What are lenses, and how are they used in functional programming?

Lenses are composable getters and setters used for manipulating immutable data structures in functional programming.

In more detail, a lens is a first-class value that combines two operations: viewing (or getting) a subpart of a data structure, and updating (or setting) that part. They are a powerful tool in functional programming languages, particularly those that emphasise immutability, such as Haskell or Scala.

The concept of lenses comes from the field of category theory in mathematics, but in practical terms, you can think of a lens as a way to zoom in on a specific part of a data structure. For example, if you have a complex nested data structure like a JSON object, you might use a lens to focus on a specific nested field. This allows you to work with that field as if it were a top-level entity, simplifying your code.

The real power of lenses comes from their composability. You can combine lenses to focus on deeper and deeper parts of a data structure, and the resulting lens will still be a first-class value that you can pass around in your program. This makes lenses a very flexible tool for working with complex data.

Lenses are used in functional programming to maintain the principles of immutability and pure functions. In an imperative language, you might update a field of an object by simply assigning a new value to it. But in a functional language, data structures are often immutable, meaning that you can't change them once they're created. Instead, you have to create a new copy of the data structure with the updated value. This can be cumbersome, especially for deeply nested data structures. Lenses provide a way to handle these updates in a clean and efficient manner.

In summary, lenses are a powerful tool in functional programming for working with immutable data structures. They allow you to focus on specific parts of a data structure, and to update those parts in a way that respects the principles of functional programming.