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EntityRelationshipAttribute Designs And Sketches
 Theory Appl. Categ
, 2002
"... EntityRelationshipAttribute ideas are commonly used to specify and design information systems. They use a graphical technique for displaying the objects of the system and relationships among them. The design process can be enhanced by specifying constraints of the system and the natural environmen ..."
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Cited by 6 (1 self)
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EntityRelationshipAttribute ideas are commonly used to specify and design information systems. They use a graphical technique for displaying the objects of the system and relationships among them. The design process can be enhanced by specifying constraints of the system and the natural environment for these is the categorical notion of sketch. Here we argue that the finitelimit, finitesum sketches with a terminal node are the appropriate class and call them EA sketches. A model for an EA sketch in a lextensive category is a `snapshot' of a database with values in that category. The category of models of an EA sketch is an object of models of the sketch in a 2category of lextensive categories. Moreover, modelling the same sketch in certain objects in other 2categories defines both the query language for the database and the updates (the dynamics) for the database. 1.
Fibrations and universal view updatability
"... Maintainability and modifiability of information system software can be enhanced by the provision of comprehensive support for views, since view support allows application programs to continue to operate unchanged when the underlying information system is modified. Supporting views depends upon a so ..."
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Cited by 4 (1 self)
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Maintainability and modifiability of information system software can be enhanced by the provision of comprehensive support for views, since view support allows application programs to continue to operate unchanged when the underlying information system is modified. Supporting views depends upon a solution to the view update problem. This paper presents a new treatment of view updates for formally specified semantic data models based on the category theoretic sketch data model. The sketch data model has been the basis of a number of successful major information system consultancies. We define view updates by a universal property in models of the formal specification, and explain why this indeed gives a complete and correct treatment of view updatability, including a solution to the view update problem. However, a definition of updatability which is based on models causes some inconvenience in applications, so we prove that in a variety of circumstances updatability is guaranteed independently of the current model. This is done first with a very general criterion, and then for some specific cases relevant to applications. We include some detail about the sketch data model, noting that it involves extensions of algebraic data specification techniques.
Sketch Data Models, Relational Schema and Data Specifications
 ENTCS, Volume
, 2001
"... When different mathematical models are used for software analysis and development it is important to understand their relationships. When the models are truly mathematical, and when the aspects of reality that they seek to model are common, it may be possible to express their relationships in precis ..."
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Cited by 4 (3 self)
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When different mathematical models are used for software analysis and development it is important to understand their relationships. When the models are truly mathematical, and when the aspects of reality that they seek to model are common, it may be possible to express their relationships in precise mathematical terms. This paper studies three mathematical models: The sketch data model, the relational data model, and the data specifications of Piessens and Steegmans, and determines their relationships mathematically and in detail. The constructions presented here answer reasonably longstanding theoretical questions, and offer techniques that promise to be practically useful in integrating data models.
Constant Complements, Reversibility and Universal View Updates ⋆
"... Abstract. The algebraic specification of information systems (including databases) has been advanced by the introduction of category theoretic sketches and in particular by the authors ’ Sketch Data Model (SkDM). The SkDM led to a new treatment of view updating using universal properties already stu ..."
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Cited by 3 (1 self)
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Abstract. The algebraic specification of information systems (including databases) has been advanced by the introduction of category theoretic sketches and in particular by the authors ’ Sketch Data Model (SkDM). The SkDM led to a new treatment of view updating using universal properties already studied in category theory. We call the new treatment succinctly ”universal updating”. This paper outlines the theory of universal updating and studies the relationships between it and recent theoretical results of Hegner and Lechtenbörger which in turn studied the classical ”constant complement ” approach to view updates. The main results demonstrate that constant complement updates are universal, that on the other hand there are sometimes universal updates even in the absence of constant complements, and that in the SkDM constant complement updates are reversible. We show further that there may be universal updates which are reversible even for views which have no complement. In short, the universal updates provide an attractive option including reversibility, even when constant complements are not available. The paper is predominantly theoretical studying different algebraic approaches to information system software but it also has important practical implications since it shows that universal updates have important properties in common with classical updates but they may be available even when classical approaches fail.
Update Algorithms for the Sketch Data Model
 Proceedings of CSCWD 2001, the Sixth International Conference on Computer Supported Cooperative Work in Design, 367–376, NRC and IEEE
, 2001
"... The authors have developed a new approach to database interoperability using the sketch data model. That technique has now been used in a number of applications, but an important question remains: What are the algorithms that support updates in the sketch data model? The question has significant con ..."
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Cited by 2 (1 self)
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The authors have developed a new approach to database interoperability using the sketch data model. That technique has now been used in a number of applications, but an important question remains: What are the algorithms that support updates in the sketch data model? The question has significant content since the sketch data model uses EAsketches to specify data structures, and these include constraint and other information not normally supported by relational database management systems. In this paper we answer the question by using the framework of EA sketches to give a detailed mathematical treatment of database updates, providing a formal definition of insert update together with an algorithm which provably achieves updates. The algorithm is new as it is the first to treat data and constraints on an equal categorical footing. We also note that further exactness properties (limits and colimits) can aid specification, and we provide algorithms for updates of EA sketched databases with finite limits. These are the first update algorithms for such databases. The sketch data model is being used in industry for designing interoperations for computer supported cooperative workand computer assisted software engineering (CASE) tools are under development. The paper is predominantly theoretical, and provides an important link needed for CASE tool development. Keywords: Category theory, data model, mathematical specification, database interoperation 1.
Three Approaches to Partiality in the Sketch Data Model
, 2002
"... Partial information is common in realworld databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit suppor ..."
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Cited by 2 (0 self)
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Partial information is common in realworld databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit support for nulls.