是否有可能表达以下Haskell程序 没有FlexibleInstances,即纯粹的Haskell2010?
{-# LANGUAGE FlexibleInstances #-}
class Funk a where truth :: a -> [Bool]
instance Funk [Bool] where truth = \x -> x
instance Funk Bool where truth = \x -> [x]
instance Funk b => Funk (Bool -> b) where
truth f = concat [truth (f True), truth (f False)]
这是受到答案的启发 如何编写一个以可变函数作为参数的Haskell函数。
我怀疑问题是,那 truth
返回除了作为参数的函数之外的其他东西(返回 Bool
不是 [Bool]
)。
这个片段的目的是给出一个布尔函数的所有可能配置的所有评估的列表,即
Main> truth (\x y -> x && y)
[True,False,False,False]
Main> truth (\x y -> x || y)
[True,True,True,False]
最后,要打印一个真值表,如下所示(参见本文末尾的样板,看看产生这个的代码):
Main> main
T T T | T
T T F | T
T F T | T
T F F | F
F T T | T
F T F | F
F F T | T
F F F | T
以下是一些用于测试和可视化的样板代码,该功能的用途是:
class TruthTable a where
truthTable :: Funk f => f -> a
instance TruthTable [String] where
truthTable f = zipWith (++) (hCells (div (length t) 2)) (map showBool $ truth f)
where
showBool True = "| T"
showBool False = "| F"
hCells 1 = ["T ", "F "]
hCells n = ["T " ++ x | x <- hCells (div n 2)] ++ ["F " ++ x | x <- hCells (div n 2)]
instance TruthTable [Char] where
truthTable f = foldl1 join (truthTable f)
where join a b = a ++ "\n" ++ b
instance TruthTable (IO a) where
truthTable f = putStrLn (truthTable f) >> return undefined
main :: IO ()
main = truthTable (\x y z -> x `xor` y ==> z)
xor :: Bool -> Bool -> Bool
xor a b = not $ a == b
(==>) :: Bool -> Bool -> Bool
a ==> b = not $ a && not b