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(1)
Diagrammatic logic and exceptions: an introduction
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Diagrammatic Specifications
Diagrammatic Specifications,10.1017/S0960129503003979,Mathematical Structures in Computer Science,Dominique Duval
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Diagrammatic Specifications
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Citations: 12
)
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Dominique Duval
Journal:
Mathematical Structures in Computer Science  MSCS
, vol. 13, no. 6, pp. 857890, 2003
DOI:
10.1017/S0960129503003979
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www.informatik.unitrier.de
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Citation Context
(5)
...The following result is easy to check directly, it can also be obtained from an adjunction [
4
]...
JeanGuillaume Dumas
,
et 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 setvalued 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 Duval
,
et 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
]...
JeanGuillaume Dumas
,
et al.
Sequential products in effect categories
...More about this point of view on deduction rules can be found in [4,
5
]...
JeanGuillaume Dumas
,
et 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 ´ inguez
,
et al.
Towards Diagrammatic Specifications of Symbolic Computation Systems
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Citations
(12)
Diagrammatic logic applied to a parameterisation process
(
Citations: 1
)
César Domínguez
,
Dominique Duval
Journal:
Mathematical Structures in Computer Science  MSCS
, vol. 20, no. 4, pp. 639654, 2010
States and exceptions are dual effects
JeanGuillaume Dumas
,
Dominique Duval
,
Laurent Fousse
,
JeanClaude Reynaud
Journal:
Computing Research Repository  CORR
, vol. abs/1001.1, 2010
Deduction as Reduction
Dominique Duval
Journal:
Computing Research Repository  CORR
, vol. abs/1011.1, 2010
Diagrammatic logic applied to a parameterization process
(
Citations: 4
)
César Domínguez
,
Dominique Duval
Journal:
Computing Research Repository  CORR
, vol. abs/0908.3, 2009
A parameterization process as a categorical construction
(
Citations: 2
)
Dominique Duval
,
César Dominguez
Journal:
Computing Research Repository  CORR
, vol. abs/0908.3, 2009