Fōrmulæ is a web-based visual environment for composing, conversing, and computing with tree-structured expressions. You build expressions by navigating and editing a tree — never by typing syntax — and they are rendered as mathematical and scientific notation on an HTML canvas. It runs entirely in the browser; there is nothing to install.
🌐 Live at formulae.org · 📦 Organization: formulae-org
This repository is the main program — the part that is always present, whatever fields you work in:
- The engine that visualizes, edits and manipulates expressions.
- The editing interface, a read–eval–print loop: each input expression is followed by its result. Unlike a typical REPL, you can select an earlier input, modify it, and request the result again. Scripts can be saved as local files to be retrieved later or shared.
- The reduction engine that evaluates expressions and returns results to be displayed.
- AI connections for the Converse mode (OpenAI, Anthropic, Google, and local models via Ollama).
- Message files (JSON) for several human languages, plus the HTML, CSS, images and icons the web app needs.
- Compose — present expressions: paragraphs, tables, equations, images, links, colors and lists. Because composing and computing share the same expressions, one file is both a runnable program and a formatted, human-readable document.
- Converse — send an expression to an AI model as a prompt. The model replies with a Fōrmulæ expression that renders in place, so equations, tables, code and inline images can appear in both the prompt and the response. Seet the AI Converse demo.
- Compute — evaluate expressions: arithmetic, symbolic algebra, logic, lists, strings, control flow, and more.
The main program handles expressions only in the abstract; the expressions for a specific field — arithmetic, typesetting, programming, … — live in separate packages, each in its own repository (package-{name}-js, listed under formulae-org). The program loads a base set of packages at startup and can load others on demand. Because the programming package makes Fōrmulæ Turing-complete and its expressions are pretty-printed, Fōrmulæ is also a visual programming language. To build your own package, see the Developer's guide for packages.
The entire formulae.org website — articles, showcases, examples and reference — is authored as Fōrmulæ .formulae files, not HTML, in the separate web-content repository.
The easiest way to use Fōrmulæ is at formulae.org. The app is plain JavaScript ES modules with no build step — to run a copy locally, serve this directory with any static HTTP server.