6 Related Work 5.2 Faithfulness

The problem of passing restrictions more general than a binding to a set of constants has been the subject of some other recent research. Ramakrishnan ((Ram88]) introduced Magic Templates to pass restrictions due to the presence of function symbols and the relationships between otherwise free arguments. However, the method generates non-range-restricted rules from range-restricted programs, and therefore cannot be applied in most database systems. Also, as we remarked in Section 5, the Bf adornment class used in Ram88] is not faithful and is less descriptive than the bcf adornment class. Where non-range-restricted programs are acceptable, the Templates approach can beneet from the use of bcf class. Balbin, Kemp, Meenakshi and Ramamoha-narao ((BKMR89]) propose a folding/unfolding algorithm to push conditions into recursions. While our objectives are similar, our approach diiers in many important ways. Balbin et al. assume that an adorned program (using the bf adornments) is given as input, and rewrite the program with the conditions pushed into lower strata. However, a bf adornment done without regard to conditions can cause their algorithm to fail, and their algorithm can ben-eet from our extension to the bcf adornment pattern. Our GMT algorithm ooers an alternative to their algorithm for pushing conditions. For many programs (such as the program P in Example 1.1), the results of the two algorithms are similar, assuming we use the bcf adornments in both algorithms. However, there are cases where their algorithm is not applicable , while GMT is, and other cases where GMT has better behavior. For example, their algorithm cannot push conditions from built-in literals in a rule body into recursive subgoals, such as the condition W > V on p cf in rule P1 of Example 4.3; GMT clearly can. GMT has better behavior when conditions are pushed into a common subexpression. Their algorithm repli-cates the rules of the common predicate for each condition pushed, while GMT only replicates the grounding subgoals of the common predicate. There are also cases (grounding by recursive subgoals) where GMT, as presented here, is not applicable, while their algorithm is. However, as we noted in Section 4.2.1, GMT could be extended to allow grounding by re-cursive subgoals. 7 Conclusions In this paper we have shown that the magic-sets techniques can be extended to deal with conditions. We have integrated (and partially implemented) an Extended Magic-sets algorithm into the rewrite optimization phase of the SQL-based Star-burst prototype DBMS at …