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Lenses, Folds and Traversals

Limits and Colimits in a Category of Lenses

Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

Project Cambria: Translate your data with lenses

Changing schemas in distributed software is hard. Could adopting bidirectional lenses help?

Symmetric lenses | Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

A lens is a bidirectional transformation between a pair of connected data structures, capable of translating an edit on one structure into an appropriate edit on the other. Many varieties of lenses have been studied, but none, to date, has offered a ...

NONS SL660

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A Review of the Ray-ban Meta AI Glasses for People With Low Vision

In the small group of professional certified vision rehabilitation therapists (CVRT), to which I belong, it is not uncommon for us to use the term “magic glasses.” These are the glasses some of our clients hope to find that will improve or restore their vision. It makes sense—in that for many of them, a new prescription once brought things back into focus. Vision loss from macular degeneration, glaucoma, diabetes, and other conditions is usually something that can be managed with proper care, but vision is not typically restored to what it once was. Still, the myth or hope for the magic glasses persists.

Bsky Post Lens

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Quotient lenses | Proceedings of the 13th ACM SIGPLAN international conference on Functional programming

Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well ...

Delta Lenses over Inductive Types

Existing bidirectional languages are either state-based or operation-based, depending on whether they represent updates as mere states or as sequences of edit operations.In-between both worlds are delta-based frameworks, where updates are represented using alignment relationships between states.In this paper, we formalize delta lenses over inductive types using dependent type theory and develop a point-free delta lens language with an explicit separation of shape and data.In contrast with the already known issue of data alignment, we identify the new problem of shape alignment and solve it by lifting standard recursion patterns such as folds and unfolds to delta lenses that use alignment to infer meaningful shape updates.

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