loeb.scala

loeb.scala

// http://blog.sigfpe.com/2006/11/from-l-theorem-to-spreadsheet.html

import cats._
import cats.implicits._


object Foo {
  def main(args: Array[String]): Unit = {
    // loeb :: Functor f => f (f x -> x) -> f x
    // loeb x = fmap (\a -> a (loeb x)) x

    type LF[F[_], A] = Eval[F[Eval[A]]]
    type LL[A] = Eval[List[Eval[A]]]

    def loeb[F[_]: Functor, A](ex: Eval[F[LF[F, A] => Eval[A]]]): Eval[F[Eval[A]]] = {
      ex.map(x => x.fmap(a => loeb(ex).flatMap(l => a(Now(l)))))
    }

    import Eval._
    val ex =
      now(
        List(
          (_: LL[Int]) => now(1),
          (xs: LL[Int]) => xs.map(ys => ys.length),
        )
      )

    //  test3 = [ (!!5), 3, (!!0)+(!!1), (!!2)*2, sum . take 3, 17]
    val test3 =
      now(
        List(
          (xs: LL[Int]) => xs.flatMap(_(5)),
          (_: LL[Int]) => now(3),
          (xs: LL[Int]) => xs.flatMap(xxs => xxs(0).flatMap(z => xxs(1).map(o => o + z))),
          (xs: LL[Int]) => xs.flatMap(xxs => xxs(2).map(_ * 2)),
          (xs: LL[Int]) => xs.map(_.take(3).map(_.value).sum),
          (_: LL[Int]) => now(17),
        )
      )
    println(loeb(test3).value.map(_.value))
    println(loeb(ex).value.map(_.value))
  }
}