functional-programming - 树上的尾递归

Question

我有一个数据结构，

datatype 'a tree = Leaf | Branch of 'a tree * 'a * 'a tree

并且我想编写一个函数以某种顺序遍历这棵树。它做什么并不重要，所以它可以是一个 treefold : ('a * 'b -> 'b) -> 'b -> 'a tree -> 'b。我可以这样写这个函数:

fun treefold f acc1 Leaf = acc1
  | treefold f acc1 (Branch (left, a, right)) =
    let val acc2 = treefold f acc1 left
        val acc3 = f (a, acc2)
        val acc4 = treefold f acc3 right
    in acc4 end

但是因为我在最后一种情况下不可避免地有两个分支，所以这不是尾递归函数。

如果允许扩展类型签名，是否可以创建一个，代价是什么？我也想知道它是否值得尝试；也就是说，它在实践中会带来任何速度优势吗？

Answer 1

您可以使用连续传递样式实现尾递归树折叠:

fun treefold1 f Leaf acc k = k acc
  | treefold1 f (Branch (left, a, right)) acc k =
    treefold1 f left acc (fn x => treefold1 f right (f(a, x)) k)

fun treefold f t b = treefold1 f t b (fn x => x)

例如:

fun sumtree t = treefold op+ t 0

val t1 = Branch (Branch(Leaf, 1, Leaf), 2, Branch (Leaf, 3, Leaf))

val n = sumtree t1

结果如预期的那样 n = 6。