Constructive Logics Part I: A Tutorial on Proof Systems and Typed Lambda-Calculi

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dc.contributor.authorGallier, Jean H
dc.date2023-05-17T01:09:23.000
dc.date.accessioned2023-05-22T12:55:55Z
dc.date.available2023-05-22T12:55:55Z
dc.date.issued1991-10-01
dc.date.submitted2007-08-10T07:40:52-07:00
dc.description.abstractThe purpose of this paper is to give an exposition of material dealing with constructive logic, typed λ-calculi, and linear logic. The emergence in the past ten years of a coherent field of research often named "logic and computation" has had two major (and related) effects: firstly, it has rocked vigorously the world of mathematical logic; secondly, it has created a new computer science discipline, which spans from what is traditionally called theory of computation, to programming language design. Remarkably, this new body of work relies heavily on some "old" concepts found in mathematical logic, like natural deduction, sequent calculus, and λ-calculus (but often viewed in a different light), and also on some newer concepts. Thus, it may be quite a challenge to become initiated to this new body of work (but the situation is improving, there are now some excellent texts on this subject matter). This paper attempts to provide a coherent and hopefully "gentle" initiation to this new body of work. We have attempted to cover the basic material on natural deduction, sequent calculus, and typed λ-calculus, but also to provide an introduction to Girard's linear logic, one of the most exciting developments in logic these past five years. The first part of these notes gives an exposition of background material (with the exception of the Girard-translation of classical logic into intuitionistic logic, which is new). The second part is devoted to linear logic and proof nets.
dc.description.commentsUniversity of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-91-74.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/7337
dc.legacy.articleid1427
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1427&context=cis_reports&unstamped=1
dc.source.issue410
dc.source.journalTechnical Reports (CIS)
dc.source.statuspublished
dc.subject.otherGRASP
dc.titleConstructive Logics Part I: A Tutorial on Proof Systems and Typed Lambda-Calculi
dc.typeReport
digcom.contributor.authorisAuthorOfPublication|email:jean@cis.upenn.edu|institution:University of Pennsylvania|Gallier, Jean H
digcom.identifiercis_reports/410
digcom.identifier.contextkey336741
digcom.identifier.submissionpathcis_reports/410
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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