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‎README.md‎

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<sub>The project has been moved from https://code.google.com/archive/p/visual-lambda/<br/>and from https://bitbucket.org/bntr/visual-lambda as well.</sub>
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<sub>The project was migrated from https://code.google.com/archive/p/visual-lambda/ and from https://bitbucket.org/bntr/visual-lambda.</sub>
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# Visual Lambda Calculus
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![logo](https://bntr.planet.ee/lambda/loop_.gif)
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The Visual Lambda environment enables intuitive manipulation of lambda calculus expressions.
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Visual Lambda is a graphical environment and visual programming tool
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for exploring pure lambda calculus using Bubble Notation.
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It represents lambda expressions as colorful, tree-like 2D structures
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and animates beta-reduction steps smoothly, making reductions easy to follow.
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![](https://raw.githubusercontent.com/bntre/visual-lambda/master/screenshot.png)
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**Try it live**: https://bntr.itch.io/visual-lambda
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Also available online at: [https://bntr.itch.io/visual-lambda](https://bntr.itch.io/visual-lambda)
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The project started as a master's thesis (2008); see the thesis for details:
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[visual_lambda.pdf](https://bntr.planet.ee/lambda/work/visual_lambda.pdf).
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## Notation
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- [Basics](https://bntr.planet.ee/lambda/visual_lambda_bubble_notation.gif)
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- More detailed in this thesis: [visual_lambda.pdf](https://bntr.planet.ee/lambda/work/visual_lambda.pdf)
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This might be useful for students, educators and researchers who want
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an intuitive, interactive way to explore λ‑calculus and reduction strategies.
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## Examples
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- Pairs, construction, reduction: [https://www.youtube.com/watch?v=YEyyyzUuUJQ](https://www.youtube.com/watch?v=YEyyyzUuUJQ)
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- Predecessors: [https://www.youtube.com/watch?v=CWzn2ucPMdg](https://www.youtube.com/watch?v=CWzn2ucPMdg)
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- ['MULT 3 2' evaluation](https://bntr.planet.ee/lambda/visual_lambda_MULT_3_2_=_6.gif) (gif)
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- ['((λgm.m(gg))(λgm.m(gg)))M' building and evaluation](https://bntr.planet.ee/lambda/lambda_F_anim.gif) (gif)
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- ['Y I' evaluation](https://bntr.planet.ee/lambda/Y_I.gif) (gif)
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![Screenshot](https://raw.githubusercontent.com/bntre/visual-lambda/master/screenshot.png)
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## Bubble Notation
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## Dependencies
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- python 3
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![Basics](https://bntr.planet.ee/lambda/visual_lambda_bubble_notation.gif)
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Watch a short demo to get an idea of how Bubble Notation works:
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https://www.youtube.com/watch?v=aRgu8S3Pnb8
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<p><a href="https://www.youtube.com/watch?v=aRgu8S3Pnb8" title="Factorial 3">
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<img src="https://img.youtube.com/vi/aRgu8S3Pnb8/maxresdefault.jpg" width="600" alt="Factorial 3"/>
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</a></p>
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Other video examples:
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- Pairs, construction and reduction: https://www.youtube.com/watch?v=YEyyyzUuUJQ
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- Predecessors: https://www.youtube.com/watch?v=CWzn2ucPMdg
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- Recursion: https://www.youtube.com/watch?v=bGG9exO2kew
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Old GIF examples:
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- 'MULT 3 2' evaluation: [MULT_3_2_=_6.gif](https://bntr.planet.ee/lambda/visual_lambda_MULT_3_2_=_6.gif)
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- 'Y I' evaluation: [Y_I.gif](https://bntr.planet.ee/lambda/Y_I.gif)
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## Requirements
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Dependencies
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- Python 3.8+
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- pygame-ce 2.5.6
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## Runningpython
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python main.py
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Install and run locally:
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```
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pip install pygame-ce==2.5.6
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python main.py
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```
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## Controls
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- [controls.txt](controls.txt)
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## Predefined expression library
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- [library.txt](library.txt)
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See the full UI control reference in [controls.txt](controls.txt).
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## Expression library
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The repository includes a small library of predefined expressions that
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you can paste into the console: see [library.txt](library.txt).
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## Related work
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## Related works
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- [Programming with Visual Expressions, Wayne Citrin](https://web.archive.org/web/20110524135539/users.encs.concordia.ca/~haarslev/vl95www/html-papers/citrin/citrin.html)
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- [A Graphical Notation for the Lambda Calculus, Dave Keenan](https://dkeenan.com/Lambda/)
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- [Alligator Eggs, Bret Victor](http://worrydream.com/AlligatorEggs/) ([browser game](https://tibordp.github.io/gator-calculus/))
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- More in [Prathyvsh's catalog](https://github.com/prathyvsh/lambda-calculus-visualizations)
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## Future work
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I still think Bubble Notation is a promising way to represent lambda terms, but this implementation is a bit dated.
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A modern reimplementation could improve interaction and visuals.
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Possible directions:
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- Make terms feel more "springy" and react to dragging with natural, physics-like motion.
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- Revisit the lazy-evaluation visualization to make it clearer and more robust.

‎controls.txt‎

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--------------------------------------------------------
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Controls
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Visual Lambda environment mouse/keyboard controls
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View
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Zoom Mouse Wheel, +/-
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Move Middle mouse button, Arrow buttons
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Refresh F5
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Items
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Input from console I
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Examples:
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>> \x y. (\x. x)
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>> FACT 3 (see library.txt)
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>> "Label"
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Items on screen (lambda terms or text labels)
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Select, Drag Left mouse button
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With selected item
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Delete D
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Copy C
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Add Free Variable V
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Zoom View Mouse Wheel, +/-
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Move View Middle mouse button, Arrows
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Refresh View F5
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Reduce Selected Enter
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Nonstop reduction Ctrl+Enter
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Input from console I
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Examples:
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>> \x y. (\x. x) add lambda term
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>> FACT 3 add predefined lambda term, see library.txt
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>> "Label" add text label
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Modes of reduction
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Applicative/Normal Alt+A
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Lazy/Pure Alt+L, Alt+P
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Inside selection Alt+S
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Quick Mode Q
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Pick for reduction
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Construction of lambda terms
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Construction of terms
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Expand selection Space
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Add Free Variable V
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Add free variable V
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With selected sub-term
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Delete Delete
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Insert Application before Insert, A
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Insert Application after Ctrl+Insert, Ctrl+A
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Insert Lambda Alt+Insert, L
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Delete Del
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Insert application before Ins or A
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Insert application after Ctrl+Ins or Ctrl+A
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Insert lambda Alt+Ins or L
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Bind Variable/Lambda with
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selected Lambda/Variable RClick or Ctrl+LClick
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Applicate Drop Item onto another
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Expand selection Space
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Create application (apply) Drop one term onto another
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Substitute a free variable
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with a term Drop the term onto the free variable
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Reduction
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Substitute for free variable
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with Item Drop Item onto free variable
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Reduce single step Enter
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Full reduction Ctrl+Enter
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Modes of reduction
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Applicative/Normal Alt+A
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Lazy/Pure Alt+L, Alt+P
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Inside selection only Alt+S
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Quick (Finger) Mode Q
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Pick a term for reduction
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History
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Undo Ctrl+Z, Alt+Left, Backspace
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Workspace
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Save Ctrl+S
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Load Ctrl+O
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Zoom Wheel
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Save screen to png F12
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Mode of export frames Alt+E
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Saving images/frames
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Save screen to png F12
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Mode of export frames Alt+E

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