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Showing content from https://en.cppreference.com/w/cpp/language/../keywords/../language/extending_std.html below:

Extending the namespace std - cppreference.com

[edit] Adding declarations to std

It is undefined behavior to add declarations or definitions to namespace std or to any namespace nested within std, with a few exceptions noted below.

#include <utility>
 
namespace std
{
    // a function definition added to namespace std: undefined behavior
    pair<int, int> operator+(pair<int, int> a, pair<int, int> b)
    {
        return {a.first + b.first, a.second + b.second};
    }
}
[edit] Adding template specializations [edit] Class templates

It is allowed to add template specializations for any standard library class template to the namespace std only if the declaration depends on at least one program-defined type and the specialization satisfies all requirements for the original template, except where such specializations are prohibited.

// Get the declaration of the primary std::hash template.
// We are not permitted to declare it ourselves.
// <typeindex> is guaranteed to provide such a declaration, 
// and is much cheaper to include than <functional>.
 
#include <typeindex> 
 
// Specialize std::hash so that MyType can be used as a key in 
// std::unordered_set and std::unordered_map.  Opening namespace
// std can accidentally introduce undefined behavior, and is not
// necessary for specializing class templates.
template<>
struct std::hash<MyType>
{
    std::size_t operator()(const MyType& t) const { return t.hash(); }
};

It is undefined behavior to declare a full or partial specialization of any member class template of a standard library class or class template.

[edit] Function templates and member functions of templates

It is allowed to add template specializations for any standard library function template to the namespace std only if the declaration depends on at least one program-defined type and the specialization satisfies all requirements for the original template, except where such specializations are prohibited.

(until C++20)

It is undefined behavior to declare a full specialization of any standard library function template.

(since C++20)

It is undefined behavior to declare a full specialization of any member function of a standard library class template:

It is undefined behavior to declare a full specialization of any member function template of a standard library class or class template:

[edit] Variable templates

It is undefined behavior to declare a full or partial specialization of any standard library variable template, except where explicitly allowed.

(since C++14) [edit] Explicit instantiation of templates

It is allowed to explicitly instantiate a class (since C++20)template defined in the standard library only if the declaration depends on the name of at least one program-defined type and the instantiation meets the standard library requirements for the original template.

[edit] Other restrictions

The namespace std may not be declared as an inline namespace.

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior LWG 120 C++98 users could explicitly instantiate standard
library templates for non-user defined types prohibited LWG 232 C++98 users could explicitly specialize standard library templates
if the declaration depends on a user-defined name of
external linkage (which can refer to a non-user-defined type) only allowed for
user-defined types LWG 422 C++98 users could specialize individual members or member templates
without specializing the whole standard library class or class template the behavior is
undefined in this case

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