Information system software productivity can be increased by improving the maintainability and modifiability of the software produced. This latter in turn can be achieved 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. But, supporting views depends upon a solution to the view update problem, and proposed solutions to date have only had limited, rather than comprehensive, applicability. This paper presents a new treatment of view updates for formally specified information systems. The formal specification technique we use is based on category theory and has been the basis of a number of successful major information system consultancies. We define view updates by a universal property in a subcategory of models of the formal specification, and explain why this indeed gives a comprehensive 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. The paper is predominantly theoretical, as it develops the theoretical basis of a formal methods technique, but the methods described here are currently being used in a large consultancy for a government Department of Health. Because the application area, information systems, is rarely treated by formal methods, we include some detail about the formal methods used. In fact they are extensions of the usual category theoretic specification techniques, and the solution to the view update problem can be seen as requiring the existence of an...

The Sketch Data Model (SkDM) is a new semantic modelling paradigm based on category theory (specifically on categorical universal algebra), which has been used successfully in several consultancies with major Australian companies. This paper describes the sketch data model and investigates the view update problem (VUP) in the sketch data model paradigm. It proposes an approach to the VUP in the SkDM, and presents a range of examples to illustrate the scope of the proposed technique. In common with previously proposed approaches, we define under what circumstances a view update can be propagated to the underlying database. Unlike many previously proposed approaches the definition is succinct and consistent, with no ad hoc exceptions, and the propagatable updates form a broad class. We argue that we avoid ad hoc exceptions by basing the definition of propagatable on the state of the underlying database. The examples demonstrate that under a range of circumstances a view schema can be shown to have propagatable views in all states, and thus state-independence can frequently be recovered. Keywords: View update, category theory, data model, semantic data modelling 1

For successful information systems development, conceptual data modeling is essential. Nowadays a plethora of techniques for conceptual data modeling exist. Many of these techniques lack a formal foundation and a lot of theory, e.g. concerning updates or schema transformations, is highly data model specific. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper the use of category theory for this purpose is addressed. Well-known conceptual data modeling concepts, such as relationship types, generalization, specialization, and collection types are discussed from a categorical point of view. An important advantage of this framework is its "configurable semantics". Features such as null values, uncertainty, and temporal behavior can be added by selecting appropriate instance categories. The addition of these features usually requires a complete redesign of the formalization in traditional set-based approaches to semantics...

For successful information systems development, conceptual data modeling is essential. Nowadays many techniques for conceptual data modeling exist. In-depth comparisons of concepts of these techniques are very difficult as the mathematical formalizations of these techniques, if they exist at all, are very different. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper the use of category theory for this purpose is addressed. Well-known conceptual data modeling concepts, such as relationship types, generalization, specialization, collection types, and constraint types, such as the total role constraint and the uniqueness constraint, are discussed from a categorical point of view. An important advantage of this framework is its "configurable semantics". Features such as null values, uncertainty, and temporal behavior can be added by selecting appropriate instance categories. The addition of these features usually requir...

Entity-Relationship-Attribute 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 finite-limit, finite-sum 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 2-category of lextensive categories. Moreover, modelling the same sketch in certain objects in other 2-categories defines both the query language for the database and the updates (the dynamics) for the database. 1.

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 long-standing theoretical questions, and offer techniques that promise to be practically useful in integrating data models.

Entity-Relationship models are a common tool for specification and design of information systems. They use a graphical technique for displaying the objects of the system and relatioships 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 finite-limit, finite-coproduct sketches with a terminal node are the appropriate class and call them ER sketches. A model for an ER sketch is a `snapshot' of a database. The models of an ER sketch in a lextensive category are a category with determined values on the entities and additional properties in case the entities have key attributes. Among the models is the query language associated to the ER sketch. We also show that database updates are simply spans of models. Moreover the category of updates of models of an ER sketch is the category of models of the sketch in the 2-category of spans. Research partially supp...

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 EA-sketches 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.

s people in their characterizations of the situation. Nevertheless, several main threads can be identified, and one of the most evident is that one depicted in the figure: computational procedures began to operate on extremely rich data structures while databases tend to be more flexible and involved from the computational view point. In fact, to manage modern distributed information systems effectively one is forced to think in terms of semantically valid computational procedures, while classical computations over classical ADTs should be moved to the level of implementation. Such a setting seems to be close to the paradigm of object-orientation which is actively inculcated in both programming and database technology as well. Figure 1. The evolution of information technologies (IT) As for the Theory-line and its relations to PL and DB, the picture we present is much more speculative. It appears that in computation

. A graph-based 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...