Modeling inheritance as coercion in a symbolic computation system

Domínguez, César; Rubio, Julio

doi:10.1145/384101.384117

Cited by 7 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the one hand, the institutional description could be extended to other parts of the EAT system or introduced into the specification of structures in the Kenzo system [11], an objectoriented Sergeraert's program (successor of EAT). For example, in [10] the specification of the functorial relationship between data structures of EAT is studied and in [9] the inheritance relationship between Kenzo structures is tackled, although both works lack an institutional description (if such a thing is possible). Besides, it should be established whether the theoretical results obtained here can be applied to other symbolic computation systems apart from EAT or Kenzo.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Object oriented institutions to specify symbolic computation systems

Domínguez¹,

Lambán²,

Rubio³

2007

RAIRO-Theor. Inf. Appl.

Self Cite

View full text Add to dashboard Cite

The specification of the data structures used in EAT, a software system for symbolic computation in algebraic topology, is based on an operation that defines a link among different specification frameworks like hidden algebras and coalgebras. In this paper, this operation is extended using the notion of institution, giving rise to three institution encodings. These morphisms define a commutative diagram which shows three possible views of the same construction, placing it in an equational algebraic institution, in a hidden institution or in a coalgebraic institution. Moreover, these morphisms can be used to obtain a new description of the final objects of the categories of algebras in these frameworks, which are suitable abstract models for the EAT data structures. Thus, our main contribution is a formalization allowing us to encode a family of data structures by means of a single algebra (which can be described as a coproduct on the image of the institution morphisms). With this aim, new particular definitions of hidden and coalgebraic institutions are presented.Mathematics Subject Classification. 68Q65, 68Q60.

show abstract

Section: Conclusion and Further Workmentioning

confidence: 99%

Object oriented institutions to specify symbolic computation systems

Domínguez¹,

Lambán²,

Rubio³

2007

RAIRO-Theor. Inf. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In view of the obtained results, some years ago, the first author of this paper began the formal study of the programs, in order to reach a good understanding on the internal calculation processes of these software systems. In particular, our study of the data types used in EAT and Kenzo [13,6,8] shows that there are two different layers of data structures in the systems. In the first layer, one finds the usual abstract data types, like the type of integers.…”

Section: Introductionmentioning

confidence: 99%

“…In [13] an operation is defined, which is called the imp construction because of its role in the implementation process in the system EAT. Starting from a specification Σ in which some operations are labelled as "pure" [8], the imp construction builds a new specification Σ A with a distinguished sort A which is added to the domain of each non-pure operation. It follows that each implementation of Σ A defines a family of implementations of Σ depending on the choice of a value in the interpretation of A.…”

Section: Introductionmentioning

confidence: 99%

A Parameterization Process: From a Functorial Point of View

Domínguez

Duval

2012

Int. J. Found. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by adding a parameter as a new variable to some operations. Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given specification is a bijection. It is proved in this paper that the parameterization process is provided by a functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits.

show abstract

“…On the other hand, the EAT and Kenzo software systems have been developed by F. Sergeraert for symbolic computation in algebraic topology [Rubio et al 2007, Dousson et al 1999. The data types used in EAT and Kenzo have been specified through a parameterization process in [Domínguez et al 2006, Domínguez et al 2007, which is described in [Lambán et al 2003] in terms of object-oriented technologies like hidden algebras [Goguen and Malcolm 2000] or coalgebras [Rutten 2000]. The parameterization process consists in adding a formal parameter to some operations in a given specification.…”

Section: Introductionmentioning

confidence: 99%

Diagrammatic logic applied to a parameterisation process

Domínguez¹,

Duval²

2010

Math. Struct. Comp. Sci.

Self Cite

View full text Add to dashboard Cite

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 ...

show abstract

Modeling inheritance as coercion in a symbolic computation system

Cited by 7 publications

References 18 publications

Object oriented institutions to specify symbolic computation systems

Object oriented institutions to specify symbolic computation systems

A Parameterization Process: From a Functorial Point of View

Diagrammatic logic applied to a parameterisation process

Contact Info

Product

Resources

About