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.

We propose a novel approach to the classical view update problem. The view update problem arises from the fact that modifications to a database view may not correspond uniquely to modifications on the underlying database; we need a means of determining an “update policy ” that guides how view updates are reflected in the database. Our approach is to define a bi-directional query language, in which every expression can be read both (from left to right) as a view definition and (from right to left) as an update policy. The primitives of this language are based on standard relational operators. Its type system, which includes recordlevel predicates and functional dependencies, plays a crucial role in guaranteeing that update policies are well-behaved, in a precise sense, and that they are total—i.e., able to handle arbitrary changes to the view.

Abstract. Domain-specific languages facilitate solving problems in a targeted domain by providing features particular to the domain. Declarative domain-specific languages have the additional benefit that users specify what something means rather than how to do something. As a result, the language compiler is free to choose the best implementation strategies and to generate multiple artifacts from a single description. PADS/ML is a declarative data description language designed to facilitate ad hoc data management. From a single description, the compiler generates a myriad of artifacts, including data structures for the in-memory representation of the data and parsers and printers. In this paper, we describe a new generic programming infrastructure for PADS/ML that allows third-party developers to define additional useful artifacts without modifying the compiler. We report on two case studies that use this infrastructure. In the first, we build a version of PADX for PADS/ML, allowing any data source with a PADS/ML description to be queried as if it were XML. In the second, we extend Harmony with the ability to synchronize any data with a PADS/ML description. 1

bidirectional programs