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A Categorical Manifesto
 Mathematical Structures in Computer Science
, 1991
"... : This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for ..."
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Cited by 100 (5 self)
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: This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical discussion. 0 Introduction This paper tries to explain why category theory is useful in computing science. The basic answer is that computing science is a young field that is growing rapidly, is poorly organised, and needs all the help it can get, and that category theory can provide help with at least the following: ffl Formulating definitions and theories. In computing science, it is often more difficult to formulate concepts and results than to give a proof. The seven guidelines of this paper can h...
Graphbased logic and sketches I: The general framework. Available by web browser from http://www.cwru.edu/1/class/mans/math/pub/wells
, 1996
"... Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic. ..."
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Cited by 8 (4 self)
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Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic.
Algebraic GraphBased Approach to Schema Integration
 In Databases and Information Systems, 2nd Int.Baltic Workshop
, 1996
"... The language of sketches is as concise and powerful as higher order logic and as handy as conventional ERdiagrams. We discuss its benefits in respect to problems of schema integration. It is evident that a chief property of the next generation information systems is their organization on cooperati ..."
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Cited by 1 (1 self)
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The language of sketches is as concise and powerful as higher order logic and as handy as conventional ERdiagrams. We discuss its benefits in respect to problems of schema integration. It is evident that a chief property of the next generation information systems is their organization on cooperative principles. Typically, applications involved in a cooperative system have to access data stored in several separate databases. These databases can be differently organized, semantically overlapping and even inconsistent, so that an application programmer encounters severe problems, moreover, in each multibase case they have to be solved specifically. In fact, as it was noted in [13], the situation is similar to the multifile situation before invention of DBs, and the analogous solution can be suggested: in order to provide applications with a single integral view of data, local DBs should be integrated into a united distributed DB. Under the latter we mean a database system which has a sc...
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 approache ..."
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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...
Scetches and Specifications User'S Gude  First . . .
, 2000
"... SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unificat ..."
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SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science. These papers are arranged in two complementary families: REFERENCE MANUAL and USER’S GUIDE. The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user’s guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics. These papers are under development, they are, or will be, available at:
Simulation Logic
"... Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory. However, the simulation condition is strictly a firstorder logic statement. We extend modal logic with modalities and axioms, the latter’s modeling conditions are the simulation ..."
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Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory. However, the simulation condition is strictly a firstorder logic statement. We extend modal logic with modalities and axioms, the latter’s modeling conditions are the simulation conditions. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The simulations are considered arrows in a category where the objects are descriptive, general frames. One can augment the simulation modalities by axioms for requiring the underlying modeling simulations to be bisimulations or to be pmorphisms. The modal systems presented are multisorted and both sound and complete with respect to their algebraic and Kripke semantics. 1
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"... Preface to the TAC reprint This is a reprint of the final version, published by the Centre de Recherche Mathématique at the Université de Montréal. We are aware of only one error, which will be corrected below. If any others are reported, we will post corrections at ftp.math.mcgill.ca/barr/pdffiles/ ..."
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Preface to the TAC reprint This is a reprint of the final version, published by the Centre de Recherche Mathématique at the Université de Montréal. We are aware of only one error, which will be corrected below. If any others are reported, we will post corrections at ftp.math.mcgill.ca/barr/pdffiles/ctcserr. pdf and at