Fōrmulæ is a web-based visual environment for computing, composing, and conversing 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.
- Compute — evaluate expressions: arithmetic, symbolic algebra, logic, lists, strings, control flow, and more.
- 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.
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.