什么是商店comonad？ [英] What is the Store comonad?

问题描述

对 Haskell中的Comonad类型类型有一些想法 ，我听说过Store的comonad。但看看 Control.Comonad.Store.Lazy ，我真的不明白。这是什么意思？它是为了什么？我听说Store = CoState是State Monad的双重身份。这意味着什么？

解决方案

如果您看一下 StoreT本身。

您可以将其视为更大结构中的地点。例如，镜头只是 a - >存储b a ;您将获得 b 字段的值，并且函数 b - >一个把一个新值放回到更大的上下文中。

考虑到它的简化，非变换形式：

data Store sa = Store（s - > a）s

实例Functor Store s）其中
fmap f（Store gs）= Store（f。g）s

实例Extend（Store s）其中
重复（Store fs）= Store（Store f）s

实例Comonad（商店）其中
提取（商店fs）= fs


即重复更改 s - > a 转换为 s - >在替换值后存储sa ，它只返回更新的地方， extract 通过放置恢复原始的 a 价值回到更大的结构。

就它与国家的关系而言，你可以这样看待它：

  type State sa = s  - > （a，s）
类型商店s a =（s  - > a，s）
  

Having some idea of what the Comonad typeclass is in Haskell, I've heard about the Store comonad. But looking at Control.Comonad.Store.Lazy, I don't really get it. What does it mean? What is it for? I've heard that Store = CoState, the dual of the State Monad. What does that mean?

解决方案

It's much easier if you look at the definition of StoreT itself.

You can think of it as a "place" in a larger structure. For instance, a lens is just a -> Store b a; you get the value of the b field, and a function b -> a to put a new value back into the larger context.

Considering it in its simplified, non-transformer form:

data Store s a = Store (s -> a) s

instance Functor (Store s) where
  fmap f (Store g s) = Store (f . g) s

instance Extend (Store s) where
  duplicate (Store f s) = Store (Store f) s

instance Comonad (Store s) where
  extract (Store f s) = f s

i.e. duplicate changes the s -> a into an s -> Store s a that just returns the "updated" place after replacing the value, and extract restores the original a by placing the value back into the larger structure.

As far as its relation to State goes, you could look at it like this:

type State s a = s -> (a, s)
type Store s a = (s -> a, s)

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