Translation with optimization from relational calculus to relational algebra having aggregate functions

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Abstract
Most of the previous translations of relational calculus to relational algebra aimed at proving that the two languages have the equivalent expressive power, thereby generating very complicated relational algebra expressions, especially when aggregate functions are introduced. This paper presents a rule-based translation method from relational calculus expressions having both aggregate functions and null values to optimized relational algebra expressions. Thus, logical optimization is carried out through translation. The translation method comprises two parts: the translational of the relational calculus kernel and the translation of aggregate functions. The former uses the familiar step-wise rewriting strategy, while the latter adopts a two-phase rewriting strategy via standard aggregate expressions. Each translation proceeds by applying a heuristic rewriting rule in preference to a basic rewriting rule. After introducing SQL-type null values, their impact on the translation is thoroughly investigated, resulting in several extensions of the translation. A translation experiment with many queries shows that the proposed translation method generates optimized relational algebra expressions. It is shown that heuristic rewriting rules play an essential role in the optimization. The correctness of the present translation is also shown. Each translation proceeds by applying a heuristic rewriting rule in preference to a basic rewriting rule. After introducing SQL-type null values, their impact on the translation is thoroughly investigated, resulting in several extensions of the translation. A translation experiment with many queries shows that the proposed translation method generates optimized relational

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