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Diagrammatic Specifications

Diagrammatic Specifications,10.1017/S0960129503003979,Mathematical Structures in Computer Science,Dominique Duval

Diagrammatic Specifications   (Citations: 12)
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Journal: Mathematical Structures in Computer Science - MSCS , vol. 13, no. 6, pp. 857-890, 2003
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    • ...The following result is easy to check directly, it can also be obtained from an adjunction [4]...

    Jean-Guillaume Dumaset al. States and exceptions are dual effects

    • ...Such a framework is provided by diagrammatic logics [5, 4]. This work does rely on the theory of diagrammatic logics, mainly for the definition of the decorated logic and for the link between the decorated logic and the explicit logic, as explained in [6, 7]. However, in this paper, the role of diagrammatic logic is hidden, and the few required notions about categories are reminded...
    • ...are usually quite happy with some programs and some theorems...More is said about this remark in the “decomposition theorem” of [5, 4]. About graphs and categories, this remark is the motivation for defining something “between” both, as follows...
    • ...In this paper, only set-valued models are considered; a more general definition of models can be found in [5, 4]. For clarity, we speak about maps (rather than functions) between sets...

    Dominique Duvalet al. About raising and handling exceptions

    • ...Moreover, with one additional level of abstraction, decorations can be obtained from morphisms between logics, in the context of diagrammatic logics [3, 2]...

    Jean-Guillaume Dumaset al. Sequential products in effect categories

    • ...More about this point of view on deduction rules can be found in [4, 5]...

    Jean-Guillaume Dumaset al. Towards a diagrammatic modeling of the LinBox C++ linear algebra libra...

    • ...In this paper we extend our interpretation of this construction and concepts using diagrammatic specifications developed by Duval and Lair [8]...
    • ...Diagrammatic specifications were introduced in [8], as summarized below...
    • ...The following theorem shows a characterization for propagators [8]...
    • ...The following theorem states some of the properties of the Yoneda morphism [8]...
    • ...Now, it is possible to define a new sketch EEq for equational categories .W e can build EEq by enriching ECat in a similar way to the process used to obtain EEq from EComp (indeed, an equational category is defined in [8] as a category with a congruence relation and in that paper some additional rules are needed to obtain that relation)...

    C. Dom ´ inguezet al. Towards Diagrammatic Specifications of Symbolic Computation Systems

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