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

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 sto