Destructor not called in inheritance

I'm totally stalled, after battling this bug for hours after hours my worst fears came true. In the sample code below, where B inherits from A but is still pointed at by an A* pointer the B destructor IS NOT called (even if they use virtual methods). Now a solution/workaround to this is not hard to make, but is this really intended (standard) behavour or is my compiler just plain insane? I can't believe I've never discovered this earlier...

Code:

#include <iostream>

class A
{
	public:
		A() { std::cout << "A::A()" << std::endl; }
		~A() { std::cout << "A::~A()" << std::endl; }

	protected:
};

class B : public A
{
	public:
		B() { std::cout << "B::B()" << std::endl; }
		~B() { std::cout << "B::~B()" << std::endl; }

	protected:
};

int main()
{
	A* b = new B();
	delete b;

	return 0;
}

You must make the destructor of the base class virtual. Then all will be well.

thanks