Yon – a topos-oriented language with a content-addressed lattice heap

12 points by amenn 2 days ago

Hello everyone. In the last two years I spent, as a dev, part of my free time stretching the limits of my knowledge. Not being a mathematician myself, I discovered that formalizing concepts in mathematical language could nonetheless be useful to improve symbolic reasoning about the concepts themselves. I made use of both books and AI, and I followed the development of the latter, mainly with a critical eye. I have several open projects, and from some observations and explorations on one of them I started asking myself what the current limits of reasoning, of logic, of mathematics itself are. So I explored categories, and topoi, above all starting from Mazzola's theory of music. I asked myself whether this could influence type theory in programming, and I ran some experiments. Out of this came this programming language, Yon, inspired by Yoneda and by morphisms. From another project I drew observations on the Leech lattice; from yet another, some experiments with mmap and coordinate-based allocation in a structure that would be advantageous, again, in a topological sense. The language certainly has mistakes here and there and I wrote the documentation in a hurry; the work took 3 weeks in total. It compiles to LLVM for performance reasons, and for now I preferred to avoid a VM and a GC. It contains unusual data structures that turn out to be performant. It's worth a look, and I hope it will win some converts, and that someone will want to help me with its development. I'd love for it to bring fresh stimuli to programming and maybe open a few new frontiers. A few concrete details, for those who want to look under the hood. The compiler is a real pipeline, not an interpreter: an OCaml frontend takes .yon source into a custom MLIR dialect I called "topos", where the categorical constructs live as first-class operations; its lowering passes take everything down to LLVM IR and from there to a native executable. A single command, yonc, drives the whole chain, and you can stop at any intermediate stage to see what a categorical construct actually becomes on its way to silicon. The runtime is where the Leech lattice observations ended up. The heap is content-addressed over Λ₂₄: every value is mapped to a lattice point and canonicalized under the Conway group Co₀ (via libmmgroup), so the same content always lives at the same address. That buys three things I would now find hard to give up: equality is a single machine comparison no matter how big the value is (string equality benches flat at ~17 ns up to 32,768-character strings, because it compares handles, never bytes); deduplication is global and automatic, with no interning logic in user code; and giving up the GC stopped being a renunciation, since cells are immutable and content-addressed, so there is nothing to trace and nothing to move. Concurrency I kept deliberately simple-minded: no threads, no shared mutable state. A program splits into isolated "Spaces" (separate processes, isolation enforced by the MMU) that talk over shared-memory channels with explicit failure semantics. About what is verified and what is just hope: the ground truth is a regression suite of 112 examples plus a cross-Space scenario suite, with exit codes identical on Linux x86-64 and macOS Apple Silicon (Intel Macs: untested). The book on the site, 21 chapters plus appendices, had every snippet compiled and run before being written down. The benchmarks appendix declares its environment and method; I tried not to publish any number without one. The limits of 1.0 are written down as well, in a baseline document that lists every fixed pool (256 heaps per chain, 64 Spaces, 16 concurrent RPC sessions, and so on), with the rationale that a hard limit that fails loudly is a specification, while a soft limit that degrades silently is a bug. For the license I went with the GCC model: compiler and toolchain are AGPLv3, the runtime is AGPLv3 with an explicit linking exception, so the language itself stays free, and the programs you write in it are entirely yours, under any license you choose.

Site + book: https://yon-lang.org Repo: https://github.com/yon-language/yon (tag v1.0.0)

Happy to answer anything: the topos dialect, why a lattice rather than a hash, what the categorical constructs lower to, what broke along the way.