diff --git a/src/librustc_mir_build/hair/pattern/const_to_pat.rs b/src/librustc_mir_build/hair/pattern/const_to_pat.rs
index 28ec2ca13d5af..9e3f75fdc078c 100644
--- a/src/librustc_mir_build/hair/pattern/const_to_pat.rs
+++ b/src/librustc_mir_build/hair/pattern/const_to_pat.rs
@@ -124,8 +124,20 @@ impl<'a, 'tcx> ConstToPat<'a, 'tcx> {
                     traits::NonStructuralMatchTy::Dynamic => {
                         "trait objects cannot be used in patterns".to_string()
                     }
+                    traits::NonStructuralMatchTy::Opaque => {
+                        "opaque types cannot be used in patterns".to_string()
+                    }
+                    traits::NonStructuralMatchTy::Generator => {
+                        "generators cannot be used in patterns".to_string()
+                    }
                     traits::NonStructuralMatchTy::Param => {
-                        bug!("use of constant whose type is a parameter inside a pattern")
+                        bug!("use of a constant whose type is a parameter inside a pattern")
+                    }
+                    traits::NonStructuralMatchTy::Projection => {
+                        bug!("use of a constant whose type is a projection inside a pattern")
+                    }
+                    traits::NonStructuralMatchTy::Foreign => {
+                        bug!("use of a value of a foreign type inside a pattern")
                     }
                 };
 
diff --git a/src/librustc_trait_selection/traits/structural_match.rs b/src/librustc_trait_selection/traits/structural_match.rs
index eb63505b69b41..b877049fcf667 100644
--- a/src/librustc_trait_selection/traits/structural_match.rs
+++ b/src/librustc_trait_selection/traits/structural_match.rs
@@ -13,6 +13,10 @@ pub enum NonStructuralMatchTy<'tcx> {
     Adt(&'tcx AdtDef),
     Param,
     Dynamic,
+    Foreign,
+    Opaque,
+    Generator,
+    Projection,
 }
 
 /// This method traverses the structure of `ty`, trying to find an
@@ -143,6 +147,22 @@ impl<'a, 'tcx> TypeVisitor<'tcx> for Search<'a, 'tcx> {
                 self.found = Some(NonStructuralMatchTy::Dynamic);
                 return true; // Stop visiting.
             }
+            ty::Foreign(_) => {
+                self.found = Some(NonStructuralMatchTy::Foreign);
+                return true; // Stop visiting.
+            }
+            ty::Opaque(..) => {
+                self.found = Some(NonStructuralMatchTy::Opaque);
+                return true; // Stop visiting.
+            }
+            ty::Projection(..) => {
+                self.found = Some(NonStructuralMatchTy::Projection);
+                return true; // Stop visiting.
+            }
+            ty::Generator(..) | ty::GeneratorWitness(..) => {
+                self.found = Some(NonStructuralMatchTy::Generator);
+                return true; // Stop visiting.
+            }
             ty::RawPtr(..) => {
                 // structural-match ignores substructure of
                 // `*const _`/`*mut _`, so skip `super_visit_with`.
@@ -159,14 +179,14 @@ impl<'a, 'tcx> TypeVisitor<'tcx> for Search<'a, 'tcx> {
                 // structural equality on `T` does not recur into the raw
                 // pointer. Therefore, one can still use `C` in a pattern.
 
-                // (But still tell caller to continue search.)
+                // (But still tell the caller to continue search.)
                 return false;
             }
             ty::FnDef(..) | ty::FnPtr(..) => {
-                // types of formals and return in `fn(_) -> _` are also irrelevant;
+                // Types of formals and return in `fn(_) -> _` are also irrelevant;
                 // so we do not recur into them via `super_visit_with`
                 //
-                // (But still tell caller to continue search.)
+                // (But still tell the caller to continue search.)
                 return false;
             }
             ty::Array(_, n)
@@ -174,17 +194,40 @@ impl<'a, 'tcx> TypeVisitor<'tcx> for Search<'a, 'tcx> {
             {
                 // rust-lang/rust#62336: ignore type of contents
                 // for empty array.
+                //
+                // (But still tell the caller to continue search.)
                 return false;
             }
-            _ => {
+            ty::Bool | ty::Char | ty::Int(_) | ty::Uint(_) | ty::Float(_) | ty::Str | ty::Never => {
+                // These primitive types are always structural match.
+                //
+                // `Never` is kind of special here, but as it is not inhabitable, this should be fine.
+                //
+                // (But still tell the caller to continue search.)
+                return false;
+            }
+
+            ty::Array(..) | ty::Slice(_) | ty::Ref(..) | ty::Tuple(..) => {
+                // First check all contained types and then tell the caller to continue searching.
                 ty.super_visit_with(self);
                 return false;
             }
+            ty::Closure(..) | ty::Infer(_) | ty::Placeholder(_) | ty::Bound(..) => {
+                bug!("unexpected type during structural-match checking: {:?}", ty);
+            }
+            ty::Error => {
+                self.tcx().sess.delay_span_bug(self.span, "ty::Error in structural-match check");
+                // We still want to check other types after encountering an error,
+                // as this may still emit relevant errors.
+                //
+                // So we continue searching here.
+                return false;
+            }
         };
 
         if !self.seen.insert(adt_def.did) {
             debug!("Search already seen adt_def: {:?}", adt_def);
-            // let caller continue its search
+            // Let caller continue its search.
             return false;
         }
 
diff --git a/src/test/ui/type-alias-impl-trait/structural-match-no-leak.rs b/src/test/ui/type-alias-impl-trait/structural-match-no-leak.rs
new file mode 100644
index 0000000000000..479d6cd9af765
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/structural-match-no-leak.rs
@@ -0,0 +1,20 @@
+#![feature(const_fn, type_alias_impl_trait)]
+
+type Bar = impl Send;
+
+// While i32 is structural-match, we do not want to leak this information.
+// (See https://github.com/rust-lang/rust/issues/72156)
+const fn leak_free() -> Bar {
+    7i32
+}
+const LEAK_FREE: Bar = leak_free();
+
+fn leak_free_test() {
+    match todo!() {
+        LEAK_FREE => (),
+        //~^ opaque types cannot be used in patterns
+        _ => (),
+    }
+}
+
+fn main() { }
diff --git a/src/test/ui/type-alias-impl-trait/structural-match-no-leak.stderr b/src/test/ui/type-alias-impl-trait/structural-match-no-leak.stderr
new file mode 100644
index 0000000000000..ae0d8e8d4239c
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/structural-match-no-leak.stderr
@@ -0,0 +1,8 @@
+error: opaque types cannot be used in patterns
+  --> $DIR/structural-match-no-leak.rs:14:9
+   |
+LL |         LEAK_FREE => (),
+   |         ^^^^^^^^^
+
+error: aborting due to previous error
+
diff --git a/src/test/ui/type-alias-impl-trait/structural-match.rs b/src/test/ui/type-alias-impl-trait/structural-match.rs
new file mode 100644
index 0000000000000..481448d64b1aa
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/structural-match.rs
@@ -0,0 +1,21 @@
+#![feature(const_fn, type_alias_impl_trait)]
+
+type Foo = impl Send;
+
+// This is not structural-match
+struct A;
+
+const fn value() -> Foo {
+    A
+}
+const VALUE: Foo = value();
+
+fn test() {
+    match todo!() {
+        VALUE => (),
+        //~^ opaque types cannot be used in patterns
+        _ => (),
+    }
+}
+
+fn main() { }
diff --git a/src/test/ui/type-alias-impl-trait/structural-match.stderr b/src/test/ui/type-alias-impl-trait/structural-match.stderr
new file mode 100644
index 0000000000000..ad9036a87d1d9
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/structural-match.stderr
@@ -0,0 +1,8 @@
+error: opaque types cannot be used in patterns
+  --> $DIR/structural-match.rs:15:9
+   |
+LL |         VALUE => (),
+   |         ^^^^^
+
+error: aborting due to previous error
+