Main functions of Databases

What are the main functions of a DB (Database) ?

1. Data definition. A DB should allow us to accept data definitions as those provided by the different types of schemas we had made to build our DB. This also includes a language processor component for each of the DDL (Data Definition Language: used to create and modifiy the logical structure (objects) of the DB)
2. Data manipulation. Users will retrieve information, as well as update and add new information. This includes a processor for DML (Data Manipulation Language: which allows the user to do such actions (retrieve, update, add); SQL is a DML).
3. Data security and integrity. Must have some mechanisms to control users requests and enforce the rules (security & integrity) defined by the DBA (Database Administrator).
4. Data recovery and concurrency. What's concurrency? That's data at the same time, okay, never though of what happens when two users are editing at the same time the same tuple? That's a concurrency problem. Also, DB must include some recovery options.
5. Data dictionary. That's data about data, meta-data. This includes the definitions of the DBs that the DBMS uses. (I.e.: a document describing a database).
6. Good performance. Obviously, a DB must be as efficient as it could be to provide all of the functions explained above.