Abstract

Bidirectional transformations provide a novel mechanism for synchronizing and maintaining the consistency of information between input and output. Despite many promising results on bidirectional transformations, they are limited to the context of relational or XML (tree-like) databases. In this paper, we challenge the problem of bidirectional transformations in the context of graphs, by proposing a formal definition of a well-behaved bidirectional semantics for UnCAL, a graph algebra for the known UnQL graph query language. The key to our successful formalization is full utilization of both recursive and bulk semantics of the structural recursion on graphs. We carefully refine the existing forward evaluation of structural recursion so that it can produce sufficient trace information for later backward evaluation. For the backward evaluation, we use the trace information to reflect in-place update and deletion on the view to the source, and adopt the universal resolving algorithm for inverse computation and the narrowing technique to tackle the difficult insertion problem. We prove the well-behavedness of our bidirectional evaluation. Our current implementation, being available online, confirms usefulness of our approach with nontrivial applications.

Citations