The classical relational algebra is incomplete, despite theorems to the contrary, in the face of advanced applications such as deductive databases, rule bases for expert systems, geographical and other spatio-temporal information systems, online analytical processing and datacubes, predictive modelling, data mining, and semistructured data. The Domain Algebra fills in much of this incompleteness, but the Aldat programming language needs a rationalization of the classical binary and unary operators as well as further facilities such as recursion, query quantification, text and pattern-matching capabilities, infinite relations, polymorphic relations, metadata, and generalized editors for end users.