How to Use Sized Types?
Let Me Count the Ways

This post is inspired by this thread from the Agda mailing list.

Because Agda treats Size like a first-class type, there’s quite a bit of freedom in how you get to use it. This makes it a bit unclear where you should start: should Size be a parameter or an index in your type? What sizes should the constructors’ recursive arguments’ and return types have? Here are two options that are usually used (and one that doesn’t work.) The recommended one is using inflationary sized types and Size<.

The State of Sized Types

Sized types hold great potential as a very practically useful way to do type-based termination checking, but sufficiently expressive sized types in dependent type theory come with a host of problems, mostly related to its incompatibility with the infinite size found in most simpler or nondependent type systems. This post attempts to describe some potential but ultimately unsatisfying solutions.

Notes on Propositional Equality

Adding LaTeX to your Jekyll Site

As it turns out, adding support to render LaTeX in a Jekyll blog isn’t all that hard, because other people have done most of the heavy lifting. There are two main ways to do this:

• Client-side rendering: After the page loads, a JS script is run to transform LaTeXy parts of the page to lovely, styled HTML.
• Build-time rendering: After Markdown files are compiled to HTML, a Jekyll plugin further transforms those LaTeXy parts to HTML as well. Here’s how you do either using $\KaTeX$.

Thulium: Disk Failure

On 24 December 2020, my home server Thulium went down. Usually the cause of downtime is my home’s public IP address changing, and I need to update the DDNS record with my domain name provider. This time it wasn’t; when I tried to SSH in through the domain, I reached something, but it wouldn’t let me in. I managed to SSH in through the local IP address and tried to reboot, but I got a segmentation fault, of all things. In the end, I rebooted the server manually by walking over to the other room and holding down the power button. I could then SSH in, my Docker containers were up, all was well.

On 27 December 2020, it happened all over again. This time, I could SSH in again, but everything was painfully slow. I checked htop: CPU and memory were doing fine. I checked my internet connection: that was fine too. It must be, then, a disk issue (obviously, since that’s the title of this post).

Interesting Problems at Small Values

This post is based on the observation that, in a variety of fields (e.g. logic, computics, mathematics, physics), while certain classes of problems can be parameterized by some natural number $n$, it appears that the interesting problems―not so simple as to be trivial, but not so complex as to be unsolvable, undecidable, intractable, or nonexistent―always occur at small $n$. Below is a collection of such problems, describing at which $n$ they are interesting, and how so.

Thulium: A One-Year Retrospective

A few months ago, on the 15th of April, was the one-year anniversary of ert.space and the Thulium server, still running happily in its desktop tower, now with an extra 2 GB of RAM. Even if I didn’t have the Thulium posts to remind me, I would always have the timely bill for the domain name. Over the past year, a multitude of services and Docker containers have risen and fallen, having been replaced or abandoned or, rarely, taken up a more permanent post. In 2018, I began with the following:

Ramblings on the Coq Kernel

Back during the summer of 2019, I worked a bit on the Coq kernel. At the same time, I posted a lot of toots on Mastodon about whatever random problems I was encountering. I’ve decided to collect them here, as it might just be that some of these will be useful to me again at some point.

Designing ShareVitalSigns for iOS

For usage notes, see the LNhealth wiki page on SVS for iOS. This post is cross-posted to the LNhealth wiki at Designing ShareVitalSigns for iOS.

Bridges of Vancouver

For reasons yet fathomable, I’ve decided to cross by foot (almost) all major pedestrian-accessible bridges crossing a body of water in Greater Vancouver. These are, courtesy of this list, as labelled on the following map, and listed as follows, in alphabetical order:

Thulium Part 3: Ghost, monitoring, backups, and a summary

This is part 3 of the Thulium series. Go back to part 2 or jump back to part 1.

Exam season has ended, and so too must this story. There are a lot more things I could self-host, but I’ve come to a point where I’m comfortable with the services I’ve set up for myself, and other ideas have larger scales and likely would deserve their own posts (setting up a mail server, for instance).

Thulium Part 2: Nextcloud (formerly Syncthing) and Gitea

This is part 2 of the Thulium series. Visit part 3 or go back to part 1.

We are now in the middle of the exam season. What better time than now to set up file syncing and a personal Git host?