Kleene's recursion theorem | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Kleene%...
00:00:43 1 Notation
00:02:31 2 Rogers's fixed-point theorem
00:03:37 2.1 Proof of the fixed-point theorem
00:09:20 2.2 Fixed-point free functions
00:10:21 3 Kleene's second recursion theorem
00:12:25 3.1 Comparison to Rogers's theorem
00:13:05 3.2 Application to quines
00:14:31 3.3 Application to elimination of recursion
00:17:53 3.4 Reflexive programming
00:18:33 4 The first recursion theorem
00:20:39 4.1 Example
00:20:46 4.2 Proof sketch for the first recursion theorem
00:24:16 4.3 Comparison to the second recursion theorem
00:24:42 5 Generalized theorem
00:26:23 6 See also
00:27:30 7 References
00:28:49 8 External links
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SUMMARY
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In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first proved by Stephen Kleene in 1938 and appear in his 1952 book Introduction to Metamathematics. A related theorem which constructs fixed points of a computable function is known as Rogers's theorem and is due to Hartley Rogers, Jr. (1967).
The recursion theorems can be applied to construct fixed points of certain operations on computable functions, to generate quines, and to construct functions defined via recursive definitions.
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