On the expressive power of database queries with intermediate types
Richard B. Hull, Jianwen Su · 1988
The set-height of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T, an intermediate type is a type which is used by some variable of the query, but which is not present in D or T. For each k, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with set-height ≤ k and using intermediate types with set-height ≤ i In particular, CALC0,0 is the relational calculus, and CALC0,1 is equivalent to the family of second-order (relational) queries