John Tromp: The Binary Lambda Calculus, The Smallest Program Language

Web Reference: 1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. 4 In him was life, and that life was the light of all mankind. 5 The light shines in the darkness, and the darkness has not overcome[a] it. John the Apostle is traditionally believed to be one of two disciples (the other being Andrew) recounted in John 1:35–39, who upon hearing the Baptist point out Jesus as the "Lamb of God", followed Jesus and spent the day with him, thus becoming the first two disciples called by Jesus. Read the Book of John online. Scripture chapters and verses with full summary, commentary meaning, and concordances for Bible study.

YouTube Excerpt: We'll discuss the Binary Lambda Calculus (BLC), an extremely simple programming language that is basically lambda calculus written in binary, whose design was motivated by the study of minimal size programs. We'll look at several example programs such as a 4-bit cat and a prime sieve. We'll show how BLC programs are at most a constant longer than those in any other language, how to define several notions of complexity of mathematical objects, and how to prove theorems about them. We'll see how to define a busy beaver function, how to define the uncomputable number known as Chaitin's constant, and how to win obfuscation contests. John Tromp is a Dutch computer scientist. He formerly worked for Dutch Centre for Mathematics and Computer Science. Tromp discovered the number of legal states of the board game Go, and co-authored with Bill Taylor the Tromp-Taylor Rules, which they call "the logical rules of Go". Paper on the Binary Lambda Calculus: http://tromp.github.io/cl/LC.pdf And check out John's LC & CL Playground: http://tromp.github.io/cl/cl.html John's Homepage is here for his other explorations: https://tromp.github.io

We'll discuss the Binary Lambda Calculus (BLC), an extremely simple programming language that is basically lambda calculus written in binary, whose...

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