如何为此数据类型编写Semigroup实例？ [英] How to write Semigroup instance for this data type?

问题描述

我正在尝试在 Haskell Book 中进行一项Semigroup练习（第15章Monoid，Semigroup ）但我卡住了。以下给出：

  newtype合并ab = 
合并{unCombine ::（a  - > b）} 
  

我应该写 Semigroup 实例为 Combine 。

然后书说它必须表现如下：

  Prelude>让f =合并$ \\\
  - >总和（n + 1）
前奏> let g = Combine $ \\\
  - > Sum（n  -  1）
 Prelude> unCombine（f<> g）$ 0 
 Sum {getSum = 0} 
 Prelude> unCombine（f< g）$ 1 
 Sum {getSum = 2} 
 Prelude> unCombine（f<> f）$ 1 
 Sum {getSum = 4} 
 Prelude> unCombine（g<> f）$ 1 
 Sum {getSum = 2} 
  

因此，我首先开始了一个错误的解决方案类型检查：

 实例Semigroup（Combine ab）where 
组合f<>合并g =合并f 
  

这当然没有预期的结果，但希望在右侧迈出一步方向。我的想法如下所示，使用伪码：

pre code实例Semigroup（Combine ab）其中
（Combine f ）<> （Combine g）= Combine（SOMETHING）

SOMETHING 为： f 和 g 附加，无论具体的附加操作是什么（它取决于 f 和 g ）;所以我认为这需要来自 Data.Monoid 的<> ，但我已经有在我的代码中导入Data.Semigroup ，因此从 Data.Monoid <> >与 Data.Semigroup 中的一致。所以我应该怎么做？

我试图找出如何说明Combine（f Monoid's< g），但不能找出。

本书还指出，除非我使用GHC 8.x，否则我必须导入 Semigroup 和我可能会从 Monoid 中隐藏<> ;但我正在努力寻找如何产生这种效果。

有什么想法？

解决方案

他们想要的可能是功能的增加。为此，输入 b 需要是一个半群：

  import Data .Semigroup 
 
 newtype Combine ab = 
 Combine {unCombine ::（a  - > b）} 
 
实例Semigroup b =>半群（Combine a b）其中
（Combine f）<> （Combine g）= Combine（\ x  - > f x> g x）
  

I'm trying to do one of the Semigroup exercises in Haskell Book (Chapter 15, "Monoid, Semigroup") but I'm stuck. The following is given:

newtype Combine a b =
  Combine { unCombine :: (a -> b) }

and I'm supposed to write the Semigroup instance for Combine.

And then book says that it must behave like the following:

 Prelude> let f = Combine $ \n -> Sum (n + 1)
 Prelude> let g = Combine $ \n -> Sum (n - 1)
 Prelude> unCombine (f <> g) $ 0
 Sum {getSum = 0}
 Prelude> unCombine (f <> g) $ 1
 Sum {getSum = 2}
 Prelude> unCombine (f <> f) $ 1
 Sum {getSum = 4}
 Prelude> unCombine (g <> f) $ 1
 Sum {getSum = 2}

So I first started with a wrong solution that type checks:

instance Semigroup (Combine a b) where
  Combine f <> Combine g = Combine f

That does not what is expected of course, but hopefully a step in the right direction. And my thinking is something like the following, in pseudocode:

 instance Semigroup (Combine a b) where
   (Combine f) <> (Combine g) = Combine (SOMETHING)

That SOMETHING being: f and g appended, whatever that concrete append operation is (it depends on f and g); so I think this requires <> from Data.Monoid, but I already have import Data.Semigroup in my code, and therefore <> from Data.Monoid coincides with the one from Data.Semigroup. So what am I supposed to do?

I tried to find out how I can state something like "Combine (f Monoid's <> g)", but couldn't find out.

The book also states unless I'm using GHC 8.x, I'll have to import Semigroup and that I might have "shadow" the <> from Monoid; but I'm struggling to find out how to have this effect.

Any ideas?

解决方案

What they want is probably the addition of functions. For that, type b needs to be a Semigroup :

import Data.Semigroup

newtype Combine a b =
  Combine { unCombine :: (a -> b) }

instance Semigroup b => Semigroup (Combine a b) where
  (Combine f) <> (Combine g) = Combine (\x -> f x <> g x)

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