Proptics[_, _]

Exchange

Exchange[A, B, S, T] is a data type shaped like a Profunctor, which characterizes the construction of an Iso and AnIso. Iso_[S, T, A, B] and AnIso_[S, T, A, B] both take two conversion functions as arguments,
view: S => A which produces an A given an S, and review: B => T which produces a T given a B.
Exchange[A, B, S, T] also takes these two function, thus making it a data type that embeds the way to construct an Iso or AnIso.

case class Exchange[A, B, S, T](view: S => A, review: B => T)

While Iso and AnIso construction is the same, their internal encodings is different.

Iso

object Iso_ {
  def apply[S, T, A, B](view: S => A)(review: B => T): Iso_[S, T, A, B]
}

Iso_[S, T, A, B] is a function P[A, B] => P[S, T] that takes a Profunctor of P[_, _].

abstract class Iso_[S, T, A, B] {
  def apply[P[_, _]](pab: P[A, B])(implicit ev: Profunctor[P]): P[S, T]
}

AnIso

object AnIso_ {
  def apply[S, T, A, B](view: S => A)(review: B => T): AnIso_[S, T, A, B]
}

AnIso_[S, T, A, B] is a function P[A, B] => P[S, T] where's the P[_, _] is a data type of Exchange

abstract class AnIso_[S, T, A, B] {
  def apply(exchange: Exchange[A, B, A, B]): Exchange[A, B, S, T]
}

In order for AnIso_[S, T, A, B] to be compatible with Iso_[S, T, A, B], an instance of Profunctor of Exchange has been introduced.

Profunctor is a type constructor that takes 2 type parameters. Exchange[A, B, S, T] is a type that has 4 type parameters, so we need to fix two of the type parameters of Exchange in order to create an instance of Profunctor of Exchange.

implicit def profunctorExchange[E, F]: Profunctor[({ type P[S, T] = Exchange[E, F, S, T] })#P] =
  new Profunctor[({ type P[S, T] = Exchange[E, F, S, T] })#P] {
    override def dimap[A, B, C, D](fab: Exchange[E, F, A, B])
                                  (f: C => A)
                                  (g: B => D): Exchange[E, F, C, D] =
      Exchange(fab.view compose f, g compose fab.review)
  }

AnIso allows us to export its internal construction logic to an Exchange using the toExchange method.

import proptics.AnIso
// import proptics.AnIso

val anIsoStringToList: AnIso[String, List[Char]] = AnIso[String, List[Char]](_.toList)(_.mkString)
// anIsoStringToList: proptics.AnIso[String,List[Char]] = proptics.AnIso_$$anon$17@74561208

val exchange = anIsoStringToList.toExchange
// exchange: proptics.internal.Exchange[List[Char],List[Char],String,String] = 
//   Exchange(scala.Function1$$Lambda$9364/0x0000000801a34040@419490d4,
//            scala.Function1$$Lambda$9364/0x0000000801a34040@78d86219)

exchange.view("Proptics")
// res0: List[Char] = List(P, r, o, p, t, i, c, s)

exchange.review("Proptics".toList)
// res1: String = Proptics

We can later on create a new instance of Iso or AnIso from the exchange instance

import proptics.Iso
// import proptics.Iso

import proptics.AnIso
// import proptics.AnIso

val anIsoFromExchange: AnIso[String, List[Char]] = 
  AnIso[String, List[Char]](exchange.view)(exchange.review)
// anIsoFromExchange: proptics.AnIso[String,List[Char]] = proptics.AnIso_$$anon$17@bf55e9c

val isoFromExchange: Iso[String, List[Char]] = Iso[String, List[Char]](exchange.view)(exchange.review)
// isoFromExchange: proptics.Iso[String,List[Char]] = proptics.Iso_$$anon$16@4c6f5ff7
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