可能吗？：行为t [行为t a] - >行为t [a] [英] Is it possible?: Behavior t [Behavior t a] -> Behavior t [a]

问题描述

有没有一种方法可以让行为t [a] ，其中t时刻[a]的值是包含在行为t [行为ta] 在时间t？ I.e，一个类型为的函数：

 行为t [行为t a]  - >行为t [a] 
  

如果这是不可能的，那是因为逻辑上的不可能性或限制在反应香蕉？

解决方案

该类型是平凡居住的任何应用程序：
$ b

 { - ＃LANGUAGE RankNTypes＃ - } 
 import Control.Applicative 
 import Control.Monad 
导入Data.Functor.Identity 
将限定的Data.Traversable导入为T 
 
 f'::（Applicative f）=> f [f a]  - > f [a] 
 f'= const $ pure [] 
  

这显然不是什么你打算。因此，让我们问一下：

 （Traversable t）=>行为u（t（行为u a）） - >行为u（ta）
  

或更普遍的适用于我们可以构建的应用程序

 （T.Traversable t）=> f（t（f a）） - > f（ta）
  

任何 f


  f ::（Monad m，T.Traversable t）=> m（t（m a）） - > m（t a）
 f =联接。 liftM T.sequence 
  

一个明显的问题出现了：如果应用程序有这样一个 f ，是否必须是monad？答案是是。我们只需将 f 应用于 Identity traversable（一元素集合 - Traversable 实例身份）和构造加入作为

  g ::（Applicative m）=> （t.Traversable t）=> m（t（m a）） - > m（t a））
  - > （m（m a） - > m a）
 g f = fmap runIdentity。 F 。 fmap Identity 
  

所以我们的函数正好适用于那些也是monad的应用程序。

结束语：您正在寻找的函数存在当且仅当 Behavior 是 Monad 。因为它不是，所以很可能没有这样的功能。 （我相信如果有办法让它成为monad，它会包含在库中）。


Is there a way to have a Behavior t [a] where the values of [a] at time t are the values contained in a Behavior t [Behavior t a] at time t? I.e, a function with the type of:

Behavior t [Behavior t a] -> Behavior t [a]

If this is not possible, is that because of a logical impossibility or a limitation in reactive-banana?

解决方案

The type is trivially inhabited for any Applicative:

{-# LANGUAGE RankNTypes #-}
import Control.Applicative
import Control.Monad
import Data.Functor.Identity
import qualified Data.Traversable as T

f' :: (Applicative f) => f [f a] -> f [a]
f' = const $ pure []

which is clearly not what you intended. So let's ask for inhabitation of

(Traversable t) => Behavior u (t (Behavior u a)) -> Behavior u (t a)

or more generally for which applicatives we can construct

(T.Traversable t) => f (t (f a)) -> f (t a)

This is inhabited for any f that is also a monad:

f :: (Monad m, T.Traversable t) => m (t (m a)) -> m (t a)
f = join . liftM T.sequence

An obvious question arises: If an applicative has such an f, does it have to be a monad? The answer is yes. We just apply f to the Identity traversable (one-element collection - the Traversable instance of Identity) and construct join as

g :: (Applicative m) => (forall t . (T.Traversable t) => m (t (m a)) -> m (t a))
                     -> (m (m a) -> m a)
g f = fmap runIdentity . f . fmap Identity

So our function is inhabited precisely for those applicatives that are also monads.

To conclude: The function you're seeking would exist if and only if Behavior were a Monad. And because it is not, most likely there is no such function. (I believe that if there were a way how to make it a monad, it'd be included in the library.)

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