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Why I am learning category theory

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Re: Why I am learning category theory

#41

Post by fdupress »

musk_micropenis wrote: post #31
hosh wrote: post #25

Earlier quoted context omitted.

In Ruby and many other languages, you have this idea of a string concatenation: "foo" + "bar" -> "foobar" "foo" + "" -> "foo" That makes it a monoid. Instead of talking about OOP patterns, knowing that the "+" operator is a monoid for string objects lets us write code that is composable. Similarly, with arrays: [:foo,:bar] + [:baz] -> [:foo,:bar,:baz] [:foo,:bar] + [] -> [:foo,:bar] Some language platforms will imple…

Most of us can go our whole careers without the "insight" that string concatenation is a "monoid". I don't know any languages that would balk at "foo" + "" or [a, b].concat([]). This all seems academic beyond belief.

Strings/lists under concatenation do not form a group since concatenation is not uniquely invertible. (In the sense of "there is no list -xs that you can concatenate onto xs to get the empty list.)

Re: Why I am learning category theory

#42

Post by schwurb »

I find CT highly fascinating, worked through parts of 7 Sketches in Composability and have a functional programming background. I see the appeal, but I came to the conclusion that my time is better spent observing, learning about and designing with abstractions like monads, applicatives and so on rather than to learn the theory behind it.

There seems to be a tiny handful of people that can use category theory as a resource to craft something relevant to software (the stereotypical example in my mind being Edward Kmett of Haskell Fame), but I am certainly not one of them, and that is not something that would change with learning more Category Theory (whatever that might mean: Proving some theorems, discovering more categories, ...)

To the author: I am looking forward to a retrospective at a later time. I wish you a good journey, happy diagram-chasing!

Re: Why I am learning category theory

#43

Post by larve »

BenoitP wrote: post #39
larve wrote: post #32

Earlier quoted context omitted.

In category theory, everything has to be defined in terms of objects and morphisms, which can be a bit challenging, but it means that you can apply those concepts to anything that has "an arrow". it's of course just playing with abstractions, and a lot of the intuitive thinking in CT goes back to using the category of sets. For me however seeing the "arrow and composition" formulation unlocks something that allows me…

> unlocks something that allows me to think in a broader fashion I believe this is what's at hand here. What is that something? What is that broad fashion? An example would be welcome

It's always hard to point out when some very abstract knowledge has guided your intuition, but I apply monads very often to compose things that go beyond "purely functional immutable data function composition". for example, composing the scheduling of PLC actions so that error handling / restarts can be abstracted away. The more recent insights of learning how to model things with just morphisms are broadening my concepts of a functor. I used to thing of a functor as some kind of data structure that you can map a function on, but in CT a functor is a morphism between categories that maps objects and morphisms while preserving identity and composition. This means I can start generating designs by thinking "I wonder if there is amorphism between my database schema category and my category of configuration files or whatever. Maybe something useful comes out, maybe not.

Re: Why I am learning category theory

#44

Post by hosh »

BenoitP wrote: post #29
hosh wrote: post #25

Earlier quoted context omitted.

In Ruby and many other languages, you have this idea of a string concatenation: "foo" + "bar" -> "foobar" "foo" + "" -> "foo" That makes it a monoid. Instead of talking about OOP patterns, knowing that the "+" operator is a monoid for string objects lets us write code that is composable. Similarly, with arrays: [:foo,:bar] + [:baz] -> [:foo,:bar,:baz] [:foo,:bar] + [] -> [:foo,:bar] Some language platforms will imple…

I see no more than Groups in your comment. Which are very useful! Also having commutative operations makes for Abelian Groups, which enable operations to be reordered, and makes for implicit parallelism. Where is Category Theory?

> But where is the Category Theory?

I have no idea. I don't think I have really yet to grok the ideas around categories and morphisms. I'm very slow at learning this stuff.

I do know that each of the small number of intuitions I have gained has sharpened how I reason about my code, that once I grokked a single intuition, they seem both simple and profound, and that there are even more that I don't yet understand.

So for example, when you wrote "Also having commutative operations makes for Abelian Groups, which enable operations to be reordered, and makes for implicit parallelism", I never thought about that. Initially, I could almost feel like something coming together. After I let that sink in for a bit, and then it starts opening doors in my mind. And then I realize it's something that I have used before, but never saw it in this way.

I was mainly answering the parent comment about why someone might want to drink the kool-aide as it were. I suppose my answer is, even though I know there are some powerful ideas with CT itself, the intuitions along the way each have many applications in my day-to-day work.

Re: Why I am learning category theory

#45

Post by picardo »

floober wrote: post #24
i_am_toaster wrote: post #21

I would be willing to drink the kool-aid if I saw it being used in a practical way. I always feel these posts are filled with category theory jargon without ever explaining why any of the jargon is relevant or useful. I’ve even watched some applied category theory courses online and have yet to feel I’ve gained anything substantive from them. However, as I started off with, I’m always willing to try something out or…

For me, I use the simple stuff (Semigroup, Monoid, Monads, Functors, ..) the most. Often times I'll be reasoning about a problem I'm working on in Haskell and realize it is a monad and I can reuse all of the existing monadic control structures. It is also helpful the other way, where you start working with someone else's code and seeing that it is a e.g. Monad immediately tells you so much concrete info about the str…

Same here. I drank the cool aid a few years back, and started using fp-ts in my frontend projects, hoping to use algebraic data types regularly. But today all I use is the Monad. I can't find any motivation to write abstract algebra to build UI widgets.

Re: Why I am learning category theory

#47

Post by zasdffaa »

wisnesky wrote: post #26
i_am_toaster wrote: post #21

I would be willing to drink the kool-aid if I saw it being used in a practical way. I always feel these posts are filled with category theory jargon without ever explaining why any of the jargon is relevant or useful. I’ve even watched some applied category theory courses online and have yet to feel I’ve gained anything substantive from them. However, as I started off with, I’m always willing to try something out or…

Category theory does provide new algorithms if you unroll all of its definitions. For example, it reveals that SQL conjunctive queries can be run both "forward" and "backward" - an algorithm that is invisible in traditional SQL literature because that literature lacks the vocabulary to even talk about what "running backward" even means - it isn't an 'inverse' relationship but an 'adjoint' one. We also use it to provi…

I see nothing in your link to justify what you say. Perhaps you can elaborate.

Re: Why I am learning category theory

#48

Post by kelseyfrog »

i_am_toaster wrote: post #21

I would be willing to drink the kool-aid if I saw it being used in a practical way. I always feel these posts are filled with category theory jargon without ever explaining why any of the jargon is relevant or useful. I’ve even watched some applied category theory courses online and have yet to feel I’ve gained anything substantive from them. However, as I started off with, I’m always willing to try something out or…

Category theory as it applies to programming is not dissimilar to learning design patterns. Some people go their whole careers never touching them and write perfectly fine programs. The same is true for category theory.

Those who learn either or both, have a larger set of mental abstractions that largely transcend any one programming language. They can say, this thing and that thing share a common salient property through a certain abstract pattern. There is a certain sense of mathematical beauty in recognizing common patterns and mechanisms. There is also the choice of subtly or drastically altering one's coding style. The same with each, a programmer can use just the right design pattern in just the right place and perhaps simplify or codify a section so that it's easier to understand the next time around (or decide not to!) or they can go completely wild and over-pattern their code. The same applies to category theory. One can recognize that some section is actually a closed reduction and accepts any semigroup and then decide to codify this into the program or not.

I tend to be a collector of ideas, so learning category theory and it's application in programming gives me all these little gems and ways to re-understabd code. Sometimes I use them and sometimes I don't, but my life is more joyful just knowing them regardless.

Re: Why I am learning category theory

#50

Post by layer8 »

BenoitP wrote: post #29
hosh wrote: post #25

Earlier quoted context omitted.

In Ruby and many other languages, you have this idea of a string concatenation: "foo" + "bar" -> "foobar" "foo" + "" -> "foo" That makes it a monoid. Instead of talking about OOP patterns, knowing that the "+" operator is a monoid for string objects lets us write code that is composable. Similarly, with arrays: [:foo,:bar] + [:baz] -> [:foo,:bar,:baz] [:foo,:bar] + [] -> [:foo,:bar] Some language platforms will imple…

I see no more than Groups in your comment. Which are very useful! Also having commutative operations makes for Abelian Groups, which enable operations to be reordered, and makes for implicit parallelism. Where is Category Theory?

It’s monoids, not groups, but yeah, it‘s just knowledge about basic algebraic structures, no particular insight from category theory here.
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