数字参数化矢量的Monad实例？ [英] Monad instance of a number-parameterised vector?

问题描述

Haskell中的静态大小载体显示在Oleg Kiselyov的数字参数化类型 a>，也可以在 Data.Param.FSVec 类型中找到-0.1.5rel =nofollow> parameterized-data module on Hackage：

  data Nat s = > FSVec sa 
  

FSVec 不是 Monad 类型类。

列表的monad实例可用于删除或重复元素：

  Prelude> [1,2,3]>> = \ i  - >情况1为1  - > [1,1]; 2  - > []; _  - > [i] 
 [1,1,3] 
  

是否与列表版本相似或不是，是否有可能从一个固定长度的向量构造monad？

解决方案

是的，如果不是自然的话，这是可能的。 / p>

单子必须对角化结果​​才能满足单子定律。

也就是说，你可以看一个向量作为 [0..n-1] - >的列表函数。 a ，然后修改monad实例的函数。

结果加入操作一个向量矢量形式的矩形矩阵，并返回其对角线。

给定

  tabulate :: Pos n => （全部m（m，m：<：n）=> m  - > a） - > FSVec na 
  

然后

  instance Pos n => Monad（FSVec n）其中
 return = copy（toNum undefined）
v>> = f = tabulate（\i-> f（v！i）！i）
  

可悲的是对此monad的使用有所限制。

我的流套件和Jeremy套件中的主题有六种版本Gibbons在这篇monad上写了一篇博客文章。

等效地，您可以将 FSVec n 视为 bindRep 和的定义来表示函数， pureRep 在我的可表示函子 pa ckage自动获得定义。

Statically sized vectors in Haskell are shown in Oleg Kiselyov's Number-parameterized types and can also be found in the Data.Param.FSVec type from the parameterized-data module on Hackage:

data Nat s => FSVec s a

FSVec is not an instance of the Monad type class.

The monad instance for lists, can be used to remove or duplicate elements:

Prelude> [1,2,3] >>= \i -> case i of 1 -> [1,1]; 2 -> []; _ -> [i]
[1,1,3]

Whether similar to the list version or not, is it possible to construct a monad from a fixed length vector?

解决方案

Yes it is possible, if not natural.

The monad has to 'diagonalize' the result in order to satisfy the monad laws.

That is to say, you can look at a vector as a tabulated function from [0..n-1] -> a and then adapt the monad instance for functions.

The resulting join operation takes a square matrix in the form of a vector of vectors and returns its diagonal.

Given

tabulate :: Pos n => (forall m. (Nat m, m :<: n) => m -> a) -> FSVec n a

then

instance Pos n => Monad (FSVec n) where
     return = copy (toNum undefined)
     v >>= f = tabulate (\i -> f (v ! i) ! i)

Sadly uses of this monad are somewhat limited.

I have a half-dozen variations on the theme in my streams package and Jeremy Gibbons wrote a blog post on this monad.

Equivalently, you can view a FSVec n as a representable functor with its representation being natural numbers bounded by n, then use the definitions of bindRep and pureRep in my representable-functors package to get the definition automatically.

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