Difference between revisions of "Lambda Calculus"

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=[[Lambda Calculus]] and [[Abstract Syntax Tree]]=
=[[Lambda Calculus]] and [[Abstract Syntax Tree]]=
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:
# [[<math>\alpha</math> conversion]]:Naming Abstraction
# [[Naming Abstraction]]:[[Naming Abstraction|<math>\alpha</math> conversion]]
# [[<math>\beta</math> conversion]]:Branching Abstraction
# [[Branching Abstraction]]:[[Branching Abstraction|<math>\beta</math> conversion]]
# [[<math>\gamma</math> conversion]]:Typing Abstraction
# [[Typing Abstraction]]:[[Typing Abstraction|<math>\gamma</math> conversion]]


This three types also relates to the reason why [[Kan Extension]] is universal.
These three types also relate to the reason why [[Kan Extension]] is universal.


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Revision as of 02:12, 19 January 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. Branching Abstraction: conversion
  3. Typing Abstraction: conversion

These three types also relate to the reason why Kan Extension is universal.


References

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

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