IndexedOptic

IndexedOptic is a type that can be used to focus on a particular element, and it's location (or index) in a deeply nested data structure. It describes a relationship between a structure S and zero, one, or many values of type (A, I), called the indexed focus (or foci) of the optic.

Definition

This is a general definition of an IndexedOptic:

/**
  * @tparam I the index of an IndexedOptic_
  * @tparam S the source of an IndexedOptic_
  * @tparam T the modified source of an IndexedOptic_
  * @tparam A the focus of an IndexedOptic_
  * @tparam B the modified focus of an IndexedOptic_
  */
trait IndexedOptic_[I, S, T, A, B] {
  def apply[P[_, _]](indexed: Indexed[P, I, A, B])(implicit ev: Profunctor[P]): P[S, T]   
}

Indexed

Indexed is a data type shaped like a Profunctor, that has is P[(A, I), B], which is similar to a P[A, B] of an Optic, but has also a notion of an index.

case class Indexed[P[_, _], I, A, B](runIndex: P[(A, I), B])

Understanding the types of an IndexedOptic

Let's assume that we want to change a NonEmptyList to NonEmptyChain. The concrete types for this IndexedOptic would be:

/**
  * Int the index of an IndexedOptic_
  * NonEmptyList[Int] the source of an IndexedOptic_
  * NonEmptyChain[Int] the modified source of an IndexedOptic_
  * Int the focus of an IndexedOptic_
  * Int the modified focus of an IndexedOptic_
  */
trait IndexedOptic_ {
  apply[P[_, _]](indexed: Indexed[P, Int, Int, Int])
                (implicit ev: Strong[P]): P[NonEmptyList[Int], NonEmptyChain[Int]]]   
}

An IndexedOptic that changes its focus/structure, is called Polymorphic IndexedOptic.

Often times you will just change the value of the focus, which means to the type of the structure will remain the same, for this specific scenario instead of using an IndexedOptic_[I, S, S, A, A] which has repeating type parameters, there is a short notation of:

type IndexedOptic[I, S, A] = IndexedOptic_[I, S, S, A, A]

An IndexedOptic that does not change its focus/structure, is called Monomorphic IndexedOptic.

While IndexedOptic_[I, S, T, A, B] is not really used for the encoding of optics in Proptics (does not serve as a base class for all optics, and it is only shown for explanation purposes), all optics are functions from Indexed[P, I, A, B] to P[S, T], where's the P[_, _] is a typeclass derived from profunctor.

List of all IndexedOptics

This table shows all pairs of indexed optics and their profunctor:

	Profunctor	Data Type
IndexedLens	Strong
AnIndexedLens		Indexed of Shop
IndexedTraversal	Wander
IndexedFold		Indexed of Forget
IndexedGetter		Indexed of Forget
IndexedSetter		Indexed of Function