Process Maths

John Baez was the first person I ever heard use the term functor. He used to (maybe he still does?) publish a newsletter called This Week's Finds in Mathematical Physics which I sometimes read with bemusement when I was in the first year of studying undergraduate maths.

This is all about representing diagrams and processes. See Two Interesting Videos on Groups.

Subscribe to Topos Institute.

Gerald Jay Sussman talking about scheme programs as wiring diagrams, ... (1986)

Subscribe to MIT Open Courseware.

Jonathan Sobel talking about Categorical Semantics (December 2004). He starts talking about the equivalence of Turing Machines and Lambda Calculus with capture-avoiding substitution. See Ian Grant's Weather Report agosto 01, 2022 for more on logical frameworks for formally specifying semantics, and Gerald Sussman on Rewriting Systems for more about ways to think of rewriting systems as biological and chemical reactions.

Att 15:24 he quotes Dana Scott on the origins of the idea of a Cartesian Closed Category (Eilenberg and Kelly, Closed Categories, 1966) which was around the time John H. Conway was giving his Cambridge course on Regular Algebra and Finite Machines. See Ian Grant's Weather Report julio 23, 2022.

As an exercise you might care to think about simulating a Universal Turing Machine using recursive Lamba expressions for each state and lists for the part of the tape behind the head and the other part underneath and in front of it. It's not too hard [NB: I'm breaking the second law!]. But defining a Turing Machine that carries out normal-order lambda reduction is not so easy.

Subscribe to William Byrd.

Comments

Post a Comment

Popular posts from this blog

Live Science - Leonardo da Vinci's Ancestry

Image
... and his posterity too? See  On Communication in Linear Time And Hypertext And The Gospel of Sophia . So it looks like El Cielo of the cistine [sic!😂] chapel is not the limit anymore.  I think I just met one of his descendents. A guy called Versailles Toledo who is from Chiapas. That might explain the murals I mention in my recent untitled post , just before the post mentioning this video. I also just took this photo of Rafael Gonzales, born here in Tecate, B.C., who told me about a spring near here called Agua Fría , half way from Tecate to Loma Tova , where, a few decades ago, people used to go to have barbecues and stuff, but now he thinks it may be private land. If someone reading this has a Facebook account, please write a link to this post onto his FB page. To see why I took the photo, look at his T-shirt and the horse-shoes and ponder this: Subscribe to BeatrizER and her video(s?) about mathematical logic, ... Sounds like Edith (II) Rix has been online all the t...
Read more

David Turner Obituary by Sarah Nicholas Fri 24 Nov 2023

Image
This was in The Guardian: David Turner obituary , only eight days after I posted  David Turner Talking About Sixty Years of Functional Programming History : This talk was given in London in 2017: See  Turner, D. A. "Some History of Functional Programming Languages" also  John Hughes - Why Functional Programming Matters  and David MacQueen's talk at ICFP 2015 in  Numberphile - Sophie Maclean on the Catalan Numbers . At 10:30 This whole discussion abut combinator reduction is especially interesting. I didn't know Arthur Norman had tried building hardware for combinator machines. I'll look that up: maybe start here A.C. Norman  Faster combinator reduction using stock hardware  in LFP '88: Proceedings of the 1988 ACM conference on LISP and functional programming. At 26:25 on the ISWIM virtual machine implemented in the PAL compacting garbage collector?! This work Reynolds and others did was at MIT in Masecheusetts and Argonne National Laboratory ...
Read more