List is a monad
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List is a monad
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Re: List is a monad
#2IDK if it ads anything to the article, but `map` is a property of Functors, and every Monad is a Functor. Well, every Monad is an Applicative Functor, and every applicative functor is a functor.
All a way of saying that, yep, you always have `map` when you have a Monad, but you don't need a Monad to have `map`.
If you want an example we can compare a regular list and a Ziplist. A regular list's Applicative instance does a cross product, while a Ziplist's applicative instance does a dot product.
(*) [2,3] [5,7, 11]
--> [10,14,22,15,21,33]
getZipList $ fmap show $ (*) ZipList [2,3] ZipList [5,7, 11]
--> ["10","21"]
For quirky reasons in Haskell, `fmap` the function implemented for every Functor instance. This is because `map` was already taken by lists. Weird, I know.
Re: List is a monad
#3U must prove it is a monoid in the category of endofuncors.
Re: List is a monad
#4I expect the author has done this knowingly, but the title is rather painful for a mathematician to read.
A list is not a monad. List is a monad. A list is an algebra for the List monad.
Re: List is a monad
#5As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes".
However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing.
A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separate lesson for every common monad instance. Start with Maybe, then IO, then maybe State and List, and so on... because ultimately, every instance of a Monad works very differently. That's why the pattern is so useful in the first place, because it applies to so many places. (Note: this is a criticism of monad tutorials in general, not this one in particular, which seems to do a decent job on this front).
In my experience, people new to Haskell focus way too much on getting the "a-ha" moment for monads in general, when really you want a bunch of separate "a-ha" moments as you realize how each instance of a monad takes advantage of the pattern differently.
I also tend to think that monads are best demonstrated in Haskell rather than in other languages, if only because the notation is so much less clunky. That may just be me though. (EDIT: well, also because almost no other languages have typeclasses, so you have to approximate it with interfaces/traits/etc)
Also FYI: in part 2, the code examples have extra newlines in between every line, which makes it hard to read (I'm on firefox, if that matters).
Re: List is a monad
#6Nit, in Haskell it's a MonadPlus. Which IIRC is a monad that supports filtering.
Re: List is a monad
#7I expect the author has done this knowingly, but the title is rather painful for a mathematician to read. A list is not a monad. List is a monad. A list is an algebra for the List monad.
I appreciate you mentioning this because I think it’s actually an important point
Re: List is a monad
#8U must prove it is a monoid in the category of endofuncors.
join has the type `m (m a) -> m a`. That's the thing that really shows off the monoidal structure. People normally implement monads in terms of bind, but you can easily define join in terms of bind for any Monad: `join ma = ma >>= id`. So really, as long as you have a lawful instance of Monad written with bind the existence of join is your proof.
Re: List is a monad
#9Let's keep up the mathiness. Look how much economics has benefitted from that.
Re: List is a monad
#10[dead]