diff --git a/libcxx/include/__algorithm/equal_range.h b/libcxx/include/__algorithm/equal_range.h
--- a/libcxx/include/__algorithm/equal_range.h
+++ b/libcxx/include/__algorithm/equal_range.h
@@ -55,7 +55,7 @@
             _ForwardIterator __mp1 = __m;
             return pair<_ForwardIterator, _ForwardIterator>
                    (
-                      _VSTD::__lower_bound_impl<_StdIterOps>(__first, __m, __value, __comp, __proj),
+                      _VSTD::__lower_bound_impl<_STLClassicAlgorithms>(__first, __m, __value, __comp, __proj),
                       _VSTD::__upper_bound<_Compare>(++__mp1, __last, __value, __comp)
                    );
         }
diff --git a/libcxx/include/__algorithm/iterator_operations.h b/libcxx/include/__algorithm/iterator_operations.h
--- a/libcxx/include/__algorithm/iterator_operations.h
+++ b/libcxx/include/__algorithm/iterator_operations.h
@@ -6,13 +6,19 @@
 //
 //===----------------------------------------------------------------------===//
 
-#ifndef _LIBCPP___ALGORIHTM_ITERATOR_OPERATIONS_H
-#define _LIBCPP___ALGORIHTM_ITERATOR_OPERATIONS_H
+#ifndef _LIBCPP___ALGORITHM_ITERATOR_OPERATIONS_H
+#define _LIBCPP___ALGORITHM_ITERATOR_OPERATIONS_H
 
+#include <__algorithm/iter_swap.h>
 #include <__config>
 #include <__iterator/advance.h>
 #include <__iterator/distance.h>
+#include <__iterator/iter_move.h>
+#include <__iterator/iter_swap.h>
 #include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
@@ -20,28 +26,63 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
+template <class _Tag> struct _IterOps;
+
 #if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
-struct _RangesIterOps {
+struct _RangesAlgorithms {};
+
+template <>
+struct _IterOps<_RangesAlgorithms> {
   static constexpr auto advance = ranges::advance;
   static constexpr auto distance = ranges::distance;
+  static constexpr auto __iter_move = ranges::iter_move;
+  static constexpr auto iter_swap = ranges::iter_swap;
+  static constexpr auto next = ranges::next;
 };
 #endif
 
-struct _StdIterOps {
+struct _STLClassicAlgorithms {};
 
-  template <class _Iterator, class _Distance>
-  _LIBCPP_HIDE_FROM_ABI static _LIBCPP_CONSTEXPR_AFTER_CXX11 void advance(_Iterator& __iter, _Distance __count) {
-    return std::advance(__iter, __count);
+template <>
+struct _IterOps<_STLClassicAlgorithms> {
+
+  // advance
+  template <class _Iter, class _Distance>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+  static void advance(_Iter& __iter, _Distance __count) {
+    std::advance(__iter, __count);
   }
 
-  template <class _Iterator>
-  _LIBCPP_HIDE_FROM_ABI static _LIBCPP_CONSTEXPR_AFTER_CXX11
-  typename iterator_traits<_Iterator>::difference_type distance(_Iterator __first, _Iterator __last) {
+  // distance
+  template <class _Iter>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+  static typename iterator_traits<_Iter>::difference_type distance(_Iter __first, _Iter __last) {
     return std::distance(__first, __last);
   }
 
+  // iter_move
+  template <class _Iter>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+  // Declaring the return type is necessary for the C++03 mode (which doesn't support placeholder return types).
+  static typename iterator_traits<typename remove_reference<_Iter>::type>::value_type&& __iter_move(_Iter&& __i) {
+    return std::move(*std::forward<_Iter>(__i));
+  }
+
+  // iter_swap
+  template <class _Iter1, class _Iter2>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+  static void iter_swap(_Iter1&& __a, _Iter2&& __b) {
+    std::iter_swap(std::forward<_Iter1>(__a), std::forward<_Iter2>(__b));
+  }
+
+  // next
+  template <class _Iter>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+  static _Iter next(const _Iter&, const _Iter& __last) {
+    return __last;
+  }
 };
 
 _LIBCPP_END_NAMESPACE_STD
 
-#endif // _LIBCPP___ALGORIHTM_ITERATOR_OPERATIONS_H
+#endif // _LIBCPP___ALGORITHM_ITERATOR_OPERATIONS_H
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
@@ -27,15 +27,15 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template <class _IterOps, class _Iter, class _Sent, class _Type, class _Proj, class _Comp>
+template <class _AlgFamily, class _Iter, class _Sent, class _Type, class _Proj, class _Comp>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
 _Iter __lower_bound_impl(_Iter __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {
-  auto __len = _IterOps::distance(__first, __last);
+  auto __len = _IterOps<_AlgFamily>::distance(__first, __last);
 
   while (__len != 0) {
     auto __l2 = std::__half_positive(__len);
     _Iter __m = __first;
-    _IterOps::advance(__m, __l2);
+    _IterOps<_AlgFamily>::advance(__m, __l2);
     if (std::__invoke(__comp, std::__invoke(__proj, *__m), __value)) {
       __first = ++__m;
       __len -= __l2 + 1;
@@ -48,17 +48,17 @@
 
 template <class _ForwardIterator, class _Tp, class _Compare>
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
-_ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value, _Compare __comp) {
+_ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value_, _Compare __comp) {
   static_assert(__is_callable<_Compare, decltype(*__first), const _Tp&>::value,
                 "The comparator has to be callable");
   auto __proj = std::__identity();
-  return std::__lower_bound_impl<_StdIterOps>(__first, __last, __value, __comp, __proj);
+  return std::__lower_bound_impl<_STLClassicAlgorithms>(__first, __last, __value_, __comp, __proj);
 }
 
 template <class _ForwardIterator, class _Tp>
 _LIBCPP_NODISCARD_EXT inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
-_ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) {
-  return std::lower_bound(__first, __last, __value,
+_ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value_) {
+  return std::lower_bound(__first, __last, __value_,
                           __less<typename iterator_traits<_ForwardIterator>::value_type, _Tp>());
 }
 
diff --git a/libcxx/include/__algorithm/ranges_binary_search.h b/libcxx/include/__algorithm/ranges_binary_search.h
--- a/libcxx/include/__algorithm/ranges_binary_search.h
+++ b/libcxx/include/__algorithm/ranges_binary_search.h
@@ -35,7 +35,7 @@
             indirect_strict_weak_order<const _Type*, projected<_Iter, _Proj>> _Comp = ranges::less>
   _LIBCPP_HIDE_FROM_ABI constexpr
   bool operator()(_Iter __first, _Sent __last, const _Type& __value, _Comp __comp = {}, _Proj __proj = {}) const {
-    auto __ret = std::__lower_bound_impl<_RangesIterOps>(__first, __last, __value, __comp, __proj);
+    auto __ret = std::__lower_bound_impl<_RangesAlgorithms>(__first, __last, __value, __comp, __proj);
     return __ret != __last && !std::invoke(__comp, __value, std::invoke(__proj, *__first));
   }
 
@@ -45,7 +45,7 @@
   bool operator()(_Range&& __r, const _Type& __value, _Comp __comp = {}, _Proj __proj = {}) const {
     auto __first = ranges::begin(__r);
     auto __last = ranges::end(__r);
-    auto __ret = std::__lower_bound_impl<_RangesIterOps>(__first, __last, __value, __comp, __proj);
+    auto __ret = std::__lower_bound_impl<_RangesAlgorithms>(__first, __last, __value, __comp, __proj);
     return __ret != __last && !std::invoke(__comp, __value, std::invoke(__proj, *__first));
   }
 };
diff --git a/libcxx/include/__algorithm/ranges_lower_bound.h b/libcxx/include/__algorithm/ranges_lower_bound.h
--- a/libcxx/include/__algorithm/ranges_lower_bound.h
+++ b/libcxx/include/__algorithm/ranges_lower_bound.h
@@ -39,7 +39,7 @@
             indirect_strict_weak_order<const _Type*, projected<_Iter, _Proj>> _Comp = ranges::less>
   _LIBCPP_HIDE_FROM_ABI constexpr
   _Iter operator()(_Iter __first, _Sent __last, const _Type& __value, _Comp __comp = {}, _Proj __proj = {}) const {
-    return std::__lower_bound_impl<_RangesIterOps>(__first, __last, __value, __comp, __proj);
+    return std::__lower_bound_impl<_RangesAlgorithms>(__first, __last, __value, __comp, __proj);
   }
 
   template <forward_range _Range, class _Type, class _Proj = identity,
@@ -49,7 +49,7 @@
                                          const _Type& __value,
                                          _Comp __comp = {},
                                          _Proj __proj = {}) const {
-    return std::__lower_bound_impl<_RangesIterOps>(ranges::begin(__r), ranges::end(__r), __value, __comp, __proj);
+    return std::__lower_bound_impl<_RangesAlgorithms>(ranges::begin(__r), ranges::end(__r), __value, __comp, __proj);
   }
 };
 } // namespace __lower_bound
diff --git a/libcxx/include/__algorithm/ranges_upper_bound.h b/libcxx/include/__algorithm/ranges_upper_bound.h
--- a/libcxx/include/__algorithm/ranges_upper_bound.h
+++ b/libcxx/include/__algorithm/ranges_upper_bound.h
@@ -40,7 +40,7 @@
       return !std::invoke(__comp, __rhs, __lhs);
     };
 
-    return std::__lower_bound_impl<_RangesIterOps>(__first, __last, __value, __comp_lhs_rhs_swapped, __proj);
+    return std::__lower_bound_impl<_RangesAlgorithms>(__first, __last, __value, __comp_lhs_rhs_swapped, __proj);
   }
 
   template <forward_range _Range, class _Type, class _Proj = identity,
@@ -54,7 +54,7 @@
       return !std::invoke(__comp, __rhs, __lhs);
     };
 
-    return std::__lower_bound_impl<_RangesIterOps>(ranges::begin(__r),
+    return std::__lower_bound_impl<_RangesAlgorithms>(ranges::begin(__r),
                                                    ranges::end(__r),
                                                    __value,
                                                    __comp_lhs_rhs_swapped,