A lens is a bidirectional program. When read from left to right, it denotes an ordinary function that maps inputs to outputs. When read from right to left, it denotes an "update translator" that takes an input together with an updated output and produces a new input that reflects the update. Many variants of this idea have been explored in the literature, but none deal fully with ordered data. If, for example, an update changes the order of a list in the output, the items in the output list and the chunks of the input that generated them can be misaligned, leading to lost or corrupted data. We attack this problem in the context of bidirectional transformations over strings, the primordial ordered data type. We first propose a collection of bidirectional string lens combinators, based on familiar operations on regular transducers (union, concatenation, Kleene-star) and with a type system based on regular expressions. We then design a new semantic space of dictionary lenses, e...
Aaron Bohannon, J. Nathan Foster, Benjamin C. Pier