A Combinatory Algebra for Sequential Functionals of Finite Type

A Combinatory Algebra for Sequential Functionals of Finite Type (1997)

by Jaap Van Oosten

Venue:	University of Utrecht
Citations:	21 - 2 self

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Datum	Value	Source
TITLE	A Combinatory Algebra for Sequential Functionals of Finite Type	user correction - Legacy Corrections
AUTHOR NAME	Jaap Van Oosten	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Mathematics; Utrecht University	SVM HeaderParse 0.2
AUTHOR ADDR	The Netherlands	SVM HeaderParse 0.1
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: Primary 03D65, 68Q55 Secondary 03B40, 03B70, 03D45, 06B35 Introduction PCF , "Godel's T with unlimited recursion", was defined in Plotkin's paper [16]. It is a simply typed -calculus with a type o for integers and constants for basic arithmetical operations, definition by cases and fixed point recursion. More importantly, there is a special reduction relation attached to it which ensures (by Plotkin's "Activity Lemma") that all PCF -definable higher-type functionals have a sequential, i.e. non-paral...	user correction - Legacy Corrections
YEAR	1997	INFERENCE
VENUE	University of Utrecht	INFERENCE
VENUE TYPE	TECHREPORT	INFERENCE
PAGES	389--406	INFERENCE
TECH	Technical Report 996	INFERENCE
CITATIONS	16 found	ParsCit 1.0