Mappings between Levels and Data Independence
The 3 levels of abstraction in the database do not exist separately of each other. There must be some correspondence, or mapping, among the levels. There are two types of mappings: the internal / conceptual mapping and the conceptual / external mapping.
The internal / conceptual mapping lies among the internal and conceptual levels, and tells the correspondence among the records and the data structures of the internal view and fields of the conceptual view and the files. If the structure of the stored database is changed, then the internal / conceptual mapping must also be changed accordingly so that the view from the conceptual level remains similar. It is this mapping that gives physical data independence for the database. For instance, we may modify the internal view of student relation by breaking the student file into two files, one containing enrolment, address and name and other containing enrolment, programme. Therefore, the mapping will make sure that the conceptual view is restored as original. The storage decision is firstly taken for optimisation purposes.
The external/conceptual view lies between the external and conceptual levels, and tells the correspondence between a particular external view and the conceptual view. Though these two levels are same, some elements discover in a particular external view may be different from the conceptual view. For example, various fields can be combined into a single (virtual) field, which can also have dissimilar names from the original fields. If the structure of the database at the conceptual level is changed, then the conceptual / external mapping must change accordingly so that the view from the external level remains constant. It is this mapping that gives logical data independence for the database. For instance, we may change the student relation to have more fields at conceptual level, yet this will never change the two user views at all.
It is also doable to have another mapping, where one external view is show in terms of other external views (this could be known as external/external mapping). This is useful if various external views are closely related to one another, as it permits you to avoid mapping each of the same external views directly to the conceptual level.