Towards an Algebraic Theory of Bidirectional Transformations

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 main-tain 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 at-tention 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.

Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

An algebraic semantics for QVT-relations check-only transformations

Fundamenta Informaticae, 114 1, Juan de Lara, Esther Guerra, An algebraic semantics for QVT-relations check-only transformations, 73-101, Copyright 2012, with permission from IOS PressQVT is the standard for model transformation defined by the OMG in the context of the Model-Driven Architecture. It is made of several transformation languages. Among them, QVT-Relations is the one with the highest level of abstraction, as it permits developing bidirectional transformations in a declarative, relational style. Unfortunately, the standard only provides a semiformal description of its semantics, which hinders analysis and has given rise to ambiguities in existing tool implementations. In order to improve this situation, we propose a formal, algebraic semantics for QVT-Relations check-only transformations, defining a notion of satisfaction of QVT-Relations specifications by models.This work has been supported by the Spanish Ministry of Science and Innovation with projects METEORIC (TIN2008-02081) and Go Lite (TIN2011-24139), and by the R&D program of the Community of Madrid with project “e-Madrid” (S2009/TIC-1650)

Calculating with lenses: optimising bidirectional transformations

This paper presents an equational calculus to reason about bidirectional transformations specified in the point-free style. In particular, it focuses on the so-called lenses as a bidirectional idiom, and shows that many standard laws characterising point-free combinators and recursion patterns are also valid in that setting. A key result is that uniqueness also holds for bidirectional folds and unfolds, thus unleashing the power of fusion as a program optimisation technique. A rewriting system for automatic lens optimisation is also presented, to prove the usefulness of the proposed calculus.(undefined

Refactoring pattern matching

Defining functions by pattern matching over the arguments is advantageous for understanding and reasoning, but it tends to expose the implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to program refactoring based on a right-invertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation, while maintaining simple and sound reasoning

Bidirectional Transformation "bx" (Dagstuhl Seminar 11031)

Bidirectional transformations bx are a mechanism for maintaining the consistency of two (or more) related sources of information. Researchers from many different areas of computer science including databases (DB), graph transformations (GT), software engineering (SE), and programming languages (PL) are actively investigating the use of bx to solve a diverse set of problems. Although researchers have been actively working on bidirectional transformations in the above mentioned communities for many years already, there has been very little cross-discipline interaction and cooperation so far. The purpose of a first International Meeting on Bidirectional Transformations (GRACE-BX), held in December 2008 near Tokyo, was therefore to bring together international elites, promising young researchers, and leading practitioners to share problems, discuss solutions, and open a dialogue towards understanding the common underpinnings of bx in all these areas. While the GRACE-BX meeting provided a starting point for exchanging ideas in different communities and confirmed our believe that there is a considerable overlap of studied problems and developed solutions in the identified communities, the Dagstuhl Seminar 11031 on ``Bidirectional Transformations\u27\u27 also aimed at providing a place for working together to define a common vocabulary of terms and desirable properties of bidirectional transformations, develop a suite of benchmarks, solve some challenging problems, and launch joint efforts to form a living bx community of cooperating experts across the identified subdisciplines. This report documents the program and the outcomes of Dagstuhl Seminar 11031 with abstracts of tutorials, working groups, and presentations on specific research topics

Quantum Turing automata

A denotational semantics of quantum Turing machines having a quantum control is defined in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore-Penrose generalized inverse, a new additive trace is introduced on the restriction of this category to isometries, which trace is carried over to directed quantum Turing machines as monoidal automata. The Joyal-Street-Verity Int construction is then used to extend this structure to a reversible bidirectional one.Comment: In Proceedings DCM 2012, arXiv:1403.757

Complex Attribute Manipulation in TGGs with Constraint-Based Programming Techniques

Model transformation plays a central role in Model-Driven Engineering (MDE) and providing bidirectional transformation languages is a current challenge with important applications.  Triple Graph Grammars (TGGs) are a formally founded,  bidirectional model transformation language shown by numerous case studies to be quite promising and successful.  Although TGGs provide adequate support for structural aspects via object  patterns in TGG rules, support for handling complex relationships between different attributes is still missing in current implementations.  For certain applications, such as bidirectional model-to-text transformations, being able to manipulate attributes via string manipulation or arithmetic operations in TGG rules is vital.  Our contribution in this paper is to formalize a TGG extension that provides a means for complex attribute manipulation in TGG rules.  Our extension is compatible with the existing TGG formalization, and retains the "single specification'' philosophy of TGGs