A Parameterization Process: From a Functorial Point of View

Domínguez, César; Duval, Dominique

doi:10.1142/s0129054112500050

Cited by 4 publications

(15 citation statements)

References 9 publications

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“…Building limit sketches for T eq and S eq is a classical exercise, and it is then easy to check that L eq is a diagrammatic logic. We will now give a simplified description -see Domínguez and Duval (2009) for a detailed construction. The starting point is the limit sketch for graphs E gr , where the points Type and Term stand for the sets of vertices (or types) and edges (or terms) and the arrows dom and codom for the functions source (or domain) and target (or codomain): Figure 1 presents the main part of the graph underlying E eq,S .…”

Section: The Diagrammatic Equational Logicmentioning

confidence: 99%

“…Since only a part of E eq,S is considered, some rules are missing, but we leave enlarging E eq,S to get them as an exercise. It should be noted that in this definition of the equational theories and specifications, the equations are identities of terms; a more subtle point of view, where the equations in a theory form a congruence, can be found in Domínguez and Duval (2009).…”

Section: The Diagrammatic Equational Logicmentioning

confidence: 99%

“…The specifications are the equational specifications together with a wide subspecification. We can build E dec,T from E eq,T , in a way that reflects the meaning of the word 'decoration' as follows -a smaller choice for E dec,T can be found in Domínguez and Duval (2009). The decorations in this context simply consist of the two keywords p for 'pure' and g for 'general'.…”

Section: Some Diagrammatic Logicsmentioning

confidence: 99%

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Diagrammatic logic applied to a parameterisation process

Domínguez¹,

Duval²

2010

Math. Struct. Comp. Sci.

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This paper provides an abstract definition of a class of logics, called diagrammatic logics, together with a definition of morphisms and 2-morphisms between them. The definition of the 2-category of diagrammatic logics relies on category theory, mainly on adjunction, categories of fractions and limit sketches. This framework is applied to the formalisation of a parameterisation process. This process, which consists of adding a formal parameter to some operations in a given specification, is presented as a morphism of logics. Then the parameter passing process for recovering a model of the given specification from a model of the parameterised specification and an actual parameter is shown to be a 2-morphism of logics.Downloaded640 types, like the type of integers, while the second layer deals with algebraic structures, like the structure of groups, which are implemented using the abstract data types in the first layer. In addition, this analysis made it clear that in EAT, groups (for instance) are not implemented individually, but are implemented through parameterised families of groups. Lambán et al. (2003) defined an operation called the imp construction -it was given this name because of its role in the implementation process in the system EAT. In fact, the imp construction is a parameterisation process: starting from a specification Σ in which some operations are labelled as 'pure ' (Domínguez et al. 2006), the imp construction builds a new specification Σ A with a distinguished sort A added to the domain of each non-pure operation. Then the parameter passing process derives an implementation of Σ from each implementation of Σ A and each value in the interpretation of A. Moreover, the exact parameterisation property was proved in Lambán et al. (2003): the implementations of EAT algebraic structures are as general as possible in the sense that they are ingredients of terminal objects in some categories of models. The parameter set in the Kenzo and EAT systems is encoded by means of a record of Common Lisp functions, which has a field for each operation in the algebraic structure to be implemented. The pure terms correspond to functions, which can be obtained from the fixed data and do not require any explicit storage, so each particular instance of the record gives rise to an algebraic structure; more details can be found in Lambán et al. (2003). Lambán et al. (2003) then reinterpreted these results for the EAT algebraic structures in terms of object-oriented techniques, like hidden algebras (Goguen and Malcolm 2000) or coalgebras (Rutten 2000). Domínguez et al. (2007) then extended these results in the algebraic framework of institutions (Goguen and Burstall 1984): the imp construction is represented through institution encodings in the sense of Tarlecki (2000). Goguen and Roşu (2002) provided a survey of the different notions of morphisms between institutions,where institution encodings are called forward institution morphisms. In fact, institution encodings are not that common in institution theories, where ...

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Section: The Diagrammatic Equational Logicmentioning

confidence: 99%

Section: The Diagrammatic Equational Logicmentioning

confidence: 99%

Section: Some Diagrammatic Logicsmentioning

confidence: 99%

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Diagrammatic logic applied to a parameterisation process

Domínguez¹,

Duval²

2010

Math. Struct. Comp. Sci.

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“…In this paper, using category theory, we argue that logical rules can be seen as fractions and logics as limit sketches, with the hope that these tools and concepts can be applied to many kinds of logics. A detailed presentation, with additional examples, can be found in [7,8,9,10]. The importance of categorical fractions for proofs and computations was recognised independently in [11].…”

Section: Introductionmentioning

confidence: 99%

Logical rules as fractions and logics as sketches

Duval

2018

Preprint

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“…In this paper we use another method for dealing with computational effects. This method has been applied to a parametrization process in [1,2] and to the states effect in [4]. It has led to the discovery of a duality between states and exceptions, briefly presented in [3].…”

Section: Introductionmentioning

confidence: 99%

Adjunctions for exceptions

Dumas¹,

Duval²,

Fousse³

et al. 2012

Preprint

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The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended semantics. We solve this apparent contradiction by defining a logic for exceptions with a proof system which is close to their syntax and where their intended semantics can be seen as a model. This requires a robust framework for logics and their morphisms, which is provided by diagrammatic logics.

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A Parameterization Process: From a Functorial Point of View

Cited by 4 publications

References 9 publications

Diagrammatic logic applied to a parameterisation process

Diagrammatic logic applied to a parameterisation process

Logical rules as fractions and logics as sketches

Adjunctions for exceptions

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