Monad连接功能 [英] Monad join function

问题描述

虽然单子在Haskell中使用绑定和返回函数表示，但它们也可以使用连接函数进行另一种表示，例如在这里讨论。我知道这个函数的类型是M（M（X）） - > M（X），但是这实际上是做什么的？

解决方案 join 就是真正发生所有魔术的地方 - （>>> =）

所有 Functor 基于的类型类使用某种类型描述额外的结构。有了 Functor 这个额外的结构通常被认为是一个容器，而 Monad 它往往被认为是作为副作用，但这些只是（偶尔具有误导性）短手 - 两种方式都是一样的，并且没有什么特别的 ^[0] 。

Monad 与其他 Functor s的区别在于它可以将控制流嵌入到额外的结构中。可以这样做的原因是，与在整个结构中应用单个扁平函数的 fmap 不同，（>> =） code>检查单个元素并从中创建新的结构。



使用一个简单的 Functor ，从每一个原始结构构建新的结构将会嵌套 Functor ，每个图层代表一个控制流点。这显然限制了效用，因为结果是混乱的，并且具有反映所使用的流量控制结构的类型。单边副作用是具有几个其他属性 [1] ：

• 两种副作用可以组合为一种（例如，do X和do Y变成do X，then Y），只要保持效果的顺序，分组的顺序就无关紧要了。


• 无所作为副作用存在（例如，do x和do nothing分组与do x分组相同）

加入函数不过是该分组操作：嵌套monad类型，如 m（ma）描述了两种副作用和它们发生的顺序， join 将它们组合在一起形成一个副作用。

因此，就一元副作用而言，绑定操作是一种与相关边效应相关的价值的简写ects和引入新副作用的函数，然后将该函数应用于该值，同时为每个副作用组合。 strong>除 IO 外。 IO 非常特殊。

[1]：如果您将这些属性与 Monoid 实例的规则进行比较，您会发现两者之间有很多相似之处 - 这不是巧合，而是事实只是一名内控官员中的幺半群，有什么问题？线是指。

While monads are represented in Haskell using the bind and return functions, they can also have another representation using the join function, such as discussed here. I know the type of this function is M(M(X))->M(X), but what does this actually do?

解决方案

Actually, in a way, join is where all the magic really happens--(>>=) is used mostly for convenience.

All Functor-based type classes describe additional structure using some type. With Functor this extra structure is often thought of as a "container", while with Monad it tends to be thought of as "side effects", but those are just (occasionally misleading) shorthands--it's the same thing either way and not really anything special^[0].

The distinctive feature of Monad compared to other Functors is that it can embed control flow into the extra structure. The reason it can do this is that, unlike fmap which applies a single flat function over the entire structure, (>>=) inspects individual elements and builds new structure from that.

With a plain Functor, building new structure from each piece of the original structure would instead nest the Functor, with each layer representing a point of control flow. This obviously limits the utility, as the result is messy and has a type that reflects the structure of flow control used.

Monadic "side effects" are structures that have a few additional properties^[1]:

• Two side effects can be grouped into one (e.g., "do X" and "do Y" become "do X, then Y"), and the order of grouping doesn't matter so long as the order of the effects is maintained.
• A "do nothing" side effect exists (e.g., "do X" and "do nothing" grouped is the same as just "do X")

The join function is nothing more than that grouping operation: A nested monad type like m (m a) describes two side effects and the order they occur in, and join groups them together into a single side effect.

So, as far as monadic side effects are concerned, the bind operation is a shorthand for "take a value with associated side effects and a function that introduces new side effects, then apply the function to the value while combining the side effects for each".

[0]: Except IO. IO is very special.

[1]: If you compare these properties to the rules for an instance of Monoid you'll see close parallels between the two--this is not a coincidence, and is in fact what that "just a monoid in the category of endofunctors, what's the problem?" line is referring to.

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