lens.kt

data class Lens<S, A>(val get: (S) -> A, val set: (A, S) -> S)

fun <A, B, C> Lens<A, B>.compose(that: Lens<C, A>): Lens<C, B> =
    Lens({ this.get(that.get(it)) }, { c, a -> that.set(this.set(c, that.get(a)), a) })

fun <A, B> Lens<A, B>.traverse(): Lens<List<A>, List<B>> =
    Lens({ it.map { get(it) } }, { bs, aas -> bs.zip(aas).map { this.set(it.first, it.second) } })

object Play {
  data class Point(val x: Double, val y: Double) {
    companion object {
      val x = Lens<Point, Double>({ it.x }, { x, p -> Point(x, p.y) })
    }
  }

  data class Circle(val p: Point, val r: Double) {
    companion object {
      val p = Lens<Circle, Point>({ it.p }, { p, c -> Circle(p, c.r) })
    }
  }

  data class Surface(val ps: List<Point>) {
    companion object {
      val ps = Lens<Surface, List<Point>>({ it.ps }, { ps, s -> Surface(ps) })
    }
  }

  val x: Lens<Circle, Double> = Point.x.compose(Circle.p)
  val y: Lens<Surface, List<Double>> = Point.x.traverse().compose(Surface.ps)
}