What is PLUS times PLUS?

An exploration of lambda calculus and Church encodings using John Tromp's visual lambda diagrams to analyze complex expressions.

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: youtube.com/playlist?list=PLi8_XqluS5xc7GL-bgVrxpA2Uww6nK0gV, 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 server about math, computer science, and other miscellaneous nerd stuff! discord.gg/XDb7x2BZAE Support us! 2swap: patreon.com/2swap 6884: ko-fi.com/iam6884 Sources and Links: Tromp's Diagrams, showcased throughout the video: 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: dkeenan.com/Lambda/ (Top Center) A notation I found on Robin Piedeleu's site, but which is likely much older: piedeleu.com/posts/diagrammatic-lambda-calculus/ (Top Right) de Brujin indices: en.wikipedia.org/wiki/De_Bruijn_index (Bottom Left) Vex (Wayne Citrin, Richard Hall, Benjamin Zorn): researchgate.net/publication/2726047_Programming_with_Visual… (Bottom Right) Visual Lambda Calculus (Viktor Massalõgin): bntr.planet.ee/lambda/work/visual_lambda.pdf / github.com/bntre/visual-lambda Lecture Notes on the Lambda Calculus (book): amazon.com/Lecture-Notes-Lambda-Calculus-Selinger/dp/0359158… 6884's Music: 6884.bandcamp.com/ A viewer-made Tromp Diagram applet: cruzgodar.com/applets/lambda-calculus/?expression-textarea=*… (By Cruz Godar) A viewer-made desmos Tromp Diagram calculator: desmos.com/calculator/rviihyo72n (By div140) This video was rendered using SwapTube! 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 :) Als