关于单半群类的进一步问题

Question

我试图利用Semigroup类型化来玩玩单子，并且我试图在自然数上定义一个单子。我将以下类和实例声明放入GHCI中

Prelude:{
Prelude| class Semigroup a where
Prelude|    (<>) :: a -> a -> a)
Prelude| newtype Sum a = Sum { getSum :: a }
Prelude|     deriving (Eq, Ord, Show)
Prelude| instance Num a => Monoid (Sum a) where
Prelude|    (<>) = coerce ((+) :: a -> a -> a)
Prelude| instance Num a => Monoid (Sum a) where
Prelude|     mempty = Sum 0
Prelude| :} 

我收到这样的信息：

<interactive>:7:4: error:
Ambiguous occurrence ‘<>’
It could refer to either ‘Prelude.<>’,
                         imported qualified from ‘Prelude’
                         (and originally defined in ‘GHC.Base’)
                      or ‘<>’, defined at <interactive>:3:4

然后我输入了import qualified Prelude as P，以避免冲突，但这不起作用，我得到了错误消息：

code<interactive>:26:19: error:
Not in scope: type constructor or class ‘Monoid’
Perhaps you meant one of these:
  ‘P.Monoid’ (imported from Prelude),
  ‘P.Monad’ (imported from Prelude) 

Answer 1

你不应该自己定义类型。它已经被定义了，通过定义另一个函数，这意味着您的所有(<>)函数等等现在都可以指向您定义的Semigroup或在Prelude中定义的那个。

因此，您可以定义您的类型并使其成为Semigroup和Monoid的实例，并使用：

import Data.Semigroup

newtype Sum a = Sum { getSum :: a } deriving (Eq, Ord, Show)

instance Num a => Semigroup (Sum a) where
    Sum a <> Sum b = Sum (a + b)

instance Num a => Monoid (Sum a) where
    mempty = Sum 0
    mappend = (<>)

因此，如果我们在shell中运行这个程序，就会得到：

Prelude> import Data.Semigroup
Prelude Data.Semigroup> :{
Prelude Data.Semigroup| newtype Sum a = Sum { getSum :: a } deriving (Eq, Ord, Show)
Prelude Data.Semigroup| 
Prelude Data.Semigroup| instance Num a => Semigroup (Sum a) where
Prelude Data.Semigroup|     Sum a <> Sum b = Sum (a + b)
Prelude Data.Semigroup| 
Prelude Data.Semigroup| instance Num a => Monoid (Sum a) where
Prelude Data.Semigroup|     mempty = Sum 0
Prelude Data.Semigroup|     mappend = (<>)
Prelude Data.Semigroup| :}
Prelude Data.Semigroup> Sum 0 <> Sum 1 <> Sum 4 <> Sum 5
Sum {getSum = 10}