Your second link is repeated though, I assume it should be this: Another interesting one about databases and category theory: And hopefully my anecdotal experience will lend some credibility to using category theory to help with programming. That is the point and the pattern I am trying to convey. You are probably aware that functional languages are closer to math than the more popular imperative languages. The morphisms in this category are closed under association because B . Take advantage of this course called Category Theory for Programmers to improve your Others skills and better understand Theory for Programmers.. So here's a "folk theorem" that explains why you should care about such abstract structures. Then you can bring in powerful OOP tools, but the only things they help you with are understanding the excess complication you added in. Again the implementation was not my point. what kind of book that teaches programming could possibly have no code in it? Find books For any natural transformation NatAB between the functors Fb: C -> D and Fa: C -> D such that NatAB: Fb -> Fa, the Yoneda embedding maps it to the natural transformation: NYoneda operates on [C, D](Fa, -) by post-composing NatAB to the natural transformations in the output NatAX, which maps the output set to NatBX, which maps ([C, D](Fa, -): Fx -> NatAX) -> ([C, D](Fb, -): Fx -> NatBX). T. By the definition of a bicategory there exist invertible 2-cells mapping each of these endo-1-cells to T. Associativity Law Solution I used it because it's easier to read then regexp. I don't understand why you are chafed. The things I do end up creating come from a much deeper place of true need. This blog-style format does work overall however, I found myself wanting more proof details for the more sophisticated topics at the end. I avoid a lot more pointless building; sometimes entire projects. It’s pretty easy to see why this is the case - a function of the form f: () -> x is essentially a container for a single value of x. I have repeatedly said that the implementation WAS not the point and that all performance metrics are negligible as the are under O(N). The language of categories is not achieving anything here but obfuscation. > > The only serious argument I hear against strong static type check- ing is that it might eliminate some programs that are semantically cor- rect. I'm still new, heh). You should know if you're "experienced" that a C++ binary is a "magnitude" faster than python just running a for loop counting to 100. It may be a good pre-req for looking at (or conjuring up your own) more detailed applications within CS specifically. The analog of a type checker would go even further by making sure that, once Romeo is declared a human being, he doesn’t sprout leaves or trap photons in his powerful gravitational field.”, https://github.com/hmemcpy/milewski-ctfp-pdf, Goodreads Members Suggest: Favorite Very Quick Reads. For any functor F from the discrete category to Set, there are N morphisms (the item-selection morphisms) between the singleton set and F a, where N is the number of elements of F a. For anyone else looking to get started with Category Theory, I'd also highly recommend choosing a functional library (i.e. The reason you care, then, is that once you have traced out these paths, when you are looking at a problem your brain will automatically try to draw you back towards the thread of regular structures. You do get dramatic speed up if you do it in SQL this is provable. There's no way I'd even be able to approach the subject with his efforts. You'll have to elucidate, I don't follow. This is just a guess, and I'm pretty sure both of us are too lazy to generate actual specs to prove it either way. m since m must be a morphism from D -> C. Therefore C is not the product of A,B. They also offer more abstracting power. Or a pure mathematician who wants to imagine what sorts of applications their work might have. Recognizing that allows you to build abstractions that work for any monad, rather than re-discovering and re-implementing the same idea for each one separately. Keep your attitude in check, this kind of attitude can ruin your whole career after you get your ass fired. You are probably aware that functional languages are closer to math than the more popular imperative languages. This course is adapted to your level as well as all Theory for Programmers pdf courses to better enrich your knowledge. You are invoking OS and CPU architectural level concepts which are so far away from python it has basically nothing to do with it. For some morphism f :: d -> R c, we can apply εc * L to form the morphism: Solution Since you are not inexperienced my advice is unlikely to be helpful. To be caricatural, one is just piling frameworks and libraries on a language where you don't even master the basics, filling in the blank from examples and snippets from the net. Start by marking “Category Theory for Programmers” as Want to Read: Error rating book. A string literal "abc" has order and preserves it by nature of having order as a property. Solution Maybe the sheer scale of that structure is beautiful to someone, but we're discussing whether scientists should bother learning it. Solution People who like this may also be interested in the awesome applied category theory list, And Conal Elliott's Compiling to Categories, which I've seen discussed here before, Highly recommend the lecture series. Imagine you have some type, like in the initial example. Granted, this really may not be useful to a working chemist. This is hostile to productivity and serves only my early commitment to having a type prover guard my every move. Things are of course not so black-and-white. h = h, so C (a, f) h = h, and C (a, f) is the identity morphism as well. Since there are no functions that map non-empty sets into the empty set, we see that if C(a, x) is nonempty, then C(b, x) must be nonempty as well. In the best cases it gives me a feeling of a super power - something that was previously impossible or extremely difficult is now elegant and clear. Solution Be the first to ask a question about Category Theory for Programmers. That is the point I am trying to make. Base Case, Solution Say K: Set -> FinSet is a functor that embeds a set into FinSet, such that for any finite set n in Set, K n = n. Then FinSet(K n, a) is a hom-set between elements in FinSet, and so FinSet(K n, a) = a^(K n) = a^n. But, after all, it is a maths book on a highly abstract topic, therefore the reader should have some previous exposure to maths and mathematical texts, and expect to struggle, from the very first pages. What this does is to add rigor to something that you (or a chemist) may understand intuitively. Too informal for a subject that needs formality. That’s just an analogy that’s sometimes useful when describing them to imperative programmers to aid intuition. The types are there even if you don't have to type them in and they are significantly constraining your set of accepted programs. Yes, thanks for this. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Finally, after going through 10 chapters I skipped to the end to see if there was some culminating breakthrough that we were striving towards... and I found more definitions stacked upon other definitions. m, so m factorizes p and q. OP is not claiming that the benefit of type inference is that it automatically "types characters". Take advantage of this course called Category Theory for Programmers to improve your Others skills and better understand Theory for Programmers. I believe that the first time I got as far as, one of the best journeys I had (another one was with "operating systems: design and implementation"), This is an ambitious book that dares to tackle concepts usually reserved for graduate Algebra courses and makes them presentable for those with a functional programming background. The converted json type fit the parameter of a library json function and thus the result was a query that executed 10x faster then the other implimentation. Most people still use python because in the end because it Doesn't even matter. You are saying that it's hard to satisfy the type checker when porting a dynamically-typed program; OP says this happens very rarely. I love new ways of thinking about things. Since this is category theory for programmers I will illustrate all major concepts using computer code. A graph with one node and one (directed) edge (hint: this edge can be composed with itself) The file preamble.tex contains all the configuration and style declarations. they are completely stuck. > I'm not sure in the context of reaction networks whether modeling the system with compositionality guarantees and a clean mapping between graph representation and differential equations gives scientists something new or not. I ended up building an odd variation of lattices to describe genome annotations because of this, and it was an exercise in finding what about the domain drew me out of strict regularity rather than trying to find my way into it, which is a lot easier. ), The best way to build the book is using the Nix package manager. * Identity: The identity is False Then αB Fb = αA Fa, but we can’t conclude that Fb = Fa, because it’s possible that G is the constant functor. While it's quite interesting and educative - I still don't get the "for programmers" part of it.