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, these have been limited to the context of relational or XML (tree-like) databases. We challenge the problem of bidirectional transformations within the context of graphs, by proposing a formal definition of a well-behaved bidirectional semantics for UnCAL, i.e., a graph algebra for the known UnQL graph query language. The key to our successful formalization is full utilization of both the recursive and bulk semantics of 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. We use the trace information for backward evaluation to reflect in-place updates and deletions on the view to the source, and adopt the universal resolving algorithm for inverse computation and the narrowing technique to tackle the difficult problem with insertion. We prove our bidirectional evaluation is well-behaved. Our current implementation is available online and confirms the usefulness of our approach with nontrivial applications.
With the increasing popularity of parallel programming environments such as PC clusters, more and more sequential programmers, with little knowledge about parallel architectures and parallel programming, are hoping to write parallel programs. Numerous attempts have been made to develop high-level parallel programming libraries that use abstraction to hide low-level concerns and reduce difficulties in parallel programming. Among them, libraries of parallel skeletons have emerged as a promising way towards this direction. Unfortunately, these libraries are not well accepted by sequential programmers, because of incomplete elimination of lower-level details, ad-hoc selection of library functions, unsatisfactory performance, or lack of convincing application examples. This paper addresses principle of designing skeleton libraries of parallel programming and reports implementation details and practical applications of a skeleton library SkeTo. The SkeTo library is unique in its feature that it has a solid theoretical foundation based on the theory of Constructive Algorithmics, and is practical to be used to describe various parallel computations in a sequential manner.
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