Towards an Algebraic Theory of Bidirectional Transformations

Stevens, Perdita

doi:10.1007/978-3-540-87405-8_1

Cited by 19 publications

(5 citation statements)

References 7 publications

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“…Note that we do not consider AOM approaches that support full code generation (e.g., [10,37]), as these are not considered to be representative for AOM [16]. We also do not take into account MDE approaches that allow immediate code modifications by automatically reflecting those changes at the model level (e.g., [26,41]), as the support for round trip engineering in AOM is currently very limited.…”

Section: Introductionmentioning

confidence: 99%

From aspect-oriented models to aspect-oriented code?

Hovsepyan

Scandariato

Baelen

et al. 2010

Proceedings of the 9th International Conference on Aspect-Oriented Software Development

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Aspect-Oriented Modeling (AOM) provides support for separating concerns at the design level. Even though most AOM approaches provide means to execute the composition of the modularized concerns to obtain a composed model, it is also possible to keep the concerns modularized at the implementation level by targeting an aspect-oriented platform. Model-driven approaches have emerged to support both alternatives via tools. Clearly, these choices are not equivalent. Rather, they have a direct impact on several dimensions, including maintainability. Hence, the main research problem addressed by this work is to figure out which alternative provides for shorter maintenance time. To answer this question, we have conducted a series of quantitative studies and experiments.

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Section: Introductionmentioning

confidence: 99%

From aspect-oriented models to aspect-oriented code?

Hovsepyan

Scandariato

Baelen

et al. 2010

Proceedings of the 9th International Conference on Aspect-Oriented Software Development

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“…Other important work related to delta lenses has appeared in [22], [21], [19] and, relating delta lenses to triple graph grammars, [7].…”

Section: Related Workmentioning

confidence: 99%

Symmetric delta lenses and spans of asymmetric delta lenses.

Johnson¹,

Rosebrugh²

2017

JOT

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Bidirectional Transformations provide mechanisms for maintaining synchronization between updatable data sources. Lenses are certain mathematically specified bidirectional transformations. As part of a project to unify the treatment of symmetric lenses (of various kinds) as equivalence classes of spans of asymmetric lenses (of corresponding kinds), we relate symmetric delta lenses with spans of asymmetric delta lenses. Because delta lenses are based on state spaces which are categories rather than sets, there is further structure that needs to be accounted for. One of the main findings in this paper is that the required equivalence relation among spans is compatible with, but coarser than, the one expected. The main result is an isomorphism of categories between a category whose morphisms are equivalence classes of symmetric delta lenses (here called fb-lenses) and the category of spans of delta lenses modulo the new equivalence.

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“…This generalization is significantly more expressive than any previously known: although symmetric variants of lenses have been studied [10,23,28], they all lack a notion of sequential composition of lenses, a significant technical and practical limitation (see Section 10). As we will see, the extra structure that we need to support composition is nontrivial; in particular, constructions involving symmetric lenses need to be proved correct modulo a notion of behavioral equivalence (Section 3).…”

Section: Introductionmentioning

confidence: 97%

Symmetric lenses

2011

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Lenses-bidirectional transformations between pairs of connected structures-have been extensively studied and are beginning to find their way into industrial practice. However, some aspects of their foundations remain poorly understood. In particular, most previous work has focused on the special case of asymmetric lenses, where one of the structures is taken as primary and the other is thought of as a projection, or view. A few studies have considered symmetric variants, where each structure contains information not present in the other, but these all lack the basic operation of composition. Moreover, while many domain-specific languages based on lenses have been designed, lenses have not been thoroughly explored from an algebraic perspective.We offer two contributions to the theory of lenses. First, we present a new symmetric formulation, based on complements, an old idea from the database literature. This formulation generalizes the familiar structure of asymmetric lenses, and it admits a good notion of composition. Second, we explore the algebraic structure of the space of symmetric lenses. We present generalizations of a number of known constructions on asymmetric lenses and settle some longstanding questions about their properties-in particular, we prove the existence of (symmetric monoidal) tensor products and sums and the non-existence of full categorical products or sums in the category of symmetric lenses. We then show how the methods of universal algebra can be applied to build iterator lenses for structured data such as lists and trees, yielding lenses for operations like mapping, filtering, and concatenation from first principles. Finally, we investigate an even more general technique for constructing mapping combinators, based on the theory of containers.

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Towards an Algebraic Theory of Bidirectional Transformations

Cited by 19 publications

References 7 publications

From aspect-oriented models to aspect-oriented code?

From aspect-oriented models to aspect-oriented code?

Symmetric delta lenses and spans of asymmetric delta lenses.

Symmetric lenses

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