Innocent Game Models of Untyped &lambda;-Calculus

Innocent Game Models of Untyped λ-Calculus (2000)

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by Andrew D. Ker , Hanno Nickau , C.-H. Luke Ong

Venue:	Theoretical Computer Science
Citations:	3 - 1 self

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Datum	Value	Source
TITLE	Innocent Game Models of Untyped λ-Calculus	user correction - Legacy Corrections
AUTHOR NAME	Andrew D. Ker	user correction - Legacy Corrections
AUTHOR AFFIL	Oxford University Computing Laboratory, Parks Road, Oxford	user correction - Legacy Corrections
AUTHOR ADDR	OX1 3QD	user correction - Legacy Corrections
AUTHOR NAME	Hanno Nickau	user correction - Legacy Corrections
AUTHOR AFFIL	Oxford University Computing Laboratory, Parks Road, Oxford	user correction - Legacy Corrections
AUTHOR ADDR	OX1 3QD	user correction - Legacy Corrections
AUTHOR NAME	C.-H. Luke Ong	user correction - Legacy Corrections
AUTHOR AFFIL	Oxford University Computing Laboratory, Parks Road, Oxford	user correction - Legacy Corrections
AUTHOR ADDR	OX1 3QD	user correction - Legacy Corrections
ABSTRACT	We present a new denotational model for the untyped -calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [9] and Nickau [17], but the traditional distinction between \question" and \answer" moves is removed. We rst construct models D and DREC as global sections of a reexive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible -algebras but are neither extensional nor universal. We then introduce a new representation of innocent strategies in an economical form. We show a strong connexion between the economical form of the denotation of a term in the game models and a variable-free form of the Nakajima tree of the term. Using this we show that the denable elements of DREC are precisely what we call eectively almost-everywhere copycat (EAC) strategies. The category A EAC with these strategies as morphisms gives rise to a -model D...	user correction - Legacy Corrections
YEAR	2000	user correction - Legacy Corrections
VENUE	Theoretical Computer Science	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	200--1	INFERENCE
VOLUME	277	INFERENCE
TECH	Ph.D. Thesis	INFERENCE
CITATIONS	19 found	ParsCit 1.0

Innocent Game Models of Untyped &lambda;-Calculus (2000)

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Innocent Game Models of Untyped λ-Calculus (2000)