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: https://www.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! https://discord.gg/XDb7x2BZAE Support us! 2swap: https://www.patreon.com/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/diagrammatic-lambda-calculus/ (Top Right) de Brujin indices: https://en.wikipedia.org/wiki/De_Bruijn_index (Bottom Left) Vex (Wayne Citrin, Richard Hall, Benjamin Zorn): https://www.researchgate.net/pu