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

class template

std::unary_function

template <class Arg, class Result> struct unary_function;

template <class Arg, class Result> struct unary_function; // deprecated

Unary function object base class

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

This is a base class for standard unary 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 unary function objects, this operator() member function takes a single parameter.

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

template <class Arg, class Result>
  struct unary_function {
    typedef Arg argument_type;
    typedef Result result_type;
  };

Member types member type definition notes argument_type The first template parameter (Arg) Type of the argument in member operator() result_type The second template parameter (Result) Type returned by member operator()
Example

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

struct IsOdd : public std::unary_function<int,bool> {
  bool operator() (int number) {return (number%2!=0);}
};

int main () {
  IsOdd IsOdd_object;
  IsOdd::argument_type input;
  IsOdd::result_type result;

  std::cout << "Please enter a number: ";
  std::cin >> input;

  result = IsOdd_object (input);

  std::cout << "Number " << input << " is " << (result?"odd":"even") << ".\n";

  return 0;
}

Possible output:

Please enter a number: 2
Number 2 is even.