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Showing content from https://cplusplus.com/reference/functional/binary_function/ below:

class template

std::binary_function

template <class Arg1, class Arg2, class Result> struct binary_function;

template <class Arg1, class Arg2, class Result> struct binary_function; // deprecated

Binary function object base class

Note: This class has been deprecated in C++11.

This is a base class for standard binary function objects.

Generically, function objects are instances of a class with member function operator() defined. This member function allows the object to be used with the same syntax as a regular function call, and therefore its type can be used as template parameter when a generic function type is expected.

In the case of binary function objects, this operator() member function takes two parameters.

binary_function is just a base class, from which specific binary function objects are derived. It has no operator() member defined (which derived classes are expected to define) - it simply has three public data members that are typedefs of the template parameters. It is defined as:

template <class Arg1, class Arg2, class Result>
  struct binary_function {
    typedef Arg1 first_argument_type;
    typedef Arg2 second_argument_type;
    typedef Result result_type;
  };

Members member type definition notes first_argument_type The first template parameter (Arg1) Type of the first argument in member operator() second_argument_type The second template parameter (Arg2) Type of the second argument in member operator() return_type The third template parameter (Result) Type returned by member operator()
Example

// binary_function example
#include <iostream>     // std::cout, std::cin
#include <functional>   // std::binary_function

struct Compare : public std::binary_function<int,int,bool> {
  bool operator() (int a, int b) {return (a==b);}
};

int main () {
  Compare Compare_object;
  Compare::first_argument_type input1;
  Compare::second_argument_type input2;
  Compare::result_type result;

  std::cout << "Please enter first number: ";
  std::cin >> input1;
  std::cout << "Please enter second number: ";
  std::cin >> input2;

  result = Compare_object (input1,input2);

  std::cout << "Numbers " << input1 << " and " << input2;
  if (result)
	  std::cout << " are equal.\n";
  else
	  std::cout << " are not equal.\n";

  return 0;
}

Possible output:

Please enter first number: 2
Please enter second number: 33
Numbers 2 and 33 are not equal.