By applying the [H.sub.(r)] statistic on our data set of size n = 342, we find that the discrepancy between the assumed

algebraic form and the empirical distribution exceeds the optimal [s.sup.*] = 0.86 at r + 1 = 4, which leads to an estimate of [[alpha].sub.r] = 0.72.

The functionality of an algebraic form can be better understood if we use a stream-based interpretation in which a stream of tuples flows from the leaves to the root of the tree.

The algebraic form of QUERY B after unnesting is shown in Figure 8.B.

The algebraic form of QUERY C is shown in Figure 8.C.

The algebraic form of this query is shown in Figure 8.D.

Every comprehension is first normalized and then translated into an algebraic form consisting of regular joins, selections, unnests, and reductions--the last being the root of the algebraic form.

Thus, T(e, (), (), {()}) translates the term e into an algebraic form. Terms are tree-like data structures that represent both calculus and algebraic terms.