I found that binary_function is removed from C++11. I am wondering why.
C++98:
template <class T> struct less : binary_function <T,T,bool> {
  bool operator() (const T& x, const T& y) const {return x<y;}
};
C++11:
template <class T> struct less {
  bool operator() (const T& x, const T& y) const {return x<y;}
  typedef T first_argument_type;
  typedef T second_argument_type;
  typedef bool result_type;
};
MODIFIED----------------------------------------------------------------------------
template<class arg,class result>
struct unary_function
{
       typedef arg argument_type;
       typedef result result_type;
};
For example, if we want to write our adapter for function even in C++98,
template <class T> struct even : unary_function <T,bool> {
  bool operator() (const T& x) const {return 0==x%2;}
};
find_if(bgn,end,even<int>()); //find even number
//adapter
template<typename adaptableFunction >
class unary_negate
{
   private:
       adaptableFunction fun_;
   public:
       typedef adaptableFunction::argument_type argument_type;
       typedef adaptableFunction::result_type result_type;  
       unary_negate(const adaptableFunction &f):fun_(f){}
       bool operator()(const argument_type&x) 
       {
           return !fun(x);
       }
}
find_if(bgn,end, unary_negate< even<int> >(even<int>()) ); //find odd number
How can we improve this in C++11 without unary_function? 
With variadic templates, a lot of general function composing can be expressed much more simply and consistently, so all of the old cruft is no longer necessary:
Do use:
std::functionstd::bindstd::mem_fnstd::result_ofDon't use:
std::unary_function, std::binary_function
std::mem_funstd::bind1st, std::bind2nd
It isn't removed, it's just deprecated in C++11. It's still part of the C++11 standard. You can still use it in your own code. It was removed in C++17 though.
It isn't used in the standard any more because requiring implementations to derive from binary_function is over-specification.
Users should not care whether less derives from binary_function, they only need to care that it defines first_argument_type, second_argument_type and result_type. It should be up to the implementation how it provides those typedefs.
Forcing the implementation to derive from a specific type means that users might start relying on that derivation, which makes no sense and is not useful.
Edit
How can we improve this in c++11 without unary_function?
You don't need it.
template<typename adaptableFunction>
class unary_negate
{
   private:
       adaptableFunction fun_;
   public:
       unary_negate(const adaptableFunction& f):fun_(f){}
       template<typename T>
           auto operator()(const T& x)  -> decltype(!fun_(x))
           {
               return !fun_(x);
           }
}
In fact you can do even better, see not_fn: a generalized negator
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