Kleene,s s-m-n Theorem
المؤلف:
Davis, M
المصدر:
Computability and Unsolvability. New York: Dover, 1982.
الجزء والصفحة:
...
18-1-2022
1256
Kleene's s-m-n Theorem
A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let 
denote the recursive function of 
variables with Gödel number 
(where (1) is normally omitted). Then for every 
and 
, there exists a primitive recursive function 
such that for all 
, 
, ..., 
,
A direct application of the 
-
-
theorem is the fact that there exists a primitive recursive function 
such that
for all 
and 
.
The 
-
-
theorem is applied in the proof of the recursion theorem. The 
-
-
theorem is the theoretical premise for a branch of computer science known as partial evaluation.
REFERENCES
Davis, M. Computability and Unsolvability. New York: Dover, 1982.
Kleene, S. C. Introduction to Metamathematics. Princeton, NJ: Van Nostrand, 1964.Rogers, H. Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press, 1987.
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