Why can't static_cast be used to down-cast when virtual inheritance is involved?

Consider the following code:

struct Base {};
struct Derived : public virtual Base {};

void f()
{
    Base* b = new Derived;
    Derived* d = static_cast<Derived*>(b);
}

This is prohibited by the standard ([n3290: 5.2.9/2]) so the code does not compile, because Derived virtually inherits from Base. Removing the virtual from the inheritance makes the code valid.

What's the technical reason for this rule to exist?

The technical problem is that there's no way to work out from a Base* what the offset is between the start of the Base sub-object and the start of the Derived object.

In your example it appears OK, because there's only one class in sight with a Base base, and so it appears irrelevant that the inheritance is virtual. But the compiler doesn't know whether someone defined another class Derived2 : public virtual Base, public Derived {}, and is casting a Base* pointing at the Base subobject of that. In general[*], the offset between the Base subobject and the Derived subobject within Derived2 might not be the same as the offset between the Base subobject and the complete Derived object of an object whose most-derived type is Derived, precisely because Base is virtually inherited.

So there's no way to know the dynamic type of the complete object, and different offsets between the pointer you've given the cast, and the required result, depending what that dynamic type is. Hence the cast is impossible.

Your Base has no virtual functions and hence no RTTI, so there certainly is no way to tell the type of the complete object. The cast is still banned even if Base does have RTTI (I don't immediately know why), but I guess without checking that a dynamic_cast is possible in that case.

[*] by which I mean, if this example doesn't prove the point then keep adding more virtual inheritance until you find a case where the offsets are different ;-)

static_cast can perform only those casts where memory layout between the classes is known at compile-time. dynamic_cast can check information at run-time, which allows to more accurately check for cast correctness, as well as read run-time information regarding the memory layout.

Virtual inheritance puts a run-time information into each object which specifies what is the memory layout between the Base and Derived. Is one right after another or is there an additional gap? Because static_cast cannot access such information, the compiler will act conservatively and just give a compiler error.

In more detail:

Consider a complex inheritance structure, where - due to multiple inheritance - there are multiple copies of Base. The most typical scenario is a diamond inheritance:

class Base {...};
class Left : public Base {...};
class Right : public Base {...};
class Bottom : public Left, public Right {...};

In this scenario Bottom consists of Left and Right, where each has its own copy of Base. The memory structure of all the above classes is known at compile time and static_cast can be used without a problem.

Let us now consider the similar structure but with virtual inheritance of Base:

class Base {...};
class Left : public virtual Base {...};
class Right : public virtual Base {...};
class Bottom : public Left, public Right {...};

Using the virtual inheritance ensures that when Bottom is created, it contains only one copy of Base that is shared between object parts Left and Right. The layout of Bottom object can be for example:

Base part
Left part
Right part
Bottom part

Now, consider that you cast Bottom to Right (that is a valid cast). You obtain a Right pointer to an object that is in two pieces: Base and Right have a memory gap in between, containing the (now-irrelevant) Left part. The information about this gap is stored at run-time in a hidden field of Right (typically referred to as vbase_offset). You can read the details for example here.

However, the gap would not exist if you would just create a standalone Right object.

So, if I give you just a pointer to Right you do not know at compile time if it is a standalone object, or a part of something bigger (e.g. Bottom). You need to check the run-time information to properly cast from Right to Base. That is why static_cast will fail and dynamic_cast will not.

Note on dynamic_cast:

While static_cast does not use run-time information about the object, dynamic_cast uses and requires it to exist! Thus, the latter cast can be used only on those classes which contain at least one virtual function (e.g. a virtual destructor)