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. | ||
A list of them can be found here: | |||
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This video series seems to be taken in the same day, a total of 5 hours. Prof. Scott offered many anecdotal insights on how <math>\lambda</math> calculus was invented and formed. It directly relates to the notion of [[function]] and [[combinator]]s. Particularly, the [[SK Combinators]]. | |||
=Lecture 1= | =Lecture 1= | ||
This starting lecture talks about the name of Lambda came from<ref name="Scott Part 1">{{:Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 1 of 5 - λC 2017}}</ref>. | |||
=Lecture 2= | =Lecture 2= | ||
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=Lecture 3= | =Lecture 3= | ||
This lecture<ref name="Scott Part 3">{{:Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5 - λC 2017}}</ref> starts to mention the notion of [[algebraic closure]] and [[fixed point]]s. | |||
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Revision as of 02:32, 20 January 2022
Prof. Dana Scott gave a few talks on Lambda Calculus, and some of them are available on Youtube.
A list of them can be found here:
This video series seems to be taken in the same day, a total of 5 hours. Prof. Scott offered many anecdotal insights on how calculus was invented and formed. It directly relates to the notion of function and combinators. Particularly, the SK Combinators.
Lecture 1
This starting lecture talks about the name of Lambda came from[1].
Lecture 2
Godel Numbering
Think about variables in terms of special numbers. This is an insight from Godel[2]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
This lecture[3] starts to mention the notion of algebraic closure and fixed points.
References
- ↑ Scott, Dana (Oct 12, 2017). Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 1 of 5 - λC 2017. local page: LambdaConf.
- ↑ 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.
- ↑ Scott, Dana (Oct 12, 2017). Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5 - λC 2017. local page: LambdaConf.