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This paper considers the theory of database queries on the complex value data model with external functions. Motivated by concerns regarding query evaluation, we first identify recursive sets of formulas, called embedded allowed, which is a class with desirable properties of "reasonable" queries. We then show that all embedded allowed calculus (or fix-point) queries are domain independent and continuous. An algorithm for translating embedded allowed queries into equivalent algebraic expressionsdoi:10.1016/j.ins.2008.02.005 fatcat:vqcwzpztxzf3xjl2regoiywm2a