namespace std {
  // invoke:
  template <class F, class... Args>
  invoke_result_t<F, Args...> invoke(F&& f, Args&&... args);
 
  // 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:
  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:
  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:
  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:
  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>;
 
  // function template not_fn:
  template <class F> /*unspecified*/ not_fn(F&& f);
 
  // 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
    /* implementation-defined */ _1;
    /* implementation-defined */ _2;
    ...
    /* implementation-defined */ _M;
  }
 
  // member function adaptors:
  template<class R, class T> /*unspecified*/ mem_fn(R T::*) noexcept;
 
  // polymorphic function wrappers:
  class bad_function_call;
  template<class> class function; // undefined
  template<class R, class... ArgTypes> class function<R(ArgTypes...)>;
  template<class R, class... ArgTypes>
  void swap(function<R(ArgTypes...)>&, function<R(ArgTypes...)>&);
  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;
 
  // 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;
  template<class ForwardIterator, class BinaryPredicate = equal_to<>>
  default_searcher<ForwardIterator, BinaryPredicate>
  make_default_searcher(ForwardIterator pat_first, ForwardIterator pat_last,
                        BinaryPredicate pred = BinaryPredicate());
  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
  boyer_moore_searcher<RandomAccessIterator, Hash, BinaryPredicate>
  make_boyer_moore_searcher(RandomAccessIterator pat_first,
                            RandomAccessIterator pat_last,
                            Hash hf = Hash(), BinaryPredicate pred = BinaryPredicate());
  template<class RandomAccessIterator,
           class Hash = hash<typename iterator_traits<RandomAccessIterator>::value_type>,
           class BinaryPredicate = equal_to<>>
  boyer_moore_horspool_searcher<RandomAccessIterator, Hash, BinaryPredicate>
  make_boyer_moore_horspool_searcher(RandomAccessIterator pat_first,
                                     RandomAccessIterator pat_last,
                                     Hash hf = Hash(),
                                     BinaryPredicate pred = BinaryPredicate());
 
  // hash function primary template:
  template <class T> struct hash;
 
  // 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;
}

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;
  };
}

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

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

class bad_function_call : public std::exception {
public:
    // constructor:
    bad_function_call() noexcept;
};

namespace std {
  template<class> class function; // undefined
  template<class R, class... ArgTypes>
  class function<R(ArgTypes...)> {
    public:
    using result_type = R;
    // 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();
    // function modifiers:
    void swap(function&) noexcept;
    // function capacity:
    explicit operator bool() const noexcept;
    // function invocation:
    R operator()(ArgTypes...) const;
    // function target access:
    const type_info& target_type() const noexcept;
    template<class T> T* target() noexcept;
    template<class T> const T* target() const noexcept;
  };
  // 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;
  // specialized algorithms:
  template <class R, class... ArgTypes>
  void swap(function<R(ArgTypes...)>&, function<R(ArgTypes...)>&);
}