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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.
Prototyping a Categorical Database in P/FDM
 In Second International Workshop on Advances in Databases and Information Systems ADBIS'95
, 1995
"... The relational data model uses set theory to provide a formal background, thus ensuring a rigorous mathematical data model with support for manipulation. The newer generation database models are based on the objectoriented programming paradigm, and so fall short of having a formal background, espe ..."
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Cited by 13 (2 self)
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The relational data model uses set theory to provide a formal background, thus ensuring a rigorous mathematical data model with support for manipulation. The newer generation database models are based on the objectoriented programming paradigm, and so fall short of having a formal background, especially in some of the more complex data manipulation areas. We use category theory to provide a formalism for object databases, known as the product model. This paper will describe our formal model for the key aspects of object databases. In particular, we will examine how this model deals with three of the most important problems inherent in object databases, those of queries, closure and views. As well as this, we investigate the more common database concepts, such as keys, relationships, aggregation, etc. We will implement a prototype of this model using P/FDM, a semantic data model database system based on the functional model of Shipman, with objectoriented extensions. 1 Introduction ...
A Framework for Modular Formal Specification and Verification
, 1997
"... This paper presents a specification formalism that combines temporal logic with actions and algebraic modules. This formalism allows to write modular specifications of complex systems and is supported by a tool. We show that we can also exploit the structure of the specification in order to real ..."
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Cited by 11 (6 self)
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This paper presents a specification formalism that combines temporal logic with actions and algebraic modules. This formalism allows to write modular specifications of complex systems and is supported by a tool. We show that we can also exploit the structure of the specification in order to realize modular verifications. It is applied to a telecommunication example.
Conceptual Data Modeling from a Categorical Perspective
 The Computer Journal
, 1996
"... For successful information systems development, conceptual data modeling is essential. Nowadays many techniques for conceptual data modeling exist. Indepth comparisons of concepts of these techniques are very difficult as the mathematical formalizations of these techniques, if they exist at all, ar ..."
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Cited by 9 (4 self)
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For successful information systems development, conceptual data modeling is essential. Nowadays many techniques for conceptual data modeling exist. Indepth 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. Wellknown 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...
Algebraic Models for Homotopy Types
 Homology, Homotopy and Applications
"... As yet we are ignorant of an effective method of computing the cohomology of a Postnikov complex from πn and k n+1 [7]. The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produce ..."
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Cited by 8 (4 self)
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As yet we are ignorant of an effective method of computing the cohomology of a Postnikov complex from πn and k n+1 [7]. The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produced, the simplest one being entirely solved by the notion of SSEHstructure, due to the authors. Other tentative solutions, Postnikov towers and E∞chain complexes are considered and compared with the SSEHstructures. In particular, which looks like a severe error about the usual understanding of the kinvariants is explained; which implies we seem far from a solution for the ideal statement of our problem. At the positive side, the problem stated above in the title inscription is solved. 1 Introduction.
Coalgebraic semantics for derivations in logic programming
 In CALCO’11
, 2011
"... Abstract. Every variablefree logic program induces a PfPfcoalgebra on the set of atomic formulae in the program. The coalgebra p sends an atomic formula A to the set of the sets of atomic formulae in the antecedent of each clause for which A is the head. In an earlier paper, we identified a variab ..."
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Abstract. Every variablefree logic program induces a PfPfcoalgebra on the set of atomic formulae in the program. The coalgebra p sends an atomic formula A to the set of the sets of atomic formulae in the antecedent of each clause for which A is the head. In an earlier paper, we identified a variablefree logic program with a PfPfcoalgebra on Set and showed that, if C(PfPf) is the cofree comonad on PfPf, then given a logic program P qua PfPfcoalgebra, the corresponding C(PfPf)coalgebra structure describes the parallel andor derivation trees of P. In this paper, we extend that analysis to arbitrary logic programs. That requires a subtle analysis of lax natural transformations between Posetvalued functors on a Lawvere theory, of locally ordered endofunctors and comonads on locally ordered categories, and of coalgebras, oplax maps of coalgebras, and the relationships between such for locally ordered endofunctors and the cofree comonads on them.
A Unifying Framework for Conceptual Data Modelling Concepts
 Information and Software Technology
, 1997
"... For succesful information systems development, conceptual data modelling is essential. Nowadays many techniques for conceptual data modelling exist, examples are NIAM, FORM, PSM, many (E)ER variants, IFO, and FDM. Indepth comparisons of concepts of these techniques is very difficult as the mathemat ..."
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Cited by 6 (2 self)
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For succesful information systems development, conceptual data modelling is essential. Nowadays many techniques for conceptual data modelling exist, examples are NIAM, FORM, PSM, many (E)ER variants, IFO, and FDM. Indepth comparisons of concepts of these techniques is very difficult as the mathematical formalisations of these techniques, if existing 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. Wellknown conceptual data modelling concepts are discussed from a category theoretic point of view. Advantages and disadvantages of the approach chosen will be outlined. Keywords: Conceptual Data Modelling, Category Theory, Meta Modelling Classification: 68P99 (AMS1991), H.1.0. (CR1991) 1 Introduction It seems an undisputed fact that, opposed to most mature scientific disciplines, the discipline of information systems does not hav...
The Open Calculus of Constructions: An Equational Type Theory with Dependent Types for Programming, Specification, and Interactive Theorem Proving
"... The open calculus of constructions integrates key features of MartinLöf's type theory, the calculus of constructions, Membership Equational Logic, and Rewriting Logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equatio ..."
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Cited by 5 (0 self)
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The open calculus of constructions integrates key features of MartinLöf's type theory, the calculus of constructions, Membership Equational Logic, and Rewriting Logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equational theories. We explore the open calculus of constructions as a uniform framework for programming, specification and interactive verification in an equational higherorder style. By having equational logic and rewriting logic as executable sublogics we preserve the advantages of a firstorder semantic and logical framework and especially target applications involving symbolic computation and symbolic execution of nondeterministic and concurrent systems.
GraphGrammar Semantics of a HigherOrder Programming Language for Distributed Systems
 Graph Transformations in Computer Science: Proceedings of the International Workshop, number 776 in Lecture Notes in Computer Science
, 1994
"... . We will consider a new tiny, yet powerful, programming language for distributed systems, called DHOP, which has its operational semantics given as algebraic graph rewrite rules in a certain category of labeled graphs. Our approach allows to separate actions which affect several processes from loca ..."
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Cited by 5 (2 self)
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. We will consider a new tiny, yet powerful, programming language for distributed systems, called DHOP, which has its operational semantics given as algebraic graph rewrite rules in a certain category of labeled graphs. Our approach allows to separate actions which affect several processes from local changes such as variable bindings. We also sketch how to derive an implementation from this specification. 1 Introduction There are already many calculi for programming distributed systems. Roughly, they can be divided into three groups: 1. Fully fledged programming languages (like occam2 [12], POOL [1], and SR [2]) contain a lot of features useful in practical applications. Their semantics is usually given informally. 2. Small languages (like CSP [11], DNP [7], extended typed calculus [18], and Facile [19]) could be used for programming tasks, although they concentrate on the main ideas. Their semantics is formally defined. 3. Process algebras (like ACP [5], CCS [14], ßcalculus [15], a...
Coalgebraic Minimisation of HDautomata for the πCalculus in a Polymorphic λCalculus
 Theoretical Computer Science
, 2004
"... We introduce finitestate verification techniques for the πcalculus whose design and correctness are justified coalgebraically. In particular, we formally specify and implement a minimisation algorithm for HDautomata derived from πcalculus agents. The algorithm is a generalisation of the partitio ..."
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We introduce finitestate verification techniques for the πcalculus whose design and correctness are justified coalgebraically. In particular, we formally specify and implement a minimisation algorithm for HDautomata derived from πcalculus agents. The algorithm is a generalisation of the partition refinement algorithm for classical automata and is specified as a coalgebraic construction defined using λ →,Π,Σ, a polymorphic λcalculus with dependent types. The convergence of the algorithm is proved; moreover, the correspondence of the specification and the implementation is shown. 1