如何使用 (->) Monad 实例和关于 (->) 的混淆 [英] How to use (->) instances of Monad and confusion about (->)

问题描述

在不同的问题中，我在关于使用 (->) 实例的 Monads 实例的评论中找到了提示，例如用于实现无点样式.

At different questions I've found hints in comments concerning using the (->) instance of Monads e.g. for realizing point-free style.

对我来说，这有点太抽象了.好的，我在 (->) 上看到了 Arrow 实例，在我看来，(->) 可以用在实例符号中，但不能用在类型中声明(这本身就是另一个问题的内容).

As for me, this is a little too abstract. Ok, I've seen Arrow instances on (->) and it seems to me, that (->) can be used in instance notations but not in type declarations (that would alone be stuff for another question).

有没有使用 (->) 作为 Monad 实例的例子?或者好的链接?

Has anyone examples using (->) as instance of Monad? Or a good link?

抱歉，如果这里可能已经讨论过这个问题，但是搜索 "(->) Monad instance" 会给您带来很多您可以想象的点击次数... 因为几乎所有关于 Haskell 的问题都涉及 (->) 或Monad".

Sorry if this question may already have been discussed here, but searching for "(->) Monad instance" gives you many many hits as you can imagine ... since nearly every question about Haskell somewhere involves (->) or "Monad".

推荐答案

对于给定类型 r，r 类型的函数 ->a 可以被认为是使用类型为 r 的环境传递 a 的计算.给定两个函数 r ->a 和 a ->(r -> b)，很容易想象在给定环境(再次，r 类型)时可以组合这些.

For a given type r, the function of type r -> a can be thought of as a computation delivering an a using an environment typed r. Given two functions r -> a and a -> (r -> b), it's easy to imagine that one can compose these when given an environment (again, of type r).

等等！这正是 monad 的意义所在！

But wait! That's exactly what monads are about!

所以我们可以为 (->) r 创建一个 Monad 实例，它通过传递 r 到 f 和 g.这就是 (->) r 的 Monad 实例所做的.

So we can create an instance of Monad for (->) r that implements f >>= g by passing the r to both f and g. This is what the Monad instance for (->) r does.

要实际访问环境，可以使用 id :: r ->r，您现在可以将其视为在环境 r 中运行并提供 r 的计算.要创建本地子环境，您可以使用以下内容:

To actually access the environment, you can use id :: r -> r, which you can now think of as a computation running in an environment r and delivering an r. To create local sub-environments, you can use the following:

inLocalEnvironment :: (r -> r) -> (r -> a) -> (r -> a)
inLocalEnvironment xform f = env -> f (xform env)

这种将环境传递给计算然后可以在本地查询和修改它的模式不仅对 (->) r monad 有用，这就是为什么它被抽象为MonadReader 类，使用比我在这里使用的更合理的名称:

This pattern of having an environment passed to computations that can then query it and modify it locally is useful for not just the (->) r monad, which is why it is abstracted into the MonadReader class, using much more sensible names than what I've used here:

http://hackage.haskell.org/packages/archive/mtl/2.0.1.0/doc/html/Control-Monad-Reader-Class.html

基本上，它有两个实例:我们在这里看到的 (->) r 和 ReaderT rm，它只是一个 newtype 包裹 r ->m a，所以它与我在这里描述的 (->) r monad 相同，除了它在其他一些转换后的 monad 中提供计算.

Basically, it has two instances: (->) r that we've seen here, and ReaderT r m, which is just a newtype wrapper around r -> m a, so it's the same thing as the (->) r monad I've described here, except it delivers computations in some other, transformed monad.

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