Quotient lenses are bidirectional transformations whose correctness laws are ``loosened'' by specified equivalence relations, allowing inessential details in concrete data formats to be suppressed. For example, a programmer could use a quotient lens to define a transformation that ignores the order of fields in XML data, so that two XML files with the same fields but in different orders would be considered the same, allowing a single, simple program to handle them both.
Building on a recently published algorithm for synthesizing plain bijective lenses from high-level specifications, we show how to synthesize bijective quotient lenses in three steps. First, we introduce quotient regular expressions} (QREs), annotated regular expressions that conveniently mark inessential aspects of string data formats; each QRE specifies, simulteneously, a regular language and an equivalence relation on it. Second, we introduce QRE lenses, i.e., lenses mapping between QREs. Our key technical result is a proof that every QRE lens can be transformed into a functionally equivalent lens that canonizes source and target data only once at the “edges” then uses a bijective lens to map between the respective canonical elements; no internal canonization occurs for a lens in this normal form. Third, we leverage this normalization theorem to synthesize QRE lenses from a pair of QREs and example input-output pairs, reusing earlier work on synthesizing plain bijective lenses. We have implemented QREs and QRE lens synthesis as an extension to the bidirectional programming language Boomerang. We evaluate the effectiveness of our approach by synthesizing QRE lenses between various real-world data formats in the Optician benchmark suite.
Conference DayTue 25 SepDisplayed time zone: Guadalajara, Mexico City, Monterrey change
15:00 - 16:30
|What You Needa Know about Yoneda: Profunctor Optics and the Yoneda Lemma (Functional Pearl)|
Guillaume BoisseauUniversity of Oxford, Jeremy GibbonsDepartment of Computer Science, University of OxfordDOI
|Incremental Relational Lenses|
Rudi HornUniversity of Edinburgh, Roly PereraUniversity of Glasgow, James CheneyUniversity of Edinburgh, UKDOI
|Synthesizing Quotient Lenses|
Solomon MainaUniversity of Pennsylvania, Anders MiltnerPrinceton University, Kathleen FisherTufts University, USA, Benjamin C. PierceUniversity of Pennsylvania, Dave WalkerPrinceton University, Steve ZdancewicUniversity of PennsylvaniaDOI
|Generic Deriving of Generic Traversals|
Csongor KissImperial College London, Matthew PickeringUniversity of Bristol, Nicolas WuUniversity of Bristol, UKDOI