Anamorphism in 1 minute

An Anamorphism (from the Greek ἀνά "upwards" and μορφή "form, shape) over a type T is a function of type U → T that destructs the U in some way into a number of components. On the components that are of type U, it applies recursion to convert theme to T 's. After that it combines the recursive results with the other components to a T , by means of the constructor functions of T .

For example if we want to build List(N, N-1, …, 1) from N we would use anamorphism from Int to List[Int]. It’s the opposite operation to fold - unfold.

	type ListAnamorphism[U, T] = U => List[T]
	def listAnamorphismFactory[U, T](func: T => Option[(U, T)]): ListAnamorphism[T, U] = {
	in: T =>
	def ana(initial: T): List[U] = func(initial) match {
	case None => Nil
	case Some((current, next)) => current :: ana(next)
	}
	ana(in)
	}
	val listDestruct: ListAnamorphism[Int, Int] = listAnamorphismFactory { i: Int => if (i == 0) None else Some(i, i - 1) }

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