12 @@ impl rustc_type_ir::Placeholder for PlaceholderType {
         self.bound.var
     }
 
-    fn with_updated_universe(self, ui: UniverseIndex) -> Self {
-        Placeholder { universe: ui, ..self }
+    fn with_updated_universe(&self, ui: UniverseIndex) -> Self {
+        Placeholder { universe: ui, ..*self }
+    }
+
+    fn new(ui: UniverseIndex, var: BoundVar) -> Self {
+        Placeholder { universe: ui, bound: BoundTy { var, kind: BoundTyKind::Anon } }
     }
 }
 
@@ -1593,8 +1609,12 @@ impl rustc_type_ir::Placeholder for PlaceholderConst {
         self.bound
     }
 
-    fn with_updated_universe(self, ui: UniverseIndex) -> Self {
-        Placeholder { universe: ui, ..self }
+    fn with_updated_universe(&self, ui: UniverseIndex) -> Self {
+        Placeholder { universe: ui, ..*self }
+    }
+
+    fn new(ui: UniverseIndex, var: BoundVar) -> Self {
+        Placeholder { universe: ui, bound: var }
     }
 }
 
diff --git a/compiler/rustc_middle/src/ty/sty.rs b/compiler/rustc_middle/src/ty/sty.rs
index e221b4e8bec..ed2f8f0a6ab 100644
--- a/compiler/rustc_middle/src/ty/sty.rs
+++ b/compiler/rustc_middle/src/ty/sty.rs
@@ -6,7 +6,7 @@ use crate::infer::canonical::Canonical;
 use crate::ty::visit::ValidateBoundVars;
 use crate::ty::InferTy::*;
 use crate::ty::{
-    self, AdtDef, Discr, Term, Ty, TyCtxt, TypeFlags, TypeSuperVisitable, TypeVisitable,
+    self, AdtDef, Discr, IntoKind, Term, Ty, TyCtxt, TypeFlags, TypeSuperVisitable, TypeVisitable,
     TypeVisitableExt, TypeVisitor,
 };
 use crate::ty::{GenericArg, GenericArgs, GenericArgsRef};
@@ -1477,6 +1477,14 @@ impl ParamConst {
 #[rustc_pass_by_value]
 pub struct Region<'tcx>(pub Interned<'tcx, RegionKind<'tcx>>);
 
+impl<'tcx> IntoKind for Region<'tcx> {
+    type Kind = RegionKind<'tcx>;
+
+    fn kind(&self) -> RegionKind<'tcx> {
+        **self
+    }
+}
+
 impl<'tcx> Region<'tcx> {
     #[inline]
     pub fn new_early_param(
diff --git a/compiler/rustc_next_trait_solver/Cargo.toml b/compiler/rustc_next_trait_solver/Cargo.toml
new file mode 100644
index 00000000000..88c4b62c54c
--- /dev/null
+++ b/compiler/rustc_next_trait_solver/Cargo.toml
@@ -0,0 +1,7 @@
+[package]
+name = "rustc_next_trait_solver"
+version = "0.0.0"
+edition = "2021"
+
+[dependencies]
+rustc_type_ir = { path = "../rustc_type_ir" }
diff --git a/compiler/rustc_trait_selection/src/solve/canonicalize.rs b/compiler/rustc_next_trait_solver/src/canonicalizer.rs
similarity index 52%
rename from compiler/rustc_trait_selection/src/solve/canonicalize.rs
rename to compiler/rustc_next_trait_solver/src/canonicalizer.rs
index 469d1f5a9cb..c2e6e82f2af 100644
--- a/compiler/rustc_trait_selection/src/solve/canonicalize.rs
+++ b/compiler/rustc_next_trait_solver/src/canonicalizer.rs
@@ -1,17 +1,11 @@
 use std::cmp::Ordering;
 
-use crate::infer::InferCtxt;
-use rustc_middle::infer::canonical::Canonical;
-use rustc_middle::infer::canonical::CanonicalTyVarKind;
-use rustc_middle::infer::canonical::CanonicalVarInfo;
-use rustc_middle::infer::canonical::CanonicalVarInfos;
-use rustc_middle::infer::canonical::CanonicalVarKind;
-use rustc_middle::ty::BoundRegionKind::BrAnon;
-use rustc_middle::ty::BoundTyKind;
-use rustc_middle::ty::TyCtxt;
-use rustc_middle::ty::TypeVisitableExt;
-use rustc_middle::ty::{self, Ty};
-use rustc_middle::ty::{TypeFoldable, TypeFolder, TypeSuperFoldable};
+use rustc_type_ir::fold::{TypeFoldable, TypeFolder, TypeSuperFoldable};
+use rustc_type_ir::{
+    BoundVar, Canonical, CanonicalTyVarKind, CanonicalVarInfo, CanonicalVarKind, ConstKind,
+    ConstTy, DebruijnIndex, InferConst, InferCtxtLike, InferTy, Interner, IntoKind, Placeholder,
+    RegionKind, TyKind, UniverseIndex, INNERMOST,
+};
 
 /// Whether we're canonicalizing a query input or the query response.
 ///
@@ -38,46 +32,46 @@ pub enum CanonicalizeMode {
         ///
         /// This doesn't work for universes created inside of the query so
         /// we do remember their universe in the response.
-        max_input_universe: ty::UniverseIndex,
+        max_input_universe: UniverseIndex,
     },
 }
 
-pub struct Canonicalizer<'a, 'tcx> {
-    infcx: &'a InferCtxt<'tcx>,
+pub struct Canonicalizer<'a, Infcx: InferCtxtLike> {
+    infcx: &'a Infcx,
     canonicalize_mode: CanonicalizeMode,
 
-    variables: &'a mut Vec<ty::GenericArg<'tcx>>,
-    primitive_var_infos: Vec<CanonicalVarInfo<'tcx>>,
-    binder_index: ty::DebruijnIndex,
+    variables: &'a mut Vec<<Infcx::Interner as Interner>::GenericArg>,
+    primitive_var_infos: Vec<CanonicalVarInfo<Infcx::Interner>>,
+    binder_index: DebruijnIndex,
 }
 
-impl<'a, 'tcx> Canonicalizer<'a, 'tcx> {
-    #[instrument(level = "debug", skip(infcx), ret)]
-    pub fn canonicalize<T: TypeFoldable<TyCtxt<'tcx>>>(
-        infcx: &'a InferCtxt<'tcx>,
+impl<'a, Infcx: InferCtxtLike<Interner = I>, I: Interner> Canonicalizer<'a, Infcx> {
+    pub fn canonicalize<T: TypeFoldable<I>>(
+        infcx: &'a Infcx,
         canonicalize_mode: CanonicalizeMode,
-        variables: &'a mut Vec<ty::GenericArg<'tcx>>,
+        variables: &'a mut Vec<<I as Interner>::GenericArg>,
         value: T,
-    ) -> Canonical<'tcx, T> {
+    ) -> Canonical<I, T> {
         let mut canonicalizer = Canonicalizer {
             infcx,
             canonicalize_mode,
 
             variables,
             primitive_var_infos: Vec::new(),
-            binder_index: ty::INNERMOST,
+            binder_index: INNERMOST,
         };
 
         let value = value.fold_with(&mut canonicalizer);
-        assert!(!value.has_infer(), "unexpected infer in {value:?}");
-        assert!(!value.has_placeholders(), "unexpected placeholders in {value:?}");
+        // FIXME: Restore these assertions. Should we uplift type flags?
+        // assert!(!value.has_infer(), "unexpected infer in {value:?}");
+        // assert!(!value.has_placeholders(), "unexpected placeholders in {value:?}");
 
         let (max_universe, variables) = canonicalizer.finalize();
 
         Canonical { max_universe, variables, value }
     }
 
-    fn finalize(self) -> (ty::UniverseIndex, CanonicalVarInfos<'tcx>) {
+    fn finalize(self) -> (UniverseIndex, <I as Interner>::CanonicalVars) {
         let mut var_infos = self.primitive_var_infos;
         // See the rustc-dev-guide section about how we deal with universes
         // during canonicalization in the new solver.
@@ -94,18 +88,17 @@ impl<'a, 'tcx> Canonicalizer<'a, 'tcx> {
             CanonicalizeMode::Response { max_input_universe } => {
                 for var in var_infos.iter_mut() {
                     let uv = var.universe();
-                    let new_uv = ty::UniverseIndex::from(
-                        uv.index().saturating_sub(max_input_universe.index()),
-                    );
+                    let new_uv =
+                        UniverseIndex::from(uv.index().saturating_sub(max_input_universe.index()));
                     *var = var.with_updated_universe(new_uv);
                 }
                 let max_universe = var_infos
                     .iter()
                     .map(|info| info.universe())
                     .max()
-                    .unwrap_or(ty::UniverseIndex::ROOT);
+                    .unwrap_or(UniverseIndex::ROOT);
 
-                let var_infos = self.infcx.tcx.mk_canonical_var_infos(&var_infos);
+                let var_infos = self.infcx.interner().mk_canonical_var_infos(&var_infos);
                 return (max_universe, var_infos);
             }
         }
@@ -127,11 +120,11 @@ impl<'a, 'tcx> Canonicalizer<'a, 'tcx> {
         //
         // This algorithm runs in `O(n²)` where `n` is the number of different universe
         // indices in the input. This should be fine as `n` is expected to be small.
-        let mut curr_compressed_uv = ty::UniverseIndex::ROOT;
+        let mut curr_compressed_uv = UniverseIndex::ROOT;
         let mut existential_in_new_uv = false;
-        let mut next_orig_uv = Some(ty::UniverseIndex::ROOT);
+        let mut next_orig_uv = Some(UniverseIndex::ROOT);
         while let Some(orig_uv) = next_orig_uv.take() {
-            let mut update_uv = |var: &mut CanonicalVarInfo<'tcx>, orig_uv, is_existential| {
+            let mut update_uv = |var: &mut CanonicalVarInfo<I>, orig_uv, is_existential| {
                 let uv = var.universe();
                 match uv.cmp(&orig_uv) {
                     Ordering::Less => (), // Already updated
@@ -183,23 +176,25 @@ impl<'a, 'tcx> Canonicalizer<'a, 'tcx> {
         for var in var_infos.iter_mut() {
             if var.is_region() {
                 assert!(var.is_existential());
-                *var = var.with_updated_universe(curr_compressed_uv);
+                let compressed_var = var.with_updated_universe(curr_compressed_uv);
+                *var = compressed_var;
             }
         }
 
-        let var_infos = self.infcx.tcx.mk_canonical_var_infos(&var_infos);
+        let var_infos = self.infcx.interner().mk_canonical_var_infos(&var_infos);
         (curr_compressed_uv, var_infos)
     }
 }
 
-impl<'tcx> TypeFolder<TyCtxt<'tcx>> for Canonicalizer<'_, 'tcx> {
-    fn interner(&self) -> TyCtxt<'tcx> {
-        self.infcx.tcx
+impl<Infcx: InferCtxtLike<Interner = I>, I: Interner> TypeFolder<I> for Canonicalizer<'_, Infcx> {
+    fn interner(&self) -> I {
+        self.infcx.interner()
     }
 
-    fn fold_binder<T>(&mut self, t: ty::Binder<'tcx, T>) -> ty::Binder<'tcx, T>
+    fn fold_binder<T>(&mut self, t: I::Binder<T>) -> I::Binder<T>
     where
-        T: TypeFoldable<TyCtxt<'tcx>>,
+        T: TypeFoldable<I>,
+        I::Binder<T>: TypeSuperFoldable<I>,
     {
         self.binder_index.shift_in(1);
         let t = t.super_fold_with(self);
@@ -207,22 +202,9 @@ impl<'tcx> TypeFolder<TyCtxt<'tcx>> for Canonicalizer<'_, 'tcx> {
         t
     }
 
-    fn fold_region(&mut self, r: ty::Region<'tcx>) -> ty::Region<'tcx> {
-        if let ty::ReVar(vid) = *r {
-            let resolved_region = self
-                .infcx
-                .inner
-                .borrow_mut()
-                .unwrap_region_constraints()
-                .opportunistic_resolve_var(self.infcx.tcx, vid);
-            assert_eq!(
-                r, resolved_region,
-                "region var should have been resolved, {r} -> {resolved_region}"
-            );
-        }
-
-        let kind = match *r {
-            ty::ReBound(..) => return r,
+    fn fold_region(&mut self, r: I::Region) -> I::Region {
+        let kind = match r.kind() {
+            RegionKind::ReBound(..) => return r,
 
             // We may encounter `ReStatic` in item signatures or the hidden type
             // of an opaque. `ReErased` should only be encountered in the hidden
@@ -232,197 +214,212 @@ impl<'tcx> TypeFolder<TyCtxt<'tcx>> for Canonicalizer<'_, 'tcx> {
             // FIXME: We should investigate the perf implications of not uniquifying
             // `ReErased`. We may be able to short-circuit registering region
             // obligations if we encounter a `ReErased` on one side, for example.
-            ty::ReStatic | ty::ReErased => match self.canonicalize_mode {
-                CanonicalizeMode::Input => CanonicalVarKind::Region(ty::UniverseIndex::ROOT),
+            RegionKind::ReStatic | RegionKind::ReErased => match self.canonicalize_mode {
+                CanonicalizeMode::Input => CanonicalVarKind::Region(UniverseIndex::ROOT),
                 CanonicalizeMode::Response { .. } => return r,
             },
 
-            ty::ReLateParam(_) | ty::ReEarlyParam(_) => match self.canonicalize_mode {
-                CanonicalizeMode::Input => CanonicalVarKind::Region(ty::UniverseIndex::ROOT),
-                CanonicalizeMode::Response { .. } => bug!("unexpected region in response: {r:?}"),
-            },
+            RegionKind::ReEarlyParam(_) | RegionKind::ReLateParam(_) => {
+                match self.canonicalize_mode {
+                    CanonicalizeMode::Input => CanonicalVarKind::Region(UniverseIndex::ROOT),
+                    CanonicalizeMode::Response { .. } => {
+                        panic!("unexpected region in response: {r:?}")
+                    }
+                }
+            }
 
-            ty::RePlaceholder(placeholder) => match self.canonicalize_mode {
+            RegionKind::RePlaceholder(placeholder) => match self.canonicalize_mode {
                 // We canonicalize placeholder regions as existentials in query inputs.
-                CanonicalizeMode::Input => CanonicalVarKind::Region(ty::UniverseIndex::ROOT),
+                CanonicalizeMode::Input => CanonicalVarKind::Region(UniverseIndex::ROOT),
                 CanonicalizeMode::Response { max_input_universe } => {
                     // If we have a placeholder region inside of a query, it must be from
                     // a new universe.
-                    if max_input_universe.can_name(placeholder.universe) {
-                        bug!("new placeholder in universe {max_input_universe:?}: {r:?}");
+                    if max_input_universe.can_name(placeholder.universe()) {
+                        panic!("new placeholder in universe {max_input_universe:?}: {r:?}");
                     }
                     CanonicalVarKind::PlaceholderRegion(placeholder)
                 }
             },
 
-            ty::ReVar(_) => match self.canonicalize_mode {
-                CanonicalizeMode::Input => CanonicalVarKind::Region(ty::UniverseIndex::ROOT),
-                CanonicalizeMode::Response { .. } => {
-                    CanonicalVarKind::Region(self.infcx.universe_of_region(r))
-                }
-            },
+            RegionKind::ReVar(vid) => {
+                assert_eq!(
+                    self.infcx.root_lt_var(vid.clone()),
+                    vid,
+                    "region vid should have been resolved fully before canonicalization"
+                );
+                assert_eq!(
+                    self.infcx.probe_lt_var(vid.clone()),
+                    None,
+                    "region vid should have been resolved fully before canonicalization"
+                );
 
-            ty::ReError(_) => return r,
+                match self.canonicalize_mode {
+                    CanonicalizeMode::Input => CanonicalVarKind::Region(UniverseIndex::ROOT),
+                    CanonicalizeMode::Response { .. } => {
+                        CanonicalVarKind::Region(self.infcx.universe_of_lt(vid).unwrap())
+                    }
+                }
+            }
+            RegionKind::ReError(_) => return r,
         };
 
         let existing_bound_var = match self.canonicalize_mode {
             CanonicalizeMode::Input => None,
             CanonicalizeMode::Response { .. } => {
-                self.variables.iter().position(|&v| v == r.into()).map(ty::BoundVar::from)
+                let r = r.clone().into();
+                self.variables.iter().position(|v| v == &r).map(BoundVar::from)
             }
         };
+
         let var = existing_bound_var.unwrap_or_else(|| {
-            let var = ty::BoundVar::from(self.variables.len());
+            let var = BoundVar::from(self.variables.len());
             self.variables.push(r.into());
             self.primitive_var_infos.push(CanonicalVarInfo { kind });
             var
         });
-        let br = ty::BoundRegion { var, kind: BrAnon };
-        ty::Region::new_bound(self.interner(), self.binder_index, br)
+
+        self.interner().mk_bound_region(self.binder_index, var)
     }
 
-    fn fold_ty(&mut self, t: Ty<'tcx>) -> Ty<'tcx> {
-        let kind = match *t.kind() {
-            ty::Infer(ty::TyVar(vid)) => {
-                assert_eq!(self.infcx.root_var(vid), vid, "ty vid should have been resolved");
-                let Err(ui) = self.infcx.probe_ty_var(vid) else {
-                    bug!("ty var should have been resolved: {t}");
-                };
-                CanonicalVarKind::Ty(CanonicalTyVarKind::General(ui))
-            }
-            ty::Infer(ty::IntVar(vid)) => {
-                assert_eq!(self.infcx.opportunistic_resolve_int_var(vid), t);
-                CanonicalVarKind::Ty(CanonicalTyVarKind::Int)
-            }
-            ty::Infer(ty::FloatVar(vid)) => {
-                assert_eq!(self.infcx.opportunistic_resolve_float_var(vid), t);
-                CanonicalVarKind::Ty(CanonicalTyVarKind::Float)
-            }
-            ty::Infer(ty::FreshTy(_) | ty::FreshIntTy(_) | ty::FreshFloatTy(_)) => {
-                bug!("fresh var during canonicalization: {t:?}")
-            }
-            ty::Placeholder(placeholder) => match self.canonicalize_mode {
-                CanonicalizeMode::Input => CanonicalVarKind::PlaceholderTy(ty::Placeholder {
-                    universe: placeholder.universe,
-                    bound: ty::BoundTy {
-                        var: ty::BoundVar::from_usize(self.variables.len()),
-                        kind: ty::BoundTyKind::Anon,
-                    },
-                }),
+    fn fold_ty(&mut self, t: I::Ty) -> I::Ty
+    where
+        I::Ty: TypeSuperFoldable<I>,
+    {
+        let kind = match t.kind() {
+            TyKind::Infer(i) => match i {
+                InferTy::TyVar(vid) => {
+                    assert_eq!(
+                        self.infcx.root_ty_var(vid),
+                        vid,
+                        "ty vid should have been resolved fully before canonicalization"
+                    );
+                    assert_eq!(
+                        self.infcx.probe_ty_var(vid),
+                        None,
+                        "ty vid should have been resolved fully before canonicalization"
+                    );
+
+                    CanonicalVarKind::Ty(CanonicalTyVarKind::General(
+                        self.infcx
+                            .universe_of_ty(vid)
+                            .unwrap_or_else(|| panic!("ty var should have been resolved: {t:?}")),
+                    ))
+                }
+                InferTy::IntVar(_) => CanonicalVarKind::Ty(CanonicalTyVarKind::Int),
+                InferTy::FloatVar(_) => CanonicalVarKind::Ty(CanonicalTyVarKind::Float),
+                InferTy::FreshTy(_) | InferTy::FreshIntTy(_) | InferTy::FreshFloatTy(_) => {
+                    todo!()
+                }
+            },
+            TyKind::Placeholder(placeholder) => match self.canonicalize_mode {
+                CanonicalizeMode::Input => CanonicalVarKind::PlaceholderTy(Placeholder::new(
+                    placeholder.universe(),
+                    self.variables.len().into(),
+                )),
                 CanonicalizeMode::Response { .. } => CanonicalVarKind::PlaceholderTy(placeholder),
             },
-            ty::Param(_) => match self.canonicalize_mode {
-                CanonicalizeMode::Input => CanonicalVarKind::PlaceholderTy(ty::Placeholder {
-                    universe: ty::UniverseIndex::ROOT,
-                    bound: ty::BoundTy {
-                        var: ty::BoundVar::from_usize(self.variables.len()),
-                        kind: ty::BoundTyKind::Anon,
-                    },
-                }),
-                CanonicalizeMode::Response { .. } => bug!("param ty in response: {t:?}"),
+            TyKind::Param(_) => match self.canonicalize_mode {
+                CanonicalizeMode::Input => CanonicalVarKind::PlaceholderTy(Placeholder::new(
+                    UniverseIndex::ROOT,
+                    self.variables.len().into(),
+                )),
+                CanonicalizeMode::Response { .. } => panic!("param ty in response: {t:?}"),
             },
-            ty::Bool
-            | ty::Char
-            | ty::Int(_)
-            | ty::Uint(_)
-            | ty::Float(_)
-            | ty::Adt(_, _)
-            | ty::Foreign(_)
-            | ty::Str
-            | ty::Array(_, _)
-            | ty::Slice(_)
-            | ty::RawPtr(_)
-            | ty::Ref(_, _, _)
-            | ty::FnDef(_, _)
-            | ty::FnPtr(_)
-            | ty::Dynamic(_, _, _)
-            | ty::Closure(_, _)
-            | ty::Coroutine(_, _, _)
-            | ty::CoroutineWitness(..)
-            | ty::Never
-            | ty::Tuple(_)
-            | ty::Alias(_, _)
-            | ty::Bound(_, _)
-            | ty::Error(_) => return t.super_fold_with(self),
+            TyKind::Bool
+            | TyKind::Char
+            | TyKind::Int(_)
+            | TyKind::Uint(_)
+            | TyKind::Float(_)
+            | TyKind::Adt(_, _)
+            | TyKind::Foreign(_)
+            | TyKind::Str
+            | TyKind::Array(_, _)
+            | TyKind::Slice(_)
+            | TyKind::RawPtr(_)
+            | TyKind::Ref(_, _, _)
+            | TyKind::FnDef(_, _)
+            | TyKind::FnPtr(_)
+            | TyKind::Dynamic(_, _, _)
+            | TyKind::Closure(_, _)
+            | TyKind::Coroutine(_, _, _)
+            | TyKind::CoroutineWitness(..)
+            | TyKind::Never
+            | TyKind::Tuple(_)
+            | TyKind::Alias(_, _)
+            | TyKind::Bound(_, _)
+            | TyKind::Error(_) => return t.super_fold_with(self),
         };
 
-        let var = ty::BoundVar::from(
-            self.variables.iter().position(|&v| v == t.into()).unwrap_or_else(|| {
+        let t = t.clone().into();
+        let var =
+            BoundVar::from(self.variables.iter().position(|v| v == &t).unwrap_or_else(|| {
                 let var = self.variables.len();
-                self.variables.push(t.into());
+                self.variables.push(t);
                 self.primitive_var_infos.push(CanonicalVarInfo { kind });
                 var
-            }),
-        );
-        let bt = ty::BoundTy { var, kind: BoundTyKind::Anon };
-        Ty::new_bound(self.infcx.tcx, self.binder_index, bt)
+            }));
+
+        self.interner().mk_bound_ty(self.binder_index, var)
     }
 
-    fn fold_const(&mut self, c: ty::Const<'tcx>) -> ty::Const<'tcx> {
+    fn fold_const(&mut self, c: I::Const) -> I::Const
+    where
+        I::Const: TypeSuperFoldable<I>,
+    {
         let kind = match c.kind() {
-            ty::ConstKind::Infer(ty::InferConst::Var(vid)) => {
-                assert_eq!(
-                    self.infcx.root_const_var(vid),
-                    vid,
-                    "const var should have been resolved"
-                );
-                let Err(ui) = self.infcx.probe_const_var(vid) else {
-                    bug!("const var should have been resolved");
-                };
-                // FIXME: we should fold this ty eventually
-                CanonicalVarKind::Const(ui, c.ty())
+            ConstKind::Infer(i) => {
+                // FIXME: we should fold the ty too eventually
+                match i {
+                    InferConst::Var(vid) => {
+                        assert_eq!(
+                            self.infcx.root_ct_var(vid),
+                            vid,
+                            "region vid should have been resolved fully before canonicalization"
+                        );
+                        assert_eq!(
+                            self.infcx.probe_ct_var(vid),
+                            None,
+                            "region vid should have been resolved fully before canonicalization"
+                        );
+                        CanonicalVarKind::Const(self.infcx.universe_of_ct(vid).unwrap(), c.ty())
+                    }
+                    InferConst::EffectVar(_) => CanonicalVarKind::Effect,
+                    InferConst::Fresh(_) => todo!(),
+                }
             }
-            ty::ConstKind::Infer(ty::InferConst::EffectVar(vid)) => {
-                assert_eq!(
-                    self.infcx.root_effect_var(vid),
-                    vid,
-                    "effect var should have been resolved"
-                );
-                let None = self.infcx.probe_effect_var(vid) else {
-                    bug!("effect var should have been resolved");
-                };
-                CanonicalVarKind::Effect
-            }
-            ty::ConstKind::Infer(ty::InferConst::Fresh(_)) => {
-                bug!("fresh var during canonicalization: {c:?}")
-            }
-            ty::ConstKind::Placeholder(placeholder) => match self.canonicalize_mode {
+            ConstKind::Placeholder(placeholder) => match self.canonicalize_mode {
                 CanonicalizeMode::Input => CanonicalVarKind::PlaceholderConst(
-                    ty::Placeholder {
-                        universe: placeholder.universe,
-                        bound: ty::BoundVar::from(self.variables.len()),
-                    },
+                    Placeholder::new(placeholder.universe(), self.variables.len().into()),
                     c.ty(),
                 ),
                 CanonicalizeMode::Response { .. } => {
                     CanonicalVarKind::PlaceholderConst(placeholder, c.ty())
                 }
             },
-            ty::ConstKind::Param(_) => match self.canonicalize_mode {
+            ConstKind::Param(_) => match self.canonicalize_mode {
                 CanonicalizeMode::Input => CanonicalVarKind::PlaceholderConst(
-                    ty::Placeholder {
-                        universe: ty::UniverseIndex::ROOT,
-                        bound: ty::BoundVar::from(self.variables.len()),
-                    },
+                    Placeholder::new(UniverseIndex::ROOT, self.variables.len().into()),
                     c.ty(),
                 ),
-                CanonicalizeMode::Response { .. } => bug!("param ty in response: {c:?}"),
+                CanonicalizeMode::Response { .. } => panic!("param ty in response: {c:?}"),
             },
-            ty::ConstKind::Bound(_, _)
-            | ty::ConstKind::Unevaluated(_)
-            | ty::ConstKind::Value(_)
-            | ty::ConstKind::Error(_)
-            | ty::ConstKind::Expr(_) => return c.super_fold_with(self),
+            ConstKind::Bound(_, _)
+            | ConstKind::Unevaluated(_)
+            | ConstKind::Value(_)
+            | ConstKind::Error(_)
+            | ConstKind::Expr(_) => return c.super_fold_with(self),
         };
 
-        let var = ty::BoundVar::from(
-            self.variables.iter().position(|&v| v == c.into()).unwrap_or_else(|| {
+        let ty = c.ty();
+        let c = c.clone().into();
+        let var =
+            BoundVar::from(self.variables.iter().position(|v| v == &c).unwrap_or_else(|| {
                 let var = self.variables.len();
-                self.variables.push(c.into());
+                self.variables.push(c);
                 self.primitive_var_infos.push(CanonicalVarInfo { kind });
                 var
-            }),
-        );
-        ty::Const::new_bound(self.infcx.tcx, self.binder_index, var, c.ty())
+            }));
+
+        self.interner().mk_bound_const(self.binder_index, var, ty)
     }
 }
diff --git a/compiler/rustc_next_trait_solver/src/lib.rs b/compiler/rustc_next_trait_solver/src/lib.rs
new file mode 100644
index 00000000000..e5fc8f755e0
--- /dev/null
+++ b/compiler/rustc_next_trait_solver/src/lib.rs
@@ -0,0 +1 @@
+pub mod canonicalizer;
diff --git a/compiler/rustc_trait_selection/Cargo.toml b/compiler/rustc_trait_selection/Cargo.toml
index 7d098180b93..29c0d8b5ff1 100644
--- a/compiler/rustc_trait_selection/Cargo.toml
+++ b/compiler/rustc_trait_selection/Cargo.toml
@@ -15,6 +15,7 @@ rustc_index = { path = "../rustc_index" }
 rustc_infer = { path = "../rustc_infer" }
 rustc_macros = { path = "../rustc_macros" }
 rustc_middle = { path = "../rustc_middle" }
+rustc_next_trait_solver = { path = "../rustc_next_trait_solver" }
 rustc_parse_format = { path = "../rustc_parse_format" }
 rustc_query_system = { path = "../rustc_query_system" }
 rustc_session = { path = "../rustc_session" }
diff --git a/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs b/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
index da2f16e9760..7457ba837f5 100644
--- a/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
+++ b/compiler/rustc_trait_selection/src/solve/eval_ctxt/canonical.rs
@@ -9,7 +9,6 @@
 //!
 //! [c]: https://rustc-dev-guide.rust-lang.org/solve/canonicalization.html
 use super::{CanonicalInput, Certainty, EvalCtxt, Goal};
-use crate::solve::canonicalize::{CanonicalizeMode, Canonicalizer};
 use crate::solve::{
     inspect, response_no_constraints_raw, CanonicalResponse, QueryResult, Response,
 };
@@ -27,6 +26,7 @@ use rustc_middle::traits::solve::{
 };
 use rustc_middle::traits::ObligationCause;
 use rustc_middle::ty::{self, BoundVar, GenericArgKind, Ty, TyCtxt, TypeFoldable};
+use rustc_next_trait_solver::canonicalizer::{CanonicalizeMode, Canonicalizer};
 use rustc_span::DUMMY_SP;
 use std::iter;
 use std::ops::Deref;
diff --git a/compiler/rustc_trait_selection/src/solve/mod.rs b/compiler/rustc_trait_selection/src/solve/mod.rs
index cf3f94e26e4..0ab099ef0c8 100644
--- a/compiler/rustc_trait_selection/src/solve/mod.rs
+++ b/compiler/rustc_trait_selection/src/solve/mod.rs
@@ -30,7 +30,6 @@ use rustc_middle::ty::{
 
 mod alias_relate;
 mod assembly;
-mod canonicalize;
 mod eval_ctxt;
 mod fulfill;
 pub mod inspect;
diff --git a/compiler/rustc_type_ir/src/canonical.rs b/compiler/rustc_type_ir/src/canonical.rs
index d2768703297..514658046b7 100644
--- a/compiler/rustc_type_ir/src/canonical.rs
+++ b/compiler/rustc_type_ir/src/canonical.rs
@@ -162,7 +162,7 @@ impl<I: Interner> CanonicalVarInfo<I> {
     }
 
     #[must_use]
-    pub fn with_updated_universe(self, ui: UniverseIndex) -> CanonicalVarInfo<I> {
+    pub fn with_updated_universe(&self, ui: UniverseIndex) -> CanonicalVarInfo<I> {
         CanonicalVarInfo { kind: self.kind.with_updated_universe(ui) }
     }
 
@@ -324,13 +324,13 @@ impl<I: Interner> CanonicalVarKind<I> {
     ///
     /// In case this is a float or int variable, this causes an ICE if
     /// the updated universe is not the root.
-    pub fn with_updated_universe(self, ui: UniverseIndex) -> CanonicalVarKind<I> {
+    pub fn with_updated_universe(&self, ui: UniverseIndex) -> CanonicalVarKind<I> {
         match self {
             CanonicalVarKind::Ty(CanonicalTyVarKind::General(_)) => {
                 CanonicalVarKind::Ty(CanonicalTyVarKind::General(ui))
             }
             CanonicalVarKind::Region(_) => CanonicalVarKind::Region(ui),
-            CanonicalVarKind::Const(_, ty) => CanonicalVarKind::Const(ui, ty),
+            CanonicalVarKind::Const(_, ty) => CanonicalVarKind::Const(ui, ty.clone()),
 
             CanonicalVarKind::PlaceholderTy(placeholder) => {
                 CanonicalVarKind::PlaceholderTy(placeholder.with_updated_universe(ui))
@@ -339,12 +339,15 @@ impl<I: Interner> CanonicalVarKind<I> {
                 CanonicalVarKind::PlaceholderRegion(placeholder.with_updated_universe(ui))
             }
             CanonicalVarKind::PlaceholderConst(placeholder, ty) => {
-                CanonicalVarKind::PlaceholderConst(placeholder.with_updated_universe(ui), ty)
+                CanonicalVarKind::PlaceholderConst(
+                    placeholder.with_updated_universe(ui),
+                    ty.clone(),
+                )
             }
             CanonicalVarKind::Ty(CanonicalTyVarKind::Int | CanonicalTyVarKind::Float)
             | CanonicalVarKind::Effect => {
                 assert_eq!(ui, UniverseIndex::ROOT);
-                self
+                self.clone()
             }
         }
     }
diff --git a/compiler/rustc_type_ir/src/const_kind.rs b/compiler/rustc_type_ir/src/const_kind.rs
index 409033a2d8d..fb5b2a4437f 100644
--- a/compiler/rustc_type_ir/src/const_kind.rs
+++ b/compiler/rustc_type_ir/src/const_kind.rs
@@ -146,15 +146,15 @@ impl<I: Interner> DebugWithInfcx<I> for InferConst {
         this: WithInfcx<'_, Infcx, &Self>,
         f: &mut core::fmt::Formatter<'_>,
     ) -> core::fmt::Result {
-        match this.infcx.universe_of_ct(*this.data) {
-            None => write!(f, "{:?}", this.data),
-            Some(universe) => match *this.data {
-                InferConst::Var(vid) => write!(f, "?{}_{}c", vid.index(), universe.index()),
-                InferConst::EffectVar(vid) => write!(f, "?{}_{}e", vid.index(), universe.index()),
-                InferConst::Fresh(_) => {
-                    unreachable!()
-                }
+        match *this.data {
+            InferConst::Var(vid) => match this.infcx.universe_of_ct(vid) {
+                None => write!(f, "{:?}", this.data),
+                Some(universe) => write!(f, "?{}_{}c", vid.index(), universe.index()),
             },
+            InferConst::EffectVar(vid) => write!(f, "?{}e", vid.index()),
+            InferConst::Fresh(_) => {
+                unreachable!()
+            }
         }
     }
 }
diff --git a/compiler/rustc_type_ir/src/debug.rs b/compiler/rustc_type_ir/src/debug.rs
index db29ec9da8c..1732d311cb4 100644
--- a/compiler/rustc_type_ir/src/debug.rs
+++ b/compiler/rustc_type_ir/src/debug.rs
@@ -1,37 +1,58 @@
-use crate::{InferConst, InferTy, Interner, UniverseIndex};
+use crate::{ConstVid, InferCtxtLike, Interner, TyVid, UniverseIndex};
 
 use core::fmt;
 use std::marker::PhantomData;
 
-pub trait InferCtxtLike {
-    type Interner: Interner;
-
-    fn universe_of_ty(&self, ty: InferTy) -> Option<UniverseIndex>;
-
-    fn universe_of_lt(
-        &self,
-        lt: <Self::Interner as Interner>::InferRegion,
-    ) -> Option<UniverseIndex>;
-
-    fn universe_of_ct(&self, ct: InferConst) -> Option<UniverseIndex>;
-}
-
 pub struct NoInfcx<I>(PhantomData<I>);
 
 impl<I: Interner> InferCtxtLike for NoInfcx<I> {
     type Interner = I;
 
-    fn universe_of_ty(&self, _ty: InferTy) -> Option<UniverseIndex> {
-        None
+    fn interner(&self) -> Self::Interner {
+        unreachable!()
     }
 
-    fn universe_of_ct(&self, _ct: InferConst) -> Option<UniverseIndex> {
+    fn universe_of_ty(&self, _ty: TyVid) -> Option<UniverseIndex> {
         None
     }
 
     fn universe_of_lt(&self, _lt: <I as Interner>::InferRegion) -> Option<UniverseIndex> {
         None
     }
+
+    fn universe_of_ct(&self, _ct: ConstVid) -> Option<UniverseIndex> {
+        None
+    }
+
+    fn root_ty_var(&self, vid: TyVid) -> TyVid {
+        vid
+    }
+
+    fn probe_ty_var(&self, _vid: TyVid) -> Option<<Self::Interner as Interner>::Ty> {
+        None
+    }
+
+    fn root_lt_var(
+        &self,
+        vid: <Self::Interner as Interner>::InferRegion,
+    ) -> <Self::Interner as Interner>::InferRegion {
+        vid
+    }
+
+    fn probe_lt_var(
+        &self,
+        _vid: <Self::Interner as Interner>::InferRegion,
+    ) -> Option<<Self::Interner as Interner>::Region> {
+        None
+    }
+
+    fn root_ct_var(&self, vid: ConstVid) -> ConstVid {
+        vid
+    }
+
+    fn probe_ct_var(&self, _vid: ConstVid) -> Option<<Self::Interner as Interner>::Const> {
+        None
+    }
 }
 
 pub trait DebugWithInfcx<I: Interner>: fmt::Debug {
diff --git a/compiler/rustc_type_ir/src/infcx.rs b/compiler/rustc_type_ir/src/infcx.rs
new file mode 100644
index 00000000000..681f129a50b
--- /dev/null
+++ b/compiler/rustc_type_ir/src/infcx.rs
@@ -0,0 +1,40 @@
+use crate::{ConstVid, Interner, TyVid, UniverseIndex};
+
+pub trait InferCtxtLike {
+    type Interner: Interner;
+
+    fn interner(&self) -> Self::Interner;
+
+    fn universe_of_ty(&self, ty: TyVid) -> Option<UniverseIndex>;
+
+    /// Resolve `TyVid` to its root `TyVid`.
+    fn root_ty_var(&self, vid: TyVid) -> TyVid;
+
+    /// Resolve `TyVid` to its inferred type, if it has been equated with a non-infer type.
+    fn probe_ty_var(&self, vid: TyVid) -> Option<<Self::Interner as Interner>::Ty>;
+
+    fn universe_of_lt(
+        &self,
+        lt: <Self::Interner as Interner>::InferRegion,
+    ) -> Option<UniverseIndex>;
+
+    /// Resolve `InferRegion` to its root `InferRegion`.
+    fn root_lt_var(
+        &self,
+        vid: <Self::Interner as Interner>::InferRegion,
+    ) -> <Self::Interner as Interner>::InferRegion;
+
+    /// Resolve `InferRegion` to its inferred region, if it has been equated with a non-infer region.
+    fn probe_lt_var(
+        &self,
+        vid: <Self::Interner as Interner>::InferRegion,
+    ) -> Option<<Self::Interner as Interner>::Region>;
+
+    fn universe_of_ct(&self, ct: ConstVid) -> Option<UniverseIndex>;
+
+    /// Resolve `ConstVid` to its root `ConstVid`.
+    fn root_ct_var(&self, vid: ConstVid) -> ConstVid;
+
+    /// Resolve `ConstVid` to its inferred type, if it has been equated with a non-infer type.
+    fn probe_ct_var(&self, vid: ConstVid) -> Option<<Self::Interner as Interner>::Const>;
+}
diff --git a/compiler/rustc_type_ir/src/interner.rs b/compiler/rustc_type_ir/src/interner.rs
index 300b0bf090d..0acd576050f 100644
--- a/compiler/rustc_type_ir/src/interner.rs
+++ b/compiler/rustc_type_ir/src/interner.rs
@@ -2,8 +2,12 @@ use smallvec::SmallVec;
 use std::fmt::Debug;
 use std::hash::Hash;
 
-use crate::{BoundVar, DebugWithInfcx, Mutability, UniverseIndex};
+use crate::{
+    BoundVar, CanonicalVarInfo, ConstKind, DebruijnIndex, DebugWithInfcx, Mutability, RegionKind,
+    TyKind, UniverseIndex,
+};
 
+#[allow(rustc::usage_of_ty_tykind)]
 pub trait Interner: Sized {
     type DefId: Clone + Debug + Hash + Ord;
     type AdtDef: Clone + Debug + Hash + Ord;
@@ -18,10 +22,15 @@ pub trait Interner: Sized {
 
     type Binder<T>;
     type TypeAndMut: Clone + Debug + Hash + Ord;
-    type CanonicalVars: Clone + Debug + Hash + Eq;
+    type CanonicalVars: Clone + Debug + Hash + Eq + IntoIterator<Item = CanonicalVarInfo<Self>>;
 
     // Kinds of tys
-    type Ty: Clone + DebugWithInfcx<Self> + Hash + Ord;
+    type Ty: Clone
+        + DebugWithInfcx<Self>
+        + Hash
+        + Ord
+        + Into<Self::GenericArg>
+        + IntoKind<Kind = TyKind<Self>>;
     type Tys: Clone + Debug + Hash + Ord + IntoIterator<Item = Self::Ty>;
     type AliasTy: Clone + DebugWithInfcx<Self> + Hash + Ord;
     type ParamTy: Clone + Debug + Hash + Ord;
@@ -35,7 +44,13 @@ pub trait Interner: Sized {
     type AllocId: Clone + Debug + Hash + Ord;
 
     // Kinds of consts
-    type Const: Clone + DebugWithInfcx<Self> + Hash + Ord;
+    type Const: Clone
+        + DebugWithInfcx<Self>
+        + Hash
+        + Ord
+        + Into<Self::GenericArg>
+        + IntoKind<Kind = ConstKind<Self>>
+        + ConstTy<Self>;
     type AliasConst: Clone + DebugWithInfcx<Self> + Hash + Ord;
     type PlaceholderConst: Clone + Debug + Hash + Ord + Placeholder;
     type ParamConst: Clone + Debug + Hash + Ord;
@@ -44,10 +59,15 @@ pub trait Interner: Sized {
     type ExprConst: Clone + DebugWithInfcx<Self> + Hash + Ord;
 
     // Kinds of regions
-    type Region: Clone + DebugWithInfcx<Self> + Hash + Ord;
+    type Region: Clone
+        + DebugWithInfcx<Self>
+        + Hash
+        + Ord
+        + Into<Self::GenericArg>
+        + IntoKind<Kind = RegionKind<Self>>;
     type EarlyParamRegion: Clone + Debug + Hash + Ord;
-    type BoundRegion: Clone + Debug + Hash + Ord;
     type LateParamRegion: Clone + Debug + Hash + Ord;
+    type BoundRegion: Clone + Debug + Hash + Ord;
     type InferRegion: Clone + DebugWithInfcx<Self> + Hash + Ord;
     type PlaceholderRegion: Clone + Debug + Hash + Ord + Placeholder;
 
@@ -63,6 +83,12 @@ pub trait Interner: Sized {
     type ClosureKind: Clone + Debug + Hash + Eq;
 
     fn ty_and_mut_to_parts(ty_and_mut: Self::TypeAndMut) -> (Self::Ty, Mutability);
+
+    fn mk_canonical_var_infos(&self, infos: &[CanonicalVarInfo<Self>]) -> Self::CanonicalVars;
+
+    fn mk_bound_ty(&self, debruijn: DebruijnIndex, var: BoundVar) -> Self::Ty;
+    fn mk_bound_region(&self, debruijn: DebruijnIndex, var: BoundVar) -> Self::Region;
+    fn mk_bound_const(&self, debruijn: DebruijnIndex, var: BoundVar, ty: Self::Ty) -> Self::Const;
 }
 
 /// Common capabilities of placeholder kinds
@@ -70,7 +96,19 @@ pub trait Placeholder {
     fn universe(&self) -> UniverseIndex;
     fn var(&self) -> BoundVar;
 
-    fn with_updated_universe(self, ui: UniverseIndex) -> Self;
+    fn with_updated_universe(&self, ui: UniverseIndex) -> Self;
+
+    fn new(ui: UniverseIndex, var: BoundVar) -> Self;
+}
+
+pub trait IntoKind {
+    type Kind;
+
+    fn kind(&self) -> Self::Kind;
+}
+
+pub trait ConstTy<I: Interner> {
+    fn ty(&self) -> I::Ty;
 }
 
 /// Imagine you have a function `F: FnOnce(&[T]) -> R`, plus an iterator `iter`
diff --git a/compiler/rustc_type_ir/src/lib.rs b/compiler/rustc_type_ir/src/lib.rs
index 2aeb4230bb8..1bcb1fcff35 100644
--- a/compiler/rustc_type_ir/src/lib.rs
+++ b/compiler/rustc_type_ir/src/lib.rs
@@ -35,6 +35,7 @@ mod canonical;
 mod const_kind;
 mod debug;
 mod flags;
+mod infcx;
 mod interner;
 mod predicate_kind;
 mod region_kind;
@@ -43,8 +44,9 @@ pub use canonical::*;
 #[cfg(feature = "nightly")]
 pub use codec::*;
 pub use const_kind::*;
-pub use debug::{DebugWithInfcx, InferCtxtLike, WithInfcx};
+pub use debug::{DebugWithInfcx, WithInfcx};
 pub use flags::*;
+pub use infcx::InferCtxtLike;
 pub use interner::*;
 pub use predicate_kind::*;
 pub use region_kind::*;
@@ -337,6 +339,12 @@ impl UniverseIndex {
     }
 }
 
+impl Default for UniverseIndex {
+    fn default() -> Self {
+        Self::ROOT
+    }
+}
+
 rustc_index::newtype_index! {
     #[cfg_attr(feature = "nightly", derive(HashStable_NoContext))]
     #[encodable]
diff --git a/compiler/rustc_type_ir/src/ty_kind.rs b/compiler/rustc_type_ir/src/ty_kind.rs
index 3d4e7f77a4f..9d3a578c3e4 100644
--- a/compiler/rustc_type_ir/src/ty_kind.rs
+++ b/compiler/rustc_type_ir/src/ty_kind.rs
@@ -820,15 +820,15 @@ impl<I: Interner> DebugWithInfcx<I> for InferTy {
         this: WithInfcx<'_, Infcx, &Self>,
         f: &mut fmt::Formatter<'_>,
     ) -> fmt::Result {
-        use InferTy::*;
-        match this.infcx.universe_of_ty(*this.data) {
-            None => write!(f, "{:?}", this.data),
-            Some(universe) => match *this.data {
-                TyVar(ty_vid) => write!(f, "?{}_{}t", ty_vid.index(), universe.index()),
-                IntVar(_) | FloatVar(_) | FreshTy(_) | FreshIntTy(_) | FreshFloatTy(_) => {
-                    unreachable!()
+        match this.data {
+            InferTy::TyVar(vid) => {
+                if let Some(universe) = this.infcx.universe_of_ty(*vid) {
+                    write!(f, "?{}_{}t", vid.index(), universe.index())
+                } else {
+                    write!(f, "{:?}", this.data)
                 }
-            },
+            }
+            _ => write!(f, "{:?}", this.data),
         }
     }
 }