Haskell函数验证括号匹配

Question

我需要编写一个函数par :: String -> Bool来验证带有括号的给定字符串是否与堆栈模块匹配.

例如:

par "(((()[()])))" = True
par "((]())" = False

这是我的堆栈模块实现:

module Stack (Stack,
              push, pop, top,
              empty, isEmpty)
    where

data Stack a = Stk [a]
             deriving (Show)

push :: a -> Stack a -> Stack a
push x (Stk xs) = Stk (x:xs)

pop :: Stack a -> Stack a
pop (Stk (_:xs)) = Stk xs
pop _ = error "Stack.pop: empty stack"


top :: Stack a -> a
top (Stk (x:_)) = x
top _ = error "Stack.top: empty stack"

empty :: Stack a
empty = Stk []

isEmpty :: Stack a -> Bool
isEmpty (Stk [])= True
isEmpty (Stk _) = False

所以我需要实现一个par函数来测试一串括号,并说明它中的括号是否平衡.我怎么能用堆栈呢？

Answer 1

module Parens where

import Data.Map (Map)
import qualified Data.Map as Map

matchingParens :: Map Char Char
matchingParens = Map.fromList [
    ('(', ')')
  , ('{', '}')
  , ('[', ']')
  ]

isOpening :: Char -> Bool
isOpening c = maybe False (const True) $ Map.lookup c matchingParens

type Stack a = [a]

balanced :: String -> Bool
balanced = balanced' []

balanced' :: Stack Char -> String -> Bool
balanced' [] ""     = True
balanced' _  ""     = False
balanced' [] (c:cs) = balanced' [c] cs
balanced' (o:os) (c:cs)
  | isOpening c = balanced' (c:o:os) cs
  | otherwise   = case Map.lookup o matchingParens of
      Nothing -> False
      Just closing -> if closing == c
        then balanced' os cs
        else False