We propose a novel approach to the view update problem for tree-structured data: a domainspecific programming language in which all expressions denote bi-directional transformations on trees. In one direction, these transformations—dubbed lenses—map a “concrete ” tree into a simplified “abstract view”; in the other, they map a modified abstract view, together with the original concrete tree, to a correspondingly modified concrete tree. Our design emphasizes both robustness and ease of use, guaranteeing strong well-behavedness and totality properties for welltyped lenses. We identify a natural mathematical space of well-behaved bi-directional transformations over arbitrary structures, study definedness and continuity in this setting, and state a precise connection with the classical theory of “update translation under a constant complement ” from databases. We then instantiate this semantic framework in the form of a collection of lens combinators that can be assembled to describe transformations on trees. These combinators include familiar constructs from functional programming (composition, mapping, projection, conditionals, recursion) together with some novel primitives for manipulating trees (splitting, pruning, copying, merging, etc.). We illustrate the expressiveness of these combinators by developing a number of bi-directional listprocessing transformations as derived forms. An extended example shows how our combinators can be used to define a lens that translates between a native HTML representation of browser bookmarks and a generic abstract bookmark format.

XML is successful as a machine processable data interchange format, but it is often too verbose for human use. For this reason, many XML languages permit an alternative more legible non-XML syntax. XSLT stylesheets are often used to convert from the XML syntax to the alternative syntax; however, such transformations are not reversible since no general tool exists to automatically parse the alternative syntax back into XML. We present XSugar, which makes it possible to manage dual syntax for XML languages. An XSugar specification is built around a context-free grammar that unifies the two syntaxes of a language. Given such a specification, the XSugar tool can translate from alternative syntax to XML and vice versa. Moreover, the tool statically checks that the transformations are reversible and that all XML documents generated from the alternative syntax are valid according to a given XML schema.

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.

The need to edit data through a view arises in a host of applications across many different areas of computing. Unfortunately, few existing systems provide support for updatable views. In practice, when they are needed, updatable views are usually implemented using two separate programs: one to compute the view from the source and another to handle updates. This rudimentary design is tedious for programmers, dif�cult to reason about, and a nightmare to maintain. This dissertation describes bidirectional programming languages, which provide an elegant mechanism for describing updatable views. Unlike programs written in an ordinary language, which only work in one direction, programs written in a bidirectional language can be run both forwards and backwards: from left to right, they describe functions that map sources to views, and from right to left, they describe functions that map updated views back to updated sources. Besides eliminating redundancy, these languages can be designed to ensure correctness, guaranteeing by construction that the two functions work well together.

The experiments in this paper apply the idea of prototyping programming language tools from robust semantics: we used a partial evaluator (Similix) to turn interpreters into inverse interpreters. This way we generated inverse interpreters for several small languages including interpreters for Turing machines, an applied lambda calculus, a flowchart language, and a subset of Java bytecode. Limiting factors of offline partial evaluation were the polyvariant specialization scheme with its lack of generalization; advantages were the availability of higher-order values to specialize a breadthfirst tree traversal. This application of self-applicable partial evaluation is different from the classical Futamura projections that tell us how to translate a program by specialization of an interpreter.

Parsers and pretty-printers for a language are often quite similar, yet both are typically implemented separately, leading to redundancy and potential inconsistency. We propose a new interface of syntactic descriptions, with which both parser and pretty-printer can be described as a single program. Whether a syntactic description is used as a parser or as a pretty-printer is determined by the implementation of the interface. Syntactic descriptions enable programmers syntax once and for all, and use these descriptions for parsing or pretty-printing as needed. We also discuss the generalization of our programming technique towards an algebra of partial isomorphisms.

Abstract. We describe the XSG programming language and define a formal semantics for it. 1

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Inverse computation has many applications such as serialization/deserialization, providing support for undo, and test-case generation for software testing. In this paper, we propose an inverse computation method that always terminates for a class of functions known as parameter-linear macro tree transducers, which involve multiple data traversals and the use of accumulations. The key to our method is the observation that a function in the class can be regarded as a non-accumulative context-generating transformation without multiple data traversals. Accordingly, we demonstrate that it is easy to achieve terminating inverse computation for the class by context-wise memoization of the inverse computation results. We also show that when we use a tree automaton to express the inverse computation results, the inverse computation runs in time polynomial to the size of the original output and the textual program size.