Alpha-conversion
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-conversion is also a kind of naming abstraction. It means that by the distinguishable values of names, it serves as a kind of numbers or addresses to indicate ordering relation or quantity. The space of name (namespace) is a space of symbols, it provides a defined range of possible values to approximately represent the concepts of interest.
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."
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.