Difference between revisions of "Dana Scott on Lambda Calculus"
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Prof. Dana Scott gave a few talks on Lambda Calculus, and some of them are available on Youtube. | Prof. Dana Scott gave a few talks on Lambda Calculus, and some of them are available on Youtube. | ||
=Lecture 1= | |||
=Once you define Topology, you may define continuous functions= | =Lecture 2= | ||
==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." | |||
==Once you define Topology, you may define continuous functions== | |||
*[https://youtu.be/S1aoZb7vF4M?t=3290 Define Continuous Functions] | *[https://youtu.be/S1aoZb7vF4M?t=3290 Define Continuous Functions] | ||
*[https://youtu.be/S1aoZb7vF4M?t=3305 The main difficulty is that there are two quantifiers, forming a rational number] | *[https://youtu.be/S1aoZb7vF4M?t=3305 The main difficulty is that there are two quantifiers, forming a rational number] | ||
*[https://youtu.be/S1aoZb7vF4M?t=3315 Finite amount of information can only be represented by a finite amount of rational numbers] | *[https://youtu.be/S1aoZb7vF4M?t=3315 Finite amount of information can only be represented by a finite amount of rational numbers] | ||
=Lecture 3= | |||
A list of them can be found here: | A list of them can be found here: | ||
{{#ask: [[Category:Dana Scott on Lambda Calculus]] | {{#ask: [[Category:Dana Scott on Lambda Calculus]] | ||
Revision as of 02:47, 19 January 2022
Prof. Dana Scott gave a few talks on Lambda Calculus, and some of them are available on Youtube.
Lecture 1
Lecture 2
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."
Once you define Topology, you may define continuous functions
- Define Continuous Functions
- The main difficulty is that there are two quantifiers, forming a rational number
- Finite amount of information can only be represented by a finite amount of rational numbers
Lecture 3
A list of them can be found here:
- ↑ 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.