Bidirectional transformation is a pair of transformations: a view function and a backward transformation . A view function maps one data structure called source onto another called view. The corresponding backward transformation reflects changes in the view to the source. Its practically useful applications include replicated data synchronization, presentation-oriented editor development, tracing software development, and view updating in the database community. However, developing a bidirectional transformation is hard, because one has to give two mappings that satisfy the bidirectional properties for system consistency. In this paper, we propose a new framework for bidirectionalization that can automatically generate a useful backward transformation from a view function while guaranteeing that the two transformations satisfy the bidirectional properties. Our framework is based on two known approaches to bidirectionalization, namely the constant complement approach from the database community and the combinator approach from the programming language community, but it has three new features: (1) unlike the constant complement approach, it can deal with transformations between algebraic data structures rather than just tables; (2) unlike the combinator approach, in which primitive bidirectional transformations have to be explicitly given, it can derive them automatically; (3) it generates a view update checker to validate updates on views, which has not been well addressed so far. The new framework has been implemented and the experimental results show that our framework has promise.
Matsuda et al. [2007, ICFP] and Voigtländer [2009, POPL] introduced two techniques that given a source-to-view function provide an update propagation function mapping an original source and an updated view back to an updated source, subject to standard consistency conditions. Being fundamentally different in approach, both techniques have their respective strengths and weaknesses. Here we develop a synthesis of the two techniques to good effect. On the intersection of their applicability domains we achieve more than what a simple union of applying the techniques side by side delivers.
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This paper describes a new embedding technique of invertible programming languages, through the case of the FliPpr language. Embedded languages have the advantage of inheriting host languages' features and supports; and one of the influential methods of embedding is the tagless-final style, which enables a high level of programmability and extensibility. However, it is not straightforward to apply the method to the family of invertible/reversible/bidirectional languages, due to the different ways functions in such domains are represented. We consider FliPpr, an invertible pretty-printing system, as a representative of such languages, and show that Atkey et al.'s unembedding technique can be used to address the problem. Together with a reformulation of FliPpr, our embedding achieves a high level of interoperability with the host language Haskell, which is not found in any other invertible languages. We implement the idea and demonstrate the benefits of the approach with examples.
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