This page is a resume-like overview of my open-source work, describing the purpose and the extent of my contributions for selected projects. Most of them also have an adequate README file, but these are intended for a typical user of the project and may require niche knowledge (e.g. of J) to understand.

BQN (BQN, mainly)

BQN is my second major programming language, driven by the frustration that no one seems to have captured the appeal of APL in a modern design with things like closures and namespaces. Some problems notwithstanding, I consider BQN a success on these grounds already, and it’s gathered a small community of users.

I implemented as much of BQN as practical in the language itself, making it easy to port to new platforms. The compiler is array-based, advancing the methods used in Co-dfns. I’ve implemented the easy Javascript VM, but a few programmers have taken up the challenge of hosting BQN in lower-level languages. The main offline implementation, CBQN, is mostly dzaima’s work.

I’ve written the documentation, specification, and tutorials, including a markdown processor in BQN to build the website and BQN code to generate the diagrams. But I must credit razetime for all the help… you know, the help pages for primitives you get if you middle-click one of the symbols buttons.


Miscellaneous BQN utilities, and the closest thing it has to a standard library right now.


To make learning BQN easier, I cloned Adám Brudzewsky’s APLcart, translating many APL examples to BQN and adding other snippets.

Singeli (BQN)

A domain-specific language for building fast array language algorithms. Designed in collaboration with dzaima, who built an initial Java implementation. The current implementation is my rewrite in BQN.

ILanguage (C)

I is an experimental (avant-garde, even) programming language inspired by J. I began creating it after the stunning realization that my two favorite features of J—rank and forks—were actually the same concept! A paper describing this idea, a generalization of what Haskell calls the Functor typeclass, is shown in the I repository. It assumes no knowledge of any specific language. The language uses a number of other interesting ideas which are described in its documentation and guided examples.

Some features of the implementation include:

  • Memory management implemented with reference counts.
  • A soft-typing framework built into the language. Any type can be a combination of elementary types, in which case values of that type are type-value pairs.
  • JIT compilation targetting x86 directly for pretty large portions of the language.

CrinGraph (Javascript)

Headphone reviewer Crinacle had measurements of hundreds (like, a lot of hundreds) of in-ear monitors with no easy way to put two of them in the same graph. I volunteered to make a comparison tool to do just this, and it’s now a popular feature of the site and used by over 20 other measurers to share their own data. In addition to the README, this project has pretty extensive documentation which really should stand on its own but you’re obviously here to read about me so I’ll get in a few bullet points worth of bragging that don’t belong in the docs:

  • That smoothing spline’s no easy feat. I wrote my own diagonal LDL decomposition and solver. The results are noticeably cleaner and more faithful than typical octave smoothing.
  • Normalizing the headphones requires solving what volume would give you a specific target loudness. How to find this? Newton’s method. I took the derivative of ISO 226:2003.

Crinacle helped guide the design, and I also took input from Discord user space_wadet, who is a professional UI designer.

BQNoise (BQN)

Utilities for music mixing, mastering, synthesis, and sequencing in BQN. Documented only in comments in the source files. My tracks on Bandcamp have been produced in J up to 2021 and BQN after.

Music (BQN)

Framework and source for synthesized music.

BQN Musician (BQN)

Teaches music synthesis and theory using BQN.

JSound (J)

The older utilities in J, which I have now left behind.

Sorting (C, Singeli)

I’ve done some research on modern sorting algorithms for CPU-native types (that is, integers and floats). I keep notes on this page. My main focus is now on Singeli Sort, a many-way hybrid with the goal of combining the advantages of as many known methods as possible. I’ve also made minor contributions to fluxsort and published some initial research for Singeli Sort as distribution crumsort.

Robin Hood Sort (C)

A new distribution sorting algorithm that beats all other methods I know of to sort 1e5 or fewer uniformly random 4-byte elements. Its performance gets better or worse based on the clumpiness of the input distribution.

JtoLaTeX (J)

The coolest J code I’ve written, in my opinion: a half-compiler, half-preprocessor to create LaTeX using J code. It replaces J operations with symbolic counterparts to build a syntax tree, and then turns the tree into LaTeX code. A particular design goal is to make the output code look natural even when the input is idiomatic J, so it uses knowledge about order of operations and mathematical convention to parenthesize only when necessary. Addons provide other utilities like matrix handling, uncertainty calculation, greek and other symbols, and set notation. Base code and the more important addons are well documented in the doc folder.

htmllint (Javascript)

A school project that I and three other students designed for a class at UNC, with input from a small team at IBM.

J programming language (C)

I made some contributions to the J source code around 2016 and have since stopped (I am now using BQN rather than J for my own programming when possible). Commits scattered across:

  • jsource: the official Github mirror of J’s source.
  • unbox: a fork of the J source code. I prefer to work with it over the official J source since the build system is nicer, and my changes appear here first.
  • openj/core: defunct. I keep it around because there are still some changes which I have not added to unbox.