There are several advantages to writing code at that level of abstraction.
It's a great way to encourage code reuse, even in fairly disparate domains. Haskell has some of the most versatile libraries of any language I've used by using mathematical abstractions like this. As a concrete example, there are functions like foldM which is like a normal fold except it can handle errors, state, nondeterminism or even parsing!
The abstractions are well-understood, which makes it easier to reason about. You get a bunch of theorems and conclusions for free just by formulating your program in mathematical terms. You can then easily take advantage of these to simplify, verify or optimize your code. For example, if you know that your data type forms a valid functor, you can always rewrite fmap a . fmap b as fmap (a . b), turning two passes into one! If you wrote a map-like function separately for each different type, taking advantage of this pattern would be more difficult.
You are also restricted in what you can do--any code that is generic across all categories can only use composition. This leaves you less room to make mistakes. If you write a function just for strings, you can accidentally add characters or always return an empty string or any number of string-specific behaviors. If you write a function against some abstraction like a functor, you cannot make any of those mistakes--there is simply no way to formulate them for all functors.
These abstractions are just a reification of a common pattern across a bunch of domains. Making the pattern explicit makes it easier to see and use and makes your code simpler.
This sounds promising, but it's far too abstract to be convincing. Can you give a example of a useful program where you need to do any of these things?
Thanks, but that's far too much to take in at once. How about just one simple example?
I did skim through them, so to be specific: hakyll, Pandoc, warp, and scotty are what I'd call practical programs, though they approximate more popular programs written in other languages, so there's the question of why someone who wasn't already a Haskell programmer should choose them. Pipes, conduits, and most of the stuff by Kmett appear to be libraries implementing other abstractions that themselves would have be justified by use in a practical program.
> Pipes, conduits, and most of the stuff by Kmett appear to be libraries implementing other abstractions that themselves would have be justified by use in a practical program.
I'm not sure I understand what you mean by "practical programming".
This may just be a cultural difference but one of the big ideas of Haskell is using a library whose "core calculus" is provably correct and then combining them in ways that preserve that correctness. So I would argue that the justification of the libraries is not in the practical ( if I understand your usage of the word?) usage but in the thoroughness and compositional semantics that they provide. That's where the category theory inspired patterns ( zippers, monads, arrows, etc ) become important.
Okay, let's define "practical programming" as creating programs that will be of use to someone who doesn't know the programming language that the program was written in. So in this case, this means writing Haskell programs that will be used by people who don't know Haskell.
This isn't the only reason to write a program of course. You can do it just for fun or to explore the mathematics. But I'm mostly interested in abstractions that might be useful for solving problems outside mathematics.
None of the libraries or patterns I mentioned above are designed for the purpose of exploring category theory. Though some people do do that, but they tend to live in their own world.
A lot of Haskellers just happen to exploit bits of CT it because its a great framework for writing and reasoning about code. Some people do use Haskell as a way to explore category theory but for example Tekmo isn't writing pipes as a means to explore the theory of free monads, they've been well studied since the 80s. I believe he just happens to find that they are an excellent way of chaining together bits of control flow.
At that heart of the problem he's tackling is very practical problem that's tied to data flow and resource management. For example, I've written a library against pipes which handles resource management of ZeroMQ sockets for a large distributed system and find that my code under pipes is much more manageable.
Okay, sure, resource management is what I'd call a practical problem, and pipelines are familiar from Unix (and Go). It looks like this pipe library has a nice practical example: enforcing the category laws means that it handles terminating pipelines consistently:
It's a great way to encourage code reuse, even in fairly disparate domains. Haskell has some of the most versatile libraries of any language I've used by using mathematical abstractions like this. As a concrete example, there are functions like foldM which is like a normal fold except it can handle errors, state, nondeterminism or even parsing!
The abstractions are well-understood, which makes it easier to reason about. You get a bunch of theorems and conclusions for free just by formulating your program in mathematical terms. You can then easily take advantage of these to simplify, verify or optimize your code. For example, if you know that your data type forms a valid functor, you can always rewrite fmap a . fmap b as fmap (a . b), turning two passes into one! If you wrote a map-like function separately for each different type, taking advantage of this pattern would be more difficult.
You are also restricted in what you can do--any code that is generic across all categories can only use composition. This leaves you less room to make mistakes. If you write a function just for strings, you can accidentally add characters or always return an empty string or any number of string-specific behaviors. If you write a function against some abstraction like a functor, you cannot make any of those mistakes--there is simply no way to formulate them for all functors.
These abstractions are just a reification of a common pattern across a bunch of domains. Making the pattern explicit makes it easier to see and use and makes your code simpler.