Semantic bidirectionalization revisited

Abstract

A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations, essentially allowing the programmers to construct one mapping of the pair and have the other automatically generated.As an alternative to creating specialized new languages, one can try to analyse and transform programs written in general purpose languages, and "bidirectionalize" them. Among others, a technique termed as semantic bidirectionalization [16] stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorem that follows from the polymorphic type of the program allows a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic.In this paper, we revisit the idea of semantic bidirectionalization and reveal the elegant principles behind the current state-of-theart techniques. Guided by the findings, we derive much simpler implementations that scale easily.

Applicative bidirectional programming with lenses

“…For example, Q5 of Use Case "STRING" in XML Query Use Case ( http://www. w3.org/TR/xquery-use-cases) which involves concatenation of strings in the transformation, can be handled by our technique, but not previously with bidirectionalization [21,22,33,41]. We believe that with the proposal in this paper, all queries in XML Query Use Case can now be bidirectionalized.…”

“…For readers familiar with the literature of bidirectional transformation, this restriction to in-place updates is very similar to that in semantic bidirectionalization [21,33,41]. We will discuss the connection in Section 7.1.…”

“…It essentially defines compositional (or modular) bidirectionalization [20,21,33,41] of programs that are monomorphic in type and use higher-order functions in definitionsomething that has not been achieved in bidirectional-transformation research so far.…”

“…Different flavors of bidirectionalization have been proposed: syntactic [20], semantic [21,22,33,41], and a combination of the two [35,36]. Syntactic bidirectionalization inspects a forward function definition written in a somehow restricted syntactic representation and synthesizes a definition for the backward version.…”

“…We discuss related techniques in Section 7, in particularly making connection to semantic bidirectionalization [21,22,33,41] and conclude in Section 8. An implementation of our idea is available from https://hackage.haskell.…”