Synthesizing quotient lenses

Abstract

Quotient lenses are bidirectional transformations whose correctness laws are łloosenedž 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 just at the łedgesž and that uses a bijective lens to map between the respective canonical elements; no internal canonization occurs in 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. CCS Concepts: • Software and its engineering → Domain specific languages; Application specific development environments;

Synthesizing symmetric lenses

“…We also show they are expressive enough for many practical uses by adding simple symmetric lenses to the Boomerang language [Bohannon et al 2008] and applying them to a range of real-world applications. This exercise also demonstrates that simple symmetric lenses can coexist with, and be extended by, other advanced lens features provided by Boomerang, including quotient lenses Maina et al 2018] and matching lenses [Barbosa et al 2010].…”

“…Following existing work on bidirectional program synthesis [Maina et al 2018], we split our algorithm into two communicating search procedures. The first, Expand, navigates the space of semantically equivalent regular expressions by applying rewrite rules that preserve both semantics and probability distributions.…”

“…As discussed in the introduction, the Optician tool [Maina et al 2018;] was a building block for our work. Optician synthesized bijective transformations and bijections modulo quotients [Maina et al 2018], but could not synthesize more complex bidirectional transformations where one format contains important information not present in the other-a common situation in the real world. From a technical perspective, the first key novelty in our work involves the definition, theory, analysis, and implementation of a new class of simple symmetric lenses, designed for synthesis.…”

Visualization by example

“…In this respect, our method is similar to prior efforts on compositional program synthesis [Feser et al 2015;Maina et al 2018;Phothilimthana et al 2016;Polikarpova et al 2016;Polozov and Gulwani 2015;Raza et al 2015]. Among these techniques, λ 2 uses domain knowledge about the DSL constructs to infer input-output examples for sub-expressions whenever feasible [Feser et al 2015], FlashMeta (and its variants) use inverse semantics of DSL constructs to propagate examples backwards [Polozov and Gulwani 2015], and Optician [Maina et al 2018;] decomposes the synthesis process using DNF regular expression outlines. Synqid also tries to decompose the overall specification into sub-goals using a technique referred to as "round-trip type checking" [Polikarpova et al 2016].…”

Bidirectional evaluation with direct manipulation

“…The "point-free" combinator-style programming model-which prohibits giving names to the results of intermediate computations-can pose significant usability challenges. One line of recourse is to forgo programming transformations at all, instead synthesizing them from specifications of the desired input and output data formats and examples connecting the two; and Maina et al [2018] present such techniques for useful classes of bidirectional string transformations. Several other approaches aim to provide programming conveniences for writing bidirectional transformations.…”