Algebraic and calculus query languages for recursively typed complex objects

Abstract

Algebraic and calculus database query languages for recursively typed complex objects based on the set and tuple constructs are studied. A fundamental characteristic of such complex objects is that, in them, sets may contain members with arbitrarily deep nesting of tuple and/or set constructs. Relative to mappings from flat relations to flat relations, the algebra without while has the expressive power of the algebra on conventional complex objects with non-recursive types. The algebra plus while has the power of the computable queries. The calculus has power equivalent to the arithmetical hierarchy and also to the calculus with countable invention for conventional complex objects. A technical tool, called “domain Turing machine,” is introduced and applied to characterize the expressive power of several classes of relational queries.