haskell - 定义函数的未定义错误

Question

我正在尝试实现一个乘以多项式的函数(使用列表表示 -- 3x^2 + 5x + 2 = P [2,5,3]):

newtype Poly a = P [a]

plus :: Num a => Poly a -> Poly a -> Poly a
plus (P a) (P b) = P (map (\(y,z) -> z + y) (zipWithPadding 0 a b))
    where
        zipWithPadding :: (Num a) => a -> [a] -> [a] -> [(a, a)]
        zipWithPadding e (aa: as) (bb: bs) = ((aa, bb): zipWithPadding e as bs)
        zipWithPadding e [] bs = zip (repeat e) bs
        zipWithPadding e as [] = zip as (repeat e)

times :: Num a => Poly a -> Poly a -> Poly a
times (P a) (P b) = sum $ multList 0 [] a b
    where
        multList :: Num a => Int -> [Poly a] -> [a] -> [a] -> [Poly a]
        multList _ s [] _ = s
        multList e s (aa:as) bs = multList (e + 1) (s ++ (multElement e aa bs)) as bs

        multElement :: Num a => Int -> a -> [a] -> [Poly a]
        multElement e aa bs = [P $ replicate e 0 ++ (map (*aa) bs)]


instance Num a => Num (Poly a) where
    (+) = plus
    (*) = times
    negate      = undefined
    fromInteger = undefined
    -- No meaningful definitions exist
    abs    = undefined
    signum = undefined

但是，当我尝试运行时，出现了一个undefined 错误:

*HW04> times (P [1,2,2]) (P [1,2])
*** Exception: Prelude.undefined

我很困惑。

Answer 1

很明显，您正在调用 Poly 的 Num 实例中的 undefined 方法之一。

您可以使用这些定义来确定调用的是哪个:

negate      = error "Poly negate undefined"
fromInteger = error "Poly fromInteger undefined"
abs    = error "Poly abs undefined"
signum = error "Poly signum undefined"

运行测试表达式产生:

Poly *** Exception: Poly fromInteger undefined

问题出在您对 sum 的使用上，它本质上定义为:

sum xs = foldl (+) 0 xs

因此调用 fromInteger 0。您可以通过以下方式解决此问题:

fromInteger x = P [ fromInteger x ]

更新

Poly a 的 fromInteger 需要这样定义的原因是因为我们需要构造一个 Num a 值列表，以及 fromInteger x是从整数值 x 创建 Num a 的方法。