Multiset types - SQL

An SQL multiset is what in mathematics is also known as a bag-something like a set except that the same element can appear more than once. The body of an SQL table is in general a bag of rows, rather than a set of rows, because SQL does indeed permit the same row to appear more than once in the same table. Although SQL has no names for table types, it does support multisets in general and it does have names for multiset types. A multiset type name consists of a type name followed by the key word MULTISET. For example, INTEGER MULTISET is the name of the type each of whose values is either (a) a bag, consisting of zero or more appearances of each value of type INTEGER and zero or more appearances of the null value of type INTEGER, or (b) the null value of type INTEGER MULTISET.

It would seem at first glance, then, that we perhaps do have a type name for a table type after all. For example, our enrolments table could perhaps be of type

ROW ( Name VARCHAR(50), StudentId VARCHAR(5),

CourseId VARCHAR(5) ) MULTISET

In fact one could declare a local variable to be of this type and its value could indeed consist of the rows. However, such a type cannot be the declared type of a base table, in spite of the fact that the elements of a base table are indeed rows of the same type. Moreover, as I have already mentioned, there is such a thing as the null value of that multiset type, whereas NULL can never appear in place of a table-no table expression in SQL can ever evaluate to NULL-nor can NULL appear in place of a row in a table. So the set of values of a multiset type whose element type is a row type includes bags that are not tables as well as bags that are.