Abstract
Conventional database query languages are considered in the context of untyped sets. The algebra without while has the expressive power of the typed complex object algebra. The algebra plus while, and COL with untyped sets (under stratified semantics or inflationary semantics) have the power of the computable queries. The calculus has power beyond the computable queries; and is characterized using the typed complex object calculus with invention. The Bancilhon-Khoshafian calculus is also discussed. A technical tool, called “generic Turing machine”, is introduced and used in several of the proofs.
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