Recursion theorems and effective domains
نویسندگان
چکیده
منابع مشابه
Independence Results for n-Ary Recursion Theorems
The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic t...
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We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene’s second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene’s second recursion theorem and Smullyan’s double recursion theorem. This leads us to define four classes of viruses, two of them being polymorphic. The...
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Following the program of Moggi, the semantics of a simple non-deterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle non-termination properly. Instead, a novel construction is proposed and investigated. It embodies both non-determinism (choice and failure) and...
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Erdos, F eller, and Pollard [2] pro ved that if the greatest common divi or of the k's with c,,>O is 1, then , Other theorems of the same type as theorem 1 were proved by T . Kaluza [4] . Assuming (1) , he showed for instance, that j (2) > 0, j (n l )j (n + 1) > p(n ) (n = 2,3, . .. ) imply that the c's are positive. Furthermore, he proved that j (I ),j(2), ... is a moment equence if, and only ...
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Register machine programs provide explicit proofs of the sn -Theorem, Kleene’s Second Recursion Theorem, and Smullyan’s Double Recursion Theorem. Thus these programs provide a pedagogically useful approach. We develop this topic from scratch, hence without appeal to the existence of universal programs, pairing, quotation, or any form of coding device. None of the results are new from the point ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1988
ISSN: 0168-0072
DOI: 10.1016/0168-0072(88)90029-2