如何在Haskell中定义二部图

module BipartiteGraph where

import Data.Set (Set)
import qualified Data.Set as Set

-- 定义二部图的数据类型
data BipartiteGraph a b = BipartiteGraph (Set a) (Set b) (Set (a, b))

-- 定义二部图的类型类
class Graph g where
  -- 添加顶点到二部图中
  addVertex :: (Ord a, Ord b) => a -> b -> g a b -> g a b
  -- 添加边到二部图中
  addEdge :: (Ord a, Ord b) => a -> b -> g a b -> g a b
  -- 判断二部图中是否存在某个顶点
  hasVertex :: (Ord a, Ord b) => a -> b -> g a b -> Bool
  -- 判断二部图中是否存在某条边
  hasEdge :: (Ord a, Ord b) => a -> b -> g a b -> Bool

-- 实现二部图的类型类
instance Graph BipartiteGraph where
  addVertex a b (BipartiteGraph as bs es) = BipartiteGraph (Set.insert a as) (Set.insert b bs) es
  addEdge a b (BipartiteGraph as bs es) = BipartiteGraph as bs (Set.insert (a, b) es)
  hasVertex a b (BipartiteGraph as bs _) = Set.member a as && Set.member b bs
  hasEdge a b (BipartiteGraph _ _ es) = Set.member (a, b) es

-- 示例用法
exampleGraph :: BipartiteGraph Int Char
exampleGraph = addVertex 1 'A' $ addVertex 2 'B' $ addEdge 1 'A' $ addEdge 2 'B' $ BipartiteGraph Set.empty Set.empty Set.empty

main :: IO ()
main = do
  putStrLn $ "Has vertex 1 'A': " ++ show (hasVertex 1 'A' exampleGraph)
  putStrLn $ "Has vertex 3 'C': " ++ show (hasVertex 3 'C' exampleGraph)
  putStrLn $ "Has edge 1 'A': " ++ show (hasEdge 1 'A' exampleGraph)
  putStrLn $ "Has edge 2 'B': " ++ show (hasEdge 2 'B' exampleGraph)