feat: add notes on Brzozowski derivatives

Author: SKalt

content/notes/techniques/brzozowski_derivatives.md

@@ -0,0 +1,24 @@
+---
+title: you can take the derivative of a regular expression?!
+link: https://jvns.ca/blog/2016/04/24/how-regular-expressions-go-fast/
+date: 2016-04-24
+---
+
+> But we can describe some of the ideas in words. Let's say we have a regular expression which is supposed to match the strings ('a', 'abab', 'aaaabb', 'bbc').
+>
+> The derivative of those strings with respect to `'a'` is ('', 'bab', 'aaabb') – you strip off the `a` from every string.
+>
+> It turns out (which is not totally obvious to me, but I think if you go through all the cases it's not too bad) that you can take the derivative of any regular expression in a pretty straightforward way – like if you have `(a+)|(b+)`, the derivative with respect to `a` is `(a+)`. These derivatives turn out to combine in nice ways which is I guess why they are called derivatives.
+
+Generally, I think this means you can fashion a RegExp matching library out of a simple recursive descent parser:
+
+1. take the first letter of the string
+2. take the derivative of the regular expression with respect to that letter
+3. recur with the rest of the string and the derivative of the original RegExp
+
+This post later lead me to reading up on [Brzozowski derivatives][wiki], which in turn pointed me towards [Parsing with Derivatives][pwd-11].
+
+<!-- links -->
+
+[wiki]: https://en.wikipedia.org/wiki/Brzozowski_derivative
+[pwd-11]: https://dl.acm.org/doi/abs/10.1145/2034574.2034801