Finally, it starts to get interesting! This example shows how you can add plus and other operations to sequences of data without creating temporaries and allocating memory.

	Note
	In this example, we see a terminal type that owns the storage of its value, a std::vector<double>. See the Vector example later on to see a terminal type that does not.

// Defining this allows the assignment below of an expression to a double
// without writing any specific code to do so.
#include <boost/yap/expression.hpp>

#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>


template <boost::yap::expr_kind Kind, typename Tuple>
struct lazy_vector_expr;


// This transform turns a terminal of std::vector<double> into a terminal
// containing the nth double in that vector.  Think of it as turning our
// expression of vectors into an expression of scalars.
struct take_nth
{
    boost::yap::terminal<lazy_vector_expr, double>
    operator() (boost::yap::terminal<lazy_vector_expr, std::vector<double>> const & expr);

    std::size_t n;
};

// A custom expression template that defines lazy + and - operators that
// produce expressions, and an eager [] operator that returns the nth element
// of the expression.
template <boost::yap::expr_kind Kind, typename Tuple>
struct lazy_vector_expr
{
    static const boost::yap::expr_kind kind = Kind;

    Tuple elements;

    // Note that this does not return an expression; it is greedily evaluated.
    auto operator[] (std::size_t n) const;
};

BOOST_YAP_USER_BINARY_OPERATOR(plus, lazy_vector_expr, lazy_vector_expr)
BOOST_YAP_USER_BINARY_OPERATOR(minus, lazy_vector_expr, lazy_vector_expr)

template <boost::yap::expr_kind Kind, typename Tuple>
auto lazy_vector_expr<Kind, Tuple>::operator[] (std::size_t n) const
{ return boost::yap::evaluate(boost::yap::transform(*this, take_nth{n})); }

boost::yap::terminal<lazy_vector_expr, double>
take_nth::operator() (boost::yap::terminal<lazy_vector_expr, std::vector<double>> const & expr)
{
    double x = boost::yap::value(expr)[n];
    // This move is something of a hack; we're forcing Yap to take a copy of x
    // by using std::move().  The move indicates that the terminal should keep
    // the value of x (since, being an rvalue, it may be a temporary), rather
    // than a reference to x.  See the "How Expression Operands Are Treated"
    // section of the tutorial for details.
    return boost::yap::make_terminal<lazy_vector_expr, double>(std::move(x));
}

// In order to define the += operator with the semantics we want, it's
// convenient to derive a terminal type from a terminal instantiation of
// lazy_vector_expr.  Note that we could have written a template
// specialization here instead -- either one would work.  That would of course
// have required more typing.
struct lazy_vector :
    lazy_vector_expr<
        boost::yap::expr_kind::terminal,
        boost::hana::tuple<std::vector<double>>
    >
{
    lazy_vector () {}

    explicit lazy_vector (std::vector<double> && vec)
    { elements = boost::hana::tuple<std::vector<double>>(std::move(vec)); }

    template <boost::yap::expr_kind Kind, typename Tuple>
    lazy_vector & operator+= (lazy_vector_expr<Kind, Tuple> const & rhs)
    {
        std::vector<double> & this_vec = boost::yap::value(*this);
        for (int i = 0, size = (int)this_vec.size(); i < size; ++i) {
            this_vec[i] += rhs[i];
        }
        return *this;
    }
};

int main ()
{
    lazy_vector v1{std::vector<double>(4, 1.0)};
    lazy_vector v2{std::vector<double>(4, 2.0)};
    lazy_vector v3{std::vector<double>(4, 3.0)};

    double d1 = (v2 + v3)[2];
    std::cout << d1 << "\n";

    v1 += v2 - v3;
    std::cout << '{' << v1[0] << ',' << v1[1]
              << ',' << v1[2] << ',' << v1[3] << '}' << "\n";

    // This expression is disallowed because it does not conform to the
    // implicit grammar.  operator+= is only defined on terminals, not
    // arbitrary expressions.
    // (v2 + v3) += v1;

    return 0;
}