TY - GEN

T1 - Towards an Algebraic Theory of Bidirectional Transformations

AU - Stevens, Perdita

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=56449119123&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-87405-8_1

DO - 10.1007/978-3-540-87405-8_1

M3 - Conference contribution

SN - 978-3-540-87404-1

T3 - Lecture Notes in Computer Science

SP - 1

EP - 17

BT - Graph Transformations

A2 - Ehrig, Hartmut

A2 - Heckel, Reiko

A2 - Rozenberg, Grzegorz

A2 - Taentzer, Gabriele

PB - Springer-Verlag GmbH

ER -