Certainty by Construction Progress Report 3

The following is a progress report for Certainty by Construction, a new book I’m writing on learning and effectively wielding Agda. Writing a book is a tedious and demoralizing process, so if this is the sort of thing you’re excited about, please do let me know!

Week three, and this update is coming in hot, a whole day early! This week I worked on the ring solving chapter, realizing that I can make a very much non-toy solver, and pack it into a chapter. We now build a multivariate semiring solver, discuss how and why it works, and then do some dependent-type shenanigans to put a delightful user interface in front of the whole thing.

In addition, it came with some excellent opportunities to discuss where semantics come from, and let me talk about homomorphisms earlier than I was otherwise hoping to.

My plan for the week was to tackle the remainder of the setoids chapter, but setoids are awful and it’s hard to motivate myself to do that, since I avoid using them in my day-to-day life whenever I can. Which is always. We’ll see what happens with this chapter, but maybe it’ll get melted down into something else. Nevertheless, understanding setoids is important for actually doing anything with the stdlib, so I dunno.

On the typesetting front, I spent an hour today fighting with Latex trying to ensure that it has glyphs for every unicode character in the book. I’ve got all but one of them sorted out now, and in the process, learned way more about Latex than any human should need to know.

The plan for next week is to cleanup the extremely WIP backmatter chapters. There’s a bunch of crap in there about me trying to do math math and failing, because math math doesn’t give two sniffs about constructability, and so none of it works out. If I’m feeling particularly plucky, I might try my hand at defining the reals, just because it might be fun.

As of today’s update, the book is now 360 pages long! I estimate it’ll be about 450 when it’s done, so we’re clearly making progress.

Anyway, that’s all for today. If you’ve already bought the book, you can get the updates for free on Leanpub. If you haven’t, might I suggest doing so? Your early support and feedback helps inspire me and ensure the book is as good as it can possibly be.