Haskell：递归数据类型 - 将[String]解析为n-ary树

Question

I am trying to parse a list of strings into a n-ary tree, defined as:

data Tree = Leaf Int | Node [Tree] deriving (Show)

If i have the [String] = ["(", "1", "(", "2", "3", ")", ")"] , I want this to be parsed into a tree with a Node with one Leaf (1) and another nested Node with the other Leafs (2, 3).

I've been trying for a couple days, but I cannot get my head around inserting an arbitrary number of children. I have previously written a AST for a simple grammar, but then I had the number of children already defined in the Data.

the [String] in "(Tree, [String])" is meant to keep track of the strings that have not yet been parsed.

data Tree = Leaf Int | Node [Tree] deriving (Show)
tree :: [String] -> (Tree, [String])
tree [] = error "I can't let you do that, Dave"
tree (x:xs) | all isDigit x = (Leaf (read x), xs)
            | -- <- Node?

I would really appreciate some help or some hints to get me a bit further.

Answer 1

Let change a bit resulting type from (Tree, [String]) to [Tree] .

We use additional argument as accumulator and use recursion:

tree :: [String] -> [Tree]
tree xs = let (Node ts, zs) = treenode (xs ++ ")") [] in ts

treenode :: [String] -> [Tree] -> (Tree, [String])
treenode []       _  = error "I can't let you do that, Dave"
treenode ("(":xs) ts = let (n, xs') = treenode xs [] in treenode xs' (n : ts)
treenode (")":xs) ts = (Node ts, xs)
treenode (x:xs)   ts = treenode xs (Leaf (read x) : ts)