Multiple inheritance and pure virtual functions

The following code:

struct interface_base
{
    virtual void foo() = 0;
};

struct interface : public interface_base
{
    virtual void bar() = 0;
};

struct implementation_base : public interface_base
{
    void foo();
};

struct implementation : public implementation_base, public interface
{   
    void bar();
};

int main()
{
    implementation x;
}

fails to compile with the following errors:

test.cpp: In function 'int main()':
test.cpp:23:20: error: cannot declare variable 'x' to be of abstract type 'implementation'
test.cpp:16:8: note:   because the following virtual functions are pure within 'implementation':
test.cpp:3:18: note:    virtual void interface_base::foo()

I have played around with it and figured out that making the 'interface -> interface_base' and 'implementation_base -> interface_base' inheritances virtual, fixes the problem, but I don't understand why. Can someone please explain what is going on?

p.s. I omitted the virtual destructors on purpose to make the code shorter. Please don't tell me to put them in, I already know :)