The Algebra of Algebraic Data Types

"This guy who is discovering it by himself" is me (the OP) about a year ago! Derivatives of types to come in part II or III (or just watch the talk on YouTube: this video )

There are two very different types of arguments typically made as to why to learn the more esoteric languages (Haskell, Lisp, Forth, others). The first is the more common: learning these languages exposes you to other ways of programming, which in turn makes you a better programmer no matter what language you're programming in. This is unquestionably true. Mainstream languages are constantly learning new things from these languages, which means you will be able to apply the techniques you learn from them to your code no matter what language you write in. I have the misfortune[1] of writing a lot of PHP at my day job, but it turns out even PHP has support for filter and map over arrays. If I hadn't learned functional programming, I would never have even looked for them. The other argument, which is made less often, is that you can actually write great software in these languages. This argument is made less often because we can obviously look at the market and the TIOBE index and see that Haskell is way down at #30 with 0.323% of the market share. However, there are really great programs made in Haskell (xmonad, for one). There are also tons of great programs made in Lisps, especially Clojure of late. So, this second argument is not entirely a dead end either. Revisiting something I mentioned in the first argument for a moment though, I would actually make a third argument that I rarely see. As I said, other languages are constantly learning new things from these languages. Has

Author of the blog post here. It's amusing to see this submitted by Don Stewart, since it was his explanation[0] of algebraic data types that first made them "click" for me! I think I forgot to mention him in this post, but I remembered in the talk[1]. If anyone's interested in this and where else it might go, I recommend read Don's SO answer[0], this SO question and the related answers[2] and these papers [3,4] on derivatives and dissections by Conor McBride. There are also several good blog posts[5] and a paper[6] by Brent Yorgey on the topic of combinatorial species, and of course Dan Piponi's blog[7] is a treasure trove of interesting insights at the intersection of math, physics and computer science. [0] link [1] this video (shitty audio for the first minute or 2 - it gets better). [2] link [3] link [4] link [5] link [6] link [7] link Edit: It should go without saying, but because a few people last time around seemed to think I was trying to pass this off as my own ideas, let me state that there is nothing original in this blog post. It's a repackaging of the ideas and work of lots of other people, all of whom are way smarter than I am.

I very much agree with you. A zip code is a string even though it looks like a number. Likewise C/Java/Go "types" are tags even though they look like types. Real types are numbers that obey type algebra, which C/Java/Go have no idea exists. The Algebra of Algebraic Data Types: this video