Tilessa🔗

Every computer you have ever used asks for your trust. Its datasheet describes what the chip is supposed to do; whether it actually does — every cycle, every corner case — is a promise backed by testing, and testing can only ever sample. The history of hardware lives in the gap between the two: errata sheets, security surprises, processors that computed the wrong answer once in a billion operations.

This book is an experiment in closing that gap. It describes Tilessa, a small parallel computer built for machine-learning workloads — and the book itself is written in a language a computer can check. Every definition in it is real, running code; every theorem is machine-verified each time the book is built. If a claim in this book were false, the book would fail to build, and you would not be reading it. We say it shortly: a page that builds cannot lie.

The design has one big idea, borrowed from mosaics. Instead of one large, complicated processor, a Tilessa is a grid of many small identical ones — tesserae, the word for the little tiles a mosaic is made of. Small things are easier to build, easier to prove correct, and easy to repeat; the interesting question, which most of this book is spent answering, is how small proved things compose into a big thing without losing what was proved. First the specification — the parts list and the rules of the game — then the semantics: what every instruction actually does, written as a program you can run. Later chapters will build the pipeline that executes instructions, prove it faithful, and compose elements into the mesh.