Show HN: Visual Lambda Calculus – a thesis project (2008) revived for the web

[bntr]

Originally built as my master's thesis in 2008, Visual Lambda is a graphical environment where lambda terms are manipulated as draggable 2D structures ("Bubble Notation"), and beta-reduction is smoothly animated.

I recently revived and cleaned up the project and published it as an interactive web version: https://bntre.github.io/visual-lambda/

GitHub repo: https://github.com/bntre/visual-lambda

It also includes a small "Lambda Puzzles" challenge, where you try to extract a hidden free variable (a golden coin) by constructing the right term: https://github.com/bntre/visual-lambda#puzzles

[bntr]

For comparison: factorial(3) visualized in two different notations.

John Tromp's Lambda Diagrams (via 2swap): https://www.youtube.com/watch?v=RcVA8Nj6HEo&t=1346s

Bubble Notation: https://www.youtube.com/watch?v=aRgu8S3Pnb8

[discarded1023]

Here's another from a long time ago: https://dkeenan.com/Lambda/

[bntr]

I like this catalog: https://github.com/prathyvsh/lambda-calculus-visualizations

And it seems that John Tromp's diagrams originate from David C. Keenan's Mockingbird (1996),

and Bubble Notation comes from Wayne Citrin's Visual Expressions (1995)

[discarded1023]

Thanks for the link! Some very pretty stuff there.

Missing AFAICT are categorical string diagrams. I'm only sort-of familiar with the notation for Haskell Arrows [1,2] but a quick google for "lambda calculus string diagrams" turns up some recent work by Dan Ghica and others that may be of interest.

[1] https://en.wikipedia.org/wiki/String_diagram

[2] Ross Paterson "A New Notation for Arrows" (2001)

[bntr]

Thanks! I liked the pics here: https://piedeleu.com/posts/diagrammatic-lambda-calculus/

I'd love to see them smoothly animated.

[the_cat_kittles]

2swap has some incredible videos

[recognity]

Really cool approach. The "Ollama for classical ML" framing makes it instantly clear what this does.

I've been building CLI-first tools myself and the pattern of wrapping complex workflows into simple terminal commands is underrated. Most devs I know would rather type one command than spin up a Jupyter notebook for a quick prediction.

Curious about the model format — do you plan to support a registry where people can publish pre-trained models, like Ollama's library? That would be the killer feature for adoption.

[bntr]

Seems like it went to the wrong post.

[bntr]

You can also construct your own puzzles and share them via URL.

Example: https://bntre.github.io/visual-lambda/#workspace=H4sIAAAAAAA...