Haskell 检查排列的函数

Question

如果我声明数据构造函数，例如

data City = Baltimore | Chicago | Seattle | Miami | Toronto
        deriving (Bounded, Enum, Eq, Ord, Show)

data Name = Orioles | Cubs | Mariners | Marlins | BlueJays
        deriving (Bounded, Enum, Eq, Ord, Show)

如何制作函数

checkPermutation :: (City -> Name) -> Bool

检查没有两个城市分配了相同的团队名称。例如，以下将 return True，但如果任何 "Name" 分配给多个城市，它将 return False。

test1 :: City -> Name
test1 c = case c of
    Baltimore  -> Orioles
    Chicago    -> Cubs
    Seattle    -> Mariners
    Miami      -> Marlins
    Toronto    -> Blue Jays

Answer 1

试试这个：

import Data.List (nub)

cities :: [City]
cities = [Baltimore..Toronto]

checkPermutation :: (City -> Name) -> Bool
checkPermutation f = (== length cities) . length . nub . map f $ cities

这基本上是检查函数 f :: City -> Name 是否为 injective。

事实上，我们可以创建一个更通用的injective谓词：

import Data.Set as Set

typeSet :: (Bounded a, Enum a, Ord a) => Set a
typeSet = fromList $ enumFrom minBound

injective :: (Enum a, Bounded a, Ord a, Ord b) => (a -> b) -> Bool
injective f = let xs = typeSet in (== size xs) . size . Set.map f $ xs

希望对您有所帮助。

Haskell 检查排列的函数

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