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Why I am learning category theory

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Re: Why I am learning category theory

#111

Post by gilmi »

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…

If you have 24 minutes, George Wilson's talk about propagators is really interesting and demonstrates how we can find solutions to problems by looking at math.

https://www.youtube.com/watch?v=nY1BCv3xn24

Re: Why I am learning category theory

#112

Post by xedrac »

yakshaving_jgt wrote: post #23
nnoitra wrote: post #4

Will it make you a better React dev tho?

I think the best way to become a better React developer is to learn Elm, and then build your React apps the same way Elm would have forced you to.

Of course Elm is closely related to Haskell, which is a playground for category theory. I think learning the why behind it all can be useful in subtle ways.

Re: Why I am learning category theory

#113

Post by franknstein »

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 feel like another application which is maybe not talked about all that much is that knowing category theory gives you power to name some design pattern, google that, and tap into that vast mathematical knowledge that humanity already discovered. This becomes incredibly valuable once you become aware of how much you don't know. Or maybe just write that bare manimum code that works, idc.

Oh and also when you recognize your design to be something from ct its probably quality. Shit code cant be described with simple math (simple as in all math is simple, not as in math that is easy to understand).

Re: Why I am learning category theory

#115

Post by yakshaving_jgt »

xedrac wrote: post #112
yakshaving_jgt wrote: post #23

Earlier quoted context omitted.

I think the best way to become a better React developer is to learn Elm, and then build your React apps the same way Elm would have forced you to.

Of course Elm is closely related to Haskell, which is a playground for category theory. I think learning the why behind it all can be useful in subtle ways.

It might be, but personally I don't know CT and I run my business on Haskell and have been writing Haskell professionally for most of my career now.

So hopefully nobody is feeling intimidated by fancy mathy stuff. Haskell is just this cool, productive programming language.

Re: Why I am learning category theory

#116

Post by i_am_toaster »

rssoconnor wrote: post #59
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…

Apologies for the jargon, but there isn't room in a comment box for a detailed explanation. "The Essence of the Iterator Pattern"[0] posed an open problem in type theory as to whether or not "lawful traversals", of type `∀ F:Applicative. (X -> F X) -> (B -> F B)` could appear for anything other than what is called a "finitary container"[1], B := ∃S. X^(P S) where the (P S) is a natural number (or equivalently a polyn…

This is a lot to digest, but I’m responding to this one because of I think this attempts to answer my question and because of your 4th reference. That being said I need to ask some questions.

Would I be correct in saying — there are less complex objects, which are defined in category theory, that are useful in a generic way in combination with one another?

If the answer to that question is yes, is there a place I look to find the mappings of these software topics/designs to these category theory objects such that I can compose them together without needing the underlying design? If that were the case, I could see the use in understanding category theory so that I could compose more modular and generically useful code.

I have to admit though, I’m still fairly speculative and my thinking on this is very abstract and probably very flawed.

Re: Why I am learning category theory

#117

Post by solomatov »

Koshkin wrote: post #80
solomatov wrote: post #75

Earlier quoted context omitted.

> As a programmer and hobbyist math reader, I found category theory to be very unrewarding (and I gave up on it) because of the lack of interesting theorems and lemmas. My takeaway was that there's Yoneda lemma and really nothing interesting before you reach that One of the most interesting things in CT are adjoints. They happen literally everywhere. For example, static analysis via abstract interpretation is an exam…

Sure, but what does the knowledge of something being an adjoint give you?

There are a lot of interesting properties:

- Adjoints preserve limits/colimits.

- Adjoint functors give rise to a monad

- They are connected to universal morphisms

Re: Why I am learning category theory

#118

Post by larve »

i_am_toaster wrote: post #116
rssoconnor wrote: post #59

Earlier quoted context omitted.

Apologies for the jargon, but there isn't room in a comment box for a detailed explanation. "The Essence of the Iterator Pattern"[0] posed an open problem in type theory as to whether or not "lawful traversals", of type `∀ F:Applicative. (X -> F X) -> (B -> F B)` could appear for anything other than what is called a "finitary container"[1], B := ∃S. X^(P S) where the (P S) is a natural number (or equivalently a polyn…

This is a lot to digest, but I’m responding to this one because of I think this attempts to answer my question and because of your 4th reference. That being said I need to ask some questions. Would I be correct in saying — there are less complex objects, which are defined in category theory, that are useful in a generic way in combination with one another? If the answer to that question is yes, is there a place I loo…

I'm not entirely sure if that is what you are asking, but for example pure functions from a type A to a type B can be compose with pure functions from a type B to a type C, to form a pure function from A to C. A lot of programmer oriented CT takes place in the category of types, with morphisms being a function from one type to another. Programming in a purely functional style makes composition of functions... trivial, compared to a function that has side-effects due to mutation.

Now of course this sounds trivial, but you can build much more refined concepts out of that simple idea. For example, creating product and sum types.

And that's where the rabbit hole starts.

Re: Why I am learning category theory

#119

Post by wisnesky »

zasdffaa wrote: post #47
wisnesky wrote: post #26

Earlier quoted context omitted.

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.

The way to run conjunctive SQL queries forward and backward is described in this paper, https://www.cambridge.org/core/journals/journal-of-functiona... , (also available on the arxiv), where they are referred to as query 'evaluation' and 'co-evaluation', respectively. We never would have been able to discover co-evaluation if not for category theory! The previous link includes this paper, and many others.

Re: Why I am learning category theory

#120

Post by bmitc »

larve wrote: post #9
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…

author here, for context, I do have a reasonable background in maths (algebra, analysis, statistics) at a CS master-ish level (self-taught and a long time ago, though), as well as spent quite some time with programming language / type theory when I was younger, and I do use monads quite a bit in my day to day programming. In fact, the fundamental algebra concepts (rings, groups, etc...) as well as fundamental CS theo…

How do you know analysis at a "CS master-ish level" (not sure what that means given it's a mathematical subject) but calculus did your head in? I'm not being judgmental but am just genuinely confused given that analysis is the foundation for calculus. :)
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