23 General utilities library [utilities]

23.14 Function objects [function.objects]

A function object type is an object type that can be the type of the postfix-expression in a function call ([expr.call], [over.match.call]).222 A function object is an object of a function object type. In the places where one would expect to pass a pointer to a function to an algorithmic template (Clause [algorithms]), the interface is specified to accept a function object. This not only makes algorithmic templates work with pointers to functions, but also enables them to work with arbitrary function objects.

222)

Such a type is a function pointer or a class type which has a member operator() or a class type which has a conversion to a pointer to function.

23.14.1 Header <functional> synopsis [functional.syn]

namespace std {
  // [func.invoke], invoke
  template <class F, class... Args>
    invoke_result_t<F, Args...> invoke(F&& f, Args&&... args)
      noexcept(is_nothrow_invocable_v<F, Args...>);

  // [refwrap], reference_wrapper
  template <class T> class reference_wrapper;

  template <class T> reference_wrapper<T> ref(T&) noexcept;
  template <class T> reference_wrapper<const T> cref(const T&) noexcept;
  template <class T> void ref(const T&&) = delete;
  template <class T> void cref(const T&&) = delete;

  template <class T> reference_wrapper<T> ref(reference_wrapper<T>) noexcept;
  template <class T> reference_wrapper<const T> cref(reference_wrapper<T>) noexcept;

  // [arithmetic.operations], arithmetic operations
  template <class T = void> struct plus;
  template <class T = void> struct minus;
  template <class T = void> struct multiplies;
  template <class T = void> struct divides;
  template <class T = void> struct modulus;
  template <class T = void> struct negate;
  template <> struct plus<void>;
  template <> struct minus<void>;
  template <> struct multiplies<void>;
  template <> struct divides<void>;
  template <> struct modulus<void>;
  template <> struct negate<void>;

  // [comparisons], comparisons
  template <class T = void> struct equal_to;
  template <class T = void> struct not_equal_to;
  template <class T = void> struct greater;
  template <class T = void> struct less;
  template <class T = void> struct greater_equal;
  template <class T = void> struct less_equal;
  template <> struct equal_to<void>;
  template <> struct not_equal_to<void>;
  template <> struct greater<void>;
  template <> struct less<void>;
  template <> struct greater_equal<void>;
  template <> struct less_equal<void>;

  // [logical.operations], logical operations
  template <class T = void> struct logical_and;
  template <class T = void> struct logical_or;
  template <class T = void> struct logical_not;
  template <> struct logical_and<void>;
  template <> struct logical_or<void>;
  template <> struct logical_not<void>;

  // [bitwise.operations], bitwise operations
  template <class T = void> struct bit_and;
  template <class T = void> struct bit_or;
  template <class T = void> struct bit_xor;
  template <class T = void> struct bit_not;
  template <> struct bit_and<void>;
  template <> struct bit_or<void>;
  template <> struct bit_xor<void>;
  template <> struct bit_not<void>;

  // [func.not_fn], function template not_fn
  template <class F>
    unspecified not_fn(F&& f);

  // [func.bind], bind
  template<class T> struct is_bind_expression;
  template<class T> struct is_placeholder;

  template<class F, class... BoundArgs>
    unspecified bind(F&&, BoundArgs&&...);
  template<class R, class F, class... BoundArgs>
    unspecified bind(F&&, BoundArgs&&...);

  namespace placeholders {
    // M is the implementation-defined number of placeholders
    see below _1;
    see below _2;
               .
               .
               .
    see below _M;
  }

  // [func.memfn], member function adaptors
  template<class R, class T>
    unspecified mem_fn(R T::*) noexcept;

  // [func.wrap], polymorphic function wrappers
  class bad_function_call;

  template<class> class function; // not defined
  template<class R, class... ArgTypes> class function<R(ArgTypes...)>;

  template<class R, class... ArgTypes>
    void swap(function<R(ArgTypes...)>&, function<R(ArgTypes...)>&) noexcept;

  template<class R, class... ArgTypes>
    bool operator==(const function<R(ArgTypes...)>&, nullptr_t) noexcept;
  template<class R, class... ArgTypes>
    bool operator==(nullptr_t, const function<R(ArgTypes...)>&) noexcept;
  template<class R, class... ArgTypes>
    bool operator!=(const function<R(ArgTypes...)>&, nullptr_t) noexcept;
  template<class R, class... ArgTypes>
    bool operator!=(nullptr_t, const function<R(ArgTypes...)>&) noexcept;

  // [func.search], searchers
  template<class ForwardIterator, class BinaryPredicate = equal_to<>>
    class default_searcher;

  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
    class boyer_moore_searcher;

  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
    class boyer_moore_horspool_searcher;

  // [unord.hash], hash function primary template
  template <class T>
    struct hash;

  // [func.bind], function object binders
  template <class T>
    inline constexpr bool is_bind_expression_v = is_bind_expression<T>::value;
  template <class T>
    inline constexpr int is_placeholder_v = is_placeholder<T>::value;
}

[ Example: If a C++ program wants to have a by-element addition of two vectors a and b containing double and put the result into a, it can do:

transform(a.begin(), a.end(), b.begin(), a.begin(), plus<double>());

— end example ]

[ Example: To negate every element of a:

transform(a.begin(), a.end(), a.begin(), negate<double>());

— end example ]

23.14.2 Definitions [func.def]

The following definitions apply to this Clause:

A call signature is the name of a return type followed by a parenthesized comma-separated list of zero or more argument types.

A callable type is a function object type or a pointer to member.

A callable object is an object of a callable type.

A call wrapper type is a type that holds a callable object and supports a call operation that forwards to that object.

A call wrapper is an object of a call wrapper type.

A target object is the callable object held by a call wrapper.

23.14.3 Requirements [func.require]

Define INVOKE(f, t1, t2, ..., tN) as follows:

(1.1)
(t1.*f)(t2, ..., tN) when f is a pointer to a member function of a class T and is_base_of_v<T, decay_t<decltype(t1)>> is true;
(1.2)
(t1.get().*f)(t2, ..., tN) when f is a pointer to a member function of a class T and decay_t<decltype(t1)> is a specialization of reference_wrapper;
(1.3)
((*t1).*f)(t2, ..., tN) when f is a pointer to a member function of a class T and t1 does not satisfy the previous two items;
(1.4)
t1.*f when N == 1 and f is a pointer to data member of a class T and is_base_of_v<T, decay_t<decltype(t1)>> is true;
(1.5)
t1.get().*f when N == 1 and f is a pointer to data member of a class T and decay_t<decltype(t1)> is a specialization of reference_wrapper;
(1.6)
(*t1).*f when N == 1 and f is a pointer to data member of a class T and t1 does not satisfy the previous two items;
(1.7)
f(t1, t2, ..., tN) in all other cases.

Define INVOKE<R>(f, t1, t2, ..., tN) as static_cast<void>(INVOKE(f, t1, t2, ..., tN)) if R is cv void, otherwise INVOKE(f, t1, t2, ..., tN) implicitly converted to R.

Every call wrapper 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 ]

23.14.4 Function template invoke [func.invoke]

template <class F, class... Args> invoke_result_t<F, Args...> invoke(F&& f, Args&&... args) noexcept(is_nothrow_invocable_v<F, Args...>);

Returns: INVOKE(std::forward<F>(f), std::forward<Args>(args)...) ([func.require]).

23.14.5 Class template reference_wrapper [refwrap]

namespace std {
  template <class T> class reference_wrapper {
  public :
    // types
    using type = T;

    // 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>
      invoke_result_t<T&, ArgTypes...>
      operator() (ArgTypes&&...) const;
  };

  template<class T>
    reference_wrapper(reference_wrapper<T>) -> reference_wrapper<T>;
}

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

reference_wrapper<T> shall be a trivially copyable type.

23.14.5.1 reference_wrapper construct/copy/destroy [refwrap.const]

reference_wrapper(T& t) noexcept;

Effects: Constructs a reference_wrapper object that stores a reference to t.

reference_wrapper(const reference_wrapper& x) noexcept;

Effects: Constructs a reference_wrapper object that stores a reference to x.get().

23.14.5.2 reference_wrapper assignment [refwrap.assign]

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

Postconditions: *this stores a reference to x.get().

23.14.5.3 reference_wrapper access [refwrap.access]

operator T& () const noexcept;

Returns: The stored reference.

T& get() const noexcept;

Returns: The stored reference.

23.14.5.4 reference_wrapper invocation [refwrap.invoke]

template <class... ArgTypes> invoke_result_t<T&, ArgTypes...> operator()(ArgTypes&&... args) const;

Returns: INVOKE(get(), std::forward<ArgTypes>(args)...). ([func.require])

23.14.5.5 reference_wrapper helper functions [refwrap.helpers]

template <class T> reference_wrapper<T> ref(T& t) noexcept;

Returns: reference_wrapper<T>(t).

template <class T> reference_wrapper<T> ref(reference_wrapper<T> t) noexcept;

Returns: ref(t.get()).

template <class T> reference_wrapper<const T> cref(const T& t) noexcept;

Returns: reference_wrapper <const T>(t).

template <class T> reference_wrapper<const T> cref(reference_wrapper<T> t) noexcept;

Returns: cref(t.get()).

23.14.6 Arithmetic operations [arithmetic.operations]

The library provides basic function object classes for all of the arithmetic operators in the language ([expr.mul], [expr.add]).

23.14.6.1 Class template plus [arithmetic.operations.plus]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x + y.

template <> struct plus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) + std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) + std::forward(u));

Returns: std::forward<T>(t) + std::forward(u).

23.14.6.2 Class template minus [arithmetic.operations.minus]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x - y.

template <> struct minus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) - std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) - std::forward(u));

Returns: std::forward<T>(t) - std::forward(u).

23.14.6.3 Class template multiplies [arithmetic.operations.multiplies]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x * y.

template <> struct multiplies<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) * std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) * std::forward(u));

Returns: std::forward<T>(t) * std::forward(u).

23.14.6.4 Class template divides [arithmetic.operations.divides]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x / y.

template <> struct divides<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) / std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) / std::forward(u));

Returns: std::forward<T>(t) / std::forward(u).

23.14.6.5 Class template modulus [arithmetic.operations.modulus]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x % y.

template <> struct modulus<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) % std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) % std::forward(u));

Returns: std::forward<T>(t) % std::forward(u).

23.14.6.6 Class template negate [arithmetic.operations.negate]

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

constexpr T operator()(const T& x) const;

Returns: -x.

template <> struct negate<void> { template <class T> constexpr auto operator()(T&& t) const -> decltype(-std::forward<T>(t)); using is_transparent = unspecified; };

template <class T> constexpr auto operator()(T&& t) const -> decltype(-std::forward<T>(t));

Returns: -std::forward<T>(t).

23.14.7 Comparisons [comparisons]

The library provides basic function object classes for all of the comparison operators in the language ([expr.rel], [expr.eq]).

For templates less, greater, less_equal, and greater_equal, the specializations for any pointer type yield a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by the built-in operators <, >, <=, >=. [ Note: When a (a, b), (a > b) == greater(a, b), and so forth. — end note ] For template specializations less<void>, greater<void>, less_equal<void>, and greater_equal<void>, if the call operator calls a built-in operator comparing pointers, the call operator yields a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by those built-in operators.

23.14.7.1 Class template equal_to [comparisons.equal_to]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x == y.

template <> struct equal_to<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) == std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) == std::forward(u));

Returns: std::forward<T>(t) == std::forward(u).

23.14.7.2 Class template not_equal_to [comparisons.not_equal_to]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x != y.

template <> struct not_equal_to<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) != std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) != std::forward(u));

Returns: std::forward<T>(t) != std::forward(u).

23.14.7.3 Class template greater [comparisons.greater]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x > y.

template <> struct greater<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) > std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) > std::forward(u));

Returns: std::forward<T>(t) > std::forward(u).

23.14.7.4 Class template less [comparisons.less]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x < y.

template <> struct less<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) < std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) < std::forward(u));

Returns: std::forward<T>(t) < std::forward(u).

23.14.7.5 Class template greater_equal [comparisons.greater_equal]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x >= y.

template <> struct greater_equal<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) >= std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) >= std::forward(u));

Returns: std::forward<T>(t) >= std::forward(u).

23.14.7.6 Class template less_equal [comparisons.less_equal]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x <= y.

template <> struct less_equal<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) <= std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) <= std::forward(u));

Returns: std::forward<T>(t) <= std::forward(u).

23.14.8 Logical operations [logical.operations]

The library provides basic function object classes for all of the logical operators in the language ([expr.log.and], [expr.log.or], [expr.unary.op]).

23.14.8.1 Class template logical_and [logical.operations.and]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x && y.

template <> struct logical_and<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) && std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) && std::forward(u));

Returns: std::forward<T>(t) && std::forward(u).

23.14.8.2 Class template logical_or [logical.operations.or]

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

constexpr bool operator()(const T& x, const T& y) const;

Returns: x || y.

template <> struct logical_or<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) || std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) || std::forward(u));

Returns: std::forward<T>(t) || std::forward(u).

23.14.8.3 Class template logical_not [logical.operations.not]

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

constexpr bool operator()(const T& x) const;

Returns: !x.

template <> struct logical_not<void> { template <class T> constexpr auto operator()(T&& t) const -> decltype(!std::forward<T>(t)); using is_transparent = unspecified; };

template <class T> constexpr auto operator()(T&& t) const -> decltype(!std::forward<T>(t));

Returns: !std::forward<T>(t).

23.14.9 Bitwise operations [bitwise.operations]

The library provides basic function object classes for all of the bitwise operators in the language ([expr.bit.and], [expr.or], [expr.xor], [expr.unary.op]).

23.14.9.1 Class template bit_and [bitwise.operations.and]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x & y.

template <> struct bit_and<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) & std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) & std::forward(u));

Returns: std::forward<T>(t) & std::forward(u).

23.14.9.2 Class template bit_or [bitwise.operations.or]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x | y.

template <> struct bit_or<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) | std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) | std::forward(u));

Returns: std::forward<T>(t) | std::forward(u).

23.14.9.3 Class template bit_xor [bitwise.operations.xor]

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

constexpr T operator()(const T& x, const T& y) const;

Returns: x ^ y.

template <> struct bit_xor<void> { template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) ^ std::forward(u)); using is_transparent = unspecified; };

template <class T, class U> constexpr auto operator()(T&& t, U&& u) const -> decltype(std::forward<T>(t) ^ std::forward(u));

Returns: std::forward<T>(t) ^ std::forward(u).

23.14.9.4 Class template bit_not [bitwise.operations.not]

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

constexpr T operator()(const T& x) const;

Returns: ~x.

template <> struct bit_not<void> { template <class T> constexpr auto operator()(T&& t) const -> decltype(~std::forward<T>(t)); using is_transparent = unspecified; };

template <class T> constexpr auto operator()(T&&) const -> decltype(~std::forward<T>(t));

Returns: ~std::forward<T>(t).

23.14.10 Function template not_fn [func.not_fn]

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

Effects: Equivalent to return call_wrapper(std::forward<F>(f)); where call_wrapper is an exposition only class defined as follows:

class call_wrapper {
  using FD = decay_t<F>;
  FD fd;

  explicit call_wrapper(F&& f);

public:
  call_wrapper(call_wrapper&&) = default;
  call_wrapper(const call_wrapper&) = default;

  template<class... Args>
    auto operator()(Args&&...) &
      -> decltype(!declval<invoke_result_t<FD&, Args...>>());

  template<class... Args>
    auto operator()(Args&&...) const&
      -> decltype(!declval<invoke_result_t<const FD&, Args...>>());

  template<class... Args>
    auto operator()(Args&&...) &&
      -> decltype(!declval<invoke_result_t<FD, Args...>>());

  template<class... Args>
    auto operator()(Args&&...) const&&
      -> decltype(!declval<invoke_result_t<const FD, Args...>>());
};

explicit call_wrapper(F&& f);

Requires: FD shall satisfy the requirements of MoveConstructible. is_constructible_v<FD, F> shall be true. fd shall be a callable object.

Effects: Initializes fd from std::forward<F>(f).

Throws: Any exception thrown by construction of fd.

template<class... Args> auto operator()(Args&&... args) & -> decltype(!declval<invoke_result_t<FD&, Args...>>()); template<class... Args> auto operator()(Args&&... args) const& -> decltype(!declval<invoke_result_t<const FD&, Args...>>());

Effects: Equivalent to:

return !INVOKE(fd, std::forward<Args>(args)...);              // see [func.require]

template<class... Args> auto operator()(Args&&... args) && -> decltype(!declval<invoke_result_t<FD, Args...>>()); template<class... Args> auto operator()(Args&&... args) const&& -> decltype(!declval<invoke_result_t<const FD, Args...>>());

Effects: Equivalent to:

return !INVOKE(std::move(fd), std::forward<Args>(args)...);   // see [func.require]

23.14.11 Function object binders [func.bind]

This subclause describes a uniform mechanism for binding arguments of callable objects.

23.14.11.1 Class template is_bind_expression [func.bind.isbind]

namespace std {
  template<class T> struct is_bind_expression;  // see below
}

The class template is_bind_expression can be used to detect function objects generated by bind. The function template bind uses is_bind_expression to detect subexpressions.

Instantiations of the is_bind_expression template shall meet the UnaryTypeTrait requirements. The implementation shall provide a definition that has a base characteristic of true_type if T is a type returned from bind, otherwise it shall have a base characteristic of false_type. A program may specialize this template for a user-defined type T to have a base characteristic of true_type to indicate that T should be treated as a subexpression in a bind call.

23.14.11.2 Class template is_placeholder [func.bind.isplace]

namespace std {
  template<class T> struct is_placeholder;      // see below
}

The class template is_placeholder can be used to detect the standard placeholders _1, _2, and so on. The function template bind uses is_placeholder to detect placeholders.

Instantiations of the is_placeholder template shall meet the UnaryTypeTrait requirements. The implementation shall provide a definition that has the base characteristic of integral_constant<int, J> if T is the type of std::placeholders::_J, otherwise it shall have a base characteristic of integral_constant<int, 0>. A program may specialize this template for a user-defined type T to have a base characteristic of integral_constant<int, N> with N > 0 to indicate that T should be treated as a placeholder type.

23.14.11.3 Function template bind [func.bind.bind]

In the text that follows:

(1.1)
FD is the type decay_t<F>,
(1.2)
fd is an lvalue of type FD constructed from std::forward<F>(f),
(1.3)
$T_{i}$ is the $i^{th}$ type in the template parameter pack BoundArgs,
(1.4)
${TD}_{i}$ is the type decay_t< $T_{i}$ >,
(1.5)
$t_{i}$ is the $i^{th}$ argument in the function parameter pack bound_args,
(1.6)
${td}_{i}$ is an lvalue of type ${TD}_{i}$ constructed from std::forward< $T_{i}$ >( $t_{i}$ ),
(1.7)
$U_{j}$ is the $j^{th}$ deduced type of the UnBoundArgs&&... parameter of the forwarding call wrapper, and
(1.8)
$u_{j}$ is the $j^{th}$ argument associated with $U_{j}$ .

template<class F, class... BoundArgs> unspecified bind(F&& f, BoundArgs&&... bound_args);

Requires: is_constructible_v<FD, F> shall be true. For each $T_{i}$ in BoundArgs, is_constructible_v< ${TD}_{i}$ , $T_{i}$ > shall be true. INVOKE(fd, $w_{1}$ , $w_{2}$ , …, $w_{N}$ ) ([func.require]) shall be a valid expression for some values $w_{1}$ , $w_{2}$ , …, $w_{N}$ , where N has the value sizeof...(bound_args). The cv-qualifiers cv of the call wrapper g, as specified below, shall be neither volatile nor const volatile.

Returns: A forwarding call wrapper g. The effect of g( $u_{1}$ , $u_{2}$ , …, $u_{M}$ ) shall be

INVOKE(fd, std::forward< $V_{1}$ >( $v_{1}$ ), std::forward< $V_{2}$ >( $v_{2}$ ), …, std::forward< $V_{N}$ >( $v_{N}$ ))

where the values and types of the bound arguments $v_{1}$ , $v_{2}$ , …, $v_{N}$ 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 ${TD}_{i}$ throws an exception.

Throws: Nothing unless the construction of fd or of one of the values ${td}_{i}$ throws an exception.

Remarks: The return type shall satisfy the requirements of MoveConstructible. If all of FD and ${TD}_{i}$ satisfy the requirements of CopyConstructible, then the return type shall satisfy the requirements of CopyConstructible. [ Note: This implies that all of FD and ${TD}_{i}$ are MoveConstructible. — end note ]

template<class R, class F, class... BoundArgs> unspecified bind(F&& f, BoundArgs&&... bound_args);

Requires: is_constructible_v<FD, F> shall be true. For each $T_{i}$ in BoundArgs, is_constructible_v< ${TD}_{i}$ , $T_{i}$ > shall be true. INVOKE(fd, $w_{1}$ , $w_{2}$ , …, $w_{N}$ ) shall be a valid expression for some values $w_{1}$ , $w_{2}$ , …, $w_{N}$ , where N has the value sizeof...(bound_args). The cv-qualifiers cv of the call wrapper g, as specified below, shall be neither volatile nor const volatile.

Returns: A forwarding call wrapper g. The effect of g( $u_{1}$ , $u_{2}$ , …, $u_{M}$ ) shall be

INVOKE<R>(fd, std::forward< $V_{1}$ >( $v_{1}$ ), std::forward< $V_{2}$ >( $v_{2}$ ), …, std::forward< $V_{N}$ >( $v_{N}$ ))

Throws: Nothing unless the construction of fd or of one of the values ${td}_{i}$ throws an exception.

The values of the bound arguments $v_{1}$ , $v_{2}$ , …, $v_{N}$ and their corresponding types $V_{1}$ , $V_{2}$ , …, $V_{N}$ depend on the types ${TD}_{i}$ derived from the call to bind and the cv-qualifiers cv of the call wrapper g as follows:

(10.1)
if ${TD}_{i}$ is reference_wrapper<T>, the argument is ${td}_{i}$ .get() and its type $V_{i}$ is T&;
(10.2)
if the value of is_bind_expression_v< ${TD}_{i}$ > is true, the argument is ${td}_{i}$ (std::forward< $U_{j}$ >( $u_{j}$ )...) and its type $V_{i}$ is invoke_result_t< ${TD}_{i}$ cv &, $U_{j}$ ...>&&;
(10.3)
if the value j of is_placeholder_v< ${TD}_{i}$ > is not zero, the argument is std::forward< $U_{j}$ >( $u_{j}$ ) and its type $V_{i}$ is $U_{j}$ &&;
(10.4)
otherwise, the value is ${td}_{i}$ and its type $V_{i}$ is ${TD}_{i}$ cv &.

23.14.11.4 Placeholders [func.bind.place]

namespace std::placeholders {
  // M is the implementation-defined number of placeholders
  see below _1;
  see below _2;
              .
              .
              .
  see below _M;
}

All placeholder types shall be DefaultConstructible and CopyConstructible, and their default constructors and copy/move constructors shall not throw exceptions. It is implementation-defined whether placeholder types are CopyAssignable. CopyAssignable placeholders' copy assignment operators shall not throw exceptions.

Placeholders should be defined as:

inline constexpr unspecified _1{};

If they are not, they shall be declared as:

extern unspecified _1;

23.14.12 Function template mem_fn [func.memfn]

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

Returns: A simple call wrapper fn such that the expression fn(t, a2, ..., aN) is equivalent to INVOKE(pm, t, a2, ..., aN) ([func.require]).

23.14.13 Polymorphic function wrappers [func.wrap]

This subclause describes a polymorphic wrapper class that encapsulates arbitrary callable objects.

23.14.13.1 Class bad_function_call [func.wrap.badcall]

An exception of type bad_function_call is thrown by function::operator() ([func.wrap.func.inv]) when the function wrapper object has no target.

namespace std {
  class bad_function_call : public exception {
  public:
    // [func.wrap.badcall.const], constructor
    bad_function_call() noexcept;
  };
}

23.14.13.1.1 bad_function_call constructor [func.wrap.badcall.const]

bad_function_call() noexcept;

Effects: Constructs a bad_function_call object.

Postconditions: what() returns an implementation-defined ntbs.

23.14.13.2 Class template function [func.wrap.func]

namespace std {
  template<class> class function; // not defined

  template<class R, class... ArgTypes>
  class function<R(ArgTypes...)> {
  public:
    using result_type = R;

    // [func.wrap.func.con], construct/copy/destroy
    function() noexcept;
    function(nullptr_t) noexcept;
    function(const function&);
    function(function&&);
    template<class F> function(F);

    function& operator=(const function&);
    function& operator=(function&&);
    function& operator=(nullptr_t) noexcept;
    template<class F> function& operator=(F&&);
    template<class F> function& operator=(reference_wrapper<F>) noexcept;

    ~function();

    // [func.wrap.func.mod], function modifiers
    void swap(function&) noexcept;

    // [func.wrap.func.cap], function capacity
    explicit operator bool() const noexcept;

    // [func.wrap.func.inv], function invocation
    R operator()(ArgTypes...) const;

    // [func.wrap.func.targ], function target access
    const type_info& target_type() const noexcept;
    template<class T>       T* target() noexcept;
    template<class T> const T* target() const noexcept;
  };

  template<class R, class... ArgTypes>
    function(R(*)(ArgTypes...)) -> function<R(ArgTypes...)>;

  template<class F> function(F) -> function<see below>;

  // [func.wrap.func.nullptr], Null pointer comparisons
  template <class R, class... ArgTypes>
    bool operator==(const function<R(ArgTypes...)>&, nullptr_t) noexcept;

  template <class R, class... ArgTypes>
    bool operator==(nullptr_t, const function<R(ArgTypes...)>&) noexcept;

  template <class R, class... ArgTypes>
    bool operator!=(const function<R(ArgTypes...)>&, nullptr_t) noexcept;

  template <class R, class... ArgTypes>
    bool operator!=(nullptr_t, const function<R(ArgTypes...)>&) noexcept;

  // [func.wrap.func.alg], specialized algorithms
  template <class R, class... ArgTypes>
    void swap(function<R(ArgTypes...)>&, function<R(ArgTypes...)>&) noexcept;
}

The function class template provides polymorphic wrappers that generalize the notion of a function pointer. Wrappers can store, copy, and call arbitrary callable objects, given a call signature, allowing functions to be first-class objects.

A callable type F is Lvalue-Callable for argument types ArgTypes and return type R if the expression INVOKE<R>(declval<F&>(), declval<ArgTypes>()...), considered as an unevaluated operand, is well formed ([func.require]).

The function class template is a call wrapper whose call signature is R(ArgTypes...).

[ Note: The types deduced by the deduction guides for function may change in future versions of this International Standard. — end note ]

23.14.13.2.1 function construct/copy/destroy [func.wrap.func.con]

function() noexcept;

Postconditions: !*this.

function(nullptr_t) noexcept;

Postconditions: !*this.

function(const function& f);

Postconditions: !*this if !f; otherwise, *this targets a copy of f.target().

Throws: shall not throw exceptions if f's target is a specialization of reference_wrapper or a function pointer. Otherwise, may throw bad_alloc or any exception thrown by the copy constructor of the stored callable object. [ Note: Implementations are encouraged to avoid the use of dynamically allocated memory for small callable objects, for example, where f's target is an object holding only a pointer or reference to an object and a member function pointer. — end note ]

function(function&& f);

Postconditions: If !f, *this has no target; otherwise, the target of *this is equivalent to the target of f before the construction, and f is in a valid state with an unspecified value.

Throws: shall not throw exceptions if f's target is a specialization of reference_wrapper or a function pointer. Otherwise, may throw bad_alloc or any exception thrown by the copy or move constructor of the stored callable object. [ Note: Implementations are encouraged to avoid the use of dynamically allocated memory for small callable objects, for example, where f's target is an object holding only a pointer or reference to an object and a member function pointer. — end note ]

template<class F> function(F f);

Requires: F shall be CopyConstructible.

Remarks: This constructor template shall not participate in overload resolution unless F is Lvalue-Callable for argument types ArgTypes... and return type R.

Postconditions: !*this if any of the following hold:

(9.1)
f is a null function pointer value.
(9.2)
f is a null member pointer value.
(9.3)
F is an instance of the function class template, and !f.

Otherwise, *this targets a copy of f initialized with std::move(f). [ Note: Implementations are encouraged to avoid the use of dynamically allocated memory for small callable objects, for example, where f is an object holding only a pointer or reference to an object and a member function pointer. — end note ]

Throws: shall not throw exceptions when f is a function pointer or a reference_wrapper<T> for some T. Otherwise, may throw bad_alloc or any exception thrown by F's copy or move constructor.

template<class F> function(F) -> function<see below>;

Remarks: This deduction guide participates in overload resolution only if &F::operator() is well-formed when treated as an unevaluated operand. In that case, if decltype(&F::operator()) is of the form R(G::*)(A...) cv & $_{o p t}$ noexcept $_{o p t}$ for a class type G, then the deduced type is function<R(A...)>.

[ Example:

void f() {
  int i{5};
  function g = [&](double) { return i; }; // deduces function<int(double)>
}

— end example ]

function& operator=(const function& f);

Effects: As if by function(f).swap(*this);

Returns: *this.

function& operator=(function&& f);

Effects: Replaces the target of *this with the target of f.

Returns: *this.

function& operator=(nullptr_t) noexcept;

Effects: If *this != nullptr, destroys the target of this.

Postconditions: !(*this).

Returns: *this.

template<class F> function& operator=(F&& f);

Effects: As if by: function(std::forward<F>(f)).swap(*this);

Returns: *this.

Remarks: This assignment operator shall not participate in overload resolution unless decay_t<F> is Lvalue-Callable for argument types ArgTypes... and return type R.

template<class F> function& operator=(reference_wrapper<F> f) noexcept;

Effects: As if by: function(f).swap(*this);

Returns: *this.

~function();

Effects: If *this != nullptr, destroys the target of this.

23.14.13.2.2 function modifiers [func.wrap.func.mod]

void swap(function& other) noexcept;

Effects: interchanges the targets of *this and other.

23.14.13.2.3 function capacity [func.wrap.func.cap]

explicit operator bool() const noexcept;

Returns: true if *this has a target, otherwise false.

23.14.13.2.4 function invocation [func.wrap.func.inv]

R operator()(ArgTypes... args) const;

Returns: INVOKE<R>(f, std::forward<ArgTypes>(args)...) ([func.require]), where f is the target object of *this.

Throws: bad_function_call if !*this; otherwise, any exception thrown by the wrapped callable object.

23.14.13.2.5 function target access [func.wrap.func.targ]

const type_info& target_type() const noexcept;

Returns: If *this has a target of type T, typeid(T); otherwise, typeid(void).

template<class T> T* target() noexcept; template<class T> const T* target() const noexcept;

Returns: If target_type() == typeid(T) a pointer to the stored function target; otherwise a null pointer.

23.14.13.2.6 null pointer comparison functions [func.wrap.func.nullptr]

template <class R, class... ArgTypes> bool operator==(const function<R(ArgTypes...)>& f, nullptr_t) noexcept; template <class R, class... ArgTypes> bool operator==(nullptr_t, const function<R(ArgTypes...)>& f) noexcept;

Returns: !f.

template <class R, class... ArgTypes> bool operator!=(const function<R(ArgTypes...)>& f, nullptr_t) noexcept; template <class R, class... ArgTypes> bool operator!=(nullptr_t, const function<R(ArgTypes...)>& f) noexcept;

Returns: (bool)f.

23.14.13.2.7 specialized algorithms [func.wrap.func.alg]

template<class R, class... ArgTypes> void swap(function<R(ArgTypes...)>& f1, function<R(ArgTypes...)>& f2) noexcept;

Effects: As if by: f1.swap(f2);

23.14.14 Searchers [func.search]

This subclause provides function object types for operations that search for a sequence [pat_first, pat_last) in another sequence [first, last) that is provided to the object's function call operator. The first sequence (the pattern to be searched for) is provided to the object's constructor, and the second (the sequence to be searched) is provided to the function call operator.

Each specialization of a class template specified in this subclause [func.search] shall meet the CopyConstructible and CopyAssignable requirements. Template parameters named

(2.1)
ForwardIterator,
(2.2)
ForwardIterator1,
(2.3)
ForwardIterator2,
(2.4)
RandomAccessIterator,
(2.5)
RandomAccessIterator1,
(2.6)
RandomAccessIterator2, and
(2.7)
BinaryPredicate

of templates specified in this subclause [func.search] shall meet the same requirements and semantics as specified in [algorithms.general]. Template parameters named Hash shall meet the requirements as specified in [hash.requirements].

The Boyer-Moore searcher implements the Boyer-Moore search algorithm. The Boyer-Moore-Horspool searcher implements the Boyer-Moore-Horspool search algorithm. In general, the Boyer-Moore searcher will use more memory and give better runtime performance than Boyer-Moore-Horspool.

23.14.14.1 Class template default_searcher [func.search.default]

template <class ForwardIterator1, class BinaryPredicate = equal_to<>>
  class default_searcher {
  public:
    default_searcher(ForwardIterator1 pat_first, ForwardIterator1 pat_last,
                     BinaryPredicate pred = BinaryPredicate());

    template <class ForwardIterator2>
      pair<ForwardIterator2, ForwardIterator2>
        operator()(ForwardIterator2 first, ForwardIterator2 last) const;

  private:
    ForwardIterator1 pat_first_;        // exposition only
    ForwardIterator1 pat_last_;         // exposition only
    BinaryPredicate pred_;              // exposition only
  };

default_searcher(ForwardIterator pat_first, ForwardIterator pat_last, BinaryPredicate pred = BinaryPredicate());

Effects: Constructs a default_searcher object, initializing pat_first_ with pat_first, pat_last_ with pat_last, and pred_ with pred.

Throws: Any exception thrown by the copy constructor of BinaryPredicate or ForwardIterator1.

template<class ForwardIterator2> pair<ForwardIterator2, ForwardIterator2> operator()(ForwardIterator2 first, ForwardIterator2 last) const;

Effects: Returns a pair of iterators i and j such that

(3.1)
i == search(first, last, pat_first_, pat_last_, pred_), and
(3.2)
if i == last, then j == last, otherwise j == next(i, distance(pat_first_, pat_last_)).

23.14.14.2 Class template boyer_moore_searcher [func.search.bm]

template <class RandomAccessIterator1,
          class Hash = hash<typename iterator_traits<RandomAccessIterator1>::value_type>,
          class BinaryPredicate = equal_to<>>
  class boyer_moore_searcher {
  public:
    boyer_moore_searcher(RandomAccessIterator1 pat_first,
                         RandomAccessIterator1 pat_last,
                         Hash hf = Hash(),
                         BinaryPredicate pred = BinaryPredicate());

    template <class RandomAccessIterator2>
      pair<RandomAccessIterator2, RandomAccessIterator2>
        operator()(RandomAccessIterator2 first, RandomAccessIterator2 last) const;

  private:
    RandomAccessIterator1 pat_first_;   // exposition only
    RandomAccessIterator1 pat_last_;    // exposition only
    Hash hash_;                         // exposition only
    BinaryPredicate pred_;              // exposition only
  };

boyer_moore_searcher(RandomAccessIterator1 pat_first, RandomAccessIterator1 pat_last, Hash hf = Hash(), BinaryPredicate pred = BinaryPredicate());

Requires: The value type of RandomAccessIterator1 shall meet the DefaultConstructible requirements, the CopyConstructible requirements, and the CopyAssignable requirements.

Requires: For any two values A and B of the type iterator_traits<RandomAccessIterator1>::value_type, if pred(A, B) == true, then hf(A) == hf(B) shall be true.

Effects: Constructs a boyer_moore_searcher object, initializing pat_first_ with pat_first, pat_last_ with pat_last, hash_ with hf, and pred_ with pred.

Throws: Any exception thrown by the copy constructor of RandomAccessIterator1, or by the default constructor, copy constructor, or the copy assignment operator of the value type of RandomAccessIterator1, or the copy constructor or operator() of BinaryPredicate or Hash. May throw bad_alloc if additional memory needed for internal data structures cannot be allocated.

template <class RandomAccessIterator2> pair<RandomAccessIterator2, RandomAccessIterator2> operator()(RandomAccessIterator2 first, RandomAccessIterator2 last) const;

Requires: RandomAccessIterator1 and RandomAccessIterator2 shall have the same value type.

Effects: Finds a subsequence of equal values in a sequence.

Returns: A pair of iterators i and j such that

(7.1)
i is the first iterator in the range [first, last - (pat_last_ - pat_first_)) such that for every non-negative integer n less than pat_last_ - pat_first_ the following condition holds: pred(*(i + n), *(pat_first_ + n)) != false, and
(7.2)
j == next(i, distance(pat_first_, pat_last_)).

Returns make_pair(first, first) if [pat_first_, pat_last_) is empty, otherwise returns make_pair(last, last) if no such iterator is found.

Complexity: At most (last - first) * (pat_last_ - pat_first_) applications of the predicate.

23.14.14.3 Class template boyer_moore_horspool_searcher [func.search.bmh]

template <class RandomAccessIterator1,
          class Hash = hash<typename iterator_traits<RandomAccessIterator1>::value_type>,
          class BinaryPredicate = equal_to<>>
  class boyer_moore_horspool_searcher {
  public:
    boyer_moore_horspool_searcher(RandomAccessIterator1 pat_first,
                                  RandomAccessIterator1 pat_last,
                                  Hash hf = Hash(),
                                  BinaryPredicate pred = BinaryPredicate());

    template <class RandomAccessIterator2>
      pair<RandomAccessIterator2, RandomAccessIterator2>
        operator()(RandomAccessIterator2 first, RandomAccessIterator2 last) const;

  private:
    RandomAccessIterator1 pat_first_;   // exposition only
    RandomAccessIterator1 pat_last_;    // exposition only
    Hash hash_;                         // exposition only
    BinaryPredicate pred_;              // exposition only
  };

boyer_moore_horspool_searcher(RandomAccessIterator1 pat_first, RandomAccessIterator1 pat_last, Hash hf = Hash(), BinaryPredicate pred = BinaryPredicate());

Requires: The value type of RandomAccessIterator1 shall meet the DefaultConstructible, CopyConstructible, and CopyAssignable requirements.

Requires: For any two values A and B of the type iterator_traits<RandomAccessIterator1>::value_type, if pred(A, B) == true, then hf(A) == hf(B) shall be true.

Effects: Constructs a boyer_moore_horspool_searcher object, initializing pat_first_ with pat_first, pat_last_ with pat_last, hash_ with hf, and pred_ with pred.

Throws: Any exception thrown by the copy constructor of RandomAccessIterator1, or by the default constructor, copy constructor, or the copy assignment operator of the value type of RandomAccessIterator1 or the copy constructor or operator() of BinaryPredicate or Hash. May throw bad_alloc if additional memory needed for internal data structures cannot be allocated.

template <class RandomAccessIterator2> pair<RandomAccessIterator2, RandomAccessIterator2> operator()(RandomAccessIterator2 first, RandomAccessIterator2 last) const;

Requires: RandomAccessIterator1 and RandomAccessIterator2 shall have the same value type.

Effects: Finds a subsequence of equal values in a sequence.

Returns: A pair of iterators i and j such that

(7.1)
i is the first iterator i in the range [first, last - (pat_last_ - pat_first_)) such that for every non-negative integer n less than pat_last_ - pat_first_ the following condition holds: pred(*(i + n), *(pat_first_ + n)) != false, and
(7.2)
j == next(i, distance(pat_first_, pat_last_)).

Returns make_pair(first, first) if [pat_first_, pat_last_) is empty, otherwise returns make_pair(last, last) if no such iterator is found.

Complexity: At most (last - first) * (pat_last_ - pat_first_) applications of the predicate.

23.14.15 Class template hash [unord.hash]

The unordered associative containers defined in [unord] use specializations of the class template hash ([functional.syn]) as the default hash function.

Each specialization of hash is either enabled or disabled, as described below. [ Note: Enabled specializations meet the requirements of Hash, and disabled specializations do not. — end note ] Each header that declares the template hash provides enabled specializations of hash for nullptr_t and all cv-unqualified arithmetic, enumeration, and pointer types. For any type Key for which neither the library nor the user provides an explicit or partial specialization of the class template hash, hash<Key> is disabled.

If the library provides an explicit or partial specialization of hash<Key>, that specialization is enabled except as noted otherwise, and its member functions are noexcept except as noted otherwise.

If H is a disabled specialization of hash, these values are false: is_default_constructible_v<H>, is_copy_constructible_v<H>, is_move_constructible_v<H>, is_copy_assignable_v<H>, and is_move_assignable_v<H>. Disabled specializations of hash are not function object types. [ Note: This means that the specialization of hash exists, but any attempts to use it as a Hash will be ill-formed. — end note ]

An enabled specialization hash<Key> will:

(5.1)
satisfy the Hash requirements, with Key as the function call argument type, the DefaultConstructible requirements, the CopyAssignable requirements,
(5.2)
be swappable for lvalues,
(5.3)
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;
(5.4)
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.

23 General utilities library [utilities]

23.14 Function objects [function.objects]

23.14.1 Header <functional> synopsis [functional.syn]

23.14.2 Definitions [func.def]

23.14.3 Requirements [func.require]

23.14.4 Function template invoke [func.invoke]

23.14.5 Class template reference_­wrapper [refwrap]

23.14.5.1 reference_­wrapper construct/copy/destroy [refwrap.const]

23.14.5.2 reference_­wrapper assignment [refwrap.assign]

23.14.5.3 reference_­wrapper access [refwrap.access]

23.14.5.4 reference_­wrapper invocation [refwrap.invoke]

23.14.5.5 reference_­wrapper helper functions [refwrap.helpers]

23.14.6 Arithmetic operations [arithmetic.operations]

23.14.6.1 Class template plus [arithmetic.operations.plus]

23.14.6.2 Class template minus [arithmetic.operations.minus]

23.14.6.3 Class template multiplies [arithmetic.operations.multiplies]

23.14.6.4 Class template divides [arithmetic.operations.divides]

23.14.6.5 Class template modulus [arithmetic.operations.modulus]

23.14.6.6 Class template negate [arithmetic.operations.negate]

23.14.7 Comparisons [comparisons]

23.14.7.1 Class template equal_­to [comparisons.equal_to]

23.14.7.2 Class template not_­equal_­to [comparisons.not_equal_to]

23.14.7.3 Class template greater [comparisons.greater]

23.14.7.4 Class template less [comparisons.less]

23.14.7.5 Class template greater_­equal [comparisons.greater_equal]

23.14.7.6 Class template less_­equal [comparisons.less_equal]

23.14.8 Logical operations [logical.operations]

23.14.8.1 Class template logical_­and [logical.operations.and]

23.14.8.2 Class template logical_­or [logical.operations.or]

23.14.8.3 Class template logical_­not [logical.operations.not]

23.14.9 Bitwise operations [bitwise.operations]

23.14.9.1 Class template bit_­and [bitwise.operations.and]

23.14.9.2 Class template bit_­or [bitwise.operations.or]

23.14.9.3 Class template bit_­xor [bitwise.operations.xor]

23.14.9.4 Class template bit_­not [bitwise.operations.not]

23.14.10 Function template not_­fn [func.not_fn]

23.14.11 Function object binders [func.bind]

23.14.11.1 Class template is_­bind_­expression [func.bind.isbind]

23.14.11.2 Class template is_­placeholder [func.bind.isplace]

23.14.11.3 Function template bind [func.bind.bind]

23.14.11.4 Placeholders [func.bind.place]

23.14.12 Function template mem_­fn [func.memfn]

23.14.13 Polymorphic function wrappers [func.wrap]

23.14.13.1 Class bad_­function_­call [func.wrap.badcall]

23.14.13.1.1 bad_­function_­call constructor [func.wrap.badcall.const]

23.14.13.2 Class template function [func.wrap.func]

23.14.13.2.1 function construct/copy/destroy [func.wrap.func.con]

23.14.13.2.2 function modifiers [func.wrap.func.mod]

23.14.13.2.3 function capacity [func.wrap.func.cap]

23.14.13.2.4 function invocation [func.wrap.func.inv]

23.14.13.2.5 function target access [func.wrap.func.targ]

23.14.13.2.6 null pointer comparison functions [func.wrap.func.nullptr]

23.14.13.2.7 specialized algorithms [func.wrap.func.alg]

23.14.14 Searchers [func.search]

23.14.14.1 Class template default_­searcher [func.search.default]

23.14.14.2 Class template boyer_­moore_­searcher [func.search.bm]

23.14.14.3 Class template boyer_­moore_­horspool_­searcher [func.search.bmh]

23.14.15 Class template hash [unord.hash]

23.14.5 Class template reference_wrapper [refwrap]

23.14.5.1 reference_wrapper construct/copy/destroy [refwrap.const]

23.14.5.2 reference_wrapper assignment [refwrap.assign]

23.14.5.3 reference_wrapper access [refwrap.access]

23.14.5.4 reference_wrapper invocation [refwrap.invoke]

23.14.5.5 reference_wrapper helper functions [refwrap.helpers]

23.14.7.1 Class template equal_to [comparisons.equal_to]

23.14.7.2 Class template not_equal_to [comparisons.not_equal_to]

23.14.7.5 Class template greater_equal [comparisons.greater_equal]

23.14.7.6 Class template less_equal [comparisons.less_equal]

23.14.8.1 Class template logical_and [logical.operations.and]

23.14.8.2 Class template logical_or [logical.operations.or]

23.14.8.3 Class template logical_not [logical.operations.not]

23.14.9.1 Class template bit_and [bitwise.operations.and]

23.14.9.2 Class template bit_or [bitwise.operations.or]

23.14.9.3 Class template bit_xor [bitwise.operations.xor]

23.14.9.4 Class template bit_not [bitwise.operations.not]

23.14.10 Function template not_fn [func.not_fn]

23.14.11.1 Class template is_bind_expression [func.bind.isbind]

23.14.11.2 Class template is_placeholder [func.bind.isplace]

23.14.12 Function template mem_fn [func.memfn]

23.14.13.1 Class bad_function_call [func.wrap.badcall]

23.14.13.1.1 bad_function_call constructor [func.wrap.badcall.const]

23.14.14.1 Class template default_searcher [func.search.default]

23.14.14.2 Class template boyer_moore_searcher [func.search.bm]

23.14.14.3 Class template boyer_moore_horspool_searcher [func.search.bmh]