A

Abstract

A A relationally complete, “reduced instruction set” form of relational algebra with just two primitive operator—REMOVE (essentially projection on all attributes but one) and an algebraic analog of either NOR or NAND, q.v. The name is a doubly recursive acronym: It stands for ALGEBRA, which in turn stands for A Logical Genesis Explains Basic Relational Algebra. As this expanded name suggests, it is designed in such a way as to emphasize its close relationship to, and solid foundation in, the discipline of predicate logic, q.v. Further details can be found in the book Databases, Types, and the Relational Model: The Third Manifesto (3rd edition), by C. J. Date and Hugh Darwen (Addison-Wesley, 2006). Note: That book uses solid arrowheads, ◂ and ▸, to delimit A operator names, as in ◂ NOR ▸, in order to distinguish those operators from operators with the same name in predicate logic or Tutorial D or both, but those arrowheads are deliberately omitted here. More to the point, that book doesn't actually define either NOR or NAND as a primitive A operator, rather, it defines A as including explicit NOT, OR, and AND operators. But it then goes on to show that (a) either OR or AND could be removed without loss, and (b) NOT and whichever of OR and AND is retained could be collapsed into a single operator—NOT and OR into NOR, or NOT and AND into NAND.