GCC error: explicit specialization in non-namespace scope

You just have to move your specializations of the member templates outside of the class body.

class VarData
{
public:
    template < typename T > bool IsTypeOf (int index) const
    {
        return IsTypeOf_f<T>::IsTypeOf(this, index);
    }
};

template <> bool VarData::IsTypeOf < int > (int index) const
{
    return false;
}

template <> bool VarData::IsTypeOf < double > (int index) const
{
    return false;
}