Theory and Applications of Lenses and Optics

This is a list of papers studying the theory and application of lenses and optics, as they're used in category theory and functional programming. Many of papers are in multiple fields and some of these fields overlap. Let me know what's missing! (preferably by creating a pull request)

Lenses, Optics

• Categories of Optics
• Generalized Lens Categories via functors Cᵒᵖ→Cat
• Profunctor Optics, a Categorical Update
• Dependent Optics
• Fibre Optics
• Limits of Bimorphic Lenses
• Compound Optics
• What you needa know about Yoneda: profunctor optics and the Yoneda lemma (functional pearl)
• String Diagrams for Optics
• Higher Lenses
• A clear picture of lens laws
• Lenses, fibrations and universal translations
• Relating algebraic and coalgebraic descriptions of lenses

Poly/Containers/Dependent Lenses

• A reference for categorical structures on Poly
• Categories of Containers
• Higher-Order Containers
• Directed Categories as Containers

Delta Lenses

• Limits and colimits in a category of lenses
• A diagrammatic approach to symmetric lenses
• Delta lenses as coalgebra for a comonad
• Delta lenses and opfibration
• Unifying Set-Based, Delta-Based, and Edit-Based Lenses
• The category of asymmetric lenses and its proxy pullbacks
• Internal lenses as functors and cofunctors

Dialectica Categories

• Meta-link to Valeria de Paiva's github repo on Dialectica Categories

Applications

• Lenses: applications and generalizations
• Category Theory in Machine Learning
• Categorical Foundations of Gradient-Based Learning
• Backprop as Functor
• Lenses and Learners
• Dioptics
• Compositional Game Theory
• Bayesian Open Games
• Bayesian Updates Compose Optically
• Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
• Learning as Change Propagation with Delta Lenses
• Learners Languages
• Towards foundations of categorical cybernetics
• Escrows are Optics
• Lenses for Composable Servers
• Poly: An abundant categorical setting for mode-dependent dynamics
• Polynomial Functors: A General Theory of Interaction
• Symmetric edit lenses: a new foundation for bidirectional languages
• Lifting couplings in Wassterstein Spaces

Blog posts

• Lenses for Philosophers
• Optics vs Lenses, Operationally
• Lenses to the left of me, Prisms to the right
• Towards Categorical Foundations of Learning
• Lens
• Towards dependent optics
• Lenses, Stores, and Yoneda
• Profunctor Optics: The Categorical View