diff --git a/libcxx/include/__algorithm/comp_ref_type.h b/libcxx/include/__algorithm/comp_ref_type.h
--- a/libcxx/include/__algorithm/comp_ref_type.h
+++ b/libcxx/include/__algorithm/comp_ref_type.h
@@ -10,7 +10,6 @@
 #define _LIBCPP___ALGORITHM_COMP_REF_TYPE_H
 
 #include <__config>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -73,7 +72,7 @@
   // Pass the comparator by lvalue reference. Or in debug mode, using a
   // debugging wrapper that stores a reference.
 #ifndef _LIBCPP_DEBUG
-  typedef typename add_lvalue_reference<_Comp>::type type;
+  typedef _Comp& type;
 #else
   typedef __debug_less<_Comp> type;
 #endif
diff --git a/libcxx/include/__algorithm/equal.h b/libcxx/include/__algorithm/equal.h
--- a/libcxx/include/__algorithm/equal.h
+++ b/libcxx/include/__algorithm/equal.h
@@ -14,7 +14,6 @@
 #include <__algorithm/comp.h>
 #include <__iterator/distance.h>
 #include <__iterator/iterator_traits.h>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -61,14 +60,14 @@
   if (_VSTD::distance(__first1, __last1) != _VSTD::distance(__first2, __last2))
     return false;
   return _VSTD::equal<_RandomAccessIterator1, _RandomAccessIterator2,
-                      typename add_lvalue_reference<_BinaryPredicate>::type>(__first1, __last1, __first2, __pred);
+                      _BinaryPredicate&>(__first1, __last1, __first2, __pred);
 }
 
 template <class _InputIterator1, class _InputIterator2, class _BinaryPredicate>
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 bool
 equal(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _InputIterator2 __last2,
       _BinaryPredicate __pred) {
-  return _VSTD::__equal<typename add_lvalue_reference<_BinaryPredicate>::type>(
+  return _VSTD::__equal<_BinaryPredicate&>(
       __first1, __last1, __first2, __last2, __pred, typename iterator_traits<_InputIterator1>::iterator_category(),
       typename iterator_traits<_InputIterator2>::iterator_category());
 }
diff --git a/libcxx/include/__algorithm/find_end.h b/libcxx/include/__algorithm/find_end.h
--- a/libcxx/include/__algorithm/find_end.h
+++ b/libcxx/include/__algorithm/find_end.h
@@ -13,7 +13,6 @@
 #include <__config>
 #include <__algorithm/comp.h>
 #include <__iterator/iterator_traits.h>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -134,7 +133,7 @@
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 _ForwardIterator1
 find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1, _ForwardIterator2 __first2, _ForwardIterator2 __last2,
          _BinaryPredicate __pred) {
-  return _VSTD::__find_end<typename add_lvalue_reference<_BinaryPredicate>::type>(
+  return _VSTD::__find_end<_BinaryPredicate&>(
       __first1, __last1, __first2, __last2, __pred, typename iterator_traits<_ForwardIterator1>::iterator_category(),
       typename iterator_traits<_ForwardIterator2>::iterator_category());
 }
diff --git a/libcxx/include/__algorithm/is_permutation.h b/libcxx/include/__algorithm/is_permutation.h
--- a/libcxx/include/__algorithm/is_permutation.h
+++ b/libcxx/include/__algorithm/is_permutation.h
@@ -15,7 +15,6 @@
 #include <__iterator/distance.h>
 #include <__iterator/iterator_traits.h>
 #include <__iterator/next.h>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -137,15 +136,14 @@
   if (_VSTD::distance(__first1, __last1) != _VSTD::distance(__first2, __last2))
     return false;
   return _VSTD::is_permutation<_RandomAccessIterator1, _RandomAccessIterator2,
-                               typename add_lvalue_reference<_BinaryPredicate>::type>(__first1, __last1, __first2,
-                                                                                      __pred);
+                               _BinaryPredicate&>(__first1, __last1, __first2, __pred);
 }
 
 template <class _ForwardIterator1, class _ForwardIterator2, class _BinaryPredicate>
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 bool
 is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1, _ForwardIterator2 __first2,
                _ForwardIterator2 __last2, _BinaryPredicate __pred) {
-  return _VSTD::__is_permutation<typename add_lvalue_reference<_BinaryPredicate>::type>(
+  return _VSTD::__is_permutation<_BinaryPredicate&>(
       __first1, __last1, __first2, __last2, __pred, typename iterator_traits<_ForwardIterator1>::iterator_category(),
       typename iterator_traits<_ForwardIterator2>::iterator_category());
 }
diff --git a/libcxx/include/__algorithm/lower_bound.h b/libcxx/include/__algorithm/lower_bound.h
--- a/libcxx/include/__algorithm/lower_bound.h
+++ b/libcxx/include/__algorithm/lower_bound.h
@@ -51,8 +51,7 @@
 _ForwardIterator
 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value_, _Compare __comp)
 {
-    typedef typename add_lvalue_reference<_Compare>::type _Comp_ref;
-    return _VSTD::__lower_bound<_Comp_ref>(__first, __last, __value_, __comp);
+    return _VSTD::__lower_bound<_Compare&>(__first, __last, __value_, __comp);
 }
 
 template <class _ForwardIterator, class _Tp>
diff --git a/libcxx/include/__algorithm/partition.h b/libcxx/include/__algorithm/partition.h
--- a/libcxx/include/__algorithm/partition.h
+++ b/libcxx/include/__algorithm/partition.h
@@ -13,7 +13,6 @@
 #include <__iterator/iterator_traits.h>
 #include <__utility/swap.h>
 #include <utility> // pair
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -77,8 +76,8 @@
 _ForwardIterator
 partition(_ForwardIterator __first, _ForwardIterator __last, _Predicate __pred)
 {
-    return _VSTD::__partition<typename add_lvalue_reference<_Predicate>::type>
-                            (__first, __last, __pred, typename iterator_traits<_ForwardIterator>::iterator_category());
+    return _VSTD::__partition<_Predicate&>(
+        __first, __last, __pred, typename iterator_traits<_ForwardIterator>::iterator_category());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/remove_if.h b/libcxx/include/__algorithm/remove_if.h
--- a/libcxx/include/__algorithm/remove_if.h
+++ b/libcxx/include/__algorithm/remove_if.h
@@ -12,7 +12,6 @@
 #include <__config>
 #include <__algorithm/find_if.h>
 #include <utility>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -27,8 +26,7 @@
 _LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_AFTER_CXX17 _ForwardIterator
 remove_if(_ForwardIterator __first, _ForwardIterator __last, _Predicate __pred)
 {
-    __first = _VSTD::find_if<_ForwardIterator, typename add_lvalue_reference<_Predicate>::type>
-                           (__first, __last, __pred);
+    __first = _VSTD::find_if<_ForwardIterator, _Predicate&>(__first, __last, __pred);
     if (__first != __last)
     {
         _ForwardIterator __i = __first;
diff --git a/libcxx/include/__algorithm/search.h b/libcxx/include/__algorithm/search.h
--- a/libcxx/include/__algorithm/search.h
+++ b/libcxx/include/__algorithm/search.h
@@ -13,7 +13,6 @@
 #include <__algorithm/comp.h>
 #include <__config>
 #include <__iterator/iterator_traits.h>
-#include <type_traits>
 #include <utility>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
@@ -101,7 +100,7 @@
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 _ForwardIterator1
 search(_ForwardIterator1 __first1, _ForwardIterator1 __last1, _ForwardIterator2 __first2, _ForwardIterator2 __last2,
        _BinaryPredicate __pred) {
-  return _VSTD::__search<typename add_lvalue_reference<_BinaryPredicate>::type>(
+  return _VSTD::__search<_BinaryPredicate&>(
              __first1, __last1, __first2, __last2, __pred,
              typename iterator_traits<_ForwardIterator1>::iterator_category(),
              typename iterator_traits<_ForwardIterator2>::iterator_category()).first;
diff --git a/libcxx/include/__algorithm/search_n.h b/libcxx/include/__algorithm/search_n.h
--- a/libcxx/include/__algorithm/search_n.h
+++ b/libcxx/include/__algorithm/search_n.h
@@ -13,7 +13,7 @@
 #include <__config>
 #include <__algorithm/comp.h>
 #include <__iterator/iterator_traits.h>
-#include <type_traits>
+#include <type_traits>  // __convert_to_integral
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -97,7 +97,7 @@
 template <class _ForwardIterator, class _Size, class _Tp, class _BinaryPredicate>
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 _ForwardIterator search_n(
     _ForwardIterator __first, _ForwardIterator __last, _Size __count, const _Tp& __value_, _BinaryPredicate __pred) {
-  return _VSTD::__search_n<typename add_lvalue_reference<_BinaryPredicate>::type>(
+  return _VSTD::__search_n<_BinaryPredicate&>(
       __first, __last, _VSTD::__convert_to_integral(__count), __value_, __pred,
       typename iterator_traits<_ForwardIterator>::iterator_category());
 }
diff --git a/libcxx/include/__algorithm/sort.h b/libcxx/include/__algorithm/sort.h
--- a/libcxx/include/__algorithm/sort.h
+++ b/libcxx/include/__algorithm/sort.h
@@ -17,7 +17,6 @@
 #include <__algorithm/unwrap_iter.h>
 #include <__utility/swap.h>
 #include <memory>
-#include <type_traits> // swap
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -131,9 +130,7 @@
     _BidirectionalIterator __lm1 = __last;
     for (--__lm1; __first != __lm1; ++__first)
     {
-        _BidirectionalIterator __i = _VSTD::min_element<_BidirectionalIterator,
-                                                        typename add_lvalue_reference<_Compare>::type>
-                                                       (__first, __last, __comp);
+        _BidirectionalIterator __i = _VSTD::min_element<_BidirectionalIterator, _Compare&>(__first, __last, __comp);
         if (__i != __first)
             swap(*__first, *__i);
     }
diff --git a/libcxx/include/__algorithm/stable_partition.h b/libcxx/include/__algorithm/stable_partition.h
--- a/libcxx/include/__algorithm/stable_partition.h
+++ b/libcxx/include/__algorithm/stable_partition.h
@@ -85,8 +85,7 @@
     // recurse on [__first, __m), *__first know to be false
     // F?????????????????
     // f       m         l
-    typedef typename add_lvalue_reference<_Predicate>::type _PredRef;
-    _ForwardIterator __first_false = _VSTD::__stable_partition<_PredRef>(__first, __m, __pred, __len2, __p, __fit);
+    _ForwardIterator __first_false = _VSTD::__stable_partition<_Predicate&>(__first, __m, __pred, __len2, __p, __fit);
     // TTTFFFFF??????????
     // f  ff   m         l
     // recurse on [__m, __last], except increase __m until *(__m) is false, *__last know to be true
@@ -101,7 +100,7 @@
     }
     // TTTFFFFFTTTF??????
     // f  ff   m  m1     l
-    __second_false = _VSTD::__stable_partition<_PredRef>(__m1, __last, __pred, __len_half, __p, __fit);
+    __second_false = _VSTD::__stable_partition<_Predicate&>(__m1, __last, __pred, __len_half, __p, __fit);
 __second_half_done:
     // TTTFFFFFTTTTTFFFFF
     // f  ff   m    sf   l
@@ -137,8 +136,7 @@
         __p = _VSTD::get_temporary_buffer<value_type>(__len);
         __h.reset(__p.first);
     }
-    return _VSTD::__stable_partition<typename add_lvalue_reference<_Predicate>::type>
-                             (__first, __last, __pred, __len, __p, forward_iterator_tag());
+    return _VSTD::__stable_partition<_Predicate&>(__first, __last, __pred, __len, __p, forward_iterator_tag());
 }
 
 template <class _Predicate, class _BidirectionalIterator, class _Distance, class _Pair>
@@ -222,8 +220,7 @@
     }
     // F???TFFF?????????T
     // f   m1  m        l
-    typedef typename add_lvalue_reference<_Predicate>::type _PredRef;
-    __first_false = _VSTD::__stable_partition<_PredRef>(__first, __m1, __pred, __len_half, __p, __bit);
+    __first_false = _VSTD::__stable_partition<_Predicate&>(__first, __m1, __pred, __len_half, __p, __bit);
 __first_half_done:
     // TTTFFFFF?????????T
     // f  ff   m        l
@@ -240,7 +237,7 @@
     }
     // TTTFFFFFTTTF?????T
     // f  ff   m  m1    l
-    __second_false = _VSTD::__stable_partition<_PredRef>(__m1, __last, __pred, __len_half, __p, __bit);
+    __second_false = _VSTD::__stable_partition<_Predicate&>(__m1, __last, __pred, __len_half, __p, __bit);
 __second_half_done:
     // TTTFFFFFTTTTTFFFFF
     // f  ff   m    sf  l
@@ -285,8 +282,7 @@
         __p = _VSTD::get_temporary_buffer<value_type>(__len);
         __h.reset(__p.first);
     }
-    return _VSTD::__stable_partition<typename add_lvalue_reference<_Predicate>::type>
-                             (__first, __last, __pred, __len, __p, bidirectional_iterator_tag());
+    return _VSTD::__stable_partition<_Predicate&>(__first, __last, __pred, __len, __p, bidirectional_iterator_tag());
 }
 
 template <class _ForwardIterator, class _Predicate>
@@ -294,8 +290,7 @@
 _ForwardIterator
 stable_partition(_ForwardIterator __first, _ForwardIterator __last, _Predicate __pred)
 {
-    return _VSTD::__stable_partition<typename add_lvalue_reference<_Predicate>::type>
-                             (__first, __last, __pred, typename iterator_traits<_ForwardIterator>::iterator_category());
+    return _VSTD::__stable_partition<_Predicate&>(__first, __last, __pred, typename iterator_traits<_ForwardIterator>::iterator_category());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/unique.h b/libcxx/include/__algorithm/unique.h
--- a/libcxx/include/__algorithm/unique.h
+++ b/libcxx/include/__algorithm/unique.h
@@ -14,7 +14,6 @@
 #include <__algorithm/adjacent_find.h>
 #include <__iterator/iterator_traits.h>
 #include <__utility/move.h>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -31,8 +30,7 @@
 _LIBCPP_NODISCARD_EXT _LIBCPP_CONSTEXPR_AFTER_CXX17 _ForwardIterator
 unique(_ForwardIterator __first, _ForwardIterator __last, _BinaryPredicate __pred)
 {
-    __first = _VSTD::adjacent_find<_ForwardIterator, typename add_lvalue_reference<_BinaryPredicate>::type>
-                                 (__first, __last, __pred);
+    __first = _VSTD::adjacent_find<_ForwardIterator, _BinaryPredicate&>(__first, __last, __pred);
     if (__first != __last)
     {
         // ...  a  a  ?  ...
diff --git a/libcxx/include/__algorithm/unique_copy.h b/libcxx/include/__algorithm/unique_copy.h
--- a/libcxx/include/__algorithm/unique_copy.h
+++ b/libcxx/include/__algorithm/unique_copy.h
@@ -13,7 +13,6 @@
 #include <__algorithm/comp.h>
 #include <__iterator/iterator_traits.h>
 #include <utility>
-#include <type_traits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
@@ -91,8 +90,7 @@
 _OutputIterator
 unique_copy(_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryPredicate __pred)
 {
-    return _VSTD::__unique_copy<typename add_lvalue_reference<_BinaryPredicate>::type>
-                              (__first, __last, __result, __pred,
+    return _VSTD::__unique_copy<_BinaryPredicate&>(__first, __last, __result, __pred,
                                typename iterator_traits<_InputIterator>::iterator_category(),
                                typename iterator_traits<_OutputIterator>::iterator_category());
 }
diff --git a/libcxx/include/__algorithm/upper_bound.h b/libcxx/include/__algorithm/upper_bound.h
--- a/libcxx/include/__algorithm/upper_bound.h
+++ b/libcxx/include/__algorithm/upper_bound.h
@@ -51,8 +51,7 @@
 _ForwardIterator
 upper_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value_, _Compare __comp)
 {
-    typedef typename add_lvalue_reference<_Compare>::type _Comp_ref;
-    return _VSTD::__upper_bound<_Comp_ref>(__first, __last, __value_, __comp);
+    return _VSTD::__upper_bound<_Compare&>(__first, __last, __value_, __comp);
 }
 
 template <class _ForwardIterator, class _Tp>