church.scala

  type CBool[A]   = (=> A, => A) => A
  type CNumber[A] = (A => A, A) => A

  def ctrue[A](t: => A, f: => A): A  = t
  def cfalse[A](t: => A, f: => A): A = f

  def cond[A](c: CBool[A], x: => A, y: => A): A = c(x, y)

  def c0[A](f: A => A, x: A): A = x
  def c1[A](f: A => A, x: A): A = f(c0(f, x))
  def c2[A](f: A => A, x: A): A = f(c1(f, x))
  def c3[A](f: A => A, x: A): A = f(c2(f, x))

  def succ[A](n: CNumber[A], f: A => A, x: A): A = f(n(f, x))
  def iszero[A](n: CNumber[CBool[A]]): CBool[A]  = n(a => cfalse[A], ctrue[A])

  val hi: String  = cond(ctrue[String], "yes", "no")
  val hi2: String = cond(cfalse[String], "yes", "no")
  println(cond(iszero[String](c0), "iszero", "error"))
  println(cond(iszero[String](c1), "error", "not zero"))