9 edition of **Recursive functionals** found in the catalog.

- 5 Want to read
- 8 Currently reading

Published
**1992** by North-Holland in Amsterdam, New York .

Written in English

- Recursive functions.

**Edition Notes**

Includes bibliographical references (p. 265-267) and index.

Statement | Luis E. Sanchis. |

Series | Studies in logic and the foundations of mathematics ;, v. 131 |

Classifications | |
---|---|

LC Classifications | QA9.615 .S26 1992 |

The Physical Object | |

Pagination | xii, 277 p. : |

Number of Pages | 277 |

ID Numbers | |

Open Library | OL1708924M |

ISBN 10 | 0444894470 |

LC Control Number | 92010555 |

the well-known ﬁrst recursion theorem, the ﬁxed point theorem in untyped lambda calculus, and G¨odel’s diagonalization lemma can be obtained; while Mulry [96] introduces the recursive topos as a natural setting to consider a generalization of the Banach-Mazur functionals to all higher : Pieter Hofstra, Philip Scott. The functional looks similar to a recursive implementation of x * y given the if x = 0 return 0 and function call with x - 1, but I don't see where to go with this. To find a fixed point in a normal mathematical equation you'd just set T(f,x,y) = f(x,y) and solve, but given the format that doesn't really work. studied it with care, and presently found that it led to a contradiction. Precision was clearly needed. Kleene's subsequent research provided this, as for example, in his influential and authoritative book Introduction to Metamathematics, which was translated into Russian, Chinese, Romanian, and Spanish. One feature of this book is the clear formulation of Gödel's theorem.

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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 Cited by: 2.

This monograph carries out the program which the author formulated in earlier work, the formalization of the theory of recursive functions of type 0 and 1 and of the theory of by: 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 Book Edition: 1.

Search in this book series. Recursive Functionals. Edited by Luis E. Sanchis. VolumePages ii-ix, () Download full volume. Previous volume. Next volume. Actions for selected chapters.

Select all / Deselect all. Download PDFs Recursive functionals book citations. Show all chapter previews Show all chapter previews. Recursive functionals. [Luis E Sanchis] -- 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 of higher order. ISBN: OCLC Number: Description: xii, pages: illustrations ; 24 cm. Contents: Mappings and Domains. Functionals and Predicates. 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.

Buy Formalized Recursive Functionals & Formalized Realizability by S C Kleene, Stephen Cole Kleene online at Alibris. We have new and used copies available, in 1 editions - starting at $ Shop now. Title (HTML): Formalized Recursive Functionals and Formalized Realizability Author(s) (Product display): S.

Kleene Book Series Name: Memoirs of the American Mathematical Society. Formalized Recursive Functionals and Formalized Realizability (Amer Math Soc Memoir - # 89) by Kleene, Stephen C.

and a great selection of related books, art and collectibles available now at. Recursion on the Countable Functionals. Authors: Normann, D. Computability vs recursion.

Pages Normann, Dag. Preview. The computable structure on Ct(k) Pages *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of.

Looking for books by Stephen Cole Kleene. See all books authored by Stephen Cole Kleene, including Mathematical Logic, and Formalized Recursive Functionals and Formalized Realizability (Memoirs; No. 1/89), and more on Computability and Recursion - Volume 2 Issue 3 - Robert I.

Soare. We consider the informal concept of “computability” or “effective calculability” and two of the formalisms commonly used to define it, “(Turing) computability ” and “(general) recursiveness ”.We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed Cited by: II.

Generalized Recursion Theory Unimonotone functions of finite types (recursive Recursive functionals book and quantifiers of finite type revisited IV) STEPHEN C. KLEENE Canonical forms and hierarchies in generalized recursion theory PHOKION G. KOLAITIS Aspects of the continuous functionals DAG NORMANN Post's problem in E'-recursionFile Size: 3MB.

The following example uses a recursive function to print a string backwards. of an array, can be deﬁned as follows: • If there is only one element, the sum is the value of this element.

• Otherwise, the sum is calculated by adding the ﬁrst element and the sum of the rest. Here is the C++ implementation:File Size: KB. A Restricted Computation Model on Scott Domains and its Partial Primitive Recursive Functionals.

Karl-Heinz Niggl - - Archive for Mathematical Logic 37 (7) Effective Enumerability of Some Families of Partially Recursive Functions Connected With Computable by: 4. Recursion on the Countable Functionals. Authors; Dag Normann; Book. 34 Citations; 2 Mentions; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access.

Buy eBook. USD Computability vs recursion. Dag Normann. Pages The computable structure on Ct(k) Dag Normann. Pages In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory.

The main core of the book gives an account of the general theory of by: Functional Interpretations This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory.

RECURSIVE FUNCTIONALS AND QUANTIFIERS OF FINITE TYPES REVISITED I A function is primitive recursive in total functions 0, iff it is definable from 0 using the schemata we listed in except that (XII) (called 55 in by: Purchase Classical Recursion Theory, Volume - 1st Edition. Print Book & E-Book.

ISBNRecursive Functions in Computer Theory by PÉTER, Rózsa: and a great selection of related books, art and collectibles available now at Recursive Functions by Rozsa Peter - AbeBooks Passion for books.

Theory of Recursive Functions and Effective Computability book. Read 3 reviews from the world's largest community for readers. (Reprint of the edition)4/5. The primitive recursive functionals are the smallest collection of objects of finite type such that: The constant function f(n) = 0 is a primitive recursive functional.

The successor function g(n) = n + 1 is a primitive recursive functional. The recursive functions are characterized by the process in virtue of which the value of a function for some argument is defined in terms of the value of that function for some other (in some appropriate sense “smaller”) arguments, as well as the values of certain other functions.

In order to get the whole process started a certain class of. A Restricted Computation Model on Scott Domains and its Partial Primitive Recursive Functionals.

Karl-Heinz Niggl - - Archive for Mathematical Logic 37 (7) Equivalence of Bar Recursors in the Theory of Functionals of Finite by: 3. Primitive recursive functions. Alterations of quantifiers.

Partial and general recursive functions. Construction of indices. Reduction of the inductive definition of {z}(a) ≃ w to an explicit definition. Reduction in type of a quantifier. Predicates of order r. book Admissible sets and structures (XLIII ). This book does not pretend to be a comprehensive treatment of descriptive set theory, of recursive functionals of finite type, or of recursion on ordinals.

Instead it serves as a nice intro-duction to each of these related areas. There are numerous exercises at the end of each section. Project Euclid - mathematics and statistics online. Klein, Felix, [] Elementarmathematik vom höheren Standpunkte aus, Lithographed, Leipzig; English transl. from 3rd German ed.

Hedrick and C. Noble, eds.), Macmillan, New York, Kronecker, Leopold, [] The saying quoted in the third paragraph of the text was spoken in his lecture on 21 September before der Cited by: A primitive functional of type 1→1 does not just take primitive recursive functionals as arguments.

A functional of type ρ→τ is a function from the set of all objects of type ρ that returns objects of type τ. A primitive recursive functional is, first and foremost, a functional. Church Turing thesis highlights the equivalence between different computability models. Using recursion we don't need a mutable state while solving some problem, and this make possible to specify a semantic in simpler terms.

Thus solutions can be simpler, in a formal sense. I think that Prolog shows better than functional languages the effectiveness of recursion (it doesn't have iteration. The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs.

In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types.

The book under review, “Subrecursion: Functions and Hierarchies,” is a carefully written work, whose principal aim is to study various classes of recursive functions which can be arranged in a natural hierarchy, and as such should be of interest to students and researchers in mathematical logic.

recursive method requ iring only the use of conditional probability that is useful for characterizing Pois- son process functionals. Some applications of this technique to convex hulls, extremes. Algebraic Recursion Theory. By L.L. Ivanov, Institute of Mathematics, Bulgarian Academy of Sciences and Sofia University Faculty of Mathematics.

The book does not depend on such results and I can complete an abbreviated version of this appendix in a few days if needed.] All the ordinals in our hierarchy must have a recursive ordering relationship or we cannot not use them in recursive functionals.

This implies that there is a recursive ordinal that is the limit of everything we can. Book for recursion. Expert + P: AmberJain. HELLO, I studied recursion in C programming. But I still think that I'm unable to grab the concept of recursion.

OR better said I cannot get recursion inside my mind from the book I'm referring to. So please tell me a book which will make me feel more comfortable with concept of recursion in.

When the recursion bottoms out, the deepest call returns 0. However, that value doesn't immediately exit the recursive call chain; instead, it just hands the value back to the recursive call one layer above it. In that way, each recursive call just adds in one more number and returns it higher up in the chain, culminating with the overall.

in higher types stresses the role of xed points of certain functionals and is often cited as an example of a more general type of recursion.

(See x) The concept of recursion used here includes: (1) induction and the notion of re exive program call, (including primitive recursion and also Kleene’s. marked the first centenary of Recursion Theory, since Dedekind's paper on the nature of number.

Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a /5(10). cartesian closure, and naturality of functionals was shown to be equivalent to Bernoulli’s principle.

Further, I posed the problem of comparing this principle to practice in the speciﬁc cases of smooth and recursive mathematics. Later detailed work on those particular cases justiﬁed the classical intuition embodied in my general Size: KB.Basic Recursion Theory.

Partial Recursive Functions. Diagonalization. Partial Recursive Functionals. Effective Operations. Indices and Enumerations. Retraceable and Regressive Sets. Post's Problem and Strong Reducibilities. Post's Problem. Simple Sets and Many-One Degrees. Hypersimple Sets and Truth-Table Degrees.

Hyperhypersimple Sets and Q. Classic recursion theory asserts that all conventional programming languages are equally expressive because they can define all partial recursive functions over the natural numbers. This statement is misleading because programming languages support and enforce a more abstract view of data than by: 4.