Petri nets were invented in 1962. They predate Unix, the internet, and object-oriented programming. For most of their history, they lived in academic papers — a formalism known to theorists but invisible to working programmers.
This book argues they deserve wider use. Not because they're elegant (they are) but because they solve practical problems. A Petri net is a state machine that handles concurrency. It's a workflow engine with formal guarantees. It's a simulation model that converts to differential equations. It's a specification that can be verified, compiled to code, and proven in zero knowledge.
You define a Petri net, simulate it with ODEs, and the structure becomes a scaffold for LLM-generated code. The net is the spec that both humans and LLMs can reason about.
I use Claude Code with a skill file that enforces: sketch topology → validate with simulation → extend monotonically → never delete, only grow. The discipline works with how LLMs operate.
I've been experimenting with Petri nets as a shared representation between humans and LLMs. The model becomes the artifact—you sketch topology, validate with simulation, extend monotonically. Code is derived.
Why Petri nets? Visual (humans can reason about them), mathematical (ODEs, invariants), executable, and compositional. LLMs can manipulate the structure without losing semantic meaning.