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Abstract: It is shown that the type structure of finite-type functionals associated to a combinatory algebra of partial functions from IN to IN (in the same way as the type structure of the countable functionals is associated to the partial combinatory algebra of total functions from IN to IN), is isomorphic to the type structure generated by object N (the flat domain on the natural numbers) in Ehrhard's category of "dI-domains with coherence", or his "hypercoherences". AMS Subject Classification:... (Update)
Context of citations to this paper: More
...PCF is the extensional collapse of the sequential algorithm model. J. van Oosten and J.R. Longley proved recently similar results [vO97, Lon98] in a realizability setting where realizers are deterministic strategies encoded as partial functions from the set of natural numbers...
.... termination test on Sigma rules out models of SDT based on sequential partial combinatory algebras (such as, e.g. the ones considered in [17], 14] and [15] 4] gives a non realizability model 18 where nonetheless Axiom 4 fails) and inasmuch one is interested in...
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BibTeX entry: (Update)
J. van Oosten. A combinatory algebra for sequential functionals of finite type. Technical Report 996, University of Utrecht, 1997. http://citeseer.ist.psu.edu/vanoosten97combinatory.html More
@inproceedings{ vanoosten99combinatory,
author = "J. van Oosten",
title = "A Combinatory Algebra for Sequential Functionals of Finite Type",
booktitle = "Models and Computability",
publisher = "Cambridge University Press",
editor = "S. B. Cooper and J. K. Truss",
pages = "389--406",
year = "1999",
url = "citeseer.ist.psu.edu/vanoosten97combinatory.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard, System et al. - 1986
306 LCF considered as a programming language (context) - Plotkin - 1977
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49 Recursive Functionals and Quantifiers of Finite Type Revisit.. (context) - Kleene - 1978
49 Recursive Functionals and Quantifiers of Finite Type Revisit.. (context) - Kleene - 1980
49 Recursive Functionals and Quantifiers of Finite Type (context) - Kleene - 1959
49 Recursive Functionals and Quantifiers of Finite Type II (context) - Kleene - 1963
45 First Steps in Synthetic Domain Theory (context) - Hyland - 1991
39 The Effective Topos (context) - Hyland - 1982
26 Tripos Theory (context) - Hyland, Johnstone et al. - 1980
19 Sequentiality and strong stability (context) - Bucciarelli, Ehrhard - 1991
16 Projecting sequential algorithms on strongly stable function.. - Ehrhard - 1996
11 The Foundations of Intuitionistic Mathematics (context) - Kleene, Vesley - 1965
1 Recursion on the Countable Functionals (context) - Norman - 1980
1 A relative PCF-definability result (context) - Ehrhard - 1996
1 typeset manuscript (context) - Hyland, Ong et al. - 1994
1 A New Category (context) - Scott - 1996
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