Abstract: A computer system identifies a predicate in a computer language containing constant expressions as vacuous. The system identifies distinct variables contained in the predicate and represents the predicate by a set of bounding rectangles. The bounding rectangles are represented in a space having a number of dimensions equal to the number of variables. There are finite limits on dimensions of a bounding rectangle which represent the relationship between the variables in the predicate and the constant expressions in the predicate. The predicate is identified as vacuously FALSE where the set of bounding rectangles is empty.

Abstract: A method for typed view hierarchies for an object-relational database management (OPDBMS). The views in the hierarchy are merged into a unified hierarchy view through case expressions for mapping and wrapping of overloaded columns. During the merge, the underlying logical tables are eliminated which results in a simplified query graph. The transformation is a non-loss operation which condenses the type information within the case expressions. This allows update, delete and insert operations to be resolved on the query graph on a local level. Using query rewrite rules, the case expressions may be simplified further.