- Cite this paper as:
- Popescu A., Roşu G. (2009) Term-Generic Logic. In: Corradini A., Montanari U. (eds) Recent Trends in Algebraic Development Techniques. WADT 2008. Lecture Notes in Computer Science, vol 5486. Springer, Berlin, Heidelberg
Term-generic logic (TGL) 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. TGL has a complete Gentzen system generalizing that of first-order logic. A certain fragment of TGL, called Horn2, possesses a much simpler Gentzen system, similar to traditional typing derivation systems of λ-calculi. Horn2 appears to be sufficient for defining a whole plethora of λ-calculi as theories inside the logic. Within intuitionistic TGL, a Horn2 specification of a calculus is likely to be adequate by default. A bit of extra effort shows adequacy w.r.t. classic TGL as well, endowing the calculus with a complete loose semantics.
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