NDLI: Reflexive Scott Domains are Not Complete for the Extensional Lambda Calculus

Content Provider	IEEE Xplore Digital Library
Author	Carraro, A. Salibra, A.
Copyright Year	2009
Abstract	A longstanding open problem is whether there exists a model of the untyped lambda calculus in the category CPO of complete partial orderings and Scott continuous functions, whose theory is exactly the least lambda-theory lambda-beta or the least extensional lambda-theory lambda-beta-eta. In this paper we analyze the class of reflexive Scott domains, the models of lambda-calculus living in the category of Scott domains (a full subcategory of CPO). The following are the main results of the paper: (i) Extensional reflexive Scott domains are not complete for the beta-eta-calculus, i.e., there are equations not in lambda-beta-eta which hold in all extensional reflexive Scott domains.(ii) The order theory of an extensional reflexive Scott domain is never recursively enumerable. These results have been obtained by isolating among the reflexive Scott domains a class of webbed models arising from Scott's information systems, called iweb-models. The class of iweb-models includes all extensional reflexive Scott domains, all preordered coherent models and all filter models living in CPO. Based on a fine-grained study of an ``effective'' version of Scott's information systems, we have shown that there are equations not in lambda-beta (resp. lambda-beta-eta) which hold in all (extensional) iweb-models.
Starting Page	91
Ending Page	100
File Size	345207
Page Count	10
File Format	PDF
ISBN	9780769537467
ISSN	10436871
DOI	10.1109/LICS.2009.22
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-08-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Calculus Equations Filters Information systems Lattices Mathematical model Logic Computer science Filtering theory Kernel Filter models Lambda calculus lambda theories Reflexive Scott domains
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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