Proving Properties of Typed Lambda-Terms Using Realizability, Covers, and Sheaves (Preliminary Version)

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dc.contributor.authorGallier, Jean H
dc.date2023-05-17T00:56:13.000
dc.date.accessioned2023-05-22T12:54:05Z
dc.date.available2023-05-22T12:54:05Z
dc.date.issued1993-11-10
dc.date.submitted2007-07-12T07:20:39-07:00
dc.description.abstractWe present a general method for proving properties of typed λ-terms. This method is obtained by introducing a semantic notion of realizability which uses the notion of a cover algebra (as in abstract sheaf theory). For this, we introduce a new class of semantic structures equipped with preorders, called pre-applicative structures. These structures need not be extensional. In this framework, a general realizability theorem can be shown. Kleene's recursive realizability and a variant of Kreisel's modified realizability both fit into this framework. Applying this theorem to the special case of the term model, yields a general theorem for proving properties of typed λ-terms, in particular, strong normalization and confluence. This approach clarifies the reducibility method by showing that the closure conditions on candidates of reducibility can be viewed as sheaf conditions. The above approach is applied to the simply-typed λ-calculus (with types →, x, +, and ⊥), and to the second-order (polymorphic λ-calculus (with types → and ∀2), for which it yields a new theorem.
dc.description.commentsUniversity of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-93-91.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/7162
dc.legacy.articleid1249
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1249&context=cis_reports&unstamped=1
dc.source.issue252
dc.source.journalTechnical Reports (CIS)
dc.source.statuspublished
dc.subject.otherGRASP
dc.titleProving Properties of Typed Lambda-Terms Using Realizability, Covers, and Sheaves (Preliminary Version)
dc.typeReport
digcom.identifiercis_reports/252
digcom.identifier.contextkey323931
digcom.identifier.submissionpathcis_reports/252
digcom.typereport
dspace.entity.typePublication
relation.isAuthorOfPublication10aa4a9c-25fb-49b5-83f1-f7c15234fc86
relation.isAuthorOfPublication.latestForDiscovery10aa4a9c-25fb-49b5-83f1-f7c15234fc86
upenn.schoolDepartmentCenterTechnical Reports (CIS)
upenn.schoolDepartmentCenterGeneral Robotics, Automation, Sensing and Perception Laboratory
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