diff --git a/include/type_traits b/include/type_traits
index 345903e3..1c7b096a 100644
--- a/include/type_traits
+++ b/include/type_traits
@@ -709,6 +709,14 @@ template <class _T1, class _T2> struct _LIBCPP_VISIBLE is_convertible
 
 // is_base_of
 
+#ifdef __clang__
+
+template <class _Bp, class _Dp>
+struct _LIBCPP_VISIBLE is_base_of
+    : public integral_constant<bool, __is_base_of(_Bp, _Dp)> {};
+
+#else  // __clang__
+
 //  (C) Copyright Rani Sharoni 2003.
 //  Use, modification and distribution are subject to the Boost Software License,
 //  Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
@@ -755,6 +763,8 @@ struct _LIBCPP_VISIBLE is_base_of
 {
 };
 
+#endif  // __clang__
+
 // is_empty
 
 template <class _Tp>
diff --git a/test/utilities/meta/meta.rel/is_base_of.pass.cpp b/test/utilities/meta/meta.rel/is_base_of.pass.cpp
index 1fad33f0..0f90ae5c 100644
--- a/test/utilities/meta/meta.rel/is_base_of.pass.cpp
+++ b/test/utilities/meta/meta.rel/is_base_of.pass.cpp
@@ -46,5 +46,4 @@ int main()
     test_is_not_base_of<B&, D&>();
     test_is_not_base_of<B[3], D[3]>();
     test_is_not_base_of<int, int>();
-    test_is_not_base_of<int, int>();
 }
diff --git a/test/utilities/meta/meta.rel/is_convertible.pass.cpp b/test/utilities/meta/meta.rel/is_convertible.pass.cpp
index 8d056689..e0728543 100644
--- a/test/utilities/meta/meta.rel/is_convertible.pass.cpp
+++ b/test/utilities/meta/meta.rel/is_convertible.pass.cpp
@@ -70,8 +70,7 @@ int main()
 
     static_assert((!std::is_convertible<Function, Function>::value), "");
 
-    static_assert((!std::is_convertible<Function, Function&>::value), "");
-    static_assert((!std::is_convertible<Function, Function&>::value), "");
+    static_assert(( std::is_convertible<Function, Function&>::value), "");
 
     static_assert(( std::is_convertible<Function, Function*>::value), "");
     static_assert(( std::is_convertible<Function, Function* const>::value), "");
@@ -98,7 +97,6 @@ int main()
     static_assert((!std::is_convertible<Function&, Function>::value), "");
 
     static_assert(( std::is_convertible<Function&, Function&>::value), "");
-    static_assert(( std::is_convertible<Function&, const Function&>::value), "");
 
     static_assert(( std::is_convertible<Function&, Function*>::value), "");
     static_assert(( std::is_convertible<Function&, Function* const>::value), "");
@@ -185,7 +183,7 @@ int main()
     static_assert((!std::is_convertible<Array, Array&>::value), "");
     static_assert(( std::is_convertible<Array, const Array&>::value), "");
     static_assert((!std::is_convertible<const Array, Array&>::value), "");
-    static_assert((!std::is_convertible<const Array, const Array&>::value), "");
+    static_assert(( std::is_convertible<const Array, const Array&>::value), "");
 
     static_assert((!std::is_convertible<Array, char>::value), "");
     static_assert((!std::is_convertible<Array, const char>::value), "");