Recursive Functionals
- 1st Edition, Volume 131 - May 18, 1992
- Author: L.E. Sanchis
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 5 5 8 5 3 - 4
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 8 8 7 1 7 - 3
This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory… Read more
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Request a sales quoteThis work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.
Mappings and Domains. Functionals and Predicates. Basic Operations. Primitive Recursive Operations. Basic Recursion. Church's Thesis. Functional Recursion. Recursive Algorithms. Formalization: Structural Semantics. Formalization: Reductional Semantics. Interpreters. A Universal Interpreter. Enumeration. Continuous Functionals. A Selector Theorem. Hyperenumeration. Recursion in Normal Classes. Recursion and Church's Thesis. References. Index.
- No. of pages: 276
- Language: English
- Edition: 1
- Volume: 131
- Published: May 18, 1992
- Imprint: North Holland
- Paperback ISBN: 9780444558534
- eBook ISBN: 9780080887173
LS
L.E. Sanchis
Affiliations and expertise
School of Computer and Information Science, Syracuse University, Syracuse, NY, USARead Recursive Functionals on ScienceDirect