We discuss the philosophy, history and theory of window functions. Simply stated, a window function maps a database state and a relation scheme to a relation over the scheme.
Window functions are the basis for all existing universal scheme interfaces.
We present an assumption inherent in universal scheme interfaces, the unique role assumption . Window functions have evolved along two paths, giving rise to computational definitions and weak instance definitions. We then look at properties we feel a reasonable window function should satisfy, notably the containment condition and faithfulness . We also define implicit objects , which are relation schemes that a window function treats in a special manner, and which are useful for describing the behavior of window functions. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.