A Simple Adequate Categorical Model for PCF

A Simple Adequate Categorical Model for PCF (1997)

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by Torben Braüner

Venue:	In Proceedings of Third International Conference on Typed Lambda Calculi and Applications
Citations:	4 - 0 self

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Datum	Value	Source
TITLE	A Simple Adequate Categorical Model for PCF	user correction - Legacy Corrections
AUTHOR NAME	Torben Braüner	user correction - Legacy Corrections
AUTHOR AFFIL	BRICS; Department of Computer Science; University of Aarhus	user correction - Legacy Corrections
AUTHOR ADDR	Ny Munkegade; DK-8000 Aarhus C, Denmark	user correction - Legacy Corrections
ABSTRACT	Usually types of PCF are interpreted as cpos and terms as continuous functions. It is then the case that non-termination of a closed term of ground type corresponds to the interpretation being bottom; we say that the semantics is adequate. We shall here present an axiomatic approach to adequacy for PCF in the sense that we will introduce categorical axioms enabling an adequate semantics to be given. We assume the presence of certain "bottom" maps with the role of being the interpretation of non-terminating terms, but the order-structure is left out. This is different from previous approaches where some kind of order-theoretic structure has been considered as part of an adequate categorical model for PCF. We take the point of view that partiality is the fundamental notion from which order-structure should be derived, which is corroborated by the observation that our categorical model induces an order-theoretic model for PCF in a canonical way.	user correction - Legacy Corrections
YEAR	1997	INFERENCE
VENUE	In Proceedings of Third International Conference on Typed Lambda Calculi and Applications	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	82--98	INFERENCE
VOLUME	1210	INFERENCE
CITATIONS	20 found	ParsCit 1.0