Haskell 定义Num的实例

我有一个带有类型声明的模块和一些用于此类型的函数

module Stream where

import Prelude ((+), (-), (<), (++), (*), otherwise, id)
import qualified Prelude as P

infixr 1 :&


data Stream a = a :& Stream a


instance P.Show a => P.Show (Stream a) where
  show xs = showInfinity (P.show (take 5 xs)) where
    showInfinity xs = P.init xs ++ "..."

head :: Stream a -> a
head (x:&_) = x


tail :: Stream a -> Stream a
tail (_:&xs) = xs


(!!) :: Stream a -> P.Int -> a
(!!) xs 0 = head xs
(!!) xs n = (tail xs) !! (n - 1)


take :: P.Int -> Stream a -> [a]
take 0 xs = []
take n xs = (head xs) : (take (n - 1) (tail xs))


map :: (a -> b) -> Stream a -> Stream b
map f xs = f (head xs) :& map f (tail xs)


zipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c
zipWith f xs ys = f (head xs) (head ys) :& zipWith f (tail xs) (tail ys)


iterate :: (a -> a) -> a -> Stream a
iterate f a = a :& iterate f (f a)

函数*，-，*可以按我的要求工作，但函数否定，abs和signum不存在

GHCi, version 8.2.2: http://www.haskell.org/ghc/  :? for help
Prelude> :l Stream
[1 of 1] Compiling Stream           ( Stream.hs, interpreted )
Ok, one module loaded.
*Stream> s1 = iterate (\x -> x + 1) 1
*Stream> negate s1

<interactive>:3:1: error:
    • Variable not in scope: negate :: Stream P.Integer -> t
    • Perhaps you meant ‘P.negate’ (imported from Prelude)

---

GHCi试图提供对绑定的相同访问，就像我们在加载的模块中一样。因为模块有明确的前奏导入

然后，GHCi还要求用户键入p.negate。毕竟，模块源代码也需要这样做

在GHCi中，我想也可以导入Prelude，以便再次使用所有绑定，而不必使用p..

对它们进行限定，因为您没有导入Prelude否定。

GHCi, version 8.2.2: http://www.haskell.org/ghc/  :? for help
Prelude> :l Stream
[1 of 1] Compiling Stream           ( Stream.hs, interpreted )
Ok, one module loaded.
*Stream> s1 = iterate (\x -> x + 1) 1
*Stream> negate s1

<interactive>:3:1: error:
    • Variable not in scope: negate :: Stream P.Integer -> t
    • Perhaps you meant ‘P.negate’ (imported from Prelude)

import Prelude ((+), (-), (<), (++), (*), otherwise, id)
import qualified Prelude as P