GFOL: A Term-Generic Logic for De ning λ-Calculi
نویسندگان
چکیده
Generic rst-order logic (GFOL) is a rst-order logic parameterized with terms de ned 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, possesses a much simpler Gentzen system, similar to traditional context-based derivation systems of λ-calculi. HORN appears to be suf cient for de ning virtually any λ-calculi (including polymorphic and type-recursive ones) as theories inside the logic. GFOL endows its theories with a default loose semantics, complete for the speci ed calculi.
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