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Category Theory for Programmers (2014) [pdf]

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Re: Category Theory for Programmers (2014) [pdf]

#31

Post by edwintorok »

rubyn00bie wrote: post #22
playing_colours wrote: post #11

I liked “An Invitation to Applied Category Theory“, pdf is available here: [1] It is written in a more terse, mathematical language, but it is very clear and friendly for non-mathematicians. The authors provide interesting examples of applicability. Hardcover is quite expensive, but the quality is great [2]. [1] http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf [2] https://www.amazon.com/gp/aw/d/1108482295

I've quite literally spent the last month trying to read, digest, and apply the above to a record layer I'm writing for FoundationDB. Dr. Spivak's work has been absolutely beyond helpful and insightful. There's no way I'd even be able to approach the subject with his efforts. I'd also recommend these as they're associated with the 7 Sketches and help fill in some blanks: Functorial Data Migration - https://arxiv.org/…

You linked to the 1166.pdf twice, did you mean to link to http://math.mit.edu/~dspivak/informatics/notes/unorganized/P... for "Category Theory as Unifying Database Formalism"?

Re: Category Theory for Programmers (2014) [pdf]

#32

Post by playing_colours »

rubyn00bie wrote: post #22
playing_colours wrote: post #11

I liked “An Invitation to Applied Category Theory“, pdf is available here: [1] It is written in a more terse, mathematical language, but it is very clear and friendly for non-mathematicians. The authors provide interesting examples of applicability. Hardcover is quite expensive, but the quality is great [2]. [1] http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf [2] https://www.amazon.com/gp/aw/d/1108482295

I've quite literally spent the last month trying to read, digest, and apply the above to a record layer I'm writing for FoundationDB. Dr. Spivak's work has been absolutely beyond helpful and insightful. There's no way I'd even be able to approach the subject with his efforts. I'd also recommend these as they're associated with the 7 Sketches and help fill in some blanks: Functorial Data Migration - https://arxiv.org/…

Thank you for sharing your experience!

I think of Category theory and Abstract algebra as great upgrade kits for brain. If, say, a software engineer manages to learn, understand, and internalise those fields up to some level, she will be able to see her daily work - algorithms, architecture, approaches to solve problems - through the mental models those areas of mathematics imprinted into her brain, think and express solutions in those categories. May feel a bit like a superpower :)

Re: Category Theory for Programmers (2014) [pdf]

#33

Post by edwintorok »

rubyn00bie wrote: post #22
playing_colours wrote: post #11

I liked “An Invitation to Applied Category Theory“, pdf is available here: [1] It is written in a more terse, mathematical language, but it is very clear and friendly for non-mathematicians. The authors provide interesting examples of applicability. Hardcover is quite expensive, but the quality is great [2]. [1] http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf [2] https://www.amazon.com/gp/aw/d/1108482295

I've quite literally spent the last month trying to read, digest, and apply the above to a record layer I'm writing for FoundationDB. Dr. Spivak's work has been absolutely beyond helpful and insightful. There's no way I'd even be able to approach the subject with his efforts. I'd also recommend these as they're associated with the 7 Sketches and help fill in some blanks: Functorial Data Migration - https://arxiv.org/…

Another interesting one about databases and category theory: Relational algebra by way of adjunctions: https://dl.acm.org/citation.cfm?id=3236781

Re: Category Theory for Programmers (2014) [pdf]

#34

Post by whatshisface »

Is there any point in learning category theory without first learning the things that it generalizes? I didn't see any value in learning about geometric algebra until I had learned enough about complex analysis to appreciate what it would mean to connect it with vector calculus.

Re: Category Theory for Programmers (2014) [pdf]

#35

Post by [deleted] »

lidHanteyk wrote: post #21
dominotw wrote: post #17

Earlier quoted context omitted.

> I now find category-theoretic constructions everywhere in mathematics, i think gp might have been asking about practical use in CS ( CS majors).

And CS is merely a subfield of maths. What should I say? Scott theory, domain theory, CPOs, Galois connections? The problem here is that, as usual, folks are trying to figure out what category theory is good for, but ignoring the entire point: The definitions are the important part. Once the definitions make sense, then the rest of the system makes sense. Category theory is all about the definitions, and moreover, al…

[deleted]

Re: Category Theory for Programmers (2014) [pdf]

#36

Post by xvilka »

The book itself is constantly updated by the author and community, people add particular language flavors. Scala flavor[1] (along with the original Haskell one) is already part of the book, OCaml flavor[2] is being worked on and mostly finished.

[1] https://github.com/hmemcpy/milewski-ctfp-pdf/releases/tag/v1...

[2] https://github.com/hmemcpy/milewski-ctfp-pdf/pull/201

Re: Category Theory for Programmers (2014) [pdf]

#37

Post by philzook »

reykjavik wrote: post #24

Watched that guy's lectures and conference talks. While it's quite interesting and educative - I still don't get the "for programmers" part of it. I don't quite get how I would jump from understanding categories, morphisms, monoids etc. to building actually better systems. There are zero practical examples in his talks. Is it because i'm not using functional languages or what am I missing here?

Being into functional programming helps quite a bit I think. In particular, category theory seems to nest well and illuminate some complicated uses of polymorphism and continuation passing style transformations.

Categories are also a useful abstraction/pattern for designing interfaces to libraries. It's sort of a more mathematically flavored version of dataflow style libraries like simulink or gnuradio diagrams and stuff. Gluing together lego blocks and building up pipelines. I have been fiddling around with a categorical interface for solve linear equations which I think is pretty neat. http://www.philipzucker.com/linear-relation-algebra-of-circu...

Re: Category Theory for Programmers (2014) [pdf]

#38

Post by westoncb »

The clearest and most concise treatment I've come across on how Category Theory is used is Tai-Danae Bradley's "What is Applied Category Theory": https://arxiv.org/abs/1809.05923 (It's a 50 page PDF)

Unfortunately the examples aren't within CS, but at least for me personally, seeing it clearly applied in any context was the most important thing. It may be a good pre-req for looking at (or conjuring up your own) more detailed applications within CS specifically.

Also, if you like that, Tai-Danae Bradley has more writing at: https://www.math3ma.com/

Re: Category Theory for Programmers (2014) [pdf]

#40

Post by philzook »

philzook wrote: post #39

People who like this may also be interested in the awesome applied category theory list https://github.com/statebox/awesome-applied-ct

And Conal Elliott's Compiling to Categories, which I've seen discussed here before http://conal.net/papers/compiling-to-categories/
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