Towards an Algebraic Theory of Bidirectional Transformations

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Abstract

Bidirectional transformations are important for model-driven development, and are also of wide interest in computer science. In this paper we present early work on an algebraic presentation of bidirectional transformations. In general, a bidirectional transformation must maintain consistency between two models, either of which may be edited, and each of which may incorporate information not represented in the other. Our main focus here is on lenses [2,1,3] which provide a particularly well-understood special case, in which one model is an abstraction of the other, and either the abstraction or the full model may be edited. We show that there is a correspondence between lenses and short exact sequences of monoids of edits. We go on to show that if we restrict attention to invertible edits, very well-behaved lenses correspond to split short exact sequences of groups; this helps to elucidate the structure of the edit groups.
Original languageEnglish
Title of host publicationGraph Transformations
EditorsHartmut Ehrig, Reiko Heckel, Grzegorz Rozenberg, Gabriele Taentzer
PublisherSpringer-Verlag GmbH
Pages1-17
Number of pages17
ISBN (Print)978-3-540-87404-1
DOIs
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin / Heidelberg
Volume5214

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