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Full abstraction for nominal general references
 In LICS ’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science (Wroclaw, 2007), IEEE Computer
"... Vol. 5 (3:8) 2009, pp. 1–69 www.lmcsonline.org ..."
Towards a Coalgebraic Semantics of UML: Class Diagrams and Use Cases
, 2003
"... Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3.2 Multiple Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.5 Semantics of Class ..."
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Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3.2 Multiple Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.5 Semantics of Class Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.6 Examples in Checking Consistency of Class Diagrams . . . . . . . . . . . . . . . . . . 35 5 Use Cases 37 5.1 Discussions on Advanced Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6 Related Work 43 7 Conclusion and Discussion 44 Acknowledgments 45 List of Figures iii List of Figures 1 Different representations of a class in UML . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6 Visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 7 Representation of an association class . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 8 Qualification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 9 Aggregation and Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 10 An nary Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 11 The ternary association Record being decomposed . . . . . . . . . . . . . . . . . . . . 26 12 The decomposi...
A categorical approach to simulations, in
 of Lecture Notes in Computer Science
, 2005
"... Abstract. Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories ..."
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Abstract. Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories while the morphisms are obtained from the corresponding notion of simulation. Here we define in detail several of those categories, collect them together in various institutions, and study their most interesting properties. 1
Process Realizability
 In Foundations of Secure Computation
, 2000
"... This paper aims to give a readable and reasonably accessible account of some ideas linking the currently still largely separate worlds of concurrency theory and process algebra, on the one hand, and type theory, categorical models and realizability on the other. Background in process algebra may be ..."
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This paper aims to give a readable and reasonably accessible account of some ideas linking the currently still largely separate worlds of concurrency theory and process algebra, on the one hand, and type theory, categorical models and realizability on the other. Background in process algebra may be found in standard texts such as [Hoa85, Hen88, Mil89, Ros97]; while background in realizability, categorical models etc. is provided by texts such as [GLT89, AL91, Cro93, AC98, BW99]. A modest background in either or both of these fields should suffice to understand the main ideas. Most of the detailed verification of properties of the formal definitions we will present is left as a series of exercises. The diligent reader who attempts a number of these should get some feeling for the interplay between concrete processtheoretic notions, and more abstract logical and categorical ideas, which is characteristic of this topic. It is this interplay which makes the topic a fascinating one for the author; I hope this brief introduction, to a field which is still wide open for further development, succeeds in conveying something of this fascination to the reader.
A remark on Gel’fand duality for spectral triples.
, 2008
"... We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms ..."
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We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms
Cause and effect: type systems for effects and dependencies
, 2005
"... Type systems commonly used in practice today fail to capture essential aspects of program behavior: The effects and dependencies of the programs. In this paper, we examine a prototypical effect type system in the style of Gifford et al., and a canonical example of a dependency type system based upon ..."
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Type systems commonly used in practice today fail to capture essential aspects of program behavior: The effects and dependencies of the programs. In this paper, we examine a prototypical effect type system in the style of Gifford et al., and a canonical example of a dependency type system based upon the work of Zdancewic. Finally, we show how these two type systems can be embedded in a more general framework, a monadic type system as developed by Pfenning and Davies.
Coalg_{KPF}: Towards a Coalgebraic Calculus for componentBased Systems
"... Coalgebras of Kripke Polynomial Functors have been widely used in modelling various kinds of systems. In this paper, we give a category Coalg KPF which consists of coalgebras of KPFs. Then we present a set of constructions like sequential and parallel composition in a subcategory of Coalg KPF for a ..."
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Coalgebras of Kripke Polynomial Functors have been widely used in modelling various kinds of systems. In this paper, we give a category Coalg KPF which consists of coalgebras of KPFs. Then we present a set of constructions like sequential and parallel composition in a subcategory of Coalg KPF for a restricted family of KPFs by exploiting the canonical operations in category theory. A family of algebraic laws for the properties being satisfied by these operations is provided. Sun Meng is a Fellow at UNU/IIST on leave from the School of Mathematical Science of Beijing University, China, where he is a Ph.D candidate. His research interest include category theory, coalgebra theory, ObjectOriented method, formal method in software development, and formal semantics for modeling languages. His email address is sm@iist.unu.edu.
Process as a World Transaction
"... Transaction is process closure: for a transaction is the limiting process of process itself. In the process world view the universe is the ultimate (intensional) transaction of all its extensional limiting processes that we call reality. ANPA’s PROGRAM UNIVERSE is a computational model which can be ..."
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Transaction is process closure: for a transaction is the limiting process of process itself. In the process world view the universe is the ultimate (intensional) transaction of all its extensional limiting processes that we call reality. ANPA’s PROGRAM UNIVERSE is a computational model which can be explored empirically in commercial database transactions where there has been a wealth of activity over the real world for the last 40 years. Process category theory demonstrates formally the fundamental distinctions between the classical model of a transaction as in PROGRAMUNIVERSE and physical reality. The paper concludes with a short technical summary for those who do not wish to read all the detail. 1
A Coalgebraic Calculus for Component Based Systems ∗
"... In this paper we describe the coalgebraic models for statebased software components and componentbased systems. The behaviour patterns of components are specified by strong monads. A family of operators for combining components based on the category of coalgebras are defined and a set of algebraic ..."
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In this paper we describe the coalgebraic models for statebased software components and componentbased systems. The behaviour patterns of components are specified by strong monads. A family of operators for combining components based on the category of coalgebras are defined and a set of algebraic laws are also presented to specify the properties being satisfied by these operators. 1