The Proto Calc2 example turns the expressions from Calc1 into callable objects. Using Boost.YAP you can do this in two ways.

You can just use lambdas to wrap the expressions:

#include <boost/yap/expression.hpp>

#include <iostream>


int main ()
{
    using namespace boost::yap::literals;

    auto expr_1 = 1_p + 2.0;

    auto expr_1_fn = [expr_1](auto &&... args) {
        return evaluate(expr_1, args...);
    };

    auto expr_2 = 1_p * 2_p;

    auto expr_2_fn = [expr_2](auto &&... args) {
        return evaluate(expr_2, args...);
    };

    auto expr_3 = (1_p - 2_p) / 2_p;

    auto expr_3_fn = [expr_3](auto &&... args) {
        return evaluate(expr_3, args...);
    };

    // Displays "5"
    std::cout << expr_1_fn(3.0) << std::endl;

    // Displays "6"
    std::cout << expr_2_fn(3.0, 2.0) << std::endl;

    // Displays "0.5"
    std::cout << expr_3_fn(3.0, 2.0) << std::endl;

    return 0;
}

Or you can use make_expression_function() to make a callable object from your expression:

#include <boost/yap/expression.hpp>

#include <iostream>


int main ()
{
    using namespace boost::yap::literals;

    // Displays "5"
    std::cout << make_expression_function(1_p + 2.0)(3.0) << std::endl;

    // Displays "6"
    std::cout << make_expression_function(1_p * 2_p)(3.0, 2.0) << std::endl;

    // Displays "0.5"
    std::cout << make_expression_function((1_p - 2_p) / 2_p)(3.0, 2.0) << std::endl;

    return 0;
}