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trait BranchType[F, T] extends (BranchType[F, T] => (F => T))

object B {
  def apply[F, T](c: BranchType[F, T] => (F => T)) = new BranchType[F, T] {
    def apply(b: BranchType[F, T]): F => T = c(b)
  }
}

def Y[F, T] = (f: (F => T) => F => T) =>
  B[F, T](x => f(x(x)(_)))(B(x => f(x(x)(_))))

val factorial = Y[Int, Int](f => i => if (i <= 0) 1 else f(i - 1) * i)
factorial(6) == 720