幺半群类型的进一步问题 class

Question

我正在尝试使用 Semigroup 类型 class 来玩弄幺半群，并且我正在尝试在自然数上定义一个幺半群。我将以下 class 和实例声明放入 GHCI

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| :}

我收到消息：

<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import qualified Prelude as P，以避免冲突，但这不起作用，我得到错误信息：

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

您应该不自己定义类型类。已经定义好了，再定义一个，就意味着你所有的(<>)函数等等现在都可以指向Semigroup你定义的，或者那个在 Prelude.

中定义

您因此可以定义您的类型并使其成为 Semigroup 和 Monoid 的实例：

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 = (<>)

如果我们因此在 shell 中运行这个，我们得到：

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}

幺半群类型的进一步问题 class

Further problems with the monoid type class

haskell

monoids