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GFOL: A Term-Generic Logic for Defining Lambda-Calculi

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Title: GFOL: A Term-Generic Logic for Defining Lambda-Calculi
Author(s): Popescu, Andrei; Rosu, Grigore
Subject(s): computer science
Abstract: Generic first-order logic (GFOL) is a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. GFOL has a complete Gentzen system generalizing that of FOL. An important fragment of GFOL, called Horn^2, possesses a much simpler Gentzen system, similar to traditional context-based derivation systems of lambda-calculi. Horn^2 appears to be sufficient for defining virtually any lambda-calculi (including polymorphic and type-recursive ones) as theories inside the logic. GFOL endows its theories with a default loose semantics, complete for the specified calculi.
Issue Date: 2006-07
Genre: Technical Report
Type: Text
Other Identifier(s): UIUCDCS-R-2006-2756
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-21

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