About

A site for visualizing the λ-calculus through John Tromp's diagrammatic notation — interactive, animated, and built to be played with.

Who

Built by EmyoT, with substantial help from Claude (Anthropic). The whole project — parser, β-reducer, layout engine, animations, UI — was put together iteratively in conversation with the model.

Why

The λ-calculus is a beautiful object: small enough to fit in a paragraph, powerful enough to express all of computation. Most introductions to it lean heavily on syntax and rewrite rules, which make it feel abstract. Tromp diagrams reverse that: they give you something concrete and spatial. Watching plus 2 3 reduce, line by line, into the Church numeral for 5 is a different kind of understanding than reading the same reduction on paper.

This site is an excuse to spend more time with that visual intuition.

Credits and references

• John Tromp — Binary Lambda Calculus and Combinatory Logic (the source of the diagram notation and BLC encoding)
• Lambda calculus — Wikipedia
• Church encoding — Wikipedia
• De Bruijn indices — Wikipedia
• Fixed-point combinators — Wikipedia

Stack

Pure HTML / CSS / JavaScript — no build step, no framework, no dependencies. Just open the files in a browser. The visualizer's animation engine uses requestAnimationFrame on raw SVG elements, with line-level transitions tracked through a substitution origin map so each line "knows" where it came from after a β-reduction.

Source

The project is local-first — all your user definitions and history are stored in your browser's localStorage. Nothing is sent anywhere.

Special thanks

• Claude (Anthropic) — co-author for every line of code. Most of this site was iterated through conversation; if it weren't obvious from the dev notes, none of it would exist at this scale otherwise.
• Beta testers — friends who clicked through half-broken builds, found the rough edges, and didn't roll their eyes when the diagrams broke.
• You — for actually reading this far. Tromp diagrams are a niche within a niche; you being here is the whole point.

Contact

Bug reports, ideas, or just hello: emyotyyy@gmail.com

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If you spot a bug or have an idea, the easiest place to look is the source: open ../visualizer/ and the JS modules in js/.