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110
Inheritance and Cofree Constructions
 European Conference on ObjectOriented Programming, number 1098 in Lect. Notes Comp. Sci
, 1995
"... The coalgebraic view on classes and objects is elaborated to include inheritance. Inheritance in coalgebraic specification (of classes) will be understood dually to parametrization in algebraic specification. That is, inheritance involves restriction (specialization), where parametrization involves ..."
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Cited by 26 (7 self)
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The coalgebraic view on classes and objects is elaborated to include inheritance. Inheritance in coalgebraic specification (of classes) will be understood dually to parametrization in algebraic specification. That is, inheritance involves restriction (specialization), where parametrization involves extension. And cofree constructions are "best" restrictions, like free constructions are "best" extensions. To make this view on inheritance precise we need a suitable notion of behaviour preserving morphism between classes, which will be defined as a "coalgebra map uptobisimulation". AMS Subject Classification (1991): 18C10, 03G30 CR Subject Classification (1991): D.1.5, D.2.1, E.1, F.1.1, F.3.0 Keywords & Phrases: object, class, inheritance, coalgebraic specification, bisimulation 1. Introduction Two basic relations in objectoriented languages are: object o belongs to class C, and: class C inherits from class C 0 (see e.g. [20]). Class membership yields what is sometimes called a...
HasCASL: Towards Integrated Specification and Development of Functional Programs
, 2002
"... The development of programs in modern functional languages such as Haskell calls for a widespectrum specification formalism that supports the type system of such languages, in particular higher order types, type constructors, and parametric polymorphism, and contains a functional language as an exe ..."
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Cited by 25 (11 self)
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The development of programs in modern functional languages such as Haskell calls for a widespectrum specification formalism that supports the type system of such languages, in particular higher order types, type constructors, and parametric polymorphism, and contains a functional language as an executable subset in order to facilitate rapid prototyping. We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that is geared towards precisely this purpose. Its semantics is tuned to allow program development by specification refinement, while at the same time staying close to the settheoretic semantics of first order Casl. The number of primitive concepts in the logic has been kept as small as possible; we demonstrate how various extensions to the logic, in particular general recursion, can be formulated within the language itself.
An algebraic framework for merging incomplete and inconsistent views
, 2004
"... View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, ..."
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Cited by 24 (7 self)
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View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of endtoend analysis. View merging is complicated by incompleteness and inconsistency of views. Once views are merged, it is useful to be able to trace the elements of the merged view back to their sources. In this paper, we propose a framework for merging incomplete and inconsistent graphbased views. We introduce a formalism, called posetannotated graphs, which incorporates a systematic annotation scheme capable of modeling incompleteness and inconsistency as well as providing a builtin mechanism for ownership traceability. We show how structurepreserving maps can capture the relationships between disparate views modeled as posetannotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We use the i ∗ modeling language [26] as an example to demonstrate how our approach can be applied to existing graphbased modeling languages, especially in the domain of early Requirements Engineering. 1
ProofTheoretic Semantics Of ObjectOriented Specification Constructs
, 1990
"... this paper is to show how a collection of specification constructs may be formally defined that supports the former effort. We should stress that we shall not attempt to provide a full and practical specification language that can be used for objectoriented design. We shall have to limit ourselves ..."
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Cited by 21 (5 self)
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this paper is to show how a collection of specification constructs may be formally defined that supports the former effort. We should stress that we shall not attempt to provide a full and practical specification language that can be used for objectoriented design. We shall have to limit ourselves to concentrate on the definition of our main primitive of specification (formalising the notion of object) together with two well known specification constructs: inheritance and aggregation (complex objects). However, we do not see deep problems in extending our results to other useful constructs such as class/type grouping and parameterisation.
Combining and Representing Logical Systems Using ModelTheoretic Parchments
 In Recent Trends in Algebraic Development Techniques, volume 1376 of LNCS
, 1997
"... . The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the modeltheoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We prop ..."
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Cited by 19 (5 self)
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. The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the modeltheoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in modeltheoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of modeltheoretic parchments is complete, and their representations may be put together using categorical limits as well. However, modeltheoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessar...
Institutionalising OntologyBased Semantic Integration
, 2007
"... We address what is still a scarcity of general mathematical foundations for ontologybased semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the firstorder ontologybased approach to semantic integration and ..."
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Cited by 19 (0 self)
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We address what is still a scarcity of general mathematical foundations for ontologybased semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the firstorder ontologybased approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax and interpretationindependent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontologybased semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics.
Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
"... ..."
A Mathematical Toolbox for the Software Architect
, 1996
"... It is suggested that Category Theory provides the right level of mathematical abstraction to address languages for describing software architectures. Contrarily to most other formalisations of SA concepts, Category Theory does not promote any particular formalism for component and connector descript ..."
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Cited by 15 (4 self)
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It is suggested that Category Theory provides the right level of mathematical abstraction to address languages for describing software architectures. Contrarily to most other formalisations of SA concepts, Category Theory does not promote any particular formalism for component and connector description but provides instead the very semantics of the concepts that are related to the gross modularisation of complex systems like "interconnection", "configuration", "instantiation" and "composition". Two examples, a category of programs for a parallel program design language and a category of temporal logic specifications, together with comparisons with other work, namely by Allen and Garlan, and Moriconi and Qian, are adduced to justify this claim. 1. Introduction In a particularly stimulating panel introduction, Garlan and Perry present an overview of current research issues in Software Architecture (SA) [11]. They characterise SA to be "emerging as a significant and different design lev...
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 14 (11 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.
Management of Evolving Specifications Using Category Theory
, 1998
"... Structure is important in large specifications for understanding, testing and managing change. Category theory has been explored as framework for providing this structure, and has been successfully used to compose specifications. This work has typically adopted a "correct by construction" ..."
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Cited by 14 (0 self)
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Structure is important in large specifications for understanding, testing and managing change. Category theory has been explored as framework for providing this structure, and has been successfully used to compose specifications. This work has typically adopted a "correct by construction" approach: components are specified, proved correct and then composed together in such a way to preserve their properties. However, in a large project, it is desirable to be able to mix specification and composition steps such that at any particular moment in the process, we may have established only some of the properties of the components, and some of the composition relations. In this paper we propose adaptations to the categorical framework in order to manage evolving specifications. We demonstrate the utility of the framework on the analysis of a part of a software change request for the Space Shuttle.