在Haskell中编写传递闭包关系函数

import Data.List (nub)

type Relation a = [(a, a)]

transitiveClosure :: Eq a => Relation a -> Relation a
transitiveClosure rel = nub $ rel ++ transitiveClosure' rel rel
  where
    transitiveClosure' :: Eq a => Relation a -> Relation a -> Relation a
    transitiveClosure' _ [] = []
    transitiveClosure' orig ((x, y):rest)
      | any (\(a, b) -> b == x && (a, y) `notElem` orig) orig = transitiveClosure' orig rest
      | otherwise = (x, y) : transitiveClosure' orig rest

-- 示例用法
main :: IO ()
main = do
  let rel = [(1, 2), (2, 3), (3, 4), (4, 5)]
  let closure = transitiveClosure rel
  putStrLn $ "传递闭包关系：" ++ show closure