So far we've only seen examples with custom terminals that own the values in the expressions we operate on. What happens when you've got types that you want to operate on, non-intrusively? Here's how you might do it with std::vector<>s:

#include <boost/yap/yap.hpp>

#include <vector>
#include <iostream>


struct take_nth
{
    template <typename T>
    auto operator() (boost::yap::expr_tag<boost::yap::expr_kind::terminal>,
                     std::vector<T> const & vec)
    { return boost::yap::make_terminal(vec[n]); }

    std::size_t n;
};

// A stateful transform that records whether all the std::vector<> terminals
// it has seen are equal to the given size.
struct equal_sizes_impl
{
    template <typename T>
    auto operator() (boost::yap::expr_tag<boost::yap::expr_kind::terminal>,
                     std::vector<T> const & vec)
    {
        auto const expr_size = vec.size();
        if (expr_size != size)
            value = false;
        return 0;
    }

    std::size_t const size;
    bool value;
};

template <typename Expr>
bool equal_sizes (std::size_t size, Expr const & expr)
{
    equal_sizes_impl impl{size, true};
    boost::yap::transform(boost::yap::as_expr(expr), impl);
    return impl.value;
}


// Assigns some expression e to the given vector by evaluating e elementwise,
// to avoid temporaries and allocations.
template <typename T, typename Expr>
std::vector<T> & assign (std::vector<T> & vec, Expr const & e)
{
    decltype(auto) expr = boost::yap::as_expr(e);
    assert(equal_sizes(vec.size(), expr));
    for (std::size_t i = 0, size = vec.size(); i < size; ++i) {
        vec[i] = boost::yap::evaluate(
            boost::yap::transform(boost::yap::as_expr(expr), take_nth{i}));
    }
    return vec;
}

// As assign() above, just using +=.
template <typename T, typename Expr>
std::vector<T> & operator+= (std::vector<T> & vec, Expr const & e)
{
    decltype(auto) expr = boost::yap::as_expr(e);
    assert(equal_sizes(vec.size(), expr));
    for (std::size_t i = 0, size = vec.size(); i < size; ++i) {
        vec[i] += boost::yap::evaluate(
            boost::yap::transform(boost::yap::as_expr(expr), take_nth{i}));
    }
    return vec;
}

// Define a type trait that identifies std::vectors.
template <typename T>
struct is_vector : std::false_type {};

template <typename T, typename A>
struct is_vector<std::vector<T, A>> : std::true_type {};

// Define all the expression-returning numeric operators we need.  Each will
// accept any std::vector<> as any of its arguments, and then any value in the
// remaining argument, if any -- some of the operators below are unary.
BOOST_YAP_USER_UDT_UNARY_OPERATOR(negate, boost::yap::expression, is_vector); // -
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(multiplies, boost::yap::expression, is_vector); // *
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(divides, boost::yap::expression, is_vector); // /
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(modulus, boost::yap::expression, is_vector); // %
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(plus, boost::yap::expression, is_vector); // +
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(minus, boost::yap::expression, is_vector); // -
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(less, boost::yap::expression, is_vector); // <
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(greater, boost::yap::expression, is_vector); // >
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(less_equal, boost::yap::expression, is_vector); // <=
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(greater_equal, boost::yap::expression, is_vector); // >=
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(equal_to, boost::yap::expression, is_vector); // ==
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(not_equal_to, boost::yap::expression, is_vector); // !=
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(logical_or, boost::yap::expression, is_vector); // ||
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(logical_and, boost::yap::expression, is_vector); // &&
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(bitwise_and, boost::yap::expression, is_vector); // &
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(bitwise_or, boost::yap::expression, is_vector); // |
BOOST_YAP_USER_UDT_ANY_BINARY_OPERATOR(bitwise_xor, boost::yap::expression, is_vector); // ^

int main()
{
    int i;
    int const n = 10;
    std::vector<int> a,b,c,d;
    std::vector<double> e(n);

    for (i = 0; i < n; ++i)
    {
        a.push_back(i);
        b.push_back(2*i);
        c.push_back(3*i);
        d.push_back(i);
    }

    // After this point, no allocations occur.

    assign(b, 2);
    assign(d, a + b * c);

    a += if_else(d < 30, b, c);

    assign(e, c);
    e += e - 4 / (c + 1);

    for (i = 0; i < n; ++i)
    {
        std::cout
            << " a(" << i << ") = " << a[i]
            << " b(" << i << ") = " << b[i]
            << " c(" << i << ") = " << c[i]
            << " d(" << i << ") = " << d[i]
            << " e(" << i << ") = " << e[i]
            << std::endl;
    }

    return 0;
}

Note

Though this example only provides overloads for the operations we want to define over std::vector<>s, the result of each of those operations is an expression<>, which uses all the operator overloads. If we wanted to restrict the operations on the results too, we could have defined a custom expression template with the desired operations, and used that instead of expression<> in the operator macros.