Standard library header <type_traits> (C++11)

 

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Standard library headers

Language support <cfloat> <climits> <compare> (C++20) <coroutine> (C++20) <csetjmp> <csignal> <cstdarg> <cstddef> <cstdint> (C++11) <cstdlib> <exception> <initializer_list> (C++11)    <limits> <new> <source_location> (C++20) <stdfloat> (C++23) <typeinfo> <version> (C++20) Concepts <concepts> (C++20) Diagnostics <cassert> <cerrno> <debugging> (C++26) <stacktrace> (C++23) <stdexcept> <system_error> (C++11) Memory management <memory> <memory_resource> (C++17) <scoped_allocator> (C++11) Metaprogramming <type_traits> (C++11) <ratio> (C++11)

General utilities <any> (C++17) <bitset> <bit> (C++20) <charconv> (C++17) <expected> (C++23) <format> (C++20) <functional> <optional> (C++17) <tuple> (C++11) <typeindex> (C++11) <utility> <variant> (C++17) Containers <array> (C++11) <deque> <flat_map> (C++23) <flat_set> (C++23) <forward_list> (C++11) <inplace_vector> (C++26)    <list> <map> <mdspan> (C++23) <queue> <set> <span> (C++20) <stack> <unordered_map> (C++11) <unordered_set> (C++11) <vector> Iterators <iterator> Ranges <generator> (C++23) <ranges> (C++20)

Algorithms <algorithm> <numeric> Strings <cctype> <cstring> <cuchar> (C++11) <cwchar> <cwctype> <string_view> (C++17) <string> Text processing <clocale> <codecvt> (C++11/17/26*) <locale> <regex> (C++11) <text_encoding> (C++26)    Numerics <cfenv> (C++11) <cmath> <complex> <linalg> (C++26) <numbers> (C++20) <random> (C++11) <valarray> Time <chrono> (C++11) <ctime> C compatibility <ccomplex> (C++11/17/20*) <ciso646> (until C++20) <cstdalign> (C++11/17/20*) <cstdbool> (C++11/17/20*) <ctgmath> (C++11/17/20*)

Input/output <cinttypes> (C++11) <cstdio> <filesystem> (C++17) <fstream> <iomanip> <iosfwd> <iostream> <ios> <istream> <ostream> <print> (C++23) <spanstream> (C++23) <sstream> <streambuf> <strstream> (C++98/26*) <syncstream> (C++20) Concurrency support <atomic> (C++11) <barrier> (C++20) <condition_variable> (C++11) <future> (C++11) <hazard_pointer> (C++26) <latch> (C++20) <mutex> (C++11) <rcu> (C++26) <semaphore> (C++20) <shared_mutex> (C++14) <stdatomic.h> (C++23) <stop_token> (C++20) <thread> (C++11) Execution support <execution> (C++17)

 

This header is part of the metaprogramming library.

Classes
Helper Classes
integral_constantbool_constant (C++11)(C++17)	compile-time constant of specified type with specified value (class template)
true_type	std::integral_constant<bool, true>
false_type	std::integral_constant<bool, false>
Primary type categories
is_void (C++11)	checks if a type is void (class template)
is_null_pointer (C++14)	checks if a type is std::nullptr_t (class template)
is_integral (C++11)	checks if a type is an integral type (class template)
is_floating_point (C++11)	checks if a type is a floating-point type (class template)
is_array (C++11)	checks if a type is an array type (class template)
is_enum (C++11)	checks if a type is an enumeration type (class template)
is_union (C++11)	checks if a type is a union type (class template)
is_class (C++11)	checks if a type is a non-union class type (class template)
is_function (C++11)	checks if a type is a function type (class template)
is_pointer (C++11)	checks if a type is a pointer type (class template)
is_lvalue_reference (C++11)	checks if a type is an lvalue reference (class template)
is_rvalue_reference (C++11)	checks if a type is an rvalue reference (class template)
is_member_object_pointer (C++11)	checks if a type is a pointer to a non-static member object (class template)
is_member_function_pointer (C++11)	checks if a type is a pointer to a non-static member function (class template)
Composite type categories
is_fundamental (C++11)	checks if a type is a fundamental type (class template)
is_arithmetic (C++11)	checks if a type is an arithmetic type (class template)
is_scalar (C++11)	checks if a type is a scalar type (class template)
is_object (C++11)	checks if a type is an object type (class template)
is_compound (C++11)	checks if a type is a compound type (class template)
is_reference (C++11)	checks if a type is either an lvalue reference or rvalue reference (class template)
is_member_pointer (C++11)	checks if a type is a pointer to a non-static member function or object (class template)
Type properties
is_const (C++11)	checks if a type is const-qualified (class template)
is_volatile (C++11)	checks if a type is volatile-qualified (class template)
is_trivial (C++11)	checks if a type is trivial (class template)
is_trivially_copyable (C++11)	checks if a type is trivially copyable (class template)
is_standard_layout (C++11)	checks if a type is a standard-layout type (class template)
is_pod (C++11)(deprecated in C++20)	checks if a type is a plain-old data (POD) type (class template)
is_literal_type (C++11)(deprecated in C++17)(removed in C++20)	checks if a type is a literal type (class template)
has_unique_object_representations (C++17)	checks if every bit in the type's object representation contributes to its value (class template)
is_empty (C++11)	checks if a type is a class (but not union) type and has no non-static data members (class template)
is_polymorphic (C++11)	checks if a type is a polymorphic class type (class template)
is_abstract (C++11)	checks if a type is an abstract class type (class template)
is_final (C++14)	checks if a type is a final class type (class template)
is_aggregate (C++17)	checks if a type is an aggregate type (class template)
is_implicit_lifetime (C++23)	checks if a type is an implicit-lifetime type (class template)
is_signed (C++11)	checks if a type is a signed arithmetic type (class template)
is_unsigned (C++11)	checks if a type is an unsigned arithmetic type (class template)
is_bounded_array (C++20)	checks if a type is an array type of known bound (class template)
is_unbounded_array (C++20)	checks if a type is an array type of unknown bound (class template)
is_scoped_enum (C++23)	checks if a type is a scoped enumeration type (class template)

Supported operations
is_constructibleis_trivially_constructibleis_nothrow_constructible (C++11)(C++11)(C++11)	checks if a type has a constructor for specific arguments (class template)
is_default_constructibleis_trivially_default_constructibleis_nothrow_default_constructible (C++11)(C++11)(C++11)	checks if a type has a default constructor (class template)
is_copy_constructibleis_trivially_copy_constructibleis_nothrow_copy_constructible (C++11)(C++11)(C++11)	checks if a type has a copy constructor (class template)
is_move_constructibleis_trivially_move_constructibleis_nothrow_move_constructible (C++11)(C++11)(C++11)	checks if a type can be constructed from an rvalue reference (class template)
is_assignableis_trivially_assignableis_nothrow_assignable (C++11)(C++11)(C++11)	checks if a type has an assignment operator for a specific argument (class template)
is_copy_assignableis_trivially_copy_assignableis_nothrow_copy_assignable (C++11)(C++11)(C++11)	checks if a type has a copy assignment operator (class template)
is_move_assignableis_trivially_move_assignableis_nothrow_move_assignable (C++11)(C++11)(C++11)	checks if a type has a move assignment operator (class template)
is_destructibleis_trivially_destructibleis_nothrow_destructible (C++11)(C++11)(C++11)	checks if a type has a non-deleted destructor (class template)
has_virtual_destructor (C++11)	checks if a type has a virtual destructor (class template)
is_swappable_withis_swappableis_nothrow_swappable_withis_nothrow_swappable (C++17)(C++17)(C++17)(C++17)	checks if objects of a type can be swapped with objects of same or different type (class template)
reference_converts_from_temporary (C++23)	checks if a reference is bound to a temporary in copy-initialization (class template)
reference_constructs_from_temporary (C++23)	checks if a reference is bound to a temporary in direct-initialization (class template)

Property queries
alignment_of (C++11)	obtains the type's alignment requirements (class template)
rank (C++11)	obtains the number of dimensions of an array type (class template)
extent (C++11)	obtains the size of an array type along a specified dimension (class template)

Type relationships
is_same (C++11)	checks if two types are the same (class template)
is_base_of (C++11)	checks if a type is a base of the other type (class template)
is_virtual_base_of (C++26)	checks if a type is a virtual base of the other type (class template)
is_convertibleis_nothrow_convertible (C++11)(C++20)	checks if a type can be converted to the other type (class template)
is_layout_compatible (C++20)	checks if two types are layout-compatible (class template)
is_pointer_interconvertible_base_of (C++20)	checks if a type is a pointer-interconvertible (initial) base of another type (class template)
is_invocableis_invocable_ris_nothrow_invocableis_nothrow_invocable_r (C++17)	checks if a type can be invoked (as if by std::invoke) with the given argument types (class template)
Const-volatility specifiers
remove_cvremove_constremove_volatile (C++11)(C++11)(C++11)	removes const and/or volatile specifiers from the given type (class template)
add_cvadd_constadd_volatile (C++11)(C++11)(C++11)	adds const and/or volatile specifiers to the given type (class template)
References
remove_reference (C++11)	removes a reference from the given type (class template)
add_lvalue_referenceadd_rvalue_reference (C++11)(C++11)	adds an lvalue or rvalue reference to the given type (class template)
Pointers
remove_pointer (C++11)	removes a pointer from the given type (class template)
add_pointer (C++11)	adds a pointer to the given type (class template)
Sign modifiers
make_signed (C++11)	obtains the corresponding signed type for the given integral type (class template)
make_unsigned (C++11)	obtains the corresponding signed type for the given integral type (class template)
Arrays
remove_extent (C++11)	removes one extent from the given array type (class template)
remove_all_extents (C++11)	removes all extents from the given array type (class template)
Miscellaneous transformations
aligned_storage (C++11)(deprecated in C++23)	defines the type suitable for use as uninitialized storage for types of given size (class template)
aligned_union (C++11)(deprecated in C++23)	defines the type suitable for use as uninitialized storage for all given types (class template)
decay (C++11)	applies type transformations as when passing a function argument by value (class template)
remove_cvref (C++20)	combines std::remove_cv and std::remove_reference (class template)
enable_if (C++11)	conditionally removes a function overload or template specialization from overload resolution (class template)
conditional (C++11)	chooses one type or another based on compile-time boolean (class template)
common_type (C++11)	determines the common type of a group of types (class template)
common_referencebasic_common_reference (C++20)	determines the common reference type of a group of types (class template)
underlying_type (C++11)	obtains the underlying integer type for a given enumeration type (class template)
result_ofinvoke_result (C++11)(removed in C++20)(C++17)	deduces the result type of invoking a callable object with a set of arguments (class template)
void_t (C++17)	void variadic alias template (alias template)
type_identity (C++20)	returns the type argument unchanged (class template)
unwrap_referenceunwrap_ref_decay (C++20)(C++20)	get the reference type wrapped in std::reference_wrapper (class template)
Operations on traits
conjunction (C++17)	variadic logical AND metafunction (class template)
disjunction (C++17)	variadic logical OR metafunction (class template)
negation (C++17)	logical NOT metafunction (class template)
Functions
Member relationships
is_pointer_interconvertible_with_class (C++20)	checks if objects of a type are pointer-interconvertible with the specified subobject of that type (function template)
is_corresponding_member (C++20)	checks if two specified members correspond to each other in the common initial subsequence of two specified types (function template)
Constant evaluation context
is_constant_evaluated (C++20)	detects whether the call occurs within a constant-evaluated context (function)
is_within_lifetime (C++26)	checks whether a pointer is within the object's lifetime at compile time (function)

Synopsis

namespace std {
  // helper class
  template<class T, T v> struct integral_constant;
 
  template<bool B>
    using bool_constant = integral_constant<bool, B>;
  using true_type  = bool_constant<true>;
  using false_type = bool_constant<false>;
 
  // primary type categories
  template<class T> struct is_void;
  template<class T> struct is_null_pointer;
  template<class T> struct is_integral;
  template<class T> struct is_floating_point;
  template<class T> struct is_array;
  template<class T> struct is_pointer;
  template<class T> struct is_lvalue_reference;
  template<class T> struct is_rvalue_reference;
  template<class T> struct is_member_object_pointer;
  template<class T> struct is_member_function_pointer;
  template<class T> struct is_enum;
  template<class T> struct is_union;
  template<class T> struct is_class;
  template<class T> struct is_function;
 
  // composite type categories
  template<class T> struct is_reference;
  template<class T> struct is_arithmetic;
  template<class T> struct is_fundamental;
  template<class T> struct is_object;
  template<class T> struct is_scalar;
  template<class T> struct is_compound;
  template<class T> struct is_member_pointer;
 
  // type properties
  template<class T> struct is_const;
  template<class T> struct is_volatile;
  template<class T> struct is_trivial;
  template<class T> struct is_trivially_copyable;
  template<class T> struct is_standard_layout;
  template<class T> struct is_empty;
  template<class T> struct is_polymorphic;
  template<class T> struct is_abstract;
  template<class T> struct is_final;
  template<class T> struct is_aggregate;
 
  template<class T> struct is_signed;
  template<class T> struct is_unsigned;
  template<class T> struct is_bounded_array;
  template<class T> struct is_unbounded_array;
  template<class T> struct is_scoped_enum;
 
  template<class T, class... Args> struct is_constructible;
  template<class T> struct is_default_constructible;
  template<class T> struct is_copy_constructible;
  template<class T> struct is_move_constructible;
 
  template<class T, class U> struct is_assignable;
  template<class T> struct is_copy_assignable;
  template<class T> struct is_move_assignable;
 
  template<class T, class U> struct is_swappable_with;
  template<class T> struct is_swappable;
 
  template<class T> struct is_destructible;
 
  template<class T, class... Args> struct is_trivially_constructible;
  template<class T> struct is_trivially_default_constructible;
  template<class T> struct is_trivially_copy_constructible;
  template<class T> struct is_trivially_move_constructible;
 
  template<class T, class U> struct is_trivially_assignable;
  template<class T> struct is_trivially_copy_assignable;
  template<class T> struct is_trivially_move_assignable;
  template<class T> struct is_trivially_destructible;
 
  template<class T, class... Args> struct is_nothrow_constructible;
  template<class T> struct is_nothrow_default_constructible;
  template<class T> struct is_nothrow_copy_constructible;
  template<class T> struct is_nothrow_move_constructible;
 
  template<class T, class U> struct is_nothrow_assignable;
  template<class T> struct is_nothrow_copy_assignable;
  template<class T> struct is_nothrow_move_assignable;
 
  template<class T, class U> struct is_nothrow_swappable_with;
  template<class T> struct is_nothrow_swappable;
 
  template<class T> struct is_nothrow_destructible;
 
  template<class T> struct has_virtual_destructor;
 
  template<class T> struct has_unique_object_representations;
 
  template<class T, class U> struct reference_constructs_from_temporary;
  template<class T, class U> struct reference_converts_from_temporary;
 
  // type property queries
  template<class T> struct alignment_of;
  template<class T> struct rank;
  template<class T, unsigned I = 0> struct extent;
 
  // type relations
  template<class T, class U> struct is_same;
  template<class Base, class Derived> struct is_base_of;
  template<class Base, class Derived> struct is_virtual_base_of;
  template<class From, class To> struct is_convertible;
  template<class From, class To> struct is_nothrow_convertible;
  template<class T, class U> struct is_layout_compatible;
  template<class Base, class Derived> struct is_pointer_interconvertible_base_of;
 
  template<class Fn, class... ArgTypes> struct is_invocable;
  template<class R, class Fn, class... ArgTypes> struct is_invocable_r;
 
  template<class Fn, class... ArgTypes> struct is_nothrow_invocable;
  template<class R, class Fn, class... ArgTypes> struct is_nothrow_invocable_r;
 
  // const-volatile modifications
  template<class T> struct remove_const;
  template<class T> struct remove_volatile;
  template<class T> struct remove_cv;
  template<class T> struct add_const;
  template<class T> struct add_volatile;
  template<class T> struct add_cv;
 
  template<class T>
    using remove_const_t    = typename remove_const<T>::type;
  template<class T>
    using remove_volatile_t = typename remove_volatile<T>::type;
  template<class T>
    using remove_cv_t       = typename remove_cv<T>::type;
  template<class T>
    using add_const_t       = typename add_const<T>::type;
  template<class T>
    using add_volatile_t    = typename add_volatile<T>::type;
  template<class T>
    using add_cv_t          = typename add_cv<T>::type;
 
  // reference modifications
  template<class T> struct remove_reference;
  template<class T> struct add_lvalue_reference;
  template<class T> struct add_rvalue_reference;
 
  template<class T>
    using remove_reference_t     = typename remove_reference<T>::type;
  template<class T>
    using add_lvalue_reference_t = typename add_lvalue_reference<T>::type;
  template<class T>
    using add_rvalue_reference_t = typename add_rvalue_reference<T>::type;
 
  // sign modifications
  template<class T> struct make_signed;
  template<class T> struct make_unsigned;
 
  template<class T>
    using make_signed_t   = typename make_signed<T>::type;
  template<class T>
    using make_unsigned_t = typename make_unsigned<T>::type;
 
  // array modifications
  template<class T> struct remove_extent;
  template<class T> struct remove_all_extents;
 
  template<class T>
    using remove_extent_t      = typename remove_extent<T>::type;
  template<class T>
    using remove_all_extents_t = typename remove_all_extents<T>::type;
 
  // pointer modifications
  template<class T> struct remove_pointer;
  template<class T> struct add_pointer;
 
  template<class T>
    using remove_pointer_t = typename remove_pointer<T>::type;
  template<class T>
    using add_pointer_t    = typename add_pointer<T>::type;
 
  // other transformations
  template<class T> struct type_identity;
  template<class T> struct remove_cvref;
  template<class T> struct decay;
  template<bool, class T = void> struct enable_if;
  template<bool, class T, class F> struct conditional;
  template<class... T> struct common_type;
  template<class T, class U, template<class> class TQual, template<class> class UQual>
    struct basic_common_reference { };
  template<class... T> struct common_reference;
  template<class T> struct underlying_type;
  template<class Fn, class... ArgTypes> struct invoke_result;
  template<class T> struct unwrap_reference;
  template<class T> struct unwrap_ref_decay;
 
  template<class T>
    using type_identity_t    = typename type_identity<T>::type;
  template<class T>
    using remove_cvref_t     = typename remove_cvref<T>::type;
  template<class T>
    using decay_t            = typename decay<T>::type;
  template<bool b, class T = void>
    using enable_if_t        = typename enable_if<b, T>::type;
  template<bool b, class T, class F>
    using conditional_t      = typename conditional<b, T, F>::type;
  template<class... T>
    using common_type_t      = typename common_type<T...>::type;
  template<class... T>
    using common_reference_t = typename common_reference<T...>::type;
  template<class T>
    using underlying_type_t  = typename underlying_type<T>::type;
  template<class Fn, class... ArgTypes>
    using invoke_result_t    = typename invoke_result<Fn, ArgTypes...>::type;
  template<class T>
    using unwrap_reference_t = typename unwrap_reference<T>::type;
  template<class T>
    using unwrap_ref_decay_t = typename unwrap_ref_decay<T>::type;
  template<class...>
    using void_t             = void;
 
  // logical operator traits
  template<class... B> struct conjunction;
  template<class... B> struct disjunction;
  template<class B> struct negation;
 
  // primary type categories
  template<class T>
    inline constexpr bool is_void_v = is_void<T>::value;
  template<class T>
    inline constexpr bool is_null_pointer_v = is_null_pointer<T>::value;
  template<class T>
    inline constexpr bool is_integral_v = is_integral<T>::value;
  template<class T>
    inline constexpr bool is_floating_point_v = is_floating_point<T>::value;
  template<class T>
    inline constexpr bool is_array_v = is_array<T>::value;
  template<class T>
    inline constexpr bool is_pointer_v = is_pointer<T>::value;
  template<class T>
    inline constexpr bool is_lvalue_reference_v = is_lvalue_reference<T>::value;
  template<class T>
    inline constexpr bool is_rvalue_reference_v = is_rvalue_reference<T>::value;
  template<class T>
    inline constexpr bool is_member_object_pointer_v = is_member_object_pointer<T>::value;
  template<class T>
    inline constexpr bool is_member_function_pointer_v = is_member_function_pointer<T>::value;
  template<class T>
    inline constexpr bool is_enum_v = is_enum<T>::value;
  template<class T>
    inline constexpr bool is_union_v = is_union<T>::value;
  template<class T>
    inline constexpr bool is_class_v = is_class<T>::value;
  template<class T>
    inline constexpr bool is_function_v = is_function<T>::value;
 
  // composite type categories
  template<class T>
    inline constexpr bool is_reference_v = is_reference<T>::value;
  template<class T>
    inline constexpr bool is_arithmetic_v = is_arithmetic<T>::value;
  template<class T>
    inline constexpr bool is_fundamental_v = is_fundamental<T>::value;
  template<class T>
    inline constexpr bool is_object_v = is_object<T>::value;
  template<class T>
    inline constexpr bool is_scalar_v = is_scalar<T>::value;
  template<class T>
    inline constexpr bool is_compound_v = is_compound<T>::value;
  template<class T>
    inline constexpr bool is_member_pointer_v = is_member_pointer<T>::value;
 
  // type properties
  template<class T>
    inline constexpr bool is_const_v = is_const<T>::value;
  template<class T>
    inline constexpr bool is_volatile_v = is_volatile<T>::value;
  template<class T>
    inline constexpr bool is_trivial_v = is_trivial<T>::value;
  template<class T>
    inline constexpr bool is_trivially_copyable_v = is_trivially_copyable<T>::value;
  template<class T>
    inline constexpr bool is_standard_layout_v = is_standard_layout<T>::value;
  template<class T>
    inline constexpr bool is_empty_v = is_empty<T>::value;
  template<class T>
    inline constexpr bool is_polymorphic_v = is_polymorphic<T>::value;
  template<class T>
    inline constexpr bool is_abstract_v = is_abstract<T>::value;
  template<class T>
    inline constexpr bool is_final_v = is_final<T>::value;
  template<class T>
    inline constexpr bool is_aggregate_v = is_aggregate<T>::value;
  template<class T>
    inline constexpr bool is_signed_v = is_signed<T>::value;
  template<class T>
    inline constexpr bool is_unsigned_v = is_unsigned<T>::value;
  template<class T>
    inline constexpr bool is_bounded_array_v = is_bounded_array<T>::value;
  template<class T>
    inline constexpr bool is_unbounded_array_v = is_unbounded_array<T>::value;
  template<class T>
    inline constexpr bool is_scoped_enum_v = is_scoped_enum<T>::value;
  template<class T, class... Args>
    inline constexpr bool is_constructible_v = is_constructible<T, Args...>::value;
  template<class T>
    inline constexpr bool is_default_constructible_v = is_default_constructible<T>::value;
  template<class T>
    inline constexpr bool is_copy_constructible_v = is_copy_constructible<T>::value;
  template<class T>
    inline constexpr bool is_move_constructible_v = is_move_constructible<T>::value;
  template<class T, class U>
    inline constexpr bool is_assignable_v = is_assignable<T, U>::value;
  template<class T>
    inline constexpr bool is_copy_assignable_v = is_copy_assignable<T>::value;
  template<class T>
    inline constexpr bool is_move_assignable_v = is_move_assignable<T>::value;
  template<class T, class U>
    inline constexpr bool is_swappable_with_v = is_swappable_with<T, U>::value;
  template<class T>
    inline constexpr bool is_swappable_v = is_swappable<T>::value;
  template<class T>
    inline constexpr bool is_destructible_v = is_destructible<T>::value;
  template<class T, class... Args>
    inline constexpr bool is_trivially_constructible_v
      = is_trivially_constructible<T, Args...>::value;
  template<class T>
    inline constexpr bool is_trivially_default_constructible_v
      = is_trivially_default_constructible<T>::value;
  template<class T>
    inline constexpr bool is_trivially_copy_constructible_v
      = is_trivially_copy_constructible<T>::value;
  template<class T>
    inline constexpr bool is_trivially_move_constructible_v
      = is_trivially_move_constructible<T>::value;
  template<class T, class U>
    inline constexpr bool is_trivially_assignable_v = is_trivially_assignable<T, U>::value;
  template<class T>
    inline constexpr bool is_trivially_copy_assignable_v
      = is_trivially_copy_assignable<T>::value;
  template<class T>
    inline constexpr bool is_trivially_move_assignable_v
      = is_trivially_move_assignable<T>::value;
  template<class T>
    inline constexpr bool is_trivially_destructible_v = is_trivially_destructible<T>::value;
  template<class T, class... Args>
    inline constexpr bool is_nothrow_constructible_v
      = is_nothrow_constructible<T, Args...>::value;
  template<class T>
    inline constexpr bool is_nothrow_default_constructible_v
      = is_nothrow_default_constructible<T>::value;
  template<class T>
    inline constexpr bool is_nothrow_copy_constructible_v
      = is_nothrow_copy_constructible<T>::value;
  template<class T>
    inline constexpr bool is_nothrow_move_constructible_v
      = is_nothrow_move_constructible<T>::value;
  template<class T, class U>
    inline constexpr bool is_nothrow_assignable_v = is_nothrow_assignable<T, U>::value;
  template<class T>
    inline constexpr bool is_nothrow_copy_assignable_v = is_nothrow_copy_assignable<T>::value;
  template<class T>
    inline constexpr bool is_nothrow_move_assignable_v = is_nothrow_move_assignable<T>::value;
  template<class T, class U>
    inline constexpr bool is_nothrow_swappable_with_v = is_nothrow_swappable_with<T, U>::value;
  template<class T>
    inline constexpr bool is_nothrow_swappable_v = is_nothrow_swappable<T>::value;
  template<class T>
    inline constexpr bool is_nothrow_destructible_v = is_nothrow_destructible<T>::value;
  template<class T>
    inline constexpr bool has_virtual_destructor_v = has_virtual_destructor<T>::value;
  template<class T>
    inline constexpr bool has_unique_object_representations_v
      = has_unique_object_representations<T>::value;
  template<class T, class U>
    inline constexpr bool reference_constructs_from_temporary_v
      = reference_constructs_from_temporary<T, U>::value;
  template<class T, class U>
    inline constexpr bool reference_converts_from_temporary_v
      = reference_converts_from_temporary<T, U>::value;
 
  // type property queries
  template<class T>
    inline constexpr size_t alignment_of_v = alignment_of<T>::value;
  template<class T>
    inline constexpr size_t rank_v = rank<T>::value;
  template<class T, unsigned I = 0>
    inline constexpr size_t extent_v = extent<T, I>::value;
 
  // type relations
  template<class T, class U>
    inline constexpr bool is_same_v = is_same<T, U>::value;
  template<class Base, class Derived>
    inline constexpr bool is_base_of_v = is_base_of<Base, Derived>::value;
  template<class Base, class Derived>
    inline constexpr bool is_virtual_base_of_v = is_virtual_base_of<Base, Derived>::value;
  template<class From, class To>
    inline constexpr bool is_convertible_v = is_convertible<From, To>::value;
  template<class From, class To>
    inline constexpr bool is_nothrow_convertible_v = is_nothrow_convertible<From, To>::value;
  template<class T, class U>
    inline constexpr bool is_layout_compatible_v = is_layout_compatible<T, U>::value;
  template<class Base, class Derived>
    inline constexpr bool is_pointer_interconvertible_base_of_v
      = is_pointer_interconvertible_base_of<Base, Derived>::value;
  template<class Fn, class... ArgTypes>
    inline constexpr bool is_invocable_v = is_invocable<Fn, ArgTypes...>::value;
  template<class R, class Fn, class... ArgTypes>
    inline constexpr bool is_invocable_r_v = is_invocable_r<R, Fn, ArgTypes...>::value;
  template<class Fn, class... ArgTypes>
    inline constexpr bool is_nothrow_invocable_v = is_nothrow_invocable<Fn, ArgTypes...>::value;
  template<class R, class Fn, class... ArgTypes>
    inline constexpr bool is_nothrow_invocable_r_v
      = is_nothrow_invocable_r<R, Fn, ArgTypes...>::value;
 
  // logical operator traits
  template<class... B>
    inline constexpr bool conjunction_v = conjunction<B...>::value;
  template<class... B>
    inline constexpr bool disjunction_v = disjunction<B...>::value;
  template<class B>
    inline constexpr bool negation_v = negation<B>::value;
 
  // member relationships
  template<class S, class M>
    constexpr bool is_pointer_interconvertible_with_class(M S::*m) noexcept;
  template<class S1, class S2, class M1, class M2>
    constexpr bool is_corresponding_member(M1 S1::*m1, M2 S2::*m2) noexcept;
 
  // constant evaluation context
  constexpr bool is_constant_evaluated() noexcept;
  consteval bool is_within_lifetime(const auto*) noexcept;
}

Class template std::integral_constant

namespace std {
  template <class T, T v>
  struct integral_constant {
    static constexpr T value = v;
    using value_type = T;
    using type = integral_constant<T, v>;
    constexpr operator value_type() const noexcept { return value; }
    constexpr value_type operator()() const noexcept { return value; }
  };
}