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

48 points by bntr 4 days ago | 9 comments

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 4 days ago

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 2 days ago

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

bntr 19 hours ago

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 17 hours ago

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 13 hours ago

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

I'd love to see them smoothly animated.

the_cat_kittles 24 hours ago

2swap has some incredible videos

recognity 14 hours ago

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 14 hours ago

Seems like it went to the wrong post.

bntr 2 days ago

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

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