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63
A Coinduction Principle for Recursive Data Types Based on Bisimulation
, 1996
"... This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programmin ..."
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Cited by 37 (3 self)
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This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programming languages [SS71], but also arise explicitly as recursive data types in functional programming languages like Standard ML [MTH90] or Haskell [HPJW92]. In the latter context, the coinduction principle provides a powerful technique for establishing the equality of programs with values in recursive data types (see examples herein and in [Pit94]).
A DomainSpecific Visual Language for Domain Model Evolution
 Journal of Visual Languages and Computing
, 2004
"... Domainspecific visual languages (DSVLs) are concise and useful tools that allow the rapid development of the behavior and/or structure of applications in welldefined domains. These languages are typically developed specifically for a domain, and have a strong cohesion to the domain concepts, which ..."
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Cited by 31 (5 self)
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Domainspecific visual languages (DSVLs) are concise and useful tools that allow the rapid development of the behavior and/or structure of applications in welldefined domains. These languages are typically developed specifically for a domain, and have a strong cohesion to the domain concepts, which often appear as primitives in the language. The strong cohesion between DSVL language primitives and the domain is a benefit for development by domain experts, but can be a drawback when the domain evolves – even when that evolution appears insignificant. This paper presents a domainspecific visual language developed expressly for the evolution of domainspecific visual languages, and uses concepts from graphrewriting to specify and carry out the transformation of the models built using the original DSVL. 1.
Metamodel driven model migration
 Vanderbilt University
, 2003
"... I love you, and I’m proud of you too. Thanks for being here for me. Jon iii ACKNOWLEDGEMENTS I give many thanks to my advisor, Dr. Gabor Karsai for being the Best AllAround Advisor™. Gabor, without your excellent teaching skills and motivational abilities, I would not be in the position I am today. ..."
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Cited by 16 (3 self)
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I love you, and I’m proud of you too. Thanks for being here for me. Jon iii ACKNOWLEDGEMENTS I give many thanks to my advisor, Dr. Gabor Karsai for being the Best AllAround Advisor™. Gabor, without your excellent teaching skills and motivational abilities, I would not be in the position I am today. Vanderbilt is lucky to have you, as will be any other student under your tutelage. I also thank very heartily the other members of my committee. Dr. Janos Sztipanovits, for his political insight (and vision for my future career); Dr. Akos Ledeczi, for holding my feet to the fire when it comes to sticking up for the value of my research, and also social interactions within ISIS; Dr. Greg Nordstrom, for (as usual) providing valuable comments in the discussion of all things metamodeling related, not to mention being an allaround good guy to bounce ideas allaround with; and of course Dr. Doug
Coherent bicartesian and sesquicartesian categories, R. Kahle et al
 eds, Proof Theory in Computer Science, Lecture
"... Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the initial object with itself are the same. (Every ..."
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Cited by 11 (1 self)
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Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the initial object with itself are the same. (Every
Granulation for Graphs
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSIT'99, volume 1661 of Lecture Notes in Computer Science
, 1999
"... . In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure ..."
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Cited by 10 (6 self)
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. In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the granulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite different kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granulation leads to a new formulation of the boundarysensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discusse...
Selfadjunctions and matrices
 Journal of Pure and Applied Algebra
"... It is shown that the multiplicative monoids of TemperleyLieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a selfadjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronec ..."
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Cited by 10 (4 self)
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It is shown that the multiplicative monoids of TemperleyLieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a selfadjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. Thereby one obtains a representation of braid groups in matrices, which, though different and presumably new, is related to the standard representation of braid groups in TemperleyLieb algebras. Mathematics Subject Classification (2000): 57M99, 20F36, 18A40 1
Formalizing the Structural Semantics of DomainSpecific Modeling Languages
, 2009
"... Modelbased approaches to system design are now widespread and successful. These approaches make extensive use of model structure to describe systems using domainspecific abstractions, to specify and implement model transformations, and to analyze structural properties of models. In spite of its ge ..."
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Cited by 10 (4 self)
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Modelbased approaches to system design are now widespread and successful. These approaches make extensive use of model structure to describe systems using domainspecific abstractions, to specify and implement model transformations, and to analyze structural properties of models. In spite of its general importance the structural semantics of modeling languages are not wellunderstood. In this paper we develop the formal foundations for the structural semantics of domain specific modeling languages (DSML), including the mechanisms by which metamodels specify the structural semantics of DSMLs. Additionally, we show how our formalization can complement existing tools, and how it yields algorithms for the analysis of DSMLs and model transformations.
Mathematics of generic specifications for model management
 Encyclopedia of Database Technologies and Applications
, 2005
"... This article (further referred to as MathI), and the next one (further referred to as MathII, see p. 359), form a mathematical companion to the article in this encyclopedia on Generic Model Management (further referred to as GenMMt, see p.258). Articles MathI and II present the basics of the arro ..."
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Cited by 9 (7 self)
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This article (further referred to as MathI), and the next one (further referred to as MathII, see p. 359), form a mathematical companion to the article in this encyclopedia on Generic Model Management (further referred to as GenMMt, see p.258). Articles MathI and II present the basics of the arrow diagram machinery that provides model management with truly generic specifications. Particularly, it allows us to build a generic pattern for heterogeneous data and schema transformation, which is presented in MathII for the first time in the literature.
Fibered Manifolds, Natural Bundles, Structured Sets, GSets and all that: The Hole Story from Space Time to Elementary Particles, grqc/0505138 12
 Isenberg, J., Marsden
, 2005
"... [M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol ..."
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Cited by 8 (3 self)
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[M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol 1. No. 3, pp 235245) In this paper we review the hole argument for the spacetime points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract from differentiability and even continuity, the hole argument is applied to a much wider class of mathematical objects. We discuss the problem concerning the individuation of the objects in more general settings such that fibered manifolds, fibered
Compositional abstractions of hybrid control systems
 In Proceedings of the 40th IEEE Conference on Decision and Control
, 2001
"... Abstract. Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature ..."
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Cited by 7 (1 self)
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Abstract. Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. In this paper we present a framework for abstraction that applies to discrete, continuous, and hybrid systems. We introduce a composition operator that allows to build complex hybrid systems from simpler ones and show compatibility between abstractions and this compositional operator. Besides unifying the existing methodologies we also propose constructions to obtain abstractions of hybrid control systems.