Abstract
Practical database query languages are usually equipped with some aggregate functions. For example, “find mean of column” can be expressed in SQL. However, the manner in which aggregate functions were introduced in these query languages leaves something to be desired. Breazu-Tannen, Buneman, and Wong [3] introduced a nested relational language NRC(=) based on monads [16, 24] and structural recursion [1, 2]. It was shown in Wong [27] that this language is equivalent to the nested relational algebras of Thomas and Fischer [22], Schek and Scholl [20], and Colby [4]. NRC(=) enjoys certain advantages over these languages: it is naturally embedded in functional languages, it is readily extensible, and it has a compact equational theory. Therefore, it is used in this report as a basis for investigating aggregate functions.
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