Question

我将自己的复数数据类型定义为学习练习，我遇到了重载(/)运算符的问题。似乎我不能将它包含在Floating或Fractional的实例中，编译器说(/)不是这些类的可见方法。是否有一个（最好是数字）类型类允许我重载此运算符？例如

instance SOMECLASS a => SOMECLASS (Complex a) where
    (/) a b@(Complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b))

以下是感兴趣的人的当前实施实施：

module Complex where
data Complex a = Complex {real :: a, imaginary :: a}

i = Complex 0 1

instance Num a => Show Complex a where
    show (Complex r i)
        | i < 0 = show r ++ " - i" ++ show (negate i)
        | otherwise = show r ++ " + i" ++ show i

instance Functor Complex where
    fmap f (Complex r i) = Complex (f r) (f i)

instance Num a => Num (Complex a) where
    (+) (Complex ra ia) (Complex rb ib) = Complex (ra + rb) (ia + ib)
    (-) (Complex ra ia) (Complex rb ib) = Complex (ra - rb) (ia - ib)
    (*) (Complex ra ia) (Complex rb ib) = Complex (ra*rb - ia*ib) (ra*ib + rb*ia)

instance Floating a => Floating (Complex a) where
    (/) a b@(Complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b))

conjugate :: Num a => Complex a -> Complex a
conjugate (Complex r i) = Complex r (negate i)

Answer 1

在:t (/)中输入ghci时，您将获得：

(/) :: Fractional a => a -> a -> a

这意味着它是Fractional的成员，而不是Floating的成员。因此，您可以将其重写为：

instance Fractional a => Fractional (Complex a) where
    (/) a b@(Complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b))

由于我们在挑剔，你还必须在Show个实例中添加括号：

instance Num a => Show (Complex a) where
    show (Complex r i)
        | i < 0 = show r ++ " - i" ++ show (negate i)
        | otherwise = show r ++ " + i" ++ show i

用于超载除法的类型

1 个答案: