How can the object parameter received by an input overloading function be const

In class we're implementing vector, but I don't understand why the code for the input operator overloading is working:

istream& operator>> (istream& in, const Vector& A)
{
    for (int i = 0; i < A.size; i++)
        in >> A.data[i];
    return in;
}

I tried the code and it worked pretty well, but how can the vector reference be const even though we're inputting values for A?!

Assuming that Vector contains some T* data pointer as a member, a const Vector's member would be a T* const pointer. T* const is a const pointer to T, though T is mutable.

Therefore, in >> A.data[i]; works, since it simply writes mutable data.

If you want constness to propagate deeply to the next pointer, you have to ensure this yourself:

class Vector {
private:
    T* m_data;

public:
    T* data() {
        return m_data;
    }
    const T* data() const {
        return m_data;
    }
};

Now, in >> A.data()[i] would fail because A.data() would yield a pointer to const T.

This technique is used by containers like std::vector, see std::vector::data.

Note on language evolution

There is std::experimental::propagate_const which solves this without extra manual effort.

P2670: Non-transient constexpr allocation proposes a propconst specifier which would could be used as follows:

struct Vector {
    // propagate const one level deep
    propconst(1) T* data;
};