was held in December 2008 near Tokyo, Japan. The meeting brought together researchers and practitioners from a variety of subdisciplines of computer science to share research efforts and help create a new community. In this report, we survey the state of the art and summarize the technical presentations delivered at the meeting. We also describe some insights gathered from our discussions and introduce a new effort to establish a benchmark for bidirectional transformations. 1

Bidirectional programming languages have been proposed as a practical approach to the view update problem. Programs in these languages, often called lenses, can be read in two ways— from left to right as functions mapping sources to views, and from right to left as functions mapping updated views back to updated sources. Lenses address the view update problem by making it possible to define a view and its associated update policy together. One issue that has not received sufficient attention in the design of bidirectional languages is alignment. In general, to correctly propagate an update to a view, a lens needs to match up the pieces of the edited view with corresponding pieces of the underlying source. Unfortunately, existing bidirectional languages are extremely limited in their treatment of alignment—they only support simple strategies that do not suffice for many examples of practical interest. In this paper, we propose a novel framework of matching lenses that extends basic lenses with new mechanisms for calculating and using alignments. We enrich the types of lenses with “chunks ” that identify the locations of data that should be re-aligned after updates, and we formulate refined behavioral laws that capture essential constraints on the handling of chunks. To demonstrate the utility of our approach, we develop a core language of matching lenses for string data, and we extend it with primitives for describing a number of useful alignment heuristics.

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 studied from a more fundamental 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. 1.

Abstract. Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard point-free combinators can be lifted to lenses with suitable backward semantics, allowing us to use the point-free style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we “lensify ” some standard functions over naturals and lists, which are tricky to define directly “by-hand ” using explicit recursion.

Replace this file with prentcsmacro.sty for your meeting,

Abstract. Model-driven software development often involves several related models. When models are updated, the updates need to be propagated across all models to make them consistent. A bidirectional model transformation keeps two models consistent by updating one model in accordance with the other. However, it does not work when the two models are modified at the same time. In this paper we propose a new algorithm that wraps any bidirectional transformation into a synchronizer with the help of a model difference approach. The synchronizer enables parallel updates by taking the two original models, the two updated models as input and producing two new models where the updates are synchronized. We also examine the requirements for synchronizing parallel updates, and demonstrate that our algorithm satisfies the requirements if the bidirectional transformation satisfies the correctness property and the hippocraticness property. Implementation of our algorithm showed that it works well in a runtime management framework in practical cases. 1

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 studied from a more fundamental 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. 1.

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.