Lazy evaluation in C++

C++ does not have native support for lazy evaluation (as Haskell does).

I'm wondering if it is possible to implement lazy evaluation in C++ in a reasonable manner. If yes, how would you do it?

EDIT: I like Konrad Rudolph's answer.

I'm wondering if it's possible to implement it in a more generic fashion, for example by using a parametrized class lazy that essentially works for T the way matrix_add works for matrix.

Any operation on T would return lazy instead. The only problem is to store the arguments and operation code inside lazy itself. Can anyone see how to improve this?

I'm wondering if it is possible to implement lazy evaluation in C++ in a reasonable manner. If yes, how would you do it?

Yes, this is possible and quite often done, e.g. for matrix calculations. The main mechanism to facilitate this is operator overloading. Consider the case of matrix addition. The signature of the function would usually look something like this:

matrix operator +(matrix const& a, matrix const& b);

Now, to make this function lazy, it's enough to return a proxy instead of the actual result:

struct matrix_add;

matrix_add operator +(matrix const& a, matrix const& b) {
    return matrix_add(a, b);
}

Now all that needs to be done is to write this proxy:

struct matrix_add {
    matrix_add(matrix const& a, matrix const& b) : a(a), b(b) { }

    operator matrix() const {
        matrix result;
        // Do the addition.
        return result;
    }
private:
    matrix const& a, b;
};

The magic lies in the method operator matrix() which is an implicit conversion operator from matrix_add to plain matrix. This way, you can chain multiple operations (by providing appropriate overloads of course). The evaluation takes place only when the final result is assigned to a matrix instance.

EDIT I should have been more explicit. As it is, the code makes no sense because although evaluation happens lazily, it still happens in the same expression. In particular, another addition will evaluate this code unless the matrix_add structure is changed to allow chained addition. C++0x greatly facilitates this by allowing variadic templates (i.e. template lists of variable length).

However, one very simple case where this code would actually have a real, direct benefit is the following:

int value = (A + B)(2, 3);

Here, it is assumed that A and B are two-dimensional matrices and that dereferencing is done in Fortran notation, i.e. the above calculates one element out of a matrix sum. It's of course wasteful to add the whole matrices. matrix_add to the rescue:

struct matrix_add {
    // … yadda, yadda, yadda …

    int operator ()(unsigned int x, unsigned int y) {
        // Calculate *just one* element:
        return a(x, y) + b(x, y);
    }
};

Other examples abound. I've just remembered that I have implemented something related not long ago. Basically, I had to implement a string class that should adhere to a fixed, pre-defined interface. However, my particular string class dealt with huge strings that weren't actually stored in memory. Usually, the user would just access small substrings from the original string using a function infix. I overloaded this function for my string type to return a proxy that held a reference to my string, along with the desired start and end position. Only when this substring was actually used did it query a C API to retrieve this portion of the string.

Boost.Lambda is very nice, but Boost.Proto is exactly what you are looking for. It already has overloads of all C++ operators, which by default perform their usual function when proto::eval() is called, but can be changed.

What Konrad already explained can be put further to support nested invocations of operators, all executed lazily. In Konrad's example, he has an expression object that can store exactly two arguments, for exactly two operands of one operation. The problem is that it will only execute one subexpression lazily, which nicely explains the concept in lazy evaluation put in simple terms, but doesn't improve performance substantially. The other example shows also well how one can apply operator() to add only some elements using that expression object. But to evaluate arbitrary complex expressions, we need some mechanism that can store the structure of that too. We can't get around templates to do that. And the name for that is expression templates. The idea is that one templated expression object can store the structure of some arbitrary sub-expression recursively, like a tree, where the operations are the nodes, and the operands are the child-nodes. For a very good explanation i just found today (some days after i wrote the below code) see here.

template<typename Lhs, typename Rhs>
struct AddOp {
    Lhs const& lhs;
    Rhs const& rhs;

    AddOp(Lhs const& lhs, Rhs const& rhs):lhs(lhs), rhs(rhs) {
        // empty body
    }

    Lhs const& get_lhs() const { return lhs; }
    Rhs const& get_rhs() const { return rhs; }
};

That will store any addition operation, even nested one, as can be seen by the following definition of an operator+ for a simple point type:

struct Point { int x, y; };

// add expression template with point at the right
template<typename Lhs, typename Rhs> AddOp<AddOp<Lhs, Rhs>, Point> 
operator+(AddOp<Lhs, Rhs> const& lhs, Point const& p) {
    return AddOp<AddOp<Lhs, Rhs>, Point>(lhs, p);
} 

// add expression template with point at the left
template<typename Lhs, typename Rhs> AddOp< Point, AddOp<Lhs, Rhs> > 
operator+(Point const& p, AddOp<Lhs, Rhs> const& rhs) {
    return AddOp< Point, AddOp<Lhs, Rhs> >(p, rhs);
}

// add two points, yield a expression template    
AddOp< Point, Point > 
operator+(Point const& lhs, Point const& rhs) {
    return AddOp<Point, Point>(lhs, rhs);
}

Now, if you have

Point p1 = { 1, 2 }, p2 = { 3, 4 }, p3 = { 5, 6 };
p1 + (p2 + p3); // returns AddOp< Point, AddOp<Point, Point> >

You now just need to overload operator= and add a suitable constructor for the Point type and accept AddOp. Change its definition to:

struct Point { 
    int x, y; 

    Point(int x = 0, int y = 0):x(x), y(y) { }

    template<typename Lhs, typename Rhs>
    Point(AddOp<Lhs, Rhs> const& op) {
        x = op.get_x();
        y = op.get_y();
    }

    template<typename Lhs, typename Rhs>
    Point& operator=(AddOp<Lhs, Rhs> const& op) {
        x = op.get_x();
        y = op.get_y();
        return *this;
    }

    int get_x() const { return x; }
    int get_y() const { return y; }
};

And add the appropriate get_x and get_y into AddOp as member functions:

int get_x() const {
    return lhs.get_x() + rhs.get_x();
}

int get_y() const {
    return lhs.get_y() + rhs.get_y();
}

Note how we haven't created any temporaries of type Point. It could have been a big matrix with many fields. But at the time the result is needed, we calculate it lazily.

I have nothing to add to Konrad's post, but you can look at Eigen for an example of lazy evaluation done right, in a real world app. It is pretty awe inspiring.

Lazy evaluation in C++

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