lambda calculus

Tom Stuart's Ruby Manor 3 talk builds FizzBuzz using nothing but Ruby lambdas, working through Church encodings of numbers, booleans and data structures. It is a hands-on introduction to lambda calculus.

2swap explores lambda calculus using John Tromp's lambda diagrams, with animated beta-reductions, asking what PLUS times PLUS gives. It touches on Church encodings and the equivalence of Turing machines and lambda calculus.

The preface to Herb Gross's MIT OpenCourseWare 'Calculus Revisited: Single Variable Calculus', an older black-and-white lecture series. It introduces his approach to teaching calculus from the basics.

An AWS re:Invent 2018 session in which Holly Mesrobian and Marc Brooker explain how AWS Lambda is built, including its sandboxing, isolation and scaling architecture. It covers what happens under the hood when serverless code runs.

Jim Weirich's RubyConf 2012 talk derives the Y combinator step by step, live-coding in Ruby lambdas. It builds up an understanding of functional programming and lambda calculus from first principles.

Philip Wadler's Lambda Days talk on propositions as types, the link between logic and computation that underlies theorem provers and programming language design.

Philip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.

Aditya Siram argues that functional programming has much to learn from Smalltalk's interactivity, using Pharo and Squeak to show live, visual, explorable programming environments.

Jose Valim introduces Nx, the project bringing numerical computing to Elixir, covering multi-dimensional tensors, automatic differentiation and JIT compilation to CPU and GPU.

Meredith Patterson and Sergey Bratus argue that networked software stays insecure because protocols and inputs are too complex to recognize safely. They propose using formal language theory and grammars to build secure, verifiable input handling.

Christopher Domas's Derbycon 2015 talk on the M/o/Vfuscator, a compiler that emits only x86 mov instructions, showing mov is Turing complete. It explains how a full machine is built from mov and why the output is a nightmare to reverse engineer.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

Tom Wildenhain's guest lecture for CMU's Esoteric Programming Languages course shows that PowerPoint transitions and slides are Turing complete without macros, building up to a mind-bending fractal ending.

Matt Might's Curry On talk on ending errors in code, both software and the human genome. He covers conservative approximation of the halting problem via static analysis and a computational approach to precision medicine.

Kyle Hill of Because Science explains and demonstrates, using real cards, how Magic: The Gathering can be used to build a Turing machine, a computer inside the card game.

Eugenia Cheng gives the opening keynote at Lambda World 2017, presenting category theory as very abstract algebra whose abstraction gives it broad applicability. She applies it to everyday questions including privilege and prejudice.