Monad 连接函数 [英] Monad join function

问题描述

虽然 monad 在 Haskell 中使用 bind 和 return 函数表示，但它们也可以使用 join 函数进行另一种表示，例如 在此讨论.我知道这个函数的类型是 M(M(X))->M(X)，但这实际上是做什么的?

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?

推荐答案

实际上，在某种程度上，join 才是真正发生奇迹的地方--(>>=) 主要是为了方便.

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

所有基于 Functor 的类型类使用某种类型描述附加结构.对于 Functor，这个额外的结构通常被认为是一个容器"，而对于 Monad，它往往被认为是副作用"，但这些只是(偶尔误导)速记——无论哪种方式都是一样的，并没有什么特别的^[0].

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].

Monad 与其他 Functor 相比的显着特点是它可以将控制流嵌入到额外的结构中.它可以这样做的原因是，与 fmap 在整个结构上应用单个平面函数不同，(>>=) 检查单个元素并构建 新结构.

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.

使用普通的Functor，从原始结构的每一部分构建新结构将嵌套Functor，每一层代表一个控制流点.这显然限制了实用性，因为结果是混乱的并且具有反映所使用的流控制结构的类型.

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副作用"是具有一些附加属性的结构^[1]:

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

• 两个副作用可以归为一个(例如，做 X"和做 Y"变成做 X，然后 Y")，分组的顺序并不重要，只要效果的顺序维护.
• 存在什么都不做"的副作用(例如，做 X"和什么都不做"分组与仅做 X"相同)

join 函数只不过是分组操作:像 m (ma) 这样的嵌套 monad 类型描述了两个副作用及其出现的顺序，并且 join 将它们组合成一个副作用.

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.

因此，就monadic副作用而言，绑定操作是取一个带有相关副作用的值和一个引入新副作用的函数，然后在组合副作用的同时将该函数应用于该值"的简写每个".

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]:除了IO.IO非常很特别.

[1]:如果将这些属性与 Monoid 实例的规则进行比较，您会发现两者之间非常相似——这不是巧合，实际上是什么只是一个内函子范畴的幺半群，有什么问题?"行是指.

[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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