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

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

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.

using Rules (C11), (C10), (C8), and (C5)), which is the algebraic form shown in Figure 8.

Thus, T(e, (), (), {()}) translates the term e into an algebraic form.

We prove that the algebraic form above is equivalent to the original comprehension.

Our unnesting algorithm generates the algebraic form in Figure 12.

Hence it does not make a difference whether this query is expressed as a group-by query or a nested query; both forms are optimized to the same efficient algebraic form.

Our unnesting algorithm will generate the algebraic form shown in Figure 12.

The [Lambda]-DB system uses a polynomial-time heuristic algorithm, called GOO [Fegaras 1998a], that generates a "good quality" order of the monoid algebra operators in query algebraic form.

After the best evaluation order is derived, the algebraic form is mapped into an evaluation plan by a rule-based rewriting system.