Dana Scott on Lambda Calculus
Revision as of 03:00, 19 January 2022 by Benkoo (talk | contribs) (→Sophomores or Juniors should learn some Topology)
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...
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.