diff --git a/src/librustc/dep_graph/dep_node.rs b/src/librustc/dep_graph/dep_node.rs
index b32fa2cda80129e2d59a2646e63af51eaea1476f..61d63f4623249c21886ee2e7e260c7c079168aee 100644
--- a/src/librustc/dep_graph/dep_node.rs
+++ b/src/librustc/dep_graph/dep_node.rs
@@ -59,7 +59,7 @@
     CanonicalTypeOpAscribeUserTypeGoal, CanonicalTypeOpEqGoal, CanonicalTypeOpNormalizeGoal,
     CanonicalTypeOpProvePredicateGoal, CanonicalTypeOpSubtypeGoal,
 };
-use crate::ty::subst::SubstsRef;
+use crate::ty::subst::{GenericArg, SubstsRef};
 use crate::ty::{self, ParamEnvAnd, Ty, TyCtxt};
 
 use rustc_data_structures::stable_hasher::{HashStable, StableHasher};
diff --git a/src/librustc/query/mod.rs b/src/librustc/query/mod.rs
index 54f5103f736ec07875cb2174d5176415dbf0e1e8..86855cb0ef0c2c3e27be088b9b695c267b479c38 100644
--- a/src/librustc/query/mod.rs
+++ b/src/librustc/query/mod.rs
@@ -9,7 +9,7 @@
 };
 use crate::ty::query::queries;
 use crate::ty::query::QueryDescription;
-use crate::ty::subst::SubstsRef;
+use crate::ty::subst::{GenericArg, SubstsRef};
 use crate::ty::{self, ParamEnvAnd, Ty, TyCtxt};
 use rustc_hir::def_id::{CrateNum, DefId, LocalDefId};
 
@@ -1114,9 +1114,9 @@ fn describe_as_module(def_id: DefId, tcx: TyCtxt<'_>) -> String {
         }
 
         /// Do not call this query directly: invoke `normalize_erasing_regions` instead.
-        query normalize_ty_after_erasing_regions(
-            goal: ParamEnvAnd<'tcx, Ty<'tcx>>
-        ) -> Ty<'tcx> {
+        query normalize_generic_arg_after_erasing_regions(
+            goal: ParamEnvAnd<'tcx, GenericArg<'tcx>>
+        ) -> GenericArg<'tcx> {
             desc { "normalizing `{:?}`", goal }
         }
 
diff --git a/src/librustc/ty/normalize_erasing_regions.rs b/src/librustc/ty/normalize_erasing_regions.rs
index cbaabd8e1f1373a2c4ae788a2ad36703ece93239..e49bf6f8e67dcbe069c97d97a86a7e405ebe8f03 100644
--- a/src/librustc/ty/normalize_erasing_regions.rs
+++ b/src/librustc/ty/normalize_erasing_regions.rs
@@ -4,8 +4,8 @@
 //!
 //! The methods in this file use a `TypeFolder` to recursively process
 //! contents, invoking the underlying
-//! `normalize_ty_after_erasing_regions` query for each type found
-//! within. (This underlying query is what is cached.)
+//! `normalize_generic_arg_after_erasing_regions` query for each type
+//! or constant found within. (This underlying query is what is cached.)
 
 use crate::ty::fold::{TypeFoldable, TypeFolder};
 use crate::ty::subst::{Subst, SubstsRef};
@@ -94,6 +94,14 @@ fn tcx(&self) -> TyCtxt<'tcx> {
     }
 
     fn fold_ty(&mut self, ty: Ty<'tcx>) -> Ty<'tcx> {
-        self.tcx.normalize_ty_after_erasing_regions(self.param_env.and(ty))
+        self.tcx
+            .normalize_generic_arg_after_erasing_regions(self.param_env.and(ty.into()))
+            .expect_ty()
+    }
+
+    fn fold_const(&mut self, c: &'tcx ty::Const<'tcx>) -> &'tcx ty::Const<'tcx> {
+        self.tcx
+            .normalize_generic_arg_after_erasing_regions(self.param_env.and(c.into()))
+            .expect_const()
     }
 }
diff --git a/src/librustc/ty/query/keys.rs b/src/librustc/ty/query/keys.rs
index 6073d3a545f6db9c7b6dbb12186e188518037a06..6be1f04efca2b5366a58cfc3de30e51447cebae0 100644
--- a/src/librustc/ty/query/keys.rs
+++ b/src/librustc/ty/query/keys.rs
@@ -5,7 +5,7 @@
 use crate::traits;
 use crate::ty::fast_reject::SimplifiedType;
 use crate::ty::query::caches::DefaultCacheSelector;
-use crate::ty::subst::SubstsRef;
+use crate::ty::subst::{GenericArg, SubstsRef};
 use crate::ty::{self, Ty, TyCtxt};
 use rustc_hir::def_id::{CrateNum, DefId, LocalDefId, LOCAL_CRATE};
 use rustc_span::symbol::Symbol;
@@ -194,6 +194,17 @@ fn default_span(&self, tcx: TyCtxt<'_>) -> Span {
     }
 }
 
+impl<'tcx> Key for GenericArg<'tcx> {
+    type CacheSelector = DefaultCacheSelector;
+
+    fn query_crate(&self) -> CrateNum {
+        LOCAL_CRATE
+    }
+    fn default_span(&self, _: TyCtxt<'_>) -> Span {
+        DUMMY_SP
+    }
+}
+
 impl<'tcx> Key for &'tcx ty::Const<'tcx> {
     type CacheSelector = DefaultCacheSelector;
 
diff --git a/src/librustc/ty/query/mod.rs b/src/librustc/ty/query/mod.rs
index 32ba13b1dbe9a5cfe2740383518400befde1ad28..1094eb49403463df6842377b5a05cb344423b173 100644
--- a/src/librustc/ty/query/mod.rs
+++ b/src/librustc/ty/query/mod.rs
@@ -31,7 +31,7 @@
 use crate::traits::Clauses;
 use crate::traits::{self, Vtable};
 use crate::ty::steal::Steal;
-use crate::ty::subst::SubstsRef;
+use crate::ty::subst::{GenericArg, SubstsRef};
 use crate::ty::util::AlwaysRequiresDrop;
 use crate::ty::{self, AdtSizedConstraint, CrateInherentImpls, ParamEnvAnd, Ty, TyCtxt};
 use crate::util::common::ErrorReported;
diff --git a/src/librustc/ty/subst.rs b/src/librustc/ty/subst.rs
index a3acc14856e1febbb4b168dfe7e0877d9d4690dc..0f4485a705046dff5d33017a6fd09b8edb99d338 100644
--- a/src/librustc/ty/subst.rs
+++ b/src/librustc/ty/subst.rs
@@ -128,6 +128,14 @@ pub fn expect_ty(self) -> Ty<'tcx> {
             _ => bug!("expected a type, but found another kind"),
         }
     }
+
+    /// Unpack the `GenericArg` as a const when it is known certainly to be a const.
+    pub fn expect_const(self) -> &'tcx ty::Const<'tcx> {
+        match self.unpack() {
+            GenericArgKind::Const(c) => c,
+            _ => bug!("expected a const, but found another kind"),
+        }
+    }
 }
 
 impl<'a, 'tcx> Lift<'tcx> for GenericArg<'a> {
diff --git a/src/librustc_session/session.rs b/src/librustc_session/session.rs
index 80f59aff69137a09d365b84d8dd8090cff769c1c..b3d75143c56392bf633d50f7cb2d0d3d44721579 100644
--- a/src/librustc_session/session.rs
+++ b/src/librustc_session/session.rs
@@ -150,7 +150,7 @@ pub struct PerfStats {
     /// Total number of values canonicalized queries constructed.
     pub queries_canonicalized: AtomicUsize,
     /// Number of times this query is invoked.
-    pub normalize_ty_after_erasing_regions: AtomicUsize,
+    pub normalize_generic_arg_after_erasing_regions: AtomicUsize,
     /// Number of times this query is invoked.
     pub normalize_projection_ty: AtomicUsize,
 }
@@ -707,8 +707,8 @@ pub fn print_perf_stats(&self) {
             self.perf_stats.queries_canonicalized.load(Ordering::Relaxed)
         );
         println!(
-            "normalize_ty_after_erasing_regions:            {}",
-            self.perf_stats.normalize_ty_after_erasing_regions.load(Ordering::Relaxed)
+            "normalize_generic_arg_after_erasing_regions:   {}",
+            self.perf_stats.normalize_generic_arg_after_erasing_regions.load(Ordering::Relaxed)
         );
         println!(
             "normalize_projection_ty:                       {}",
@@ -1080,7 +1080,7 @@ fn build_session_(
             symbol_hash_time: Lock::new(Duration::from_secs(0)),
             decode_def_path_tables_time: Lock::new(Duration::from_secs(0)),
             queries_canonicalized: AtomicUsize::new(0),
-            normalize_ty_after_erasing_regions: AtomicUsize::new(0),
+            normalize_generic_arg_after_erasing_regions: AtomicUsize::new(0),
             normalize_projection_ty: AtomicUsize::new(0),
         },
         code_stats: Default::default(),
diff --git a/src/librustc_traits/normalize_erasing_regions.rs b/src/librustc_traits/normalize_erasing_regions.rs
index c2fb237a05b5476783e59a5222aac5b728ceeadb..065cf38eb249075a3c9ac3b2407c6dbcc5d5aaa0 100644
--- a/src/librustc_traits/normalize_erasing_regions.rs
+++ b/src/librustc_traits/normalize_erasing_regions.rs
@@ -1,23 +1,24 @@
 use rustc::traits::query::NoSolution;
 use rustc::ty::query::Providers;
-use rustc::ty::{self, ParamEnvAnd, Ty, TyCtxt};
+use rustc::ty::subst::GenericArg;
+use rustc::ty::{self, ParamEnvAnd, TyCtxt};
 use rustc_infer::infer::TyCtxtInferExt;
 use rustc_trait_selection::traits::query::normalize::AtExt;
 use rustc_trait_selection::traits::{Normalized, ObligationCause};
 use std::sync::atomic::Ordering;
 
 crate fn provide(p: &mut Providers<'_>) {
-    *p = Providers { normalize_ty_after_erasing_regions, ..*p };
+    *p = Providers { normalize_generic_arg_after_erasing_regions, ..*p };
 }
 
-fn normalize_ty_after_erasing_regions<'tcx>(
+fn normalize_generic_arg_after_erasing_regions<'tcx>(
     tcx: TyCtxt<'tcx>,
-    goal: ParamEnvAnd<'tcx, Ty<'tcx>>,
-) -> Ty<'tcx> {
-    debug!("normalize_ty_after_erasing_regions(goal={:#?})", goal);
+    goal: ParamEnvAnd<'tcx, GenericArg<'tcx>>,
+) -> GenericArg<'tcx> {
+    debug!("normalize_generic_arg_after_erasing_regions(goal={:#?})", goal);
 
     let ParamEnvAnd { param_env, value } = goal;
-    tcx.sess.perf_stats.normalize_ty_after_erasing_regions.fetch_add(1, Ordering::Relaxed);
+    tcx.sess.perf_stats.normalize_generic_arg_after_erasing_regions.fetch_add(1, Ordering::Relaxed);
     tcx.infer_ctxt().enter(|infcx| {
         let cause = ObligationCause::dummy();
         match infcx.at(&cause, param_env).normalize(&value) {