Doc. no. P0005R3
Date: 2015-11-10
Project: Programming Language C++
Reply to: Alisdair Meredith <ameredith1@bloomberg.net>
Stephan T. Lavavej <stl@microsoft.com>
Tomasz Kamiński <tomaszkam at gmail dot com>

Adopt not_fn from Library Fundamentals 2 for C++17

Table of Contents

Revision History

Revision 0

Original version of the paper for the 2015 pre-Kona mailing.

Revision 1

Revised to follow P0090R0, eliminating weak result type and result_type, and adding compatibility clauses to Annex C.

Additional future work item for std::reference_wrapper.

Established precedent for removing features from the standard without a period of deprecation.

Revision 2

LEWG review recommended we should keep the result_type typedef for std::function.

At LWG recommendation, renamed the fn term used in the specification of not_fn with g, the same name used in the bind specification, to minimize confusion with the term fd used in the same paragraphs.

Revision 3

Deprecate the remnants of the old adaptable function facility rather than remove it. Drafting follows the precedent for deprecating member names set by D.6 Old iostreams members [depr.ios.members] in the preceding versions of the standard.

Drop the paragraphs added to the compatiblity annex, and prune the list of names in the Zombie Names clause, as this revision does not remove any old names, and so creates no compatibility concerns.

Introduction

This paper recommends adopting the not_fn function binder from the Library Fundamentals TS v2 as a replacement for the old negators, not1 and not2. This enable the deprecation (and eventual removal) of the last parts of the legacy function binder APIs.

In the same mailing as revision 0 of this paper, Stephan Lavavej proposed removing the same typedefs, along with the weak result type wording that completed support for the deprecated (and removed) binders. This paper agrees with that direction and merges his wording to form a single, votable paper. However, following review at the eKona meeting, this paper now advocates deprecation, rather than removal.

Finally, Stephan's paper proposed a clause reserving names that are removed from the standard for previous standarization. This allows vendors to continue supporting the features removed at the April 2015 meeting in Lenexa until a time of their own choosing, to better support their customers without violating a strict interpretation of the standard.

Recommendation for Immediate Adoption

The function template not_fn was first proposed by Tomasz Kamiński for Library Fundamentals 2. However, there is extensive experience of this feature through the Boost library. The main reason cited for putting this into the Fundamentals TS v2, rather than directly into the C++ working draft, was to give users early access to the feature. However, we are already seeing new C++17 library features available in the main standard library distributions, typically guarded by an experimental C++17 build mode flag, so barring any unexpected design issues, there is a strong argument to ship this library in both the Fundamentals TS and the draft standard.

The immediate benefit of adopting this library directly into the C++ Standard is that it is the necessary missing component to allow us to deprecate the legacy negator types, unary_negate and binary_negate, and the factory functions not1 and not2. These are the last two library components that depend on the adaptable function protocol of embedding typedefs in functor classes to support adaption. The other such components from early standards (e.g., bind1st) have already been removed, following their deprecation in C++11. Adopting not_fn would allow us to deprecate, and ultimately remove, this final legacy.

Deprecate Support for the Adaptable Function Protocol

Deprecate the Classic not1 and not2 Negators

Traditionally we would start a long deprecation process before removing supported library features such as not1 and not2. However, this paper will argue that we should go further and actively remove them from the proposed C++17 standard, once the not_fn replacement is available, along with the adaptable functors have already been removed from the working paper.

The list of references at the end of this paper shows a number of other deprecated features targeted for removal in C++17, suggesting this would be an ideal time to perform cleanup, taking any hit of breaking compatibility with older code in one transition, rather than making each new version of the standard a risk.

Deprecate the typedefs that Support Adaptable Functions

Once the last of the classic binders are removed, then all of the support machinery created only for them should also be removed. That means removing all of the argument_type, first_argument_type, and second_argument_type typedefs in the standard library.

Note that the adaptable function protocol no longer functions as well when it was originally designed, due to the addition of new language features and libraries, such as lambda expressions, "diamond" functors, and more. This is not due to a lack of effort, but simply that it is not possible to have a unique set of typedefs for some of these types, such as polymorphic lambda objects. However, we do pay a cost for retaining support elsewhere in the library, due to the awkward conditionally defined member typedefs in several components, such as std::function wrapping a function type with exactly one or two parameters, or similarly for std::reference_wrapper for function references of exactly one or two arguments.

The original version of this paper recommended retaining the result_type typedefs under the mistaken impression they were part of the INVOKE protocol. Further research shows that link was severed back in 2007 with the adoption of N2194 which specified result_of entirely in terms of decltype, and so removing the link between bind-expressions and result_of when using INVOKE. With the subsequent removal of the deprecated function binders, and the proposed removal of the classic negators in this paper, there is no further use of weak result types in the standard library, other than defining them. Therefore, I agree with Stephan Lavavej in paper P0090R0 and recommend the removal weak result type and related uses of result_type from the standard library too.

One final wrinkle is that, based on review in Library Evolution, and feedback from those still actively using the feature, the result_type typedef should be retained for the two class templates std::hash and std::function. After further review, noting that the Hash concept for user-supplied hashing functors makes no requirement for result_type, it was recommended that result_type be retained for only std::function.

Allow Vendors to Support Customers

Library vendors will often choose to continue supporting customers using previous library features long after the standard has removed them, especially if they support multiple versions of the standard through the same distribution. Stephan proposed adding a subsection to clause 17 reserving certain names for use by previous standards. This continues to reserve those names for use by the library, meaning that users are not permitted to start using these names as macros. It also allows vendors to remove these identifiers at a time of their choosing, rather than immediately on the release of the new standard. This will mitigate the previous removal of deprecated features like auto_ptr.

Deprecate vs. Immediate Removal

Removing a feature directly from the standard without a period of deprecation is unusual, but not without precedent. C++11 removed exported templates and the original meaning of the keyword auto. C++14 removed gets and the implicit const on constexpr functions. The C++17 working draft has already removed support for trigraphs.

It is not clear that the features proposed for deprecation in this paper reach the same bar of minimal impact on existing code. For example, export was not implemented by most of the available compilers at the time of its immediate removal; code surveys of open source projects and large code bases confirmed that auto was not in widespread use; the removal of gets was deliberately intended to break existing usage of an unsafe function; code using trigraphs could easily be rewritten to not use trigraphs on the majority of known systems at the time of their removal.

Future Extensions

reference_wrapper for Incomplete Types

Removing the result_type typedefs would enable support for incomplete types in reference_wrapper. That is not possible today due to the need to look inside the template type parameter to sniff out the presence of a weak result type, or any of the other nested typedefs. The key difference to the current proposal is that reference_wrapper would be actively prohibited from adding the previous (conditional) typedefs for compatibility purposes otherwise permitted by the proposed zombie-names clause. Additionally, 17.6.4.8 [res.on.functions]/2.5 still holds, making it clear that we would be required to call out this support for reference_wrapper. In the meantime, implementations would be free to document and extend this guarantee as a conforming extension.

Adopting this suggestion would enable code like the following, that is currently ill-formed if the template type parameters are incomplete when instantiated: 

template<typename T, typename U>
auto my_tie(T& t, U& u) {
    return std::make_tuple(ref(t), ref(u));
}

Negated bind Expressions

A long-standing feature of the Boost library that contributed the original design for not_fn is an expansion of the bind language to return a bind expression that negates its result when called as !bind(a1, a2, ..., aN).

While this feature is desirable, it has not yet been through the LEWG process, and is slightly trickier to specify than implement as the result of a bind expression is unspecified, and the interaction works by providing an operator! overload for the unspecified bind-object type. Therefore, this is left as an extension to be proposed for the Library Fundamentals 3 TS.

Proposed Wording

Insert a new section under 17.6.4.3 [reserved.names], between 17.6.4.3.1 [macro.names] and 17.6.4.3.2 [extern.names]:

17.6.4.3.x Zombie names [zombie.names]

In namespace std, the following names are reserved for previous standardization: auto_ptr, bind1st, bind2nd, binder1st, binder2nd, mem_fun, mem_fun_ref, mem_fun_t, mem_fun1_t, mem_fun_ref_t, mem_fun1_ref_t, const_mem_fun_t, const_mem_fun1_t, const_mem_fun_ref_t, const_mem_fun1_ref_t, ptr_fun, pointer_to_unary_function, pointer_to_binary_function, random_shuffle, unary_function, and binary_function.

Amend the <function> header synopsis in 20.0p2 [function.objects]: 

  // 20.9.9, negators:
  template <class Predicate> class unary_negate;
  template <class Predicate>
    constexpr unary_negate<Predicate> not1(const Predicate&);
  template <class Predicate> class binary_negate;
  template <class Predicate>
    constexpr binary_negate<Predicate> not2(const Predicate&);

  // 20.9.9, Function template not_fn
  template <class F> unspecified not_fn(F&& f);

Strike the result_type, first_argument_type, and second_argument_type typedefs from 20.8.2.4 [util.smartptr.ownerless].

20.8.2.4 Class template owner_less [util.smartptr.ownerless]

1 The class template owner_less allows ownership-based mixed comparisons of shared and weak pointers. 

namespace std {
  template<class T> struct owner_less;

  template<class T> struct owner_less<shared_ptr<T> > {
    typedef bool result_type;
    typedef shared_ptr<T> first_argument_type;
    typedef shared_ptr<T> second_argument_type;
    bool operator()(shared_ptr<T> const&, shared_ptr<T> const&) const;
    bool operator()(shared_ptr<T> const&, weak_ptr<T> const&) const;
    bool operator()(weak_ptr<T> const&, shared_ptr<T> const&) const;
  };

  template<class T> struct owner_less<weak_ptr<T> > {
    typedef bool result_type;
    typedef weak_ptr<T> first_argument_type;
    typedef weak_ptr<T> second_argument_type;
    bool operator()(weak_ptr<T> const&, weak_ptr<T> const&) const;
    bool operator()(shared_ptr<T> const&, weak_ptr<T> const&) const;
    bool operator()(weak_ptr<T> const&, shared_ptr<T> const&) const;
  };
}

Strike the last note in 20.9p5 [function.objects]:

5 [Note: To enable adaptors and other components to manipulate function objects that take one or two arguments many of the function objects in this clause correspondingly provide typedefs argument_type and result_type for function objects that take one argument and first_argument_type, second_argument_type, and result_type for function objects that take two arguments. — end note ]

Strike the definition of weak result type from 20.9.2:

20.9.2 Requirements [func.require]

  1. Define INVOKE (f, t1, t2, ..., tN) as follows:
    1. (t1.*f)(t2, ..., tN) when f is a pointer to a member function of a class T and t1 is an object of type T or a reference to an object of type T or a reference to an object of a type derived from T;
    2. ((*t1).*f)(t2, ..., tN) when f is a pointer to a member function of a class T and t1 is not one of the types described in the previous item;
    3. t1.*f when N == 1 and f is a pointer to member data of a class T and t1 is an object of type T or a reference to an object of type T or a reference to an object of a type derived from T;
    4. (*t1).*f when N == 1 and f is a pointer to member data of a class T and t1 is not one of the types described in the previous item;
    5. f(t1, t2, ..., tN) in all other cases.
  2. Define INVOKE (f, t1, t2, ..., tN, R) as static_cast<void>(INVOKE (f, t1, t2, ..., tN)) if R is cv void, otherwise INVOKE (f, t1, t2, ..., tN) implicitly converted to R.
  3. If a call wrapper (20.9.1) has a weak result type the type of its member type result_type is based on the type T of the wrapper's target object (20.9.1):
    1. if T is a pointer to function type, result_type shall be a synonym for the return type of T;
    2. if T is a pointer to member function, result_type shall be a synonym for the return type of T;
    3. if T is a class type and the qualified-id T::result_type is valid and denotes a type (14.8.2), then result_type shall be a synonym for T::result_type;
    4. otherwise result_type shall not be defined.
  4. Every call wrapper (20.9.1) shall be MoveConstructible. A forwarding call wrapper is a call wrapper that can be called with an arbitrary argument list and delivers the arguments to the wrapped callable object as references. This forwarding step shall ensure that rvalue arguments are delivered as rvalue references and lvalue arguments are delivered as lvalue references. A simple call wrapper is a forwarding call wrapper that is CopyConstructible and CopyAssignable and whose copy constructor, move constructor, and assignment operator do not throw exceptions. [Note: In a typical implementation forwarding call wrappers have an overloaded function call operator of the form 
    template<class... UnBoundArgs>
R operator()(UnBoundArgs&&... unbound_args) cv-qual;
    — end note ]

Simplify the definition of reference_wrapper:

20.9.4 Class template reference_wrapper [refwrap]


namespace std {
  template <class T> class reference_wrapper {
  public :
    // types
    typedef T type;
    typedef see below result_type;              // not always defined
    typedef see below argument_type;            // not always defined
    typedef see below first_argument_type;      // not always defined
    typedef see below second_argument_type;     // not always defined

    // construct/copy/destroy
    reference_wrapper(T&) noexcept;
    reference_wrapper(T&&) = delete; // do not bind to temporary objects
    reference_wrapper(const reference_wrapper& x) noexcept;

    // assignment
    reference_wrapper& operator=(const reference_wrapper& x) noexcept;

    // access
    operator T& () const noexcept;
    T& get() const noexcept;

    // invocation
    template <class... ArgTypes>
    result_of_t<T&(ArgTypes&&...)>
    operator() (ArgTypes&&...) const;
  };
}

1 reference_wrapper<T> is a CopyConstructible and CopyAssignable wrapper around a reference to an object or function of type T.

2 reference_wrapper<T> shall be a trivially copyable type (3.9).

3 reference_wrapper<T> has a weak result type (20.9.2). If T is a function type, result_type shall be a synonym for the return type of T.

4 The template specialization reference_wrapper<T> shall define a nested type named argument_type as a synonym for T1 only if the type T is any of the following:

(4.1) — a function type or a pointer to function type taking one argument of type T1

(4.2) — a pointer to member function R T0::f cv (where cv represents the member function's cv-qualifiers); the type T1 is cv T0*

(4.3) — a class type where the qualified-id T::argument_type is valid and denotes a type (14.8.2); the type T1 is T::argument_type.

5 The template instantiation reference_wrapper<T> shall define two nested types named first_argument_type and second_argument_type as synonyms for T1 and T2, respectively, only if the type T is any of the following:

(5.1) — a function type or a pointer to function type taking two arguments of types T1 and T2

(5.2) — a pointer to member function R T0::f(T2) cv (where cv represents the member function's cv-qualifiers); the type T1 is cv T0*

(5.3) — a class type where the qualified-ids T::first_argument_type and T::second_argument_type are both valid and both denote types (14.8.2); the type T1 is T::first_argument_type and the type T2 is T::second_argument_type.

Strike the result_type, argument_type, first_argument_type, and second_argument_type typedefs from 20.9.5 [arithmetic.operations].

20.9.5 Arithmetic operations [arithmetic.operations]

1 The library provides basic function object classes for all of the arithmetic operators in the language (5.6, 5.7). 

template <class T = void> struct plus {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

2 operator() returns x + y. 

template <class T = void> struct minus {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

3 operator() returns x - y. 

template <class T = void> struct multiplies {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

4 operator() returns x * y. 

template <class T = void> struct divides {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

5 operator() returns x / y. 

template <class T = void> struct modulus {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

6 operator() returns x % y. 

template <class T = void> struct negate {
  constexpr T operator()(const T& x) const;
  typedef T argument_type;
  typedef T result_type;
};

7 operator() returns -x.

Strike the result_type, first_argument_type, and second_argument_type typedefs from 20.9.6 [comparisons].

20.9.6 Comparisons [comparisons]

1 The library provides basic function object classes for all of the comparison operators in the language (5.9, 5.10). 

template <class T = void> struct equal_to {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

2 operator() returns x == y. 

template <class T = void> struct not_equal_to {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

3 operator() returns x != y. 

template <class T = void> struct greater {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

4 operator() returns x > y. 

template <class T = void> struct less {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

5 operator() returns x < y. 

template <class T = void> struct greater_equal {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

6 operator() returns x >= y. 

template <class T = void> struct less_equal {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

7 operator() returns x <= y.

Strike the result_type, argument_type, first_argument_type, and second_argument_type typedefs from 20.9.7 [logical.operations].

20.9.7 Logical operations [logical.operations]

1 The library provides basic function object classes for all of the logical operators in the language (5.14, 5.15, 5.3.1). 

template <class T = void> struct logical_and {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

2 operator() returns x && y. 

template <class T = void> struct logical_or {
  constexpr bool operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};

3 operator() returns x || y. 

template <class T = void> struct logical_not {
  constexpr bool operator()(const T& x) const;
  typedef T argument_type;
  typedef bool result_type;
};

4 operator() returns !x.

Strike the result_type, argument_type, first_argument_type, and second_argument_type typedefs from 20.9.8 [bitwise.operations].

20.9.8 Bitwise operations [bitwise.operations]

1 The library provides basic function object classes for all of the bitwise operators in the language (5.11, 5.13, 5.12, 5.3.1). 

template <class T = void> struct bit_and {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

2 operator() returns x & y. 

template <class T = void> struct bit_or {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

3 operator() returns x | y. 

template <class T = void> struct bit_xor {
  constexpr T operator()(const T& x, const T& y) const;
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef T result_type;
};

4 operator() returns x ^ y. 

template <class T = void> struct bit_not {
  constexpr bool operator()(const T& x) const;
  typedef T argument_type;
  typedef T result_type;
};

5 operator() returns ~x.

Replace subclause 20.9.9 [negators] with a new subclause 20.9.9 [func.not_fn], copying everything from the Library Fundamentals 2 TS other than the struck-out note:

20.9.9 Negators [negators]

1 Negators not1 and not2 take a unary and a binary predicate, respectively, and return their complements (5.3.1). 


   template <class Predicate>
     class unary_negate {
   public:
     constexpr explicit unary_negate(const Predicate& pred);
     constexpr bool operator()(const typename Predicate::argument_type& x) const;
     typedef typename Predicate::argument_type argument_type;
     typedef bool result_type;
   };

2 operator() returns !pred(x). 


 template <class Predicate>
     constexpr unary_negate<Predicate> not1(const Predicate& pred);

3 Returns: unary_negate<Predicate>(pred). 


  template <class Predicate>
  class binary_negate {
  public:
    constexpr explicit binary_negate(const Predicate& pred);
    constexpr bool operator()(const typename Predicate::first_argument_type& x,
        const typename Predicate::second_argument_type& y) const;
  typedef typename Predicate::first_argument_type first_argument_type;
  typedef typename Predicate::second_argument_type second_argument_type;
  typedef bool result_type;
  };

4 operator() returns !pred(x,y). 


template <class Predicate>
  constexpr binary_negate<Predicate> not2(const Predicate& pred);

5 Returns: binary_negate<Predicate>(pred).

20.9.9 Function template not_fn [func.not_fn]


template <class F> unspecified not_fn(F&& f);

1 In the text that follows:

2 Requires: is_constructible<FD, F>::value shall be true. fd shall be a callable object (§20.9.1).

3 Returns: A forwarding call wrapper g such that the expression g(a1, a2, ..., aN) is equivalent to !INVOKE(fd, a1, a2, ..., aN) (§20.9.2).

4 Throws: Nothing unless the construction of fd throws an exception.

5 Remarks: The return type shall satisfy the requirements of MoveConstructible. If FD satisfies the requirements of CopyConstructible, then the return type shall satisfy the requirements of CopyConstructible. [ Note: This implies that FD is MoveConstructible. — end note ]

[ Note: Function template not_fn can usually provide a better solution than using the negators not1 and not2 — end note ]

Remove the weak result type from the type returns from bind expressions in 20.9.10.3 [func.bind.bind]:

3 Returns: A forwarding call wrapper g with a weak result type (20.9.2). The effect of g(u1, u2, ..., uM) shall be INVOKE(fd, std::forward<V1>(v1), std::forward<V2>(v2), ..., std::forward<VN>(vN), result_of_t<FD cv & (V1, V2, ..., VN)>), where cv represents the cv-qualifiers of g and the values and types of the bound arguments v1, v2, ..., vN are determined as specified below. The copy constructor and move constructor of the forwarding call wrapper shall throw an exception if and only if the corresponding constructor of FD or of any of the types TiD throws an exception.

Remove the result_type member from the type returned by bind expressions with user-specified return types in 20.9.10.3 [func.bind.bind]:

7 Returns: A forwarding call wrapper g (20.9.2) with a nested type result_type defined as a synonym for R. The effect of g(u1, u2, ..., uM) shall be INVOKE(fd, std::forward<V1>(v1), std::forward<V2>(v2), ..., std::forward<VN>(vN), R), where the values and types of the bound arguments v1, v2, ..., vN are determined as specified below. The copy constructor and move constructor of the forwarding call wrapper shall throw an exception if and only if the corresponding constructor of FD or of any of the types TiD throws an exception.

Strike the unnecessary typedefs from the unspecified return-type of mem_fn:

20.9.11 Function template mem_fn [func.memfn]

template<class R, class T> unspecified mem_fn(R T::* pm);

1 Returns: A simple call wrapper (20.9.1) fn such that the expression fn(t, a2, ..., aN) is equivalent to INVOKE (pm, t, a2, ..., aN) (20.9.2). fn shall have a nested type result_type that is a synonym for the return type of pm when pm is a pointer to member function.

2 The simple call wrapper shall define two nested types named argument_type and result_type as synonyms for cv T* and Ret, respectively, when pm is a pointer to member function with cv-qualifier cv and taking no arguments, where Ret is pm's return type.

3 The simple call wrapper shall define three nested types named first_argument_type, second_argument_type, and result_type as synonyms for cv T*, T1, and Ret, respectively, when pm is a pointer to member function with cv-qualifier cv and taking one argument of type T1, where Ret is pm's return type.

4 Throws: Nothing.

Strike the relevant typedefs from the class definition of function:

20.9.12.2 Class template function [func.wrap.func]


namespace std {
template<class> class function; // undefined
template<class R, class... ArgTypes>
class function<R(ArgTypes...)> {
public:
  typedef R result_type;
  typedef T1 argument_type;          // only if sizeof...(ArgTypes) == 1 and
                                     // the type in ArgTypes is T1
  typedef T1 first_argument_type;    // only if sizeof...(ArgTypes) == 2 and
                                     // ArgTypes contains T1 and T2
  typedef T2 second_argument_type;   // only if sizeof...(ArgTypes) == 2 and
                                     // ArgTypes contains T1 and T2

  // further details elided...
};

Strike bullet (1.3), on the definition of standard hash functors:

20.9.13 Class template hash [unord.hash]

1 The unordered associative containers defined in 23.5 use specializations of the class template hash as the default hash function. For all object types Key for which there exists a specialization hash<Key>, and for all enumeration types (7.2) Key, the instantiation hash<Key> shall:

(1.1) — satisfy the Hash requirements (17.6.3.4), with Key as the function call argument type, the DefaultConstructible requirements (Table 19), the CopyAssignable requirements (Table 23),

(1.2) — be swappable (17.6.3.2) for lvalues,

(1.3) — provide two nested types result_type and argument_type which shall be synonyms for size_t and Key, respectively,

(1.4) — satisfy the requirement that if k1 == k2 is true, h(k1) == h(k2) is also true, where h is an object of type hash<Key> and k1 and k2 are objects of type Key;

(1.5) — satisfy the requirement that the expression h(k), where h is an object of type hash<Key> and k is an object of type Key, shall not throw an exception unless hash<Key> is a user-defined specialization that depends on at least one user-defined type.

Strike the result_type, first_argument_type, and second_argument_type typedefs from the value_compare member-class of map in 23.4.4.1 [map.overview].

23.4.4 Class template map [map]

23.4.4.1 Class template map overview [map.overview]

namespace std {
  template <class Key, class T, class Compare = less<Key>,
            class Allocator = allocator<pair<const Key, T> > >
  class map {
  public:
     // types
     // details elided...

     class value_compare {
     friend class map;
     protected:
       Compare comp;
       value_compare(Compare c) : comp(c) {}
     public:
       typedef bool result_type;
       typedef value_type first_argument_type;
       typedef value_type second_argument_type;
       bool operator()(const value_type& x, const value_type& y) const {
         return comp(x.first, y.first);
       }
    };

    // 23.4.4.2, construct/copy/destroy:
    // remaining details elided...
  };
}

Strike the result_type, first_argument_type, and second_argument_type typedefs from the value_compare member-class of multimap in 23.4.5.1 [multimap.overview].

23.4.5 Class template multimap [multimap]

23.4.5.1 Class template multimap overview [multimap.overview]

namespace std {
  template <class Key, class T, class Compare = less<Key>,
            class Allocator = allocator<pair<const Key, T> > >
  class multimap {
  public:
     // types
     // details elided...

     class value_compare {
     friend class map;
     protected:
       Compare comp;
       value_compare(Compare c) : comp(c) {}
     public:
       typedef bool result_type;
       typedef value_type first_argument_type;
       typedef value_type second_argument_type;
       bool operator()(const value_type& x, const value_type& y) const {
         return comp(x.first, y.first);
       }
    };

    // 23.4.4.2, construct/copy/destroy:
    // remaining details elided...
  };
}

Insert a new clause into Annex D:

D.x Old Adaptable Function Bindings [depr.func.adaptor.binding]

D.x.1 Weak Result Types [depr.weak.result_type]

  1. If a call wrapper (20.9.1) has a weak result type, the type of its member type result_type is based on the type T of the wrapper's target object (20.9.1):
    1. if T is a pointer to function type, result_type shall be a synonym for the return type of T;
    2. if T is a pointer to member function, result_type shall be a synonym for the return type of T;
    3. if T is a class type and the qualified-id T::result_type is valid and denotes a type (14.8.2), then result_type shall be a synonym for T::result_type;
    4. otherwise result_type shall not be defined.

D.x.2 Typedefs to Support Function Binders [depr.func.adaptor.typedefs]

  1. To enable old function adaptors to manipulate function objects that take one or two arguments, many of the function objects in this standard correspondingly provide typedefs argument_type and result_type for function objects that take one argument and first_argument_type, second_argument_type, and result_type for function objects that take two arguments.
  2. The following member names are defined in addition to names specified in Clause 20: 
    namespace std {
  template<class T> struct owner_less<shared_ptr<T> > {
    typedef bool result_type;
    typedef shared_ptr<T> first_argument_type;
    typedef shared_ptr<T> second_argument_type;
  };

  template<class T> struct owner_less<weak_ptr<T> > {
    typedef bool result_type;
    typedef weak_ptr<T> first_argument_type;
    typedef weak_ptr<T> second_argument_type;
  };

  template <class T> class reference_wrapper {
  public :
    typedef see below result_type;              // not always defined
    typedef see below argument_type;            // not always defined
    typedef see below first_argument_type;      // not always defined
    typedef see below second_argument_type;     // not always defined
  };

  template <class T = void> struct plus {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct minus {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct multiplies {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct divides {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct modulus {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct negate {
    typedef T argument_type;
    typedef T result_type;
  };

  template <class T = void> struct equal_to {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct not_equal_to {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct greater {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct less {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct greater_equal {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct less_equal {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct logical_and {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct logical_or {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct logical_not {
    typedef T argument_type;
    typedef bool result_type;
  };

  template <class T = void> struct bit_and {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct bit_or {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct bit_xor {
    typedef T first_argument_type;
    typedef T second_argument_type;
    typedef T result_type;
  };

  template <class T = void> struct bit_not {
    typedef T argument_type;
    typedef T result_type;
  };

  template<class R, class... ArgTypes>
  class function<R(ArgTypes...)> {
  public:
    typedef T1 argument_type;          // only if sizeof...(ArgTypes) == 1 and
                                       // the type in ArgTypes is T1
    typedef T1 first_argument_type;    // only if sizeof...(ArgTypes) == 2 and
                                       // ArgTypes contains T1 and T2
    typedef T2 second_argument_type;   // only if sizeof...(ArgTypes) == 2 and
                                       // ArgTypes contains T1 and T2
  };
}
  3. reference_wrapper<T> has a weak result type (D.x.1). If T is a function type, result_type shall be a synonym for the return type of T.
  4. The template specialization reference_wrapper<T> shall define a nested type named argument_type as a synonym for T1 only if the type T is any of the following:
    1. - a function type or a pointer to function type taking one argument of type T1
    2. - a pointer to member function R T0::f cv (where cv represents the member function's cv-qualifiers); the type T1 is cv T0*
    3. - a class type where the qualified-id T::argument_type is valid and denotes a type (14.8.2); the type T1 is T::argument_type.
  5. The template instantiation reference_wrapper<T> shall define two nested types named first_argument_type and second_argument_type as synonyms for T1 and T2, respectively, only if the type T is any of the following:
    1. - a function type or a pointer to function type taking two arguments of types T1 and T2
    2. - a pointer to member function R T0::f(T2) cv (where cv represents the member function's cv-qualifiers); the type T1 is cv T0*
    3. - a class type where the qualified-ids T::first_argument_type and T::second_argument_type are both valid and both denote types (14.8.2); the type T1 is T::first_argument_type and the type T2 is T::second_argument_type.
  6. For all object types Key for which there exists a specialization hash<Key>, and for all enumeration types (7.2) Key, the instantiation hash<Key> shall provide two nested types, result_type and argument_type, which shall be synonyms for size_t and Key, respectively.
  7. The forwarding call wrapper g returned by a call to bind(f, bound_args...) (20.9.10.3) shall have a weak result type (D.x.1).
  8. The forwarding call wrapper g returned by a call to bind<R>(f, bound_args...) (20.9.10.3) shall have a nested type result_type defined as a synonym for R.
  9. The simple call wrapper fn returned from a call to mem_fn(pm) shall have a nested type result_type that is a synonym for the return type of pm when pm is a pointer to member function.
  10. The simple call wrapper shall define two nested types named argument_type and result_type as synonyms for cv T* and Ret, respectively, when pm is a pointer to member function with cv-qualifier cv and taking no arguments, where Ret is pm's return type.
  11. The simple call wrapper shall define three nested types named first_argument_type, second_argument_type, and result_type as synonyms for cv T*, T1, and Ret, respectively, when pm is a pointer to member function with cv-qualifier cv and taking one argument of type T1, where Ret is pm's return type.
  12. The following member names are defined in addition to names specified in Clause 23: 
    namespace std {
  template <class Key, class T, class Compare = less<Key>,
            class Allocator = allocator<pair<const Key, T>>>
  class map {
  public:
     class value_compare {
     public:
       typedef bool result_type;
       typedef value_type first_argument_type;
       typedef value_type second_argument_type;
       }
    };
  };

  template <class Key, class T, class Compare = less<Key>,
            class Allocator = allocator<pair<const Key, T>>>
  class multimap {
  public:
     class value_compare {
     public:
       typedef bool result_type;
       typedef value_type first_argument_type;
       typedef value_type second_argument_type;
    };
  };
}

D.x.3 Negators [depr.negators]

  1. The header <functional> has the following additional declarations: 
    namespace std {
  template <class Predicate> class unary_negate;
  template <class Predicate>
    constexpr unary_negate<Predicate> not1(const Predicate&);
  template <class Predicate> class binary_negate;
  template <class Predicate>
    constexpr binary_negate<Predicate> not2(const Predicate&);
}
  2. Negators not1 and not2 take a unary and a binary predicate, respectively, and return their complements (5.3.1). 

    3. 
   template <class Predicate>
     class unary_negate {
   public:
     constexpr explicit unary_negate(const Predicate& pred);
     constexpr bool operator()(const typename Predicate::argument_type& x) const;
     typedef typename Predicate::argument_type argument_type;
     typedef bool result_type;
   };

  3. operator() returns !pred(x). 

    4. 
 template <class Predicate>
     constexpr unary_negate<Predicate> not1(const Predicate& pred);

  4. Returns: unary_negate<Predicate>(pred). 

    5. 
  template <class Predicate>
  class binary_negate {
  public:
    constexpr explicit binary_negate(const Predicate& pred);
    constexpr bool operator()(const typename Predicate::first_argument_type& x,
                              const typename Predicate::second_argument_type& y) const;
    typedef typename Predicate::first_argument_type first_argument_type;
    typedef typename Predicate::second_argument_type second_argument_type;
    typedef bool result_type;
  };

  5. operator() returns !pred(x,y). 

    6. 
template <class Predicate>
  constexpr binary_negate<Predicate> not2(const Predicate& pred);

  6. Returns: binary_negate<Predicate>(pred).

References