Combinators for bi-directional tree transformations: A linguistic approach to the view update problem

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Combinators for bi-directional tree transformations: A linguistic approach to the view update problem (2005)

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by J. Nathan Foster , Michael B. Greenwald , Jonathan T. Moore , Benjamin C. Pierce , Alan Schmitt

Venue:	In ACM SIGPLAN–SIGACT Symposium on Principles of Programming Languages (POPL
Citations:	204 - 16 self

BibTeX

@INPROCEEDINGS{Foster05combinatorsfor,
    author = {J. Nathan Foster and Michael B. Greenwald and Jonathan T. Moore and Benjamin C. Pierce and Alan Schmitt},
    title = {Combinators for bi-directional tree transformations: A linguistic approach to the view update problem},
    booktitle = {In ACM SIGPLAN–SIGACT Symposium on Principles of Programming Languages (POPL},
    year = {2005},
    pages = {233--246},
    publisher = {ACM Press}
}

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Abstract

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.

Keyphrases

view update problem linguistic approach bi-directional tree transformation modified abstract view natural mathematical space bi-directional transformation arbitrary structure simplified abstract view novel approach constant complement study definedness precise connection welltyped lens totality property bi-directional listprocessing transformation extended example novel primitive well-behaved bi-directional transformation original concrete tree tree-structured data familiar construct native html representation modified concrete tree lens combinators semantic framework generic abstract bookmark format concrete tree browser bookmark update translation classical theory derived form functional programming

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