"Bidirectionalization for free" for monomorphic transformations

A bidirectional transformation is a pair of mappings between source andview data objects, one in each direction. When the view is modified, thesource is updated accordingly with respect to some laws. Over the years, alot of effort has been made to offer better language support for programmingsuch transformations. In particular, a technique known as bidirectionalizationis able to analyze and transform unidirectional programs written in generalpurpose languages, and “bidirectionalize” them.Among others, an approach termed semantic bidirectionalization pro-posed by Voigtländer stands out in terms of user-friendliness. A unidirec-tional program can be written using arbitrary language constructs, as longas the function it represents is polymorphic and the language constructs re-spect parametricity. The free theorems that follow from the polymorphictype of the program allow a kind of forensic examination of the transforma-tion, determining its effect without examining its implementation. This isconvenient, as the programmer is not restricted to using a particular syntax;but it does require the transformation to be polymorphic.In this paper, we lift this polymorphism requirement to improve the appli-cability of semantic bidirectionalization. Concretely, we provide a type classPackM γ αμ, which intuitively reads “a concrete datatype γ is abstractedto a type α, and the ‘observations’ made by a transformation on values oftype γ are recorded by a monad μ”. With PackM , we turn monomorphic Email addresses: [email protected] (Kazutaka Matsuda),[email protected] (Meng Wang) Preprint submitted to Science of Computer ProgrammingOctober 6, 2014 transformations into polymorphic ones that are ready to be bidirectionalized.We demonstrate our technique with case studies of typical applications ofbidirectional transformation, namely text processing, XML query and graphtransformation, which were commonly considered beyond semantic bidirec-tionalization because of their monomorphic nature.