This subclause contains templates that may be used to transform one
type to another following some predefined rule.

Table 52: Const-volatile modifications [tab:meta.trans.cv]

Template | Comments |

The member typedef type names
the same type as T
except that any top-level const-qualifier has been removed. | |

The member typedef type names
the same type as T
except that any top-level volatile-qualifier has been removed. | |

The member typedef type shall be the same as T
except that any top-level cv-qualifier has been removed. | |

If T is a reference, function, or top-level const-qualified
type, then type names
the same type as T, otherwise
T const. | |

If T is a reference, function, or top-level volatile-qualified
type, then type names
the same type as T, otherwise
T volatile. | |

Table 54: Sign modifications [tab:meta.trans.sign]

Template | Comments |

If T names a (possibly cv-qualified)
signed integer type then the member typedef
type names the type T; otherwise,
if T names a (possibly cv-qualified) unsigned integer
type then type names the corresponding
signed integer type, with the same cv-qualifiers as T;
otherwise, type names the signed integer type with smallest
rank for which
sizeof(T) == sizeof(type), with the same
cv-qualifiers as T. | |

If T names a (possibly cv-qualified)
unsigned integer type then the member typedef
type names the type T; otherwise,
if T names a (possibly cv-qualified) signed integer
type then type names the corresponding
unsigned integer type, with the same cv-qualifiers as T;
otherwise, type names the unsigned integer type with smallest
rank for which
sizeof(T) == sizeof(type), with the same
cv-qualifiers as T. |

[Example

: *end example*

]// the following assertions hold: assert((is_same_v<remove_extent_t<int>, int>)); assert((is_same_v<remove_extent_t<int[2]>, int>)); assert((is_same_v<remove_extent_t<int[2][3]>, int[3]>)); assert((is_same_v<remove_extent_t<int[][3]>, int[3]>));—

Table 56: Pointer modifications [tab:meta.trans.ptr]

Template | Comments |

If T has type “(possibly cv-qualified) pointer
to T1” then the member typedef type
names T1; otherwise, it names T. | |

If T names a referenceable type or a
cv void type then
the member typedef type names the same type as
remove_reference_t<T>*;
otherwise, type names T. |

Table 57: Other transformations [tab:meta.trans.other]

Template | Comments |

The value of default-alignment shall be the most
stringent alignment requirement for any object type whose size
is no greater than Len ([basic.types]). The member typedef type shall be a trivial standard-layout type
suitable for use as uninitialized storage for any object whose size
is at most Len and whose alignment is a divisor of Align. | |

The member typedef type shall be a trivial standard-layout type suitable for use as
uninitialized storage for any object whose type is listed in Types;
its size shall be at least Len. The static member alignment_value
shall be an integral constant of type size_t whose value is the
strictest alignment of all types listed in Types. Each type in the template parameter pack Types
is a complete object type. | |

[Note : ]This behavior is similar to the lvalue-to-rvalue ([conv.lval]),
array-to-pointer ([conv.array]), and function-to-pointer ([conv.func])
conversions applied when an lvalue is used as an rvalue, but also
strips cv-qualifiers from class types in order to more closely model by-value
argument passing. — end note | |

template<bool B, class T,
class F> struct conditional; | |

template<class... T> struct common_type; | Unless this trait is specialized (as specified in Note B, below),
the member type is defined or omitted as specified in Note A, below. If it is omitted, there shall be no member type. Each type in the template parameter pack T shall be
complete, cv void, or an array of unknown bound. |

Unless this trait is specialized (as specified in Note D, below),
there shall be no member type. | |

If T is an enumeration type, the member typedef type names
the underlying type of T ([dcl.enum]);
otherwise, there is no member type. | |

template<class Fn, class... ArgTypes> struct invoke_result; | If the expression INVOKE(declval<Fn>(), declval<ArgTypes>()...)
is well-formed when treated as an unevaluated operand,
the member typedef type names the type
decltype(INVOKE(declval<Fn>(), declval<ArgTypes>()...));
otherwise, there shall be no member type. Only the validity of the immediate context of the
expression is considered. [Note : ]The compilation of the expression can result in side effects such as
the instantiation of class template specializations and function
template specializations, the generation of implicitly-defined
functions, and so on. Such side effects are not in the “immediate
context” and can result in the program being ill-formed. — end notePreconditions: Fn and all types in the template parameter pack ArgTypes are complete types, cv void, or arrays of unknown bound. |

If T is
a specialization reference_wrapper<X> for some type X,
the member typedef type of unwrap_reference<T> is X&,
otherwise it is T. | |

The member typedef type of unwrap_ref_decay<T>
denotes the type unwrap_reference_t<decay_t<T>>. |

[Note

: *end note*

]A typical implementation would define aligned_storage as:

— template<size_t Len, size_t Alignment> struct aligned_storage { typedef struct { alignas(Alignment) unsigned char __data[Len]; } type; };

In addition to being available via inclusion
of the <type_traits> header, the templates
unwrap_reference,
unwrap_ref_decay,
unwrap_reference_t, and
unwrap_ref_decay_t
are available
when the header <functional> ([functional.syn]) is included.

Let:

- CREF(A) be add_lvalue_reference_t<const remove_reference_t<A>>,
- XREF(A) denote a unary alias template T such that T<U> denotes the same type as U with the addition of A's cv and reference qualifiers, for a non-reference cv-unqualified type U,
- COPYCV(FROM, TO) be an alias for type TO
with the addition of FROM's top-level cv-qualifiers,
[Example: COPYCV(const int, volatile short) is an alias for const volatile short. —]
*end example* - COND-RES(X, Y) be decltype(false ? declval<X(&)()>()() : declval<Y(&)()>()()).

Given types A and B,
let X be remove_reference_t<A>,
let Y be remove_reference_t<B>, and
let COMMON-REF(A, B) be:

- If A and B are both lvalue reference types, COMMON-REF(A, B) is COND-RES(COPYCV(X, Y) &, COPYCV(Y, X) &) if that type exists and is a reference type.
- Otherwise, let C be remove_reference_t<COMMON-REF(X&, Y&)>&&. If A and B are both rvalue reference types, C is well-formed, and is_convertible_v<A, C> && is_convertible_v<B, C> is true, then COMMON-REF(A, B) is C.
- Otherwise, let D be COMMON-REF(const X&, Y&). If A is an rvalue reference and B is an lvalue reference and D is well-formed and is_convertible_v<A, D> is true, then COMMON-REF(A, B) is D.
- Otherwise, if A is an lvalue reference and B is an rvalue reference, then COMMON-REF(A, B) is COMMON-REF(B, A).
- Otherwise, COMMON-REF(A, B) is ill-formed.

If any of the types computed above is ill-formed, then
COMMON-REF(A, B) is ill-formed.

Note A:
For the common_type trait applied to a template parameter pack T of types,
the member type shall be either defined or not present as follows:

- If sizeof...(T) is zero, there shall be no member type.
- If sizeof...(T) is one, let T0 denote the sole type constituting the pack T. The member typedef-name type shall denote the same type, if any, as common_type_t<T0, T0>; otherwise there shall be no member type.
- If sizeof...(T) is two,
let the first and second types constituting T be denoted
by T1 and T2, respectively, and
let D1 and D2 denote
the same types as decay_t<T1> and decay_t<T2>, respectively.
- If is_same_v<T1, D1> is false or is_same_v<T2, D2> is false, let C denote the same type, if any, as common_type_t<D1, D2>.
- [Note: None of the following will apply if there is a specialization common_type<D1, D2>. —]
*end note* - Otherwise, if
decay_t<decltype(false ? declval<D1>() : declval<D2>())>

denotes a valid type, let C denote that type. - Otherwise, if COND-RES(CREF(D1), CREF(D2)) denotes a type, let C denote the type decay_t<COND-RES(CREF(D1), CREF(D2))>.

- If sizeof...(T) is greater than two, let T1, T2, and R, respectively, denote the first, second, and (pack of) remaining types constituting T. Let C denote the same type, if any, as common_type_t<T1, T2>. If there is such a type C, the member typedef-name type shall denote the same type, if any, as common_type_t<C, R...>. Otherwise, there shall be no member type.

Note B: Notwithstanding the provisions of [meta.type.synop], and
pursuant to [namespace.std],
a program may specialize common_type<T1, T2>
for types T1 and T2 such that
is_same_v<T1, decay_t<T1>> and
is_same_v<T2, decay_t<T2>> are each true.

[Note

: *end note*

]Such specializations are needed when only explicit conversions
are desired between the template arguments.

—
Such a specialization need not have a member named type,
but if it does, that member shall be a typedef-name
for an accessible and unambiguous cv-unqualified non-reference type C
to which each of the types T1 and T2 is explicitly convertible.

Moreover, common_type_t<T1, T2> shall denote
the same type, if any, as does common_type_t<T2, T1>.

No diagnostic is required for a violation of this Note's rules.

Note C: For the common_reference trait applied to a parameter pack
T of types, the member type shall be either defined or not
present as follows:

- If sizeof...(T) is zero, there shall be no member type.
- Otherwise, if sizeof...(T) is one, let T0 denote the sole type in the pack T. The member typedef type shall denote the same type as T0.
- Otherwise, if sizeof...(T) is two, let T1 and T2
denote the two types in the pack T. Then
- If T1 and T2 are reference types and COMMON-REF(T1, T2) is well-formed, then the member typedef type denotes that type.
- Otherwise, if basic_common_reference<remove_cvref_t<T1>, remove_cvref_t<T2>, XREF(T1), XREF(T2)>::type is well-formed, then the member typedef type denotes that type.
- Otherwise, if COND-RES(T1, T2) is well-formed, then the member typedef type denotes that type.
- Otherwise, if common_type_t<T1, T2> is well-formed, then the member typedef type denotes that type.
- Otherwise, there shall be no member type.

- Otherwise, if sizeof...(T) is greater than two, let T1,
T2, and Rest, respectively, denote the first, second, and
(pack of) remaining types comprising T. Let C be the type
common_reference_t<T1, T2>. Then:
- If there is such a type C, the member typedef type shall denote the same type, if any, as common_reference_t<C, Rest...>.
- Otherwise, there shall be no member type.

Note D: Notwithstanding the provisions of [meta.type.synop], and
pursuant to [namespace.std], a program may partially specialize
basic_common_reference<T, U, TQual, UQual>
for types T and U such that
is_same_v<T, decay_t<T>> and
is_same_v<U, decay_t<U>> are each true.

[Note

: *end note*

]Such specializations
can be used to influence the result of common_reference, and
are needed when only explicit conversions are desired
between the template arguments.

—
Such a specialization need not have a member named type, but if it does,
that member shall be a typedef-name for an accessible and
unambiguous type C to which each of the types TQual<T> and
UQual<U> is convertible.

Moreover, basic_common_reference<T, U, TQual, UQual>::type shall denote
the same type, if any, as does
basic_common_reference<U, T, UQual, TQual>::type.

No diagnostic is required for a violation of these rules.

[Example

: *end example*

]Given these definitions:

— using PF1 = bool (&)(); using PF2 = short (*)(long); struct S { operator PF2() const; double operator()(char, int&); void fn(long) const; char data; }; using PMF = void (S::*)(long) const; using PMD = char S::*;the following assertions will hold:

static_assert(is_same_v<invoke_result_t<S, int>, short>); static_assert(is_same_v<invoke_result_t<S&, unsigned char, int&>, double>); static_assert(is_same_v<invoke_result_t<PF1>, bool>); static_assert(is_same_v<invoke_result_t<PMF, unique_ptr<S>, int>, void>); static_assert(is_same_v<invoke_result_t<PMD, S>, char&&>); static_assert(is_same_v<invoke_result_t<PMD, const S*>, const char&>);