Consider the following functions which have distinct signatures:

const std::string& identity_s(const std::string& x) // Function (as pointer).
    { return x; }

int identity_i_impl(int x) { return x; }
int (&identity_i)(int) = identity_i_impl; // Function reference.

double identity_d_impl(double x) { return x; }
boost::function<double (double)> identity_d = identity_d_impl; // Functor.

Instead of calling them using their separate names (here BOOST_TEST is equivalent to assert): ^[1]

BOOST_TEST(identity_s("abc") == "abc");
BOOST_TEST(identity_i(123) == 123);
BOOST_TEST(identity_d(1.23) == 1.23);

It is possible to use this library to create a single overloaded function object (or functor) named identity that aggregates together the calls to the specific functions (see also functor.cpp and identity.hpp):

boost::overloaded_function<
      const std::string& (const std::string&)
    , int (int)
    , double (double)
> identity(identity_s, identity_i, identity_d);

// All calls via single `identity` function.
BOOST_TEST(identity("abc") == "abc");
BOOST_TEST(identity(123) == 123);
BOOST_TEST(identity(1.23) == 1.23);

Note how the functions are called via a single overloaded function object identity instead of using their different names identity_s, identity_i, and identity_d.