C++ Double Dispatch for Equals()

When you create methods like this:

virtual bool is_equal(Shape& circle) { return false; };

And in the subclass,

virtual bool is_equal(Circle& circle) { return true; };

These are not the same method. You have two separate virtual methods, neither of which is overridden (they are overloaded not even overloaded, as Ben Voigt pointed out). When you call Shape::is_equal, there is only one version: Shape::is_equal(Shape&)… which is not overridden and always returns false.

You would have to define the separate overloaded methods in the parent class and then override them in the child class. For example,

class Shape {
    // Choice between these two methods happens at compile time...
    virtual bool is_equal(Circle& circle) { return false; };
    virtual bool is_equal(Rectangle& circle) { return false; };
};

class Rectangle : Shape {
    // Choice between this and Shape::is_equal(Rectangle&) happens at runtime...
    virtual bool is_equal(Rectangle& circle) { return true; };
};

However, using tricks like this, you will probably not approach the performance or simplicity of the way a C programmer would do it:

typedef enum {
    SHAPE_CIRCLE,
    SHAPE_RECTANGLE
} shape_type_t;

struct shape {
    shape_type_t type;
};

struct circle {
    shape_type_t type;
    ...
};

struct rectangle {
    shape_type_t type;
    ...
};

bool shape_equal(struct shape *x, struct shape *y)
{
    if (x->type != y->type)
        return false;
    switch (x->type) {
    case SHAPE_CIRCLE:
        return circle_equal((struct circle *) x, (struct circle *) y);
    case SHAPE_RECTANGLE:
        ...;
    }
}

If overloading and virtual methods are making your code more complicated than the C version, then you may wish to rethink whether you solve this particular problem with overloading and virtual methods.