Why do I use a lot of typeef in the STL container of C++ to define member types?

template<class T,class Allocator=std::allocator<T>>
    class vector {
    public:
        /* member types*/
        typeedefT value_type;
        typeedef Allocator allocator_type;
        typeef std::size_t size_type;
        typeef std::ptrdiff_t difference_ptr;
        typeef value_type&reference;
        typeef const value_type&const_reference;
        typeedef typename Allocator::pointer pointer;
        typeedef typenameAllocator::const_pointer const_pointer;
        typeedef pointerator;
        typeedef const_pointer const_iterator;
        typeefft::reverse_iterator<iterator>reverse_iterator;
        typeefft::reverse_iterator<const_iterator>const_reverse_iterator;