HOBiT: Programming Lenses Without Using Lens Combinators

We propose HOBiT, a higher-order bidirectional programming language, in which users can write bidirectional programs in the familiar style of conventional functional programming, while enjoying the full expressiveness of lenses. A bidirectional transformation, or a lens, is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws—a pattern that is found in databases, model-driven development, compiler construction, and so on. The most common way of programming lenses is with lens combinators, which are lens-to-lens functions that compose simpler lenses to form more complex ones. Lens combinators preserve the bidirectionality of lenses and are expressive; but they compel programmers to a specialised point-free style—i.e., no naming of intermediate computation results—limiting the scalability of bidirectional programming. To address this issue, we propose a new bidirectional programming language HOBiT, in which lenses are represented as standard functions, and combinators are mapped to language constructs with binders. This design transforms bidirectional programming, enabling programmers to write bidirectional programs in a flexible functional style and at the same time access the full expressiveness of lenses. We formally define the syntax, type system, and the semantics of the language, and then show that programs in HOBiT satisfy bidirectionality. Additionally, we demonstrate HOBiT ’s programmability with examples.