diff --git a/include/boost/math/tools/type_traits.hpp b/include/boost/math/tools/type_traits.hpp
index 689815a5a..b10f386e9 100644
--- a/include/boost/math/tools/type_traits.hpp
+++ b/include/boost/math/tools/type_traits.hpp
@@ -19,26 +19,475 @@ namespace math {
 
 #include <cuda/std/type_traits>
 
+// Helper classes
+using cuda::std::integral_constant;
+using cuda::std::true_type;
+using cuda::std::false_type;
+
+// Primary type categories
 using cuda::std::is_void;
+using cuda::std::is_null_pointer;
 using cuda::std::is_integral;
+using cuda::std::is_floating_point;
+using cuda::std::is_array;
+using cuda::std::is_enum;
+using cuda::std::is_union;
+using cuda::std::is_class;
+using cuda::std::is_function;
+using cuda::std::is_pointer;
+using cuda::std::is_lvalue_reference;
+using cuda::std::is_rvalue_reference;
+using cuda::std::is_member_object_pointer;
+using cuda::std::is_member_function_pointer;
+
+// Composite Type Categories
+using cuda::std::is_fundamental;
+using cuda::std::is_arithmetic;
+using cuda::std::is_scalar;
+using cuda::std::is_object;
+using cuda::std::is_compound;
+using cuda::std::is_reference;
+using cuda::std::is_member_pointer;
+
+// Type properties
+using cuda::std::is_const;
+using cuda::std::is_volatile;
+using cuda::std::is_trivial;
+using cuda::std::is_trivially_copyable;
+using cuda::std::is_standard_layout;
+using cuda::std::is_empty;
+using cuda::std::is_polymorphic;
+using cuda::std::is_abstract;
+using cuda::std::is_final;
+using cuda::std::is_signed;
+using cuda::std::is_unsigned; 
+
+// Supported Operations
+using cuda::std::is_constructible;
+using cuda::std::is_trivially_constructible;
+using cuda::std::is_nothrow_constructible;
+
+using cuda::std::is_default_constructible;
+using cuda::std::is_trivially_default_constructible;
+using cuda::std::is_nothrow_default_constructible;
+
+using cuda::std::is_copy_constructible;
+using cuda::std::is_trivially_copy_constructible;
+using cuda::std::is_nothrow_copy_constructible;
+
+using cuda::std::is_move_constructible;
+using cuda::std::is_trivially_move_constructible;
+using cuda::std::is_nothrow_move_constructible;
+
+using cuda::std::is_assignable;
+using cuda::std::is_trivially_assignable;
+using cuda::std::is_nothrow_assignable;
+
+using cuda::std::is_copy_assignable;
+using cuda::std::is_trivially_copy_assignable;
+using cuda::std::is_nothrow_copy_assignable;
+
+using cuda::std::is_move_assignable;
+using cuda::std::is_trivially_move_assignable;
+using cuda::std::is_nothrow_move_assignable;
+
+using cuda::std::is_destructible;
+using cuda::std::is_trivially_destructible;
+using cuda::std::is_nothrow_destructible;
+
+using cuda::std::has_virtual_destructor;
+
+// Property Queries
+using cuda::std::alignment_of;
+using cuda::std::rank;
+using cuda::std::extent;
+
+// Type Relationships
+using cuda::std::is_same;
+using cuda::std::is_base_of;
+using cuda::std::is_convertible;
+
+// Const-volatility specifiers
+using cuda::std::remove_cv;
+using cuda::std::remove_cv_t;
+using cuda::std::remove_const;
+using cuda::std::remove_const_t;
+using cuda::std::remove_volatile;
+using cuda::std::remove_volatile_t;
+using cuda::std::add_cv;
+using cuda::std::add_cv_t;
+using cuda::std::add_const;
+using cuda::std::add_const_t;
+using cuda::std::add_volatile;
+using cuda::std::add_volatile_t;
+
+// References
+using cuda::std::remove_reference;
+using cuda::std::remove_reference_t;
+using cuda::std::add_lvalue_reference;
+using cuda::std::add_lvalue_reference_t;
+using cuda::std::add_rvalue_reference;
+using cuda::std::add_rvalue_reference_t;
+
+// Pointers
+using cuda::std::remove_pointer;
+using cuda::std::remove_pointer_t;
+using cuda::std::add_pointer;
+using cuda::std::add_pointer_t;
+
+// Sign Modifiers
+using cuda::std::make_signed;
+using cuda::std::make_signed_t;
+using cuda::std::make_unsigned;
+using cuda::std::make_unsigned_t;
+
+// Arrays
+using cuda::std::remove_extent;
+using cuda::std::remove_extent_t;
+using cuda::std::remove_all_extents;
+using cuda::std::remove_all_extents_t;
+
+// Misc transformations
+using cuda::std::decay;
+using cuda::std::decay_t;
+using cuda::std::enable_if;
 using cuda::std::enable_if_t;
+using cuda::std::conditional;
+using cuda::std::conditional_t;
+using cuda::std::common_type;
+using cuda::std::common_type_t;
+using cuda::std::underlying_type;
+using cuda::std::underlying_type_t;
 
 #else // STD versions
 
 #include <type_traits>
 
+// Helper classes
+using std::integral_constant;
+using std::true_type;
+using std::false_type;
+
+// Primary type categories
 using std::is_void;
+using std::is_null_pointer;
 using std::is_integral;
+using std::is_floating_point;
+using std::is_array;
+using std::is_enum;
+using std::is_union;
+using std::is_class;
+using std::is_function;
+using std::is_pointer;
+using std::is_lvalue_reference;
+using std::is_rvalue_reference;
+using std::is_member_object_pointer;
+using std::is_member_function_pointer;
+
+// Composite Type Categories
+using std::is_fundamental;
+using std::is_arithmetic;
+using std::is_scalar;
+using std::is_object;
+using std::is_compound;
+using std::is_reference;
+using std::is_member_pointer;
+
+// Type properties
+using std::is_const;
+using std::is_volatile;
+using std::is_trivial;
+using std::is_trivially_copyable;
+using std::is_standard_layout;
+using std::is_empty;
+using std::is_polymorphic;
+using std::is_abstract;
+using std::is_final;
+using std::is_signed;
+using std::is_unsigned; 
+
+// Supported Operations
+using std::is_constructible;
+using std::is_trivially_constructible;
+using std::is_nothrow_constructible;
+
+using std::is_default_constructible;
+using std::is_trivially_default_constructible;
+using std::is_nothrow_default_constructible;
+
+using std::is_copy_constructible;
+using std::is_trivially_copy_constructible;
+using std::is_nothrow_copy_constructible;
+
+using std::is_move_constructible;
+using std::is_trivially_move_constructible;
+using std::is_nothrow_move_constructible;
+
+using std::is_assignable;
+using std::is_trivially_assignable;
+using std::is_nothrow_assignable;
+
+using std::is_copy_assignable;
+using std::is_trivially_copy_assignable;
+using std::is_nothrow_copy_assignable;
+
+using std::is_move_assignable;
+using std::is_trivially_move_assignable;
+using std::is_nothrow_move_assignable;
+
+using std::is_destructible;
+using std::is_trivially_destructible;
+using std::is_nothrow_destructible;
+
+using std::has_virtual_destructor;
+
+// Property Queries
+using std::alignment_of;
+using std::rank;
+using std::extent;
+
+// Type Relationships
+using std::is_same;
+using std::is_base_of;
+using std::is_convertible;
+
+// Const-volatility specifiers
+using std::remove_cv;
+using std::remove_cv_t;
+using std::remove_const;
+using std::remove_const_t;
+using std::remove_volatile;
+using std::remove_volatile_t;
+using std::add_cv;
+using std::add_cv_t;
+using std::add_const;
+using std::add_const_t;
+using std::add_volatile;
+using std::add_volatile_t;
+
+// References
+using std::remove_reference;
+using std::remove_reference_t;
+using std::add_lvalue_reference;
+using std::add_lvalue_reference_t;
+using std::add_rvalue_reference;
+using std::add_rvalue_reference_t;
+
+// Pointers
+using std::remove_pointer;
+using std::remove_pointer_t;
+using std::add_pointer;
+using std::add_pointer_t;
+
+// Sign Modifiers
+using std::make_signed;
+using std::make_signed_t;
+using std::make_unsigned;
+using std::make_unsigned_t;
+
+// Arrays
+using std::remove_extent;
+using std::remove_extent_t;
+using std::remove_all_extents;
+using std::remove_all_extents_t;
+
+// Misc transformations
+using std::decay;
+using std::decay_t;
+using std::enable_if;
 using std::enable_if_t;
+using std::conditional;
+using std::conditional_t;
+using std::common_type;
+using std::common_type_t;
+using std::underlying_type;
+using std::underlying_type_t;
 
 #endif 
 
+template <bool B>
+using bool_constant = boost::math::integral_constant<bool, B>;
+
 template <typename T>
 BOOST_MATH_INLINE_CONSTEXPR bool is_void_v = boost::math::is_void<T>::value;
 
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_null_pointer_v = boost::math::is_null_pointer<T>::value;
+
 template <typename T>
 BOOST_MATH_INLINE_CONSTEXPR bool is_integral_v = boost::math::is_integral<T>::value;
 
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_floating_point_v = boost::math::is_floating_point<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_array_v = boost::math::is_array<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_enum_v = boost::math::is_enum<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_union_v = boost::math::is_union<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_class_v = boost::math::is_class<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_function_v = boost::math::is_function<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_pointer_v = boost::math::is_pointer<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_lvalue_reference_v = boost::math::is_lvalue_reference<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_rvalue_reference_v = boost::math::is_rvalue_reference<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_member_object_pointer_v = boost::math::is_member_object_pointer<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_member_function_pointer_v = boost::math::is_member_function_pointer<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_fundamental_v = boost::math::is_fundamental<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_arithmetic_v = boost::math::is_arithmetic<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_scalar_v = boost::math::is_scalar<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_object_v = boost::math::is_object<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_compound_v = boost::math::is_compound<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_reference_v = boost::math::is_reference<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_member_pointer_v = boost::math::is_member_pointer<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_const_v = boost::math::is_const<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_volatile_v = boost::math::is_volatile<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivial_v = boost::math::is_trivial<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_copyable_v = boost::math::is_trivially_copyable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_standard_layout_v = boost::math::is_standard_layout<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_empty_v = boost::math::is_empty<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_polymorphic_v = boost::math::is_polymorphic<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_abstract_v = boost::math::is_abstract<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_final_v = boost::math::is_final<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_aggregate_v = boost::math::is_aggregate<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_signed_v = boost::math::is_signed<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_unsigned_v = boost::math::is_unsigned<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_constructible_v = boost::math::is_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_constructible_v = boost::math::is_trivially_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_constructible_v = boost::math::is_nothrow_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_default_constructible_v = boost::math::is_default_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_default_constructible_v = boost::math::is_trivially_default_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_default_constructible_v = boost::math::is_nothrow_default_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_copy_constructible_v = boost::math::is_copy_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_copy_constructible_v = boost::math::is_trivially_copy_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_copy_constructible_v = boost::math::is_nothrow_copy_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_move_constructible_v = boost::math::is_move_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_move_constructible_v = boost::math::is_trivially_move_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_move_constructible_v = boost::math::is_nothrow_move_constructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_assignable_v = boost::math::is_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_assignable_v = boost::math::is_trivially_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_assignable_v = boost::math::is_nothrow_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_copy_assignable_v = boost::math::is_copy_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_copy_assignable_v = boost::math::is_trivially_copy_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_copy_assignable_v = boost::math::is_nothrow_copy_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_move_assignable_v = boost::math::is_move_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_move_assignable_v = boost::math::is_trivially_move_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_move_assignable_v = boost::math::is_nothrow_move_assignable<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_destructible_v = boost::math::is_destructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_trivially_destructible_v = boost::math::is_trivially_destructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool is_nothrow_destructible_v = boost::math::is_nothrow_destructible<T>::value;
+
+template <typename T>
+BOOST_MATH_INLINE_CONSTEXPR bool has_virtual_destructor_v = boost::math::has_virtual_destructor<T>::value;
+
+template <typename T, typename U>
+BOOST_MATH_INLINE_CONSTEXPR bool is_same_v = boost::math::is_same<T, U>::value;
+
+template <typename T, typename U>
+BOOST_MATH_INLINE_CONSTEXPR bool is_base_of_v = boost::math::is_base_of<T, U>::value;
+
 } // namespace math
 } // namespace boost