Difference between revisions of "Dana Scott on Lambda Calculus"
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==A neighborhood of a possibly infinite set...== | ==A neighborhood of a possibly infinite set...== | ||
*[https://youtu.be/S1aoZb7vF4M?t=3140 The neighborhood of a possibly infinite set is just determined by a finite subset... and its complement] | *[https://youtu.be/S1aoZb7vF4M?t=3140 The neighborhood of a possibly infinite set is just determined by a finite subset... and its complement] | ||
*[https://youtu.be/S1aoZb7vF4M?t=3172 A stronger topology, called product topology, where its complement ...] | *[https://youtu.be/S1aoZb7vF4M?t=3172 A stronger topology, called product topology, where its complement can also be expressed with finite information... Hausdorf set taking half the topology] | ||
==Once you define Topology, you may define continuous functions== | ==Once you define Topology, you may define continuous functions== | ||
Revision as of 03:05, 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:
"You don't need Turing Machine to understand it, I hope I can convince you of that."
Scott's Universe is the Powerset of Integers
In this lectureCite error: Invalid <ref> tag; invalid names, e.g. too many, Scott explicitly stated that:
"The Universe if the Powerset of Integers."
Sophomores or Juniors should learn some Topology
Sophomores or juniors should have some topology from calculus...
A neighborhood of a possibly infinite set...
- The neighborhood of a possibly infinite set is just determined by a finite subset... and its complement
- A stronger topology, called product topology, where its complement can also be expressed with finite information... Hausdorf set taking half the topology
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:
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.