Year: 2020
Type: article
Abstract: Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define lenses as simultaneously functors and cofunctors between categories. We show that lenses may be canonically represented as a particular commuting triangle of functors, and unify the classical state-based lenses with both c-lenses and d-lenses in this framework. This new treatment of lenses leads to considerable simplifications that are important in applications, including a clear interpretation of lens composition.
DOI: 10.4204/eptcs.323.13
Author: Bryce Clarke
Institution: Macquarie University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Australian Government
OpenAlex ID: W3084840103