是否有可能实现`（Applicative m）=>应用（StateT s m）`？ [英] Is it possible to implement `(Applicative m) => Applicative (StateT s m)`?

问题描述

我目前正在研究 Data.Fresh 和 Control.Monad.Trans.Fresh ，其中，定义一个生成新变量的接口，以及一个实现这个接口的monad变换器。

我最初认为可以实现 Applicative 实例为我的 FreshT vm ，唯一要求 Applicative m 存在。但是，我被卡住了，好像我需要 Monad m 。不信任我的Haskell-fu，然后转向变形金刚包，并且对我在 Control.Monad.Trans.State.Lazy 和<$ c $中找到的内容感到惊讶c> .Strict ：

  instance（Functor m，Monad m）=>应用（StateT sm）其中
 pure =返回
（*）= ap 
  

所以，这里是我的问题：是否有可能用下面的实例头创建一个具有等价语义的实例？

 实例（应用m）=> Applicative（StateT sm）where 
  

解决方案

考虑到你有两个功能：

  f :: s  - > m（s，a  - > b）
 g :: s  - > m（s，a）
  

您要创建一个函数 h = StateT f * StateF g

  h :: s  - > m（s，b）
  

从上面可以看出 s 你可以传递给 f ，所以你有：



  f':: m（s，a  - > b）
g :: s  - > m（s，a）
  

然而，要获得 s out of f'你需要Monad（无论你使用application，它仍然是 ms g ）。

你可以使用定义并使用免费monad ，但对于状态崩溃，您需要加入。

I'm currently working on Data.Fresh and Control.Monad.Trans.Fresh, which resp. define an interface for generating fresh variables, and a monad transformer which implements this interface.

I initially thought it would be possible to implement the Applicative instance for my FreshT v m with the only requirement that Applicative m exists. However, I got stuck and it seemed like I need to require Monad m. Not trusting my Haskell-fu, I then turned to the transformers package, and was surprised by what I found in Control.Monad.Trans.State.Lazy and .Strict:

instance (Functor m, Monad m) => Applicative (StateT s m) where
    pure = return
    (<*>) = ap

So here is my question: is it possible to create an instance with equivalent semantics with the following instance head?

instance (Applicative m) => Applicative (StateT s m) where

解决方案

Consider that you have two functions:

 f :: s -> m (s, a -> b)
 g :: s -> m (s, a)

And you want to create a function h = StateT f <*> StateF g

 h :: s -> m (s, b)

From the above you have an s you can pass to f so you have:

 f' :: m (s, a -> b)
 g :: s -> m (s, a)

However to get s out of f' you need the Monad (whatever you'd do with applicative it would still be in form of m s so you would not be able to apply the value to g).

You can play with the definitions and use free monad but for the collapse of state you need join.

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