function - 检查排列的 Haskell 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)

如何创建一个函数

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

检查没有为两个城市分配相同的团队名称。例如，以下内容将返回 True，但如果将任何“名称”分配给多个城市，则会返回 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

这主要检查函数f::City -> Name是否为injective .

事实上，我们可以创建一个更通用的单射谓词:

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

希望有帮助。