It's a bit simpler in implementation; the relevant data structures are defined a bit differently, so it could give a nice alternate perspective about what a blockchain written in Haskell may look like.
I like the idea behind this article, but this isn't the way to do it. It hides the simplicity of the blockchain concept behind arcane syntax and overly complicated higher-order typing constructs.
newtype BlockF a = Block (V.Vector a) deriving (Eq, Show, Foldable, Traversable, Functor, Monoid)
type Block = BlockF Transaction
type Blockchain = Cofree MerkleF Block
Does anyone really think this is how one should write software? I think that constructions like Cofree are interesting, but I don't think they're programming.
I agree and disagree. There is nothing about the usage of Cofree and other similar concepts which is "not programming". I think it's a completely viable way to write software within a particular scope (e.g. depending on the team that will work with the internals of the code, and whether the users of the library are to be required to understand the concept). If it provides the correct abstraction and can lead to more performant, maintainable and/or readable code (which is of course subjective), then by all means.
That said, I agree that the article doesn't spend a great deal of time explaining the concepts, whether blockchain itself or the category theory it's using, leading to a sense (for me) of being overly terse and coming across as a bit pompous. Although, I realize that for a certain audience there's nothing pompous about this at all and it might seem perfectly reasonable.
"A Comonad v is a cofree Comonad for f if every comonad homomorphism from another comonad w to v is equivalent to a natural transformation from w to f.
A cofree functor is right adjoint to a forgetful functor.
Cofree is a functor from the category of functors to the category of comonads that is right adjoint to the forgetful functor from the category of comonads to the category of functors that forgets how to extract and duplicate, leaving you with only a Functor."
So I take it you believe that a degree in category theory is the bare minimum for people to expect to be able to understand other people's code? The layman interpretation of "Avoid success at all costs" comes to mind.
Although I don't disagree regarding the difficulty of understanding Cofree, at least the blog post explains what it's doing in this context. That alone was enough for me to understand that beginning snippet, convince me that there was at least some utility in the use of Cofree here, and remember this as an example of where it can be useful.
The parent^2 comment also snipped an example explained in the blog post, where he specifically chose that structure so that he could make use of built-in structures to traverse the tree. Similar to the use of Cofree (though I understand the Traversable monad far more), the reasoning was presented, it made sense, and I could move on from that without scratching my head.
You don't need to understand category theory to understand Cofree. It's not a very complicated construction. The Haskell ecosystem's provision of stuff like Free, Cofree, Fix, etc. covers a huge number of common constructions and saves you a lot of effort.
A common example of a "kind of hard problem" I see all the time on various tech sites (e.g. here) is flattening a rose tree (arbitrary depth nested array). Guess what? In Haskell, you can express the whole structure as "Free []". Hundreds of useful primitives are already written for you, including the thing you need to flatten the tree, "toList". This just goes to show that it's not a pointless masturbatory excercise in dragging math into software engineering; it's actually directly and immediately very useful.
I think this is more a failure of documentation than anything else. The definition provided there is correct and useful for a certain subset of people, but there are ways of grokking comonads and cofree comonads that don't require so much math.
It's a tricky concept no matter how you slice it (in my opinion), but I like the following article:
I belive that abstraction can be a double edged sword.
Pro. you write less code
Pro. Your code is easier to read for everyone familiar with the abstraction.
Con. You need a math degree.
Con. Harder to get contributors.
etc...
Tangentially. The docs also say that:
"In practice, cofree comonads are quite useful for annotating syntax trees, or talking about streams."
Sometimes you can learn the abstraction and one of its particualr use cases. And apply it when you find it, without needing the degree.
Also to answer your question:
"So I take it you believe that a degree in category theory is the bare minimum for people to expect to be able to understand other people's code?"
No, I don't believe so.
But the experiment of forming a team of people that knows all this to see how productive they are, would be nice to see.
This kind of language sounds intimidating if you aren't familiar with it, but it's actually not that complicated. The documentation states the universal property of the cofree comonad for a functor. You don't need a degree in math to understand it - the bits of category theory that most Haskellers use are very basic.
Cofree in general I use all the time, especially in compilers. The Generic and Binary Cofree instances were lifted straight out of a decompiler I'm supposed to be working on. The most common reason is to get Traversable and Plated instances:
For the blockchain stuff specifically, I suppose I didn't really use them too heavily in this article. So you could argue they aren't currently doing a whole lot of good.
I'm not actually certain if people prefer seeing the heavier types that I default to in real code(to avoid refactoring later), vs. types that are as simple as needed but might need to change as the program evolves. The first choice lets people who already know Haskell learn something from it, while the second makes beginners less confused.
Actually, I realized I follow the "abstract recursion out of your structures" intuition but don't really realize why you chose Cofree instead of some of the other options:
import Control.Monad.Free
import Control.Comonad.Cofree
import Data.Functor.Foldable
data A f
= ANil
| ACons f
type AList a = Cofree A a
a :: AList Int
a = 1 :< ACons (2 :< ACons (3 :< ANil))
data B a f
= B a f
type BList a = Free (B a) ()
b :: BList Int
b = Free (B 1 (Free (B 2 (Free (B 3 (Pure ()))))))
data C a f
= CCons a f
| CNil
type CList a = Fix (C a)
c :: CList Int
c = Fix (CCons 1 (Fix (CCons 2 (Fix (CCons 3 (Fix CNil))))))
You wanted to ensure it's non-empty? Something about the actual Comonad (extend, etc) interface?
I think the opposite could be said. That the C++ implementation hides the simplicity of the blockchain in a language that lacks powerful abstractions and prevents code reuse.
If cofree seems like it isn't programming, that is only because this style of code helps avoid the need for it.
It's quite a cute idea, implementing a blockchain (a fundamentally impure concept) in Haskell. If you're interested in other cool Haskell projects, check out JoeyH[1].
Impure as in "has side-effects". An append-only state that is used for synchronisation between different machines by definition has side-effects. Of course, you can have side-effects in Haskell, I just thought it was an interesting choice.
Haskell takes a stand against implicit side-effects, letting you see what a function is capable of doing in its type. It's really weird to suggest that performing side-effects in such a language is strange or awkward or cute or whatever. Doing those things is the whole point of writing programs.
It's a bit simpler in implementation; the relevant data structures are defined a bit differently, so it could give a nice alternate perspective about what a blockchain written in Haskell may look like.
Relevant video: https://www.youtube.com/watch?v=LZEHOlZY2To
That said, I agree that the article doesn't spend a great deal of time explaining the concepts, whether blockchain itself or the category theory it's using, leading to a sense (for me) of being overly terse and coming across as a bit pompous. Although, I realize that for a certain audience there's nothing pompous about this at all and it might seem perfectly reasonable.
This is about a blockchain, and is presented using Haskell and over-the-top Haskell pseudo-category-theory.. it just doesn't compute for me.
OTOH, how many elements should the reader's vocabulary have to enable him to read other's people code?
"A Comonad v is a cofree Comonad for f if every comonad homomorphism from another comonad w to v is equivalent to a natural transformation from w to f.
A cofree functor is right adjoint to a forgetful functor.
Cofree is a functor from the category of functors to the category of comonads that is right adjoint to the forgetful functor from the category of comonads to the category of functors that forgets how to extract and duplicate, leaving you with only a Functor."
So I take it you believe that a degree in category theory is the bare minimum for people to expect to be able to understand other people's code? The layman interpretation of "Avoid success at all costs" comes to mind.
The parent^2 comment also snipped an example explained in the blog post, where he specifically chose that structure so that he could make use of built-in structures to traverse the tree. Similar to the use of Cofree (though I understand the Traversable monad far more), the reasoning was presented, it made sense, and I could move on from that without scratching my head.
A common example of a "kind of hard problem" I see all the time on various tech sites (e.g. here) is flattening a rose tree (arbitrary depth nested array). Guess what? In Haskell, you can express the whole structure as "Free []". Hundreds of useful primitives are already written for you, including the thing you need to flatten the tree, "toList". This just goes to show that it's not a pointless masturbatory excercise in dragging math into software engineering; it's actually directly and immediately very useful.
It's a tricky concept no matter how you slice it (in my opinion), but I like the following article:
http://dlaing.org/cofun/posts/free_and_cofree.html
I won't claim it's easy reading, but it's a lot more grounded and motivated.
Pro. you write less code Pro. Your code is easier to read for everyone familiar with the abstraction. Con. You need a math degree. Con. Harder to get contributors. etc...
Tangentially. The docs also say that:
"In practice, cofree comonads are quite useful for annotating syntax trees, or talking about streams."
Sometimes you can learn the abstraction and one of its particualr use cases. And apply it when you find it, without needing the degree.
Also to answer your question: "So I take it you believe that a degree in category theory is the bare minimum for people to expect to be able to understand other people's code?"
No, I don't believe so.
But the experiment of forming a team of people that knows all this to see how productive they are, would be nice to see.
https://hackage.haskell.org/package/lens-4.15.4/docs/Control...
For the blockchain stuff specifically, I suppose I didn't really use them too heavily in this article. So you could argue they aren't currently doing a whole lot of good.
I'm not actually certain if people prefer seeing the heavier types that I default to in real code(to avoid refactoring later), vs. types that are as simple as needed but might need to change as the program evolves. The first choice lets people who already know Haskell learn something from it, while the second makes beginners less confused.
If cofree seems like it isn't programming, that is only because this style of code helps avoid the need for it.
[1]: http://joeyh.name/code/