2022 Project Review

27 December 2022

Here’s a review of all1 the programming projects I worked on in my spare time this year. I’m quite satisfied with the work I did. I learned a lot and had some cool ideas that I will continue to build on. I’m glad I wrote this review, because there’s some stuff in here that I’m quite proud of that I had forgotten about. This year was a pretty long one for me.




ipso is a scripting language that I started working on a bit over 2 years ago. My goal for this project is to have a scripting language that I actually enjoy using. So far I haven’t found a language that I find satisfactory for small administrative programs; Bash and Python have no types, and Haskell is a bit slow and old for interpreted use, for example. ipso is my attempt at an answer.

This year I set up a website (https://ipso.dev) and published my first few releases on GitHub.

Some of this year’s features and milestones that I’m proud of:

The language itself is pretty stable now, so now my focus will be on writing standard library functions.




An implementation of Peter Shirley’s Ray Tracing in One Weekend with some extra features. It was super fun. It’s incredibly satisfying to go from a bunch of math to beautiful images.

The most striking thing I learned was Monte Carlo integration. It’s a way to compute integrals using random numbers. Ray tracing uses it to approximate the colour of a point on a surface. Every point on a surface has a specific, well-defined colour, and that colour can be the result of contributions from an extremely large number incident rays. The point’s colour can be expressed as an integral, and we use Monte Carlo integration to compute the integral with a varying level of accuracy. For a preview render, we can use few samples, and quickly produce a noisy image. For a full render we can use many samples, which will take longer, but will give a very accurate result.




“Sylva” means “forest” in Latin (according to Google Translate). I was playing with some ideas about wikis / “document-based knowledge graphs”.

There were tree things I wanted to combine:

This was just a sketch and I don’t plan to do anything with it.




A while ago I built a toy structural code editor using Haskell (GHCJS), and the reflex FRP library. I wasn’t happy with the performance. I heard about vue.js and was curious what it would be like to use it instead of reflex. I rebuilt some of the code editor using vue.js with TypeScript, enough to get a sense of the coding style and performance of the app. I was impressed by the performance improvements, and found TypeScript tolerable (and much, much better than plain JavaScript).


March / April


nix-docs is an ongoing experiment with reference documentation for some important Nix functions. Most Nix documentation is prose paragraphs, which is pretty bad for reference docs. Reference docs need to be skimmable, terse, and interlinked. Here’s the nix-docs page for mkDerivation: https://blog.ielliott.io/nix-docs/mkDerivation.html.

This year I updated the styling to match the new NixOS design and wrote a documentation generator for the content (my first iteration was hand-edited HTML that I copied from the Nixpkgs manual).




ccc stands for cartesian closed category. I was inspired by this podcast with Conal Elliott, and revisited his compiling to categories and calculating compilers categorically papers. One important insight from “calculating compilers categorically” is that translating lambda expressions into CCC syntax sort of “sequentialises” them. The composition operation in a category implies an order of operations: g ∘ f is often read as g after f. It seems to me that CCC syntax is closer to our word-at-a-time-style imperative CPUs.

This leads to the first idea I explored in ccc was: using CCC syntax as an intermediate representation for lambda calculus. This worked out really well; I learned that the lambda to CCC translation also performs closure conversion, which is another reason that CCC syntax is easier to compile to imperative code.

The second idea builds on the first. Once we have a program in CCC syntax, a compiler can be defined as a functor from CCC syntax to another cartesian closed category. I think Conal mentioned this in the podcast episode. I wrote a messy SSA compiler as a functor from CCC syntax arrows to “SSA builder arrows” (Haskell functions of type SSA -> SSA). It was pretty straightforward because CCC syntax is sequential and closure-converted.

The last idea was to apply these techniques to substructural lambda calculi (i.e. affine and linear lambda calculus). Linear lambda calculus has its own categorical syntax (closed symmetric monoidal category - call it CSMC for short), so I wrote a program that translates lambda calculus to CSMC syntax, and rejects lambda calculus terms that have non-linear variable usages. I then used the same program structure to translate lambda terms to semicartesian monoidal category syntax, which is just CSMC syntax with a terminal object. That translation allows unused variables while rejecting variable duplication, which makes it affine. The final translation adds a dup : a -> a ⊗ a arrow to the semicartesian monoidal category, which gets us back to a cartesian closed category (but with a slightly different syntax) and unrestricted lambda calculus.

This journey lead to a style for checking lambda calculus that works for linear, affine, and unrestricted lambda calculus. I think would be interesting to create a type checker that checks in this style. My intuition says such a type checker might be easier to parallelise.

I also noticed that the CCC syntax I settled on is explicit about parallel computations. While composition (f ∘ g) can be thought of as f after g, the tensor operator (f ⊗ g) can be thought of as f and g in parallel. There’s a sense in which this CCC syntax “reveals” parallelism that’s inherient in the lambda calculus. I’m curious what it would be like to write a multi-core parallel evaluator based on this.




I wanted to check for broken local links markdown documents, and create a “move” command that works like mv but also renames links. I finished the former but not the latter.




This work was inspired by an article about the limitations of unification-based type checking. It seemed to claim that Hindley-Milner / unification-based type checking is very limited, and presented a dichotomy between bidirectional typing and unification that I don’t agree with.

I wrote a Hindley-Milner-based type checker for a language with subtyping by applying bidirectional principles. It has higher-rank polymorphism, existential types, optional record fields, and default record fields, which are all powered by the same subtyping mechanism. Unification and instantiation are also performed by the subtyping mechanism.

The key insight is to allow the subtyping check to transform terms. A type A is a subtype of B when values of type A can be used where values of type B are expected. This is often written as A :> B, and in code as something like isSubtypeOf : Type -> Type -> Bool. My type checker returns evidence that the subtyping relation holds, which could be written as (a : A) :> B ~> b, and as a function: isSubtypeOf : (Expr, Type) -> Type -> Maybe Expr. The bidirectional style means ensures that “checking” types drives subtyping. This is all perfectly compatible with unification-based inference.

This deserves a much clearer explanation in its own blog post. I think it’s a promising result for programming language design.


June / July


little is my first attempt at a Knuth-style literate programming system. I want to write documents about code that are also the source truth for the code. Systems like literate Haskell are unsatisfying to me because I have to present the code to the reader in the same order that the code appears in the source file. For example, all literate Haskell articles will begin with a preamble of imports (example article). I want to present code to the reader in a non-linear fashion, in a way that supports my explanation. I imagine that I’d often put import declarations in an appendix, for instance.

little doc generates a document that I can publish on the web, and little code generates the codebase that is described in the document. Another fun use case is “self-documenting shell scripts” (example). Rather than commenting a bash script, you can write a literate document that describes a bash script, and give the document a shebang line.

little uses XML for its markup, so that I can use whatever “presentation” markup I want (Markdown, LaTex, HTML, etc.). I was surprised by how “not terrible” it felt to use XML for this. I have a strong bias against XML in general, and now that bias has gained some nuance. XML feels alright for markup, that is, for extra information in documents that are mostly text which people will consume by reading. That’s what it was designed for; it’s the eXtensible Markup Language. What I now object to is the use of XML as a data format. This article has a good heuristic for distinguishing the two uses: if you remove all the tags from your XML document, will it still make sense to a reader? I’ve tried to apply this heuristic to the syntax of little.

The code is pretty crappy, so if I continued to work on this I’d rewrite it. I’m optimistic about what I created so far, though.




mininix is an attempt at understanding how Nix-style build systems work by writing a small one. It includes a content-addressable store, a build database (using sqlite), a parallel build executor and a typed build language.

I also wanted to improve on the naming of concepts (i.e. use a better word than “derivation”), and to keep typeability in mind from the start (Nix is very very untyped. Would types affect the build system’s design?).

One idea I’d like to explore here is a sort of “local” version of Nix. Instead of having a global store, have a per-project store for build artifacts similar to cabal’s dist[-newstyle] directories and cargo’s target directory.

I’m also interested in whether we can have build systems that reuse existing package declarations. For example, if you want to use Nix to package a Haskell project, you need to convert your .cabal file to a Nix expression (or do import from derivation, which I fundamentally disagree with). What if there was a way to use the .cabal file without the grossness of import-from-derivation?




This project shows a sort of “upside down” approach to Hindley-Milner type inference. This work was inspired by some inaccurate type errors that ipso generated, and this algorithm is my solution.

Bidirectional type checking separates inference from checking, and this distinction is important in contrasting “normal” Hindley-Milner to the “top-down” approach. Roughly speaking, Hindley-Milner constructs types through inference in a bottom-up manner, and my algorithm refines types through checking from the top down.

In Hindley-Milner, all the work is done by inference and checking is the trivial case of inference followed by unification with an expected type. In the “top-down” style, checking does all the work, and inference is performed by checking against a fresh metavariable.

I want to combine this work with the subtyping work I mentioned earier.




hover-pill is a game I created to learn the Bevy game engine. You can try an early build here. It’s a 3D puzzle/platformer where you fly around as a capsule-shaped object (I’m not a 3D artist) trying to reach the green goal square.

I haven’t done any game development for years, so this project was very refreshing. Once I had all the mechanics working, I asked my girlfriend to test the levels I designed. Each time she completed a level, I created a slightly more difficult one. She enjoyed playing it, and I’m glad that in the end I created something fun.

Bevy uses wgpu for graphics, which combined with Rusts awesome cross-compilation support means it was pretty easy for me to develop on my desktop (with x86_64 and Vulkan), and then compile a WASM and WebGL version for the web. It was a pleasant surprise, coming from Haskell and GHCJS.

This was my first time using an entity-component-system framework, and I enjoyed it. Data-Oriented Design helped me understand the history behind the patterns. I think there are ideas here that apply outside of game development, but I don’t know what they are yet. On example (and I think it’s where I learned about the DoD book) is this explanation of a “data-oriented” performance improvement in the Zig compiler.




After hover-pill I wanted to learn more about graphics APIs and GPU programming. I realised that computing the mandelbrot set was an “embarrassingly parallel” problem, so it would be a good fit for GPU programming.

The mandelbrot renderer runs in realtime. It has a satisfying “blooming” effect as the iteration count ticks up and more points are coloured. The mandelbrot calculations are performed in a compute shader, and the colours are assigned using a histogram algorithm on the CPU. I couldn’t figure out how to do histogram colouring on the GPU.

To make sense of the WebGPU API, I created this diagram which displays all relevant (Web)GPU resources and their relationships:

I have a much better sense of GPU programming fundamentals, and I think the careful design of WebGPU helped. It’s higher level than Vulkan, but more explicit than OpenGL. I’ve done a Vulkan tutorial and forgot almost all of it. Having learned the fundamentals wgpu, I think the Vulkan API would make a lot more sense to me now.




hedge is a library that makes it easier for me to write web information systems with Haskell. I’ve been developing a sense of style and a set of patterns around writing Haskell web apps, in particular using servant and focusing on server-side rendered resources, and hedge is kind of my “kitchen sink” for things that support the style.

I might create a command-line program for setting up a new project, adding endpoints, and other forms of boilerplate I find.

I’m not sure if it will ever lead to something I could call a “framework”, like Rails. Right now I have the sense that it would be more like a pattern language with automated helpers.

  1. that made it onto GitHub