1. Introduction
1.1. Example
Before going into details, below is a simple example of the core of what is proposed -- a "virtual", but statically-dispatched, non-member function that declares a logical entry point for user-customization. Users may explicitly override such a function for their type from their own namespace, in which case qualified calls to the customization point will dispatch to the user’s customized implementation whenever appropriate.
namespace std { // A customization point named "swap", including a default definition. template < class T > virtual void swap ( T & lhs , T & rhs ) { /*...*/ } } // namespace std // A user’s override (may appear in their own namespace) void swap ( foo & lhs , foo & rhs ) override : std :: swap { /*...*/ } 
1.2. Motivation
Many C++ libraries introduce simple, named, single-function customization points
through which generic code may interface with user-defined operations. Two
common techniques for implementing these customization points are nested members
of template specializations (such as with traits classes or with 
Both of the aforementioned approaches have advantages and disadvantages. The traits-based approach allows for groupings of associated types and associated functions, has a fairly clear declaration, has (relatively) simple rules when matching template arguments to specializations, but is a bit cumbersome to use directly and user-specialization often requires jumping into a foreign namespace.
The ADL-based approach applies to individual functions as opposed to groupings of associated properties, so it is a bit narrower in scope, but in that narrow scope it has some advantages. When a user needs to override such a customization point, they do not need to enter into a foreign namespace nor do they have to specialize a type-template just to customize a single function.
However, the simplicity of ADL-based customization points is in some sense an illusion. Proper creation and use of ADL customization points is so subtle that experts in C++ have written extensive articles about them[2] and they are a frequent source of questions for newcomers and experienced C++ programmers alike[3]. Ranges even goes so far as to introduce the design pattern of a "Customization Point Object" at the library level[4], whose primary purpose is to make it easier to consistently specify and invoke ADL-based customization points. A prominent programmer in the generic programming community has even gone so far as to state ADL is the one feature that he would remove from C++ if he could.[5]
The following are considered by the author of this proposal to be some core issues with customization points based on ADL.
- 
     They do not have a clear declaration in code. 
- 
     They are subtle to invoke correctly and doing so incorrectly may not always produce a compile-time error ( using std :: swap ; swap ( lhs , rhs ); 
- 
     Associated-namespace rules are rarely understood, cause confusion, and bugs. 
- 
     Lookup often leads to a large amount of overloads that must be considered. 
This proposal attempts to make function-kind customization points a directly supported part of the language, with a simpler set of rules than existing approaches that most programmers would be able to fully understand.
2. Customization Point Functions
Customization point functions are the proposed alternative to the subset of customization points that developers currently use ADL for.
2.1. Declaring a Customization Point Function
A customization point function may be declared at namespace scope just as any
other function template, but with a preceding 
template < class T > virtual constexpr void swap ( T & lhs , T & rhs ) noexcept ( std :: is_nothrow_move_constructible_v < T > && std :: is_nothrow_move_assignable_v < T > ) requires MoveConstructible < T > && MoveAssignable < T > { T temp = std :: move ( lhs ); lhs = std :: move ( rhs ); rhs = std :: move ( temp ); } 
Note that the usage of the keyword 
2.2. Overriding Customization Point Functions
A customization point function’s primary use is as a non-member function that
may be overridden. Unlike with normal function overloading, an override of a
customization point function must be explicitly declared as an override of that
specific customization point function. There are multiple ways in which a
customization point function’s override may be declared, but the simplest is to
write the function type including the 
namespace std { // A customization point function template < class T > virtual void swap ( T & lhs , T & rhs ) { /*default definition*/ } } // namespace std // A user-defined type class tensor { /*...*/ }; // A user-defined override for swap void ( tensor & lhs , tensor & rhs ) override : std :: swap // The customization point function to be overridden { /*...*/ } 
Informally, an override of a customization point function must be more
specialized or more constrained than the customization point function that it
overrides, but the return type of an override may differ if the override’s
return type is implicitly convertible to the customization point function’s
return type, or if the customization point’s return type is 
Formal details surrounding these requirements and any alterations will be explored in a future revision if the rest of the proposal is positively received.
2.2.1. Semantics of Customization Point Functions
When code attempts to call a customization point function, it is first resolved as if there were some imaginary function or function template with that declaration. If a call to such a function would be valid, then it and all of the direct overrides of that customization point function are treated as though they were all functions with the same name in some namespace with no other members. If a qualified call to a function of that name in that namespace would succeed, then the corresponding function is what is called in the actual program.
2.3. Named Customization Point Function Overrides
An override of a customization point function may optionally be given a name. To specify a name for a customization point function override, the declaration is the same as a normal function declaration, except that it includes the override specifier and the customization point function that it overrides in the same manner as for an unnamed override described above. A name given to an overriding function definition must be a unique name in its namespace (it must be unique even with respect to other functions in that namespace).
template < class It , class Distance > virtual constexpr void advance ( It & it , Distance n ) requires InputIterator < It > { for ( ; n != 0 ; -- n ) ++ it ; } template < class It , class Distance > constexpr void advance_bidirectional ( It & it , Distance n ) override requires BidirectionalIterator < It > : advance { if ( n >= 0 ) for ( ; n != 0 ; -- n ) ++ it ; else for ( ; n != 0 ; ++ n ) -- it ; } 
One advantage of specification of a name for an override is that it makes it
easier to invoke a specific override, much as it is useful to be able to invoke
a specific 
A named override is itself considered to also be a customization point function. Implications of this are described later on in this paper.
2.4. Overrides as Friend Functions
In order to limit the amount of overrides that are looked up per call, it is
suggested that a customization point function may be able to be overridden in
the body of a class definition, in a similar manner to how an inline 
2.5. Customization Point Functions as Objects
Despite the name, a customization point function is expected to behave more similar to a function object than to a function or function template. The rationale for this is to allow such a function to be able to be easily passed around to higher-order functions as a single entity. It also more accurately reflects intended behavior with respect to prohibition of "implicit" overloading and name lookup. A customization point function *cannot* be overloaded, but rather, it may only be overridden. Further, a customization point function is to not be found by ADL, and if when attempting to call a function by name a customization point function of that name is found by normal name lookup prior to ADL, then ADL is inhibited. The combination of these rules removes many of the subtleties of invoking customization points correctly.
2.6. "Pure Virtual" Customization Point Functions
Similar to 
template < class T > virtual void draw ( context & cont , T const & obj ) = 0 ; 
2.7. Final Customization Point Functions
A customization point function may be declared 
A 
template < class T > T square ( T const & arg ) final { return arg * arg ; } std :: transform ( range1 , out_it , square ); 
2.8. Hierarchical Customization Point Functions
As mentioned earlier, a named customization point function override is itself
considered to be its own customization point function. This means that such an
override may be explicitly overridden by name (it may also be pure and it may be 
template < class It , class Distance > virtual constexpr void advance ( It & it , Distance n ) requires InputIterator < It > { for ( ; n != 0 ; -- n ) ++ it ; } template < class It , class Distance > constexpr void advance_bidirectional ( It & it , Distance n ) override requires BidirectionalIterator < It > : advance { if ( n >= 0 ) for ( ; n != 0 ; -- n ) ++ it ; else for ( ; n != 0 ; ++ n ) -- it ; } template < class It , class Distance > constexpr void advance_random_access ( It & it , Distance n ) override requires RandomAccessIterator < It > : advance_bidirectional { it += n ; } 
Note that the above code example has some advantages over both traditional
concept-based overloading and of branching via 
A named customization point function override that is intended to be 
3. Suggested Polls
Should this proposal be elaborated on in a future revision?
Are the motivating problems worth solving at the language level at all?
Is the functionality of 
4. References
[1]: Matt Kulukundis: "Tip of the Week #152: AbslHashValue and You" https://abseil.io/tips/152
[2]: Eric Niebler: "Customization Point Design in C++11 and Beyond" http://ericniebler.com/2014/10/21/customization-point-design-in-c11-and-beyond/
[3]: Stack Overflow Search for ADL https://stackoverflow.com/search?q=ADL
[4]: N4762 "Working Draft, Standard for Programming Language C++" [customization.point.object]: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/n4762.pdf
[5]: Jens Weller "An Interview with Sean Parent" https://www.meetingcpp.com/blog/items/interview-with-sean-parent.html
[6]: Eric Niebler: "C++11 Library Design" https://github.com/boostcon/cppnow_presentations_2014/blob/master/files/cxx11-library-design.pdf