There are a number of proposals lately that instead of rewriting correlated queries into more efficient queries or algebraic forms, offer new evaluation algorithms that perform better than the default nested loop evaluation of embedded queries.

If we use the rules in Definition 3, this comprehension is translated into algebraic form as

2], [bar]r} that may appear at any point in a calculus form (including the ones inside other comprehensions) is translated into an algebraic form by [?

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.

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.