Difference between revisions of "Alpha-conversion"
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<math>\alpha</math> conversion is also a kind of naming abstraction. | <math>\alpha</math>-conversion is also a kind of naming abstraction. It means that by the distinguishable values of '''[[name]]s''', it serves as a kind of numbers or addresses to indicate ordering relation or quantity. The space of [[name]] ([[namespace]]) is a space of symbols, it provides a defined range of possible values to [[PAC|approximately]] [[representable|represent]] the concepts of interest. | ||
=Godel Numbering= | |||
Think about variables in terms of special numbers. This is an insight from Godel<ref name="Scott Part 2">{{:Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 2 of 5 - λC 2017}}</ref><ref extends="Scott Part 2">[https://youtu.be/S1aoZb7vF4M?t=2880 Scott said:"With a little bit of set theory and arithmetic, this can be taught to juniors."] </ref>, and later utilized to created [[Universal computation]]. | |||
=We don't need Turing Machine= | |||
In this lecture<ref extends="Scott Part 2">[https://youtu.be/S1aoZb7vF4M?t=3196 Scott:"We don't need Turing Machine."]</ref>, Scott explicitly stated that: | |||
"We don't need Turing Machine, I hope I can convince you of that." | |||
<noinclude> | <noinclude> | ||
=References= | =References= | ||
<references/> | <references/> | ||
Latest revision as of 13:42, 19 May 2022
-conversion is also a kind of naming abstraction. It means that by the distinguishable values of names, it serves as a kind of numbers or addresses to indicate ordering relation or quantity. The space of name (namespace) is a space of symbols, it provides a defined range of possible values to approximately represent the concepts of interest.
Godel Numbering
Think about variables in terms of special numbers. This is an insight from Godel[1]Cite error: Invalid <ref> tag; invalid names, e.g. too many, and later utilized to created Universal computation.
We don't need Turing Machine
In this lectureCite error: Invalid <ref> tag; invalid names, e.g. too many, Scott explicitly stated that:
"We don't need Turing Machine, I hope I can convince you of that."
References
- ↑ Scott, Dana (Oct 12, 2017). Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 2 of 5 - λC 2017. local page: LambdaConf.