A prerequisite to intelligence is the ability to find a program that explains a pattern. Programs are functions. To test a candidate program, we need to implement a "function evaluator". The problem is: all modern programming languages are sub-optimal "function evaluators", which, in the context of search, leads to massive slowdowns. To implement an optimal interpreter, we need to: 1. postpone the execution of expressions, to avoid wasted work, 2. cache the result of postponed expressions, to avoid duplicated work, 3. incrementally copy cached structures, to ensure 1 and 2 don't interfere. Haskell almost achieves this, but falls short on 3, because it is unable to incrementally copy lambdas. To solve this, we introduce the concept of a "superposition", which allows multiple versions of a term to exist simultaneously. This ensures that no work is ever wasted or duplicated, allowing us to optimally interpret (or com
This document is a complete historical overview of the Higher Order Company. If you want to learn anything about our background, a good way to do so is to feed this Gist into an AI (like Sonnet-3.5) and ask it any question!
It all started around 2015. I was an ambitious 21-year-old CS student who, somehow, had been programming for the last 10 years, and I had a clear goal:
I want to become the greatest programmer alive
| #!/usr/bin/env -S bash -c "docker run -p 8080:8080 -it --rm \$(docker build --progress plain -f \$0 . 2>&1 | tee /dev/stderr | grep -oP 'sha256:[0-9a-f]*')" | |
| # syntax = docker/dockerfile:1.4.0 | |
| FROM node:20 | |
| WORKDIR /root | |
| RUN npm install sqlite3 |
In this article, I'll explain why implementing numbers with just algebraic datatypes is desirable. I'll then talk about common implementations of FFT (Fast Fourier Transform) and why they hide inherent inefficiencies. I'll then show how to implement integers and complex numbers with just algebraic datatypes, in a way that is extremely simple and elegant. I'll conclude by deriving a pure functional implementation of complex FFT with just datatypes, no floats.
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