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recursion schemes for cats; to iterate is human, to recurse, divine

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package higherkindness.droste

import cats.Functor
import cats.syntax.functor._

object Scatter {

  def ana[F[_], A]: Scatter[F, A, A] =
    Left(_)

  def gapo[F[_]: Functor, A, B](
      coalgebra: Coalgebra[F, B]
  ): Scatter[F, A, Either[B, A]] = {
    case Left(b)  => Right(coalgebra(b).map(Left(_)))
    case Right(a) => Left(a)
  }

  def apo[F[_]: Functor, A, B](implicit
      project: Project[F, B]
  ): Scatter[F, A, Either[B, A]] =
    gapo(project.coalgebra)
}