What is PLUS times PLUS?

ERRATA:
• The "Church-Turing Thesis" is different from the "Church-Turing Theorem". The "theorem" is the claim which I discussed in the video- namely, that the Turing machine and lambda calculus are equally powerful. The "thesis" is the informal claim that the two of these systems are a sufficient formalization which capture the idea of "arbitrary computation".
• I claimed in the end of the video that this was the first example of animated beta-reductions of visual lambda expressions. Paul Brauner has some videos here:    • Lambda Diagrams  , although they do not explicitly animate the mechanics of one step of beta-reduction! I probably should have chosen my words more carefully. Sorry Paul- linked you in an info card in the top right!
• It seems that both lisp and rust blur the line between functional and imperative programming more than I realized, so take that chart at the end with a grain of salt!
• While the expression (*(+ +)), treated as a 4-argument function, yields (d^(c^b))^(a+c), inserting the 4th argument is actually not necessary! You can treat it as a 3-argument function, and it reduces to (c^b)*(a+c).

JOIN OUR DISCORD!   / discord  

Support us!
2swap:   / 2swap  
6884: https://ko-fi.com/iam6884

Sources and Links:
Tromp's Diagrams, showcased throughout the video: https://tromp.github.io/cl/diagrams.html
At 4:28, a number of visualizations for the Lambda Calculus were shown. These include:
(Top Left) David C Keenan's Graphical Notation for the Lambda Calculus: https://dkeenan.com/Lambda/
(Top Center) A notation I found on Robin Piedeleu's site, but which is likely much older: https://piedeleu.com/posts/diagrammat...
(Top Right) de Brujin indices: https://en.wikipedia.org/wiki/De_Brui...
(Bottom Left) Vex (Wayne Citrin, Richard Hall, Benjamin Zorn): https://www.researchgate.net/publicat...
(Bottom Right) Visual Lambda Calculus (Viktor Massalõgin): https://bntr.planet.ee/lambda/work/vi... / https://github.com/bntre/visual-lambda
Lecture Notes on the Lambda Calculus (book): https://www.amazon.com/Lecture-Notes-...
6884's Music: https://6884.bandcamp.com/
A viewer-made Tromp Diagram applet: https://cruzgodar.com/applets/lambda-... (By Cruz Godar)
A viewer-made desmos Tromp Diagram calculator: https://www.desmos.com/calculator/rvi... (By div140)

This video was rendered using SwapTube! https://github.com/2swap/swaptube

Oh, also, this is my first time using auto-dubbed tracks. I am VERY IRRITATED to have to use this... I happen to speak a few languages on the list and I would have preferred to dub it myself. As far as I can tell, I as a creator am not even given the opportunity to do so. If anyone else knows of a way, please comment :) Also, let me know if the AI dub in your language is particularly poor.