[fractalsea]

Author here. Thanks for the feedback!

I agree that the do notation does look nice. The on thing that I like about the >> operator is that it's clear that you are performing a combining two functions. But to be honest I don't feel strongly either way.

I definitely agree with your point on monads. I tried to keep this post more accessible, but I hope to go into a more technical post in the future on how we used monad transformers when writing these tests. We ended up using WriterT, ReaderT, LoggingT, EitherT for the "test components". Unfortunately the websocket library we used did not play well with this (it is callback based).

And I also agree with your final points. Having said that, I had very low expectations in this area going in, and it actually turned out to be not nearly as bad as I expected.

[tel]

At the risk of being a little pedantic, >> isn't combining two functions, e.g.

    Just () >> Nothing     ==     Nothing
    Nothing >> Just ()     ==     Nothing

It's perhaps viable to think of (m >> f) as modifying/continuing the m effect/computation using a continuation which is constantly the f effect. But that's about as close to "combining two functions" I can get it without specifically picking a monad that is a function.

On the other hand, >=> is absolutely combining two functions. It's exactly (flip (.)) in a Kleisli category over some monad.

[fractalsea]

By "combining" I just meant an operator that takes multiple functions and returns a new function based on those arguments. I guess these "functions" are a special case because they are constant monadic functions. Do you mean to say composition rather than combination when you are about >=>?

[tel]

Yeah, I'm happy to abide by this all when the caveats are specialized, but >=> is definitely and directly what's being appealed to.

I meant combination just so as to generalize the idea of "composition". If you're willing to call Kleisli composition "composition" generally then I won't complain :)

[innguest]

Yes, but let's be careful not to confuse beginners that thought they were on the path to understanding and then you come and say "it's not combining two functions".

Well, it is combining two morphisms - that you can't deny. And most people use the shorthand word "function" to mean "any morphism" including type constructors.

You may be technically correct but it is not incorrect for people trying to make sense of all these transformations, to say that >> combines two functions. These functions are picked up by the monadic context and executed in sequence.

[tel]

>> certainly never combines two functions! The closest you can come is to specialize the monad in context to ((->) e) and then talk about that kind of combination. The other way to go is to see >> as a special case of >=> wherein constant Kleisli functions are applied. I've got no problem with that now... Except now you're really talking about >=> and you may as well be specific?

[dllthomas]

"The closest you can come is to specialize the monad in context to ((->) e) and then talk about that kind of combination."

I think >> also feels a lot like composing functions when we've specialized the monad to State.

[tel]

Oh, that's an even better example!

[innguest]

You missed my point. Haskell beginners do not know we use the word "morphism" for the most generic "take an input, give an output" thing (the most generic map). That's why they call it "function".

It's not wrong, just not specific enough. Does (>>) not combine two maps?

[tel]

It... doesn't.

We appear to be talking past one another. How do you interpret

    (>>) :: Monad m => m a -> m b -> m b

as combining two maps of any kind without either (a) specializing `m` to a function type or (b) considering it syntax sugar for

    a >> b ===> (const a >=> const b) ()

[innguest]

> It... doesn't.

It does! :)

> How do you interpret (>>) :: Monad m => m a -> m b -> m b as combining two maps of any kind

The answer is in your question. Is -> not an arrow? Isn't there one of those arrows pointing into and out of every m x in the signature above? (for the first and last m x, there could be arrows pointing in and out, respectively). That means they are maps.

A morphism is any value that has arrows pointing to it (from other values) and out of it (to other values). Read my answer above as well.

I am not debating your arguments. I know you know what you are talking about and you are right in what you're saying otherwise. What I am saying is in Haskell everything except Bottom is a categorical morphism, and you seem to be ignoring this concept, which is helpful for those who are trying to make sense of all this.

[dllthomas]

I'm sure there's ways we can force it, but I don't think it's terribly natural to consider "Just x" or "Nothing" to be "tak[ing] an input, giv[ing] an output". "Just", certainly, but not once you've applied it.

[innguest]

I'm not forcing any definition here.

Just 5 is a map, and Nothing is a map. Let's watch:

Just 5 >> Nothing

Just is a map that accepts an input and returns that input decorated with a certain structure.

  Just ---(5)---> (Just 5)

Which means there's an arrow that shoots out of (Just), itself a map - because it has arrows coming in and going out - which we can use to arrive at (Just 5).

Then (>>) combines the Just 5 map - a map that takes a function, like (>>) in this case, and returns another function that accepts another Maybe and returns another Maybe.

Let's draw that:

  (Just 5) ---(>>)---> (\x -> (Just 5) >> x)

Which means there's an arrow that shoots out of (Just 5), itself a map, to which in this example we go to its index (>>) and retrieve the resulting value, another map: (\x -> (Just 5) >> x)

Now we give the map above, the input Nothing, and it returns the value Nothing, itself a map, because it has arrows coming in and shooting out as can be seen below:

  (\x -> (Just 5) >> x) ---(Nothing)---.====(>>)====>> (\x -> Nothing >> x)
                              ^        |
                              |________|

The ====> arrow above I've added to show other possible arrows you might want to take from Nothing onwards.

In other words, to say that a value in Haskell is not a map is to say it can't be arrived at, nor escaped from. If I understand correctly, the only value that can't be escaped from is Bottom, which has 0 arrows pointing out of it. Therefore it is not a map. But Just, Just 5 and Nothing are all maps, as they all have arrows pointing to them (which means we can arrive at them) and arrows pointing out of them (which means we can escape from them). Something that has arrows coming in and going out, we call a morphism.

[chowells]

Callbacks are more or less handled by the continuation monad transformer, `ContT`, if you want to use it.

[fractalsea]

Interesting. I think I will have to play around this before I get my head around it, but thanks for the suggestion.

[kungfooguru]

Do you plan to release any of this code? I'd love to see how the internals look for that.

[fractalsea]

We currently do not have plans to release this code, mainly because it is very specific to our system. Having said that we are working on another large Haskell project, and we do have plans to open source a central component of it.