Lambda Calculus

From PKC
Jump to navigation Jump to search

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:

A Table that Shows Representable Closure in Abstraction types
Technical Term Abstraction types Symbolic representation Description
-conversion Variable Naming abstraction A collection of symbols (names) that act as unique identifiers.
-reduction Substitution rule Function evaluations A template or executable function that can be reused in multiple contexts.
-composition Sequential composition Function composition The sequential/structural arrangements of known representable data.
  1. Naming Abstraction: conversion
  2. Functional Abstraction: reduction
  3. Composition Abstraction: reduction

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

D
J
L
P
Q
T
V
V cont.
V cont.

Retrieved from "https://pkc.pub/index.php?title=Lambda_Calculus&oldid=30823"