diff --git a/libcxx/include/map b/libcxx/include/map
--- a/libcxx/include/map
+++ b/libcxx/include/map
@@ -904,8 +904,8 @@
     typedef _Key                                     key_type;
     typedef _Tp                                      mapped_type;
     typedef pair<const key_type, mapped_type>        value_type;
-    typedef typename __identity<_Compare>::type      key_compare;
-    typedef typename __identity<_Allocator>::type    allocator_type;
+    typedef __identity_t<_Compare>                   key_compare;
+    typedef __identity_t<_Allocator>                 allocator_type;
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
@@ -1674,8 +1674,8 @@
     typedef _Key                                     key_type;
     typedef _Tp                                      mapped_type;
     typedef pair<const key_type, mapped_type>        value_type;
-    typedef typename __identity<_Compare>::type      key_compare;
-    typedef typename __identity<_Allocator>::type    allocator_type;
+    typedef __identity_t<_Compare>                   key_compare;
+    typedef __identity_t<_Allocator>                 allocator_type;
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
diff --git a/libcxx/include/set b/libcxx/include/set
--- a/libcxx/include/set
+++ b/libcxx/include/set
@@ -450,7 +450,7 @@
     typedef key_type                                 value_type;
     typedef _Compare                                 key_compare;
     typedef key_compare                              value_compare;
-    typedef typename __identity<_Allocator>::type    allocator_type;
+    typedef __identity_t<_Allocator>                 allocator_type;
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
@@ -974,11 +974,11 @@
 {
 public:
     // types:
-    typedef _Key                                      key_type;
+    typedef _Key                                     key_type;
     typedef key_type                                 value_type;
-    typedef _Compare                                  key_compare;
+    typedef _Compare                                 key_compare;
     typedef key_compare                              value_compare;
-    typedef typename __identity<_Allocator>::type    allocator_type;
+    typedef __identity_t<_Allocator>                 allocator_type;
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
diff --git a/libcxx/include/type_traits b/libcxx/include/type_traits
--- a/libcxx/include/type_traits
+++ b/libcxx/include/type_traits
@@ -525,6 +525,9 @@
 template <class _Tp>
 struct __identity { typedef _Tp type; };
 
+template <class _Tp>
+using __identity_t _LIBCPP_NODEBUG_TYPE = typename __identity<_Tp>::type;
+
 template <class _Tp, bool>
 struct _LIBCPP_TEMPLATE_VIS __dependent_type : public _Tp {};
 
@@ -4022,8 +4025,8 @@
 
 template <class _MP, class _Tp>
 struct __result_of_mp<_MP, _Tp, true>
-    : public __identity<typename __member_pointer_traits<_MP>::_ReturnType>
 {
+    using type = typename __member_pointer_traits<_MP>::_ReturnType;
 };
 
 // member data pointer
@@ -4034,13 +4037,13 @@
 template <class _Rp, class _Class, class _Tp>
 struct __result_of_mdp<_Rp _Class::*, _Tp, false>
 {
-    typedef typename __apply_cv<decltype(*_VSTD::declval<_Tp>()), _Rp>::type& type;
+    using type = typename __apply_cv<decltype(*_VSTD::declval<_Tp>()), _Rp>::type&;
 };
 
 template <class _Rp, class _Class, class _Tp>
 struct __result_of_mdp<_Rp _Class::*, _Tp, true>
 {
-    typedef typename __apply_cv<_Tp, _Rp>::type& type;
+    using type = typename __apply_cv<_Tp, _Rp>::type&;
 };
 
 template <class _Rp, class _Class, class _Tp>
diff --git a/libcxx/include/unordered_map b/libcxx/include/unordered_map
--- a/libcxx/include/unordered_map
+++ b/libcxx/include/unordered_map
@@ -920,9 +920,9 @@
     // types
     typedef _Key                                           key_type;
     typedef _Tp                                            mapped_type;
-    typedef typename __identity<_Hash>::type               hasher;
-    typedef typename __identity<_Pred>::type               key_equal;
-    typedef typename __identity<_Alloc>::type              allocator_type;
+    typedef __identity_t<_Hash>                            hasher;
+    typedef __identity_t<_Pred>                            key_equal;
+    typedef __identity_t<_Alloc>                           allocator_type;
     typedef pair<const key_type, mapped_type>              value_type;
     typedef value_type&                                    reference;
     typedef const value_type&                              const_reference;
@@ -1857,9 +1857,9 @@
     // types
     typedef _Key                                           key_type;
     typedef _Tp                                            mapped_type;
-    typedef typename __identity<_Hash>::type               hasher;
-    typedef typename __identity<_Pred>::type               key_equal;
-    typedef typename __identity<_Alloc>::type              allocator_type;
+    typedef __identity_t<_Hash>                            hasher;
+    typedef __identity_t<_Pred>                            key_equal;
+    typedef __identity_t<_Alloc>                           allocator_type;
     typedef pair<const key_type, mapped_type>              value_type;
     typedef value_type&                                    reference;
     typedef const value_type&                              const_reference;
diff --git a/libcxx/include/unordered_set b/libcxx/include/unordered_set
--- a/libcxx/include/unordered_set
+++ b/libcxx/include/unordered_set
@@ -411,9 +411,9 @@
     // types
     typedef _Value                                                     key_type;
     typedef key_type                                                   value_type;
-    typedef typename __identity<_Hash>::type                           hasher;
-    typedef typename __identity<_Pred>::type                           key_equal;
-    typedef typename __identity<_Alloc>::type                          allocator_type;
+    typedef __identity_t<_Hash>                                        hasher;
+    typedef __identity_t<_Pred>                                        key_equal;
+    typedef __identity_t<_Alloc>                                       allocator_type;
     typedef value_type&                                                reference;
     typedef const value_type&                                          const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),
@@ -1109,9 +1109,9 @@
     // types
     typedef _Value                                                     key_type;
     typedef key_type                                                   value_type;
-    typedef typename __identity<_Hash>::type                           hasher;
-    typedef typename __identity<_Pred>::type                           key_equal;
-    typedef typename __identity<_Alloc>::type                          allocator_type;
+    typedef __identity_t<_Hash>                                        hasher;
+    typedef __identity_t<_Pred>                                        key_equal;
+    typedef __identity_t<_Alloc>                                       allocator_type;
     typedef value_type&                                                reference;
     typedef const value_type&                                          const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),