Term-Generic Logic

  • Andrei Popescu
  • Grigore Roşu
Conference paper

DOI: 10.1007/978-3-642-03429-9_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5486)
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

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrei Popescu
    • 1
  • Grigore Roşu
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUSA

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