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

Popescu, Andrei; Rosu, Grigore

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https://hdl.handle.net/2142/11238 Copy

Description

Title

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

Author(s)

• Popescu, Andrei
• Rosu, Grigore

Issue Date

2006-07

Keyword(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.

Type of Resource

text

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http://hdl.handle.net/2142/11238

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