Corpus ID: 15132300

Spans of Delta Lenses

  title={Spans of Delta Lenses},
  author={Michael Johnson and R. Rosebrugh},
As part of an ongoing project to unify the treatment of symmetric lenses (of various kinds) as equivalence classes of spans of asymmetric lenses (of corresponding kinds) we relate the symmetric delta lenses of Diskin et al, 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 and one of the main findings in this paper is that the required equivalence relation among… Expand
Symmetric delta lenses and spans of asymmetric delta lenses
The main result is an isomorphism of categories between a category whose morphisms are equivalence classes of symmetric delta lenses and the category of spans of delta lenses modulo the new equivalence. Expand
Bx 2015 — Bidirectional Transformations: Proceedings of the 4th International Workshop on Bidirectional Transformations
The main result is an isomorphism of categories between a category whose morphisms are equivalence classes of symmetric delta lenses and the category of spans of delta lenses modulo the new equivalence. Expand
A diagrammatic approach to symmetric lenses
Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetricExpand
Unifying Set-Based, Delta-Based and Edit-Based Lenses
A substantial unication with concrete inter-conversions developed among the three main approaches to lenses in both their symmetric and asymmetric forms is provided. Expand
Universal Updates for Symmetric Lenses
This paper considers cospans of c-lenses and shows that they generate symmetric c- lenses with an appropriate universal property, which is further analysed and used to motivate proposed generalisations to obtain universal, least-change, properties for symmetric d-lense. Expand
Multicategories of Multiary Lenses
A class of asymmetric amendment lenses called spg-lenses (stable putget lenses) is introduced which is more general than well-behaved amendment lenses, but is closed under composition, and it is shown how to use spg -lenses to capture a wide class of mutidirectional transformations which compose well and form a well-known and long-standing structure, a multicategory — a multicategories of multiary lenses. Expand
Cospans and symmetric lenses
Those symmetric d-lenses which are representable as cospans of d- lenses which have unique corrs per pair of objects and satisfy two other technical conditions are characterized. Expand
Distributing Commas, and the Monad of Anchored Spans
The main result is the development of a distributive law, in the sense of Beck [3] but only up to isomorphism, distributing L over R, which makes RL a monad, the monad of anchored spans, thus removing the hand-waving and establishing a precise calculus for span-based transitions. Expand


Spans of lenses
These functors which exhibit a category whose arrows are spans of wellbehaved lenses as a retract of a categorywhose arrows are the corresponding symmetric lenses are related to the asymmetric lenses of Hofmann, Pierce and Wagner. Expand
Symmetric lenses
It is shown 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. Expand
From state- to delta-based bidirectional model transformations: the symmetric case
Two new algebraic laws are identified--weak undoability and weak invertibility, which capture important semantics of BX and are useful for both state- and delta-based settings. Expand
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
This paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics", and provides a toolbox of design patterns and structural principles of real practical value for MDE. Expand
From State- to Delta-Based Bidirectional Model Transformations
A novel formal framework based on a graphical language is proposed: models are nodes and updates are arrows, and it is shown how the three major problems caused by under-specification of bidirectional model transformation languages can be fixed. Expand
From State- to Delta-Based Bidirectional Model Transformations: the Asymmetric Case
Spans of Lenses. CEUR Proceedings
  • Spans of Lenses. CEUR Proceedings
  • 2014
Delta Lenses and Opfibrations
2013) Delta Lenses and Fibrations
  • Electronic Communications of the EASST