Dana Scott on Lambda Calculus
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:
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.