A bidirectional transformation consists of pairs of transformations - a forward transformation get produces a target view from a source, while a putback transformation put puts back modifications on the view to the source - satisfying sensible roundtrip properties. Existing bidirectional approaches are get-based in that one writes (an artifact resembling) a forward transformation and a corresponding backward transformation can be automatically derived. However, the unavoidable ambiguity that stems from the underspecification of put often leads to unpredictable bidirectional behavior, making it hard to solve nontrivial practical synchronization problems with existing bidirectional transformation approaches. Theoretically, this ambiguity problem could be solved by writing put directly and deriving get, but differently from programming with get it is easy to write invalid put functions. An open challenge is how to check whether the definition of a putback transformation is valid, while guaranteeing that the corresponding unique get exists. In this paper, we propose, as far as we are aware, the first safe language for supporting putback-based bidirectional programming. The key to our approach is a simple but powerful language for describing primitive putback transformations. We show that validity of putback transformations in this language is decidable and can be automatically checked. A particularly elegant and strong aspect of our design is that we can simply reuse and apply standard results for treeless functions and tree transducers in the specification of our checking algorithms.
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