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Why I am learning category theory

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Re: Why I am learning category theory

#21

Post by i_am_toaster »

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 see the reason in something. Can anyone give me a practical applied way in which category theory is a benefit to your design rather than just creating higher level jargon to label your current design with?

Re: Why I am learning category theory

#22

Post by nonrandomstring »

Tainnor wrote: post #7

As someone with a maths degree, yet who admittedly hasn't looked into category theory beyond some basic notions, I still don't quite understand why anyone would want to learn category theory before e.g. abstract algebra or even just fundamental mathematical reasoning (definition, theorem, proof). Maybe I'm missing something but it seems to me that all you can study monads in programming languages without having to al…

To me it's part of the "stretch your mind" philosophy. Plenty of exercises that add some suppleness and help with all round problem solving. It's one reason I keep up with Lisp even though nobody cares much to learn or pay me to program in it these days. Any programme of discrete and abstract maths surely has the same benefits, with a little bit of different theory areas; number, group, sets, operator... all healthy stuff unless taken to extremes :)

Re: Why I am learning category theory

#24

Post by floober »

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 structure, where in a less structured language you might need to reed through a bunch of docs to understand how to manipulate some objects. The "killer app" is all of that extra structure shared throughout all of the codebases.

Re: Why I am learning category theory

#25

Post by hosh »

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…

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 implement the first concat, but not the latter. Without the latter, you couldn't do things like, accept an empty user input. You would have to write code like:

  defaults + user_input unless user_input_array.empty?
This applies to things like, hashes, or even more complex objects -- such as ActiveRecord named scopes, even if they don't use a "+" operator. (But maybe, Hash objects can be "+" together instead of calling merge())

This is all applicable to how you can design libraries and DSLs that seem intuitive and easy to use. Instead of just thinking about bundling a number of methods together with a data structure, you can make sure that a single method within that bundle works the way you expected across a number of objects. You might even be using these ideas in your code, but don't realize it.

Re: Why I am learning category theory

#26

Post by wisnesky »

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 provide a new semantics for data integration. Link: https://www.categoricaldata.net

Re: Why I am learning category theory

#27

Post by zmgsabst »

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…

I think the real insight of category theory is you’re already doing it, eg, whiteboard diagrams.

Category theory is the language of diagrams; it studies math from that perspective. However, it turns out that category theory is equivalent to type theory (ie, what computers use). So the reason why diagrams can be reliably used to represent the semantics of type theory expressions is category theory.

My workflow of developing ubiquitous language with clients and then converting that into a diagram mapping classes of things and their relationships followed by translating that diagram into typed statements expressing the same semantics is applied category theory.

The “category theory types” are just names for patterns in those diagrams.

Trying to understand them without first getting that foundational relationship is the path to frustration — much like reading GoF before groking OOP.

Re: Why I am learning category theory

#28

Post by vosper »

hosh wrote: post #25
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…

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…

> Instead of just thinking about bundling a number of methods together with a data structure, you can make sure that a single method within that bundle works the way you expected across a number of objects. You might even be using these ideas in your code, but don't even realize it.

I think this was GP's point. They complain that no-one explains why the category theory _jargon_ is useful. As you point out, the jargon is not needed in order to use the concept. Someone might even come up with the concept independently of the jargon.

Re: Why I am learning category theory

#29

Post by BenoitP »

hosh wrote: post #25
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…

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?

Re: Why I am learning category theory

#30

Post by School-Cotton »

nonrandomstring wrote: post #22
Tainnor wrote: post #7

As someone with a maths degree, yet who admittedly hasn't looked into category theory beyond some basic notions, I still don't quite understand why anyone would want to learn category theory before e.g. abstract algebra or even just fundamental mathematical reasoning (definition, theorem, proof). Maybe I'm missing something but it seems to me that all you can study monads in programming languages without having to al…

To me it's part of the "stretch your mind" philosophy. Plenty of exercises that add some suppleness and help with all round problem solving. It's one reason I keep up with Lisp even though nobody cares much to learn or pay me to program in it these days. Any programme of discrete and abstract maths surely has the same benefits, with a little bit of different theory areas; number, group, sets, operator... all healthy…

But you can study all of that stuff without category theory.
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