Synthesizing symmetric lenses

Abstract

Lenses are programs that can be run both "front to back" and "back to front, " allowing updates to either their source or their target data to be transferred in both directions. Since their introduction by Foster et al., lenses have been extensively studied, extended, and applied. Recent work has also demonstrated how techniques from type-directed program synthesis can be used to efficiently synthesize a simple class of lenses-so-called bijective lenses over string data-given a pair of types (regular expressions) and a small number of examples.We extend this synthesis algorithm to a much broader class of lenses, called simple symmetric lenses, including all bijective lenses, all of the popular category of "asymmetric" lenses, and a rich subset of the more powerful "symmetric lenses" proposed by Hofmann et al. Intuitively, simple symmetric lenses allow some information to be present on one side but not the other and vice versa. They are of independent theoretical interest, being the largest class of symmetric lenses that do not rely on persistent internal state.Synthesizing simple symmetric lenses is substantially more challenging than synthesizing bijective lenses: Since some of the information on each side can be "disconnected" from the other side, there will, in general, be many lenses that agree with a given example. To guide the search process, we use stochastic regular expressions and ideas from information theory to estimate the amount of information propagated by a candidate lens, generally preferring lenses that propagate more information, as well as user annotations marking parts of the source and target data structures as either irrelevant or essential.We describe an implementation of simple symmetric lenses and our synthesis procedure as extensions to the Boomerang language. We evaluate its performance on 48 benchmark examples drawn from Flash Fill, Augeas, the bidirectional programming literature, and electronic file format synchronization tasks. Our implementation can synthesize each of these lenses in under 30 seconds.

Synbit: synthesizing bidirectional programs using unidirectional sketches

“…The above set-up may sound reasonable but actually omits important internal details. Optician internally tries to expand 𝑟 * into either 𝑟𝑟 * |𝜀 or 𝑟 * 𝑟 |𝜀 nondeterministically (Miltner et al 2019), which eventually transforms 𝑟𝑟 * (head-biased non-empty lists) into 𝑟 (𝑟 * 𝑟 |𝜀) = 𝑟𝑟 * 𝑟 |𝑟 (one-step expansions of last-biased nonempty lists). The core transformation involves no structural transformations after this expansion.…”

“…Optician's regular-expression-based specification matches perfectly with the simplicity of the lens languages and their close connection to advanced types, while Synbit takes full advantage of HOBiT's alignment to conventional functional programming. On a more technical note, Optician (Miltner et al 2019) is able to prioritize the generated programs by quantitative information flow. It is not clear how this may be used in Synbit as the computation of the quantitative information flow will be difficult for a language with arbitrary recursion.…”

Runners in Action

“…On the theoretical side, by developing semantics in a SubpCpoq-enriched setting [32], we plan to support recursion at all levels, and remove the distinction between ground and arbitrary types. Finally, by using proof-relevant subtyping [34] and synthesis of lenses [19], we can upgrade the subtyping relation from a simple inclusion to one that relates types by lenses.…”

Program sketching with live bidirectional evaluation

“…Programming-by-Example (PBE) for Domain-Specific Languages. Programming-by-example techniques have been developed for numerous domain-specific applications, including string transformations [Gulwani 2011] (including bidirectional ones [Miltner et al 2019]), shell scripting [Gulwani et al 2015], web scraping [Chasins et al 2018], parallel data processing [Smith and Albarghouthi 2016], and generating vector graphics [Hempel et al 2019]. See Gulwani et al [2017] for a recent survey of developments.…”