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Databases as Diagram Algebras: Specifying Queries and Views Via the GraphBased Logic of Sketches
, 1996
"... The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams ..."
Abstract

Cited by 11 (9 self)
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The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams of sets and functions. Given a signature of operations (query language), any sketch (database schema) can be extended with derived items denoting data that can be retrieved from the database. Views to a schema S are then sketch morphisms v : SV ! S 0 from some sketch (view schema) SV into an augmentation of S with derived items, S 0 . In this way one obtains a unifying graphbased formal language for data and metadata definition and manipulation. In particular, a formalized specification framework for heterogeneous multibase systems can be built. The approach is described with a number of examples and then precisely formalized. The main technical contribution is the development of alge...
Generalised Sketches as an algebraic graphbased framework for semantic modeling and database design
, 1997
"... A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached ..."
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A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached in the framework. The machinery has its origin in the classical sketches invented by Ehresmann and is close to their generalization recently proposed by Makkai. There are two essential distinctions from Makkai's sketches. One consists in a different  more direct  formalization of sketches that categorists (and database designers) usually draw. The second distinction is more fundamental and consists in introducing operational sketches specifying complex diagram operations over ordinary (predicate) sketches, correspondingly, models of operational sketches are diagram algebras. Together with the notion of parsing operational sketches, this is the main mathematical contribution of the pape...