Difference between revisions of "Lambda Calculus"

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All decision making procedures can be represented into three major kinds of branching:
All decision making procedures can be represented into three major kinds of branching:
# [[Naming Abstraction]]:[[Naming Abstraction|<math>\alpha</math> conversion]]
# [[Naming Abstraction]]:[[Naming Abstraction|<math>\alpha</math> conversion]]
# [[Branching Abstraction]]:[[Branching Abstraction|<math>\beta</math> conversion]]
# [[Functional Abstraction]]:[[Functional Abstraction|<math>\beta</math> conversion]]
# [[Typing Abstraction]]:[[Typing Abstraction|<math>\gamma</math> conversion]]
# [[Composition Abstraction]]:[[Composition Abstraction|<math>\gamma</math> conversion]]


These three types also relate to the reason why [[Kan Extension]] is universal. To understand the intricate mechanisms of [[Lambda calculus]], and why and how this simple language can be universal, please read this page:[[Dana Scott on Lambda Calculus]].
These three types also relate to the reason why [[Kan Extension]] is universal. To understand the intricate mechanisms of [[Lambda calculus]], and why and how this simple language can be universal, please read this page:[[Dana Scott on Lambda Calculus]].

Revision as of 10:37, 19 May 2022

Lambda calculus is a universal/Turing-complete language specification invented by Alonzo Church, that is considered to be mathematically elegant, due to its small size. Almost all text-based formal languages are defined using Lambda calculus. To learn about its history, it is recommended to watch this video by Dana Scott[1].

Lambda Calculus and Abstract Syntax Tree

All decision making procedures can be represented into three major kinds of branching:

  1. Naming Abstraction: conversion
  2. Functional Abstraction: conversion
  3. Composition Abstraction: conversion

These three types also relate to the reason why Kan Extension is universal. To understand the intricate mechanisms of Lambda calculus, and why and how this simple language can be universal, please read this page:Dana Scott on Lambda Calculus.

Video Playlist

  • For people who wants to learn about Lambda Calculus, this video playlist[2] would be very useful.


References

  1. ↑ Scott, Dana (Aug 24, 2012). Dana S. Scott Lambda Calculus, Then and Now. local page: princetonacademics. 
  2. ↑ Lambda Calculus Playlist on Youtube

Related Pages

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